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Blood pressure analysis on time scales from seconds to days

Westerhof, B.E.

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Citation for published version (APA):Westerhof, B. E. (2005). Blood pressure analysis on time scales from seconds to days.

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Berend E. Westerhof

Blood pressure analysis on tim

e scales from seconds to days B

erend E. Westerhof

Blood pressure analysison time scales from seconds to days

UitnodigingVoor het bijwonen van de openbare

verdediging van het proefschrift:

Blood pressure analysis on time scales

from seconds to days

van

Berend E. Westerhof

Op dinsdag 13 December 2005

om 12.00 uur

In de Aula van de Universiteit van Amsterdam, Oude Lutherse Kerk,

Singel 411 (hoek Spui)te Amsterdam

Receptie ter plaatsena afloop van de promotie

Berend E. WesterhofM. van Borsselenlaan 361181 DA Amstelveen

Tel: 020 6432746

Paranimfen:

Gabriela Montorzi-ThorellTel: +41 22 7430384

[email protected]

Claas WesterhofTel: 010 4258645

[email protected]

Blood pressure analysis

on time scales from seconds to days

Berend E. Westerhof

Blood pressure analysis on time scales from seconds to days

Thesis University of Amsterdam, the Netherlands

ISBN-10: 9090201580 ISBN-13: 9789090201580

© 2005 Berend E. Westerhof

Cover: Adapted homunculi representing the model of the systemic arterial system as

described by N. Westerhof in “Analog studies of human systemic arterial

hemodynamics”, Thesis, University of Pennsylvania, Philadelphia PA.

Financial support: BMEYE B.V.

Printed in 2005 by FEBODRUK, Enschede, the Netherlands

BLOOD PRESSURE ANALYSIS ON TIME SCALES

FROM SECONDS TO DAYS

ACADEMISCH PROEFSCHRIFT

ter verkrijging van de graad van doctor

aan de Universiteit van Amsterdam

op gezag van de Rector Magnificus

prof. mr. P.F. van der Heijden

ten overstaan van een door het college voor promoties ingestelde

commissie, in het openbaar te verdedigen in de Aula der Universiteit

op dinsdag 13 december 2005, te 12.00 uur

door

Berend Eric Westerhof

geboren te Washington DC, Verenigde Staten van Amerika

Promotiecommissie: Promotor: Prof. Dr. Ir. J.A.E. Spaan Prof. Ir. K.H. Wesseling, Emeritus Co-promotor: Dr. J.M. Karemaker Overige leden: Prof. Dr. Ir. C.A. Grimbergen

Prof. Dr. J.H. Ravesloot Prof. Dr. N. Stergiopulos Dr. W.J.W. Bos Faculteit der Geneeskunde

Aan Marleen, Marten en Rosa

7

Table of contents

1. Introduction 9

2. Sensitivity of pressure transfer to arterial parameters 29

3. Parameter adaptation to individualize pressure reconstruction 43

4. Quantification of wave reflection in the human aorta from pressure alone

59

5. Variations in cardiac oxygen supply and demand in hypertensive subjects after rising

77

6. Time-domain cross-correlation baroreflex sensitivity:

performance on the Eurobavar data set 89

7. Dynamics of baroreflex sensitivity during postural stress 109

8. Variable day/night bias in 24-h non-invasive finger pressure against intrabrachial artery pressure is removed by waveform filtering and level correction

129

9. Non-invasive blood pressure measurement in relation to a variety of basic and clinical applications

141

10. Summary and Conclusions 149

Appendix Assessing arterial baroreflex control of heart rate: new perspectives 157

Background 169

Samenvatting 179

Dankwoord 189

Overview of studies 191

9

“primum non nocere”

Chapter 1

Introduction

The maxim “First, do no harm” 1 is chosen as a motto for this thesis, as all exploration in

this work is directed towards methods that allow diagnosis based on non-invasive

measurements of blood pressure.

Blood pressure

Blood pressure is the result of the heart pumping against the arterial load. Pressure

should be maintained while different tissues tap flow according to their needs for oxygen

and nutrients. Particularly the brain and the heart muscle itself are very dependent on a

sufficient supply of oxygen at all time. Several activities influence blood pressure, for

instance tensing of the leg muscles returns venous blood to the heart which then will be

pumped out and increase pressure. Other processes may tend to decrease pressure by

requiring more flow, or in other words, by lowering the resistance. The autonomic

nervous system has several options to stabilize blood pressure. Changing venous

compliance greatly enhances filling of the heart; modulating the vascular resistance is

also very effective. Varying heart rate is less effective, but more noticeable. With fever,

the higher body temperature and thus metabolic rate requires more oxygen to be

delivered, often resulting in high heart rates and palpitations.

1 “First, do no harm” is widely believed to be part of the Hippocratic oath, which, however, it is not. Hippocrates did articulate a similar conviction in his Epidemics, Book I, Section XI: “(…) to help, or at least to do no harm”. The Greek physician Galen may have first used the phrase in Latin as cited above while working in Rome.

10

Continually interacting processes result in continually varying blood pressure and heart

rate. Simple daily activities such as talking or even breathing have an effect on blood

pressure. Blood pressure can double with anxiety, heart rate can triple with physical

activity, while cardiac output, the product of the volume pumped out by the heart per

beat (stroke volume) times heart rate can increase four- to perhaps six-fold in well-

trained athletes.

Clinical importance

When blood pressure is out of its normal range for longer periods, one speaks of high

blood pressure, hypertension, or low blood pressure, hypotension. Hypotension is

usually no threat to health in daily life as long as no light-headedness or fainting occurs.

It can pose an acute threat due to underperfusion in for instance sepsis patients.

Hypertension is an acute risk when extremely high, but even moderate hypertension is

considered to be very dangerous on the long run. Hypertension is defined when the

highest value of the pressure curve, the systolic blood pressure, exceeds 140 mmHg

(systolic hypertension) or when the lowest value, diastolic blood pressure, exceeds 90

mmHg (diastolic hypertension). Up to 30 % of the adult population in most countries

suffers from hypertension and it is one of the most important preventable causes of death

worldwide. Together with other modifiable risk factors including high cholesterol, diet,

inactive lifestyle and smoking, hypertension accounts for about 75 % of cardiovascular

diseases (WHO, Cardiovascular Disease: Prevention and Control. 2003).

Methods of measurements

Early and accurate diagnosis may be a key factor in prevention of or therapy for

hypertension. The feeling of the pulse is one of the oldest manners of diagnosis, believed

to be the invention of Herophilus (335 – 280 B.C.). It was centuries later before Hales2

performed quantitative measurements in 1733 (1). The level to which the blood of a

horse rose in the glass tubing connected to the ‘crural’ artery gave the level of blood

pressure in cmH20 (or cm blood, to be precise). Obviously this method was unfit for use

in humans. A breakthrough was made by Riva-Rocci in 1896 (2), the year when he

presented an air-inflatable arm cuff connected to a manometer; by deflating the cuff and

feeling for the pulse distal of the cuff systolic blood pressure could be determined. In

2 Often the reference to Hales’ measurement is accompanied by a well-known engraving by Cuzzo. This artist reconstruction was made in 1944 and shows the tube connected to the carotid artery in stead of to a crural artery as described by Hales.

11

1905 Korotkoff (3) refined the technique further with the auscultatory method. With the

introduction of the use of a stethoscope diastolic pressure could be determined as well.

The Riva-Rocci / Korotkoff method remains the standard for blood pressure

measurement until today. Nowadays, automated measurements, mostly with

oscillometric devices, are becoming more and more accepted. These devices measure the

pressure in a cuff, which is first inflated above systolic pressure and then deflated to

below diastolic pressure. Oscillation in the cuff pressure is maximal at mean arterial

pressure; mathematical algorithms determine systolic and diastolic values from the

oscillations. What was lost however, with these cuff methods, was the possibility to

observe the shape of the pulse wave.

Figure 1

Hales had noted the oscillation of the blood in his glass tube and later (1838) Poiseuille

designed an instrument specifically for the quantifying these variations, basically a

Ludwig’s Kymograph

12

mercury filled u-shaped tube with a scale. Ludwig (4) described the kymograph (Figure

1) in 1847 with which blood pressure oscillation could be recorded on a drum3. These

instruments measured invasively, thus restricting their use. One of the most accurate

apparatuses designed for non-invasive wave shape analysis was Marey’s (5)

sphygmograph (1860). A lever system amplified the radial pulse (Figure 2), which then

was graphed on a smoke-blackened moving strip (Figure 3).

Figure 2

Marey’s Sphygmograph

A technique that combines accuracy with maximal information is the continuous

pressure recording with the direct intra-arterial method. First mentions date back to

1914, when Bleichroeder (6) performed a catheterization of his own radial artery.

Whether he recorded his blood pressure is not clear, however, it would have been

possible at that time. Frank developed a manometer that could accurately measure

pulsatile pressure in 1903 (7). High fidelity catheter-tip manometers were introduced by

Millar in 1972 (8). Intra-arterial measurements are routinely performed in operation

theaters and intensive care settings, in other words, those circumstances in which it is

vital to continuously monitor blood pressure, mostly to prevent pressures to become too

low. When no such imperative reasons are present it may not be ethical to measure intra-

arterial pressure. If nonetheless the pressure wave shape is required, applanation

tonometry is a non-invasive alternative. Measurements are performed by placing a

3 Hoff and Geddes argue (4) that Ludwig may not have been the first to use graphic registration in physiology.

13

pressure sensor externally on a superficial artery. Usually, the radial or the carotid artery

is assessed. However, measurement over a longer period of time or during maneuvers is

difficult, and pressure values are relative, not absolute.

Figure 3

A very important development is the non-invasive measurement of finger arterial

pressure (10,11). With this method blood pressure can be continuously measured, even

during exercise, and values are calibrated. The method is well validated for various

circumstances and is in use in research and clinical investigations (12-42). A great part

of the work in this thesis is related to this method.

Blood pressure measurements in hypertension

In hypertension, the brachial systolic and diastolic pressures are the pressures on which

epidemiological studies are based and on which clinical decisions are made. Although

finger arterial pressure is well accepted now and used in studies of blood pressure

regulation, for diagnosis in hypertension, brachial pressures are the standard.

Blood pressure tracings from Marey’s Sphygmograph

14

Twenty-four hour recordings of blood pressure, or even 48 hours, are becoming more

frequent in studies on hypertension and for diagnosis (43). It is generally accepted

nowadays that 24-hour recordings of blood pressure are better predictors of

cardiovascular morbidity and mortality and to correlate closer to organ damage than

“office blood pressure”: the blood pressure determined by the doctor when examining

the patient. Here one enters the discussions of the “white coat effect” (44); the finding

that blood pressure can be elevated by the stress of the environment. Thus it plays a role

by whom and where the measurements are taken: measurement by nurse, doctor, or self,

measurement by machine at home or in the office, and combinations of all the above. A

special class is defined recently as the masked hypertensives (45): hypertensives who

remain undetected because they, for unknown reasons, have pressures below the limits

of hypertension when measured in the office, but have elevated blood pressures in daily

life. In other words, the time of measurement also plays an important role and this is why

an ambulatory method gives superior insight in the blood pressure of a person.

In the field of 24-hour recordings, patients can be classified as dippers, non-dippers, and

reverse dippers (46,47,48). Dippers lower their blood pressure by more than 10 mmHg

or by more than 10 % during the nighttime hours. Non-dippers decrease less in pressure

and reverse dippers increase their blood pressure during the night. All classes have been

associated with different levels of risk for cardiac and cerebrovascular incidents.

Ambulatory 24-hour measurements are generally carried out with oscillometric devices

on the upper arm, and usually these measurements give sufficient information for

diagnostic purposes. However, in research, continuous measurements are obviously

much more valuable. For instance, in the investigation of silent ischemia (49), i.e.

ischemia not noted by the patient but detectable from the ECG, oscillometric devices do

not have the required time-resolution. Another field in which interest is growing is sleep

apnea, known to be a risk factor for hypertension (50). The combination of continuous

blood pressure with ECG, ventilation and perhaps blood oxygenation gives much more

information needed for thorough research.

Limitations of the methods

Non-invasive pressure is, necessarily, measured in peripheral vessels, usually the

brachial, radial or finger arteries as mentioned. The amplitudes and the wave shapes of

these pressures differ from ascending aortic pressure and these differences are not

constant but variable, for instance during medication (51). It is central pressure that

forms the load on the heart during systole and that determines the perfusion pressure for

coronary circulation during diastole, the period in which most of the myocardial

15

perfusion takes place (52). Wave shape analysis, for instance to obtain a measure of

arterial stiffness, should preferably be performed on central pressure as well. Information

contained in the wave shape made available by continuous non-invasive methods from

peripheral vessels can nevertheless help to reconstruct central pressure. When only

systolic and diastolic pressures are available possibilities to reconstruct central pressure

are very limited.

Blood pressure not only varies with time within a heartbeat but also from one beat to

another and a single measurement is only of limited value. As pointed out, there is a

tendency to follow blood pressure over 24 hours or even two days, since not only the

absolute values are important, blood pressure variability is an important parameter as

well. With automated devices measurements can be taken at most every few minutes;

however, even more insight into the processes determining systemic pressure can be

obtained when beat-to-beat blood pressure values are available. In this case, heart rate

and pressure variability can be analyzed in great detail and baroreflex sensitivity can be

calculated from the relation between heart rate and blood pressure. The baroreflex is

important to stabilize blood pressure by increasing or decreasing heart rate in reaction to

pressure changes. Baroreflex sensitivity is a prognostic factor in cardiology (53,54,55).

16

This thesis

Overview

This thesis aims to improve the possibilities of retrieving information from blood

pressure measurements especially when this pressure is obtained non-invasively from the

finger.

First, an effort is made to develop and test transfer functions between central and

peripheral blood pressure. For this, continuous information on these pressures is required

and the systolic and diastolic pressure values are not sufficient. Transfer function

analysis is on a time scale of milliseconds. The main conclusion is that a single

generalized transfer function is usually sufficient to reconstruct central pressure from

peripheral pressure.

We also developed a new method to determine wave reflection in the aorta, which is a

measure of arterial stiffness, also on a time scale of milliseconds. Although this study

was performed using high fidelity central measurements of pressure and flow we expect

that the method is applicable without flow measurements with uncalibrated pressure

recording.

Having established that central pressure can be reconstructed from peripheral pressure

(15,20), this pressure signal can then be used to make a reasonable assumption about the

cardiac oxygen demand as measure of cardiac work and cardiac oxygen supply. Cardiac

oxygen supply and demand should be in balance, or else cardiac ischemia will develop.

A new method for the determination of baroreflex sensitivity is described next. The new

method is then used to investigate the dynamics of the baroreflex during orthostatic

stress. The processes related to oxygen supply/demand ratio and baroreceptor reflex take

place on the time scale of seconds.

A method to correct the pressure drop that may occur between brachial and finger

arterial pressure was examined (20,42). We showed that this method can correct the

differences between brachial and finger arterial pressure over 24 hours and it facilitates

the blood pressure measurement over days.

17

Below we will discuss the relevance of these studies in some detail.

Transfer functions

Non-invasive pressure measurements are typically obtained from peripheral sites as the

radial artery by applanation tonometry (56,57) or from the finger with the so-called

“volume-clamp”/“physiocal” method (10,11). Applanation of the carotid artery gives an

accepted “surrogate” of central arterial pressure. Pressure measurement by applanation

tonometry cannot give absolute values, since no objective criteria exist for the operator

to know if the pressure is indeed representing the intra-arterial values. Simply fitting the

measured curves to brachial diastolic and mean pressure (60) can give a reasonable

approximation. However, one can do much better using the concepts from signal

analysis directed to describing relationships between causally related signals. So-called

transfer functions form a powerful method to do so. Hence, the application of transfer

functions allows the calculation of central pressure from peripheral pressure and thereby

estimation of the inherent consequences of generated pressure for the heart. Transfer

functions are widely used in the literature nowadays and are advocated by many

(12,15,19-21,30,31,42,57-64). In contrast, some groups have proposed to distil important

parameters pertaining to cardiovascular condition directly form peripheral pressures

(65,66), thus circumventing the use of transfer functions.

In a physiological model we set out to investigate which vessel wall- and blood

properties have the largest influence on the pressure transfer. The results of this

sensitivity analysis are summarized in Chapter 2. The central to peripheral time delay of

the upstroke in pressure can be measured and we investigated the potential of this

parameter in adjusting the transfer function to improve reconstructed central pressures.

The findings of this research are presented in Chapter 3.

Reflection indices

The augmentation index (secondary rise in systolic pressure divided by pulse pressure) is

a popular construct used in trials and associated with virtually any other index in the

field of hemodynamics and hypertension. Originally, the index was devised to get an

indication of wave reflection, which in turn should give an indication of arterial stiffness.

A fundamentally better estimate of arterial stiffness is obtained by pulse wave velocity

measurement. Indeed these measurements are also performed frequently (67). The great

advantage of augmentation index measurement is that only one arterial site has to be

assessed, usually the carotid artery, whereas for pulse wave velocity measurements two

18

sites are required. Most customary sites are carotid and femoral artery, to have a

relatively large part of the aorta included in the measurement.

As will be discussed in Chapter 4 the calculation of the reflection index requires the

pressure wave as well as the flow wave. It has been suggested that the description of the

aortic valve flow wave by a triangular shape in systole would be a useful approximation

(68). This method simplifies the determination of the reflection index considerably.

Moreover, it circumvents a weakness of the augmentation index since this conventional

signal analysis cannot detect reflection when the summation of the reflected wave and

forward wave result in a waveform without discontinuity in the rising pressure

waveform. This new method opens the way to non-invasive measurements allowing

large-scale population research.

Cardiac oxygen supply and demand

Morning excess in cardiovascular incidents has always been attributed to an increase in

cardiac oxygen demand (69,70), caused by increasing blood pressure and heart rate. In

the literature, decreased oxygen supply has always been associated with increased

coronary tone, coronary vasospasm, stenosis or atherosclerosis, or heightened platelet

aggregability, but never with decreased cardiac oxygen supply potential (71). However,

we show that not only cardiac oxygen demand increases in the morning but that cardiac

oxygen supply-potential decreases as well. To estimate cardiac oxygen demand we used

the Rate-Pressure Product (52,72), an index that is well accepted; to estimate cardiac

supply potential we used the Diastolic Time Fraction, which is recently emerging as a

good indicator of subendocardial perfusion (73,74). Both indices show a strong

correlation with heart rate, oxygen demand increasing with increasing heart rate and

oxygen supply potential decreasing. In relation to the heart rate increase after rising it is

heartening to note that the hypertensive population in our study has a smaller increase

than the normotensives controls: this limits the morning imbalance between supply and

demand (Chapter 5).

Baroreflex sensitivity

Baroreflex can be calculated from changes in interbeat-interval following changes in

blood pressure. Blood pressure changes can be spontaneous or provoked. The

provocation of blood pressure changes can be accomplished by infusion of vasoactive

drugs. First, angiotensin was used (75), but this substance was shown to have a central

effect on the baroreflex. Later, phenylephrine and nitroprusside were used to increase

and decrease blood pressure, respectively (76). Both substances affect the baroreflex as

well (77,78) by changing the properties of the vascular wall where the receptors are

19

located. Another accepted method is neck suction or pressure (79). With a neck-cuff

pressure changes can be transferred to the carotid sinus, thus deceiving the system that

arterial pressure is too high or too low.

Using the spontaneous variations in interbeat interval and blood pressure allows much

more agreeable determination of baroreflex sensitivity. The so-called sequential method

(80) searches for sequences in which interbeat interval and blood pressure jointly

increase or decrease. When a sequence of three or more normal beats is recognized, the

linear regression through interbeat interval values as a function of blood pressure values

is calculated and the angle of the regression line is taken as baroreflex sensitivity.

Usually the delay between blood pressure and interbeat interval changes is prescribed at

zero or one beat.

In a recently proposed method, cross-correlations between pressure and interbeat interval

are calculated for time delays from 0 to 5 seconds of interbeat interval (41). The linear

regression with the highest coefficient of correlation renders the slope, quantifying the

baroreflex sensitivity. The time delay is not prescribed but retrieved from the

measurements, giving extra information. We call this the xBRS method for cross-

correlation baroreflex sensitivity.

This method was evaluated (Chapter 6) on a set of data of the EUROBAVAR working

group, available through the Internet for this purpose. We found that the method gives

results comparable to other methods using these data, but with a larger number of

estimations per unit of time and with less scatter. The publication was accompanied by

an editorial comment, which is included in an Appendix to this thesis.

The tilt table is an excellent method to challenge the baroreflex and we investigated

whether we could document that with our new method (Chapter 7). The baroreflex

sensitivity changed with the tilt angle, and the rate of change appears to be related to the

magnitude of change of the tilt angle. The BRS shows a linear relation to the sine of the

tilt angle as well: as vagal activity withdrew, the BRS decreased. This is associated by a

shift towards longer delays between blood pressure and interbeat interval changes.

Level correction

A transfer function is very useful in relating the waveforms measured at the periphery

and central. However, it does not entirely account for the differences in the measurement

of mean blood pressure. In Chapter 8 it is shown that finger blood pressure can be

reconstructed, with a transfer function and a level correction, to brachial blood pressure,

with acceptable errors, thus allowing the comparison to standard brachial values. The

level correction method (20) was originally developed for transversal use, i.e. for groups

20

of patients; we now show its usefulness longitudinally, i.e. over 24 hours (42). Tracking

is improved and the nocturnal dip is better described. Probably one calibration of

reconstructed pressure per day will suffice (21).

Conclusion

In this dissertation several methods are explored to advance the use of non-invasive

recording of arterial blood pressure for studies in physiology and diagnostics in

cardiovascular disease and hypertension. Ordered by increasing time scale, we will

describe a physiological model of pressure transfer, and consecutively propose a method

for individualization of a pressure transfer function.

Next a method is proposed to calculate the reflection index using pressure wave features.

Wave reflections are of interest since they are a measure of arterial stiffness and used as

a marker for cardiovascular morbidity and mortality. Usually the augmentation index is

calculated as an approximation of the reflection index. It will be show that the suggested

method gives results closer to measured reflection index than the established method of

augmentation index calculation.

Further, parameters for cardiac oxygen supply potential and cardiac oxygen demand are

studied. An accepted concept relates the elevated numbers of cardiovascular incidents in

the morning hours to increased cardiac oxygen demand after rising, However, we will

demonstrate that cardiac oxygen supply potential decreases as well.

An prognostic factor in cardiology is baroreflex sensitivity, a measure of autonomic

blood pressure control. We put forward a new method to determine baroreflex

sensitivity, giving more results per unit of time and additionally a time delay in

autonomic reaction. This delay may allow us to discriminate between the fast

parasympathetic and the slower sympathetic branch of the autonomic system. This

assumption will be considered in a study of the influence of orthostatic stress on

baroreflex sensitivity.

Finally, on a time scale of 24 hours, a method to improve the reconstruction of brachial

artery pressure from finger arterial pressure measurements is tested. We anticipate

showing that the diurnal blood pressure pattern can be more accurately described.

Dipping or non-dipping of nocturnal pressure is an issue in the classification of the

severity of hypertension and reliably discriminating dippers and non-dippers from non-

invasive pressures is a useful asset.

21

In conclusion, several new methods were investigated to advance diagnostics in

cardiovascular disease and hypertension, based on non-invasive blood pressure.

22

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29

Chapter 2

Sensitivity of pressure transfer to arterial

parameters

Berend E Westerhof1, Ilja Guelen1, Wim J Stok2,

Karel H Wesseling1, Jos AE Spaan3, Nico Westerhof4,

Willem Jan W Bos5, Nikos Stergiopulos6

Transfer functions that calculate aortic pressure from peripheral pressures give the

opportunity to non-invasively obtain information on the cardiac load. Several approaches

have been taken to arrive at transfer functions. Chen et al. and Fetics et al. (5,7) used a

special mathematical transformation to deduce transfer functions from human data and

the averaged transfer function of a group of patients was used as “standard” transfer.

Karamanoglu et al. (15,16) used a segmented model of the arterial tree. Gizdulich et al.

(9,10) proposed a method to obtain brachial pressure from finger pressure by fitting a

second order filter to averaged data. Stergiopulos et al. (23) have recently shown that

splitting the brachial pressure in its backward and forward waves and by shifting these

waves with respect to each other over the travel time between aorta and brachial artery,

an accurate wave transformation can be obtained. Another topic in this field that has

received much attention is the calibration and level correction of non-invasively obtained

pressures (1,3,10,11,12,25).

1 BMEYE, Amsterdam, The Netherlands 2 Dept of Physiology, Academic Medical Center, University of Amsterdam, The Netherlands 3 Dept of Medical Physics, Academic Medical Center, University of Amsterdam, The Netherlands 4 Dept of Physiology, ICaR-VU, VU University medical center, Amsterdam, The Netherlands 5 Dept of Internal Medicine, St Antonius Ziekenhuis, Nieuwegein, The Netherlands 6 Biomedical Engineering Laboratory, Swiss Federal Institute of Technology, Lausanne, Switzerland

30

Thus, there are several approaches to describe pressure transfer from periphery to aorta.

Although several groups report favorably about the use of transfer functions, others are

more critical (13,21). To acquire more insight into the determinants of pressure transfer

we investigated the quantitative contribution of all known contributing arterial, blood

and distal arterial load properties to the transfer function and to the systolic and diastolic

pressure. This information allows us to determine the main contributing factors and to

obtain a description of the transfer function based on these major contributing

parameters only.

Methods For evaluation of the effect of parameters changes we use models between

brachiocephalic and brachial artery.

Tube model based on anatomy

We constructed a model, representing the human subclavian, axillary and brachial artery,

based on Womersley’s theory for an artery under stiff longitudinal constraint and

including viscous fluid damping (29). The wall is taken linear and viscoelastic. Wall

viscosity is modeled with a second order polynomial; the constants are taken from

Westerhof et al. (28). The tube system has a length of 42 cm and is tapering, according

to actual anatomical data, from a diameter of 8.1 mm proximal to 4.7 mm distal given by

Westerhof et al. (27). The tube system is divided in 7 segments, with length, radius and

wall thickness given in Table 1. Wave speed and damping (wave propagation coefficient

g and characteristic impedance) follow directly from longitudinal impedance based on

Womersley’s theory and from transverse impedance that is based on the (viscoelastic)

wall properties. The tube is loaded with a three-element Windkessel (20) as shown in

Figure 1A, representing the input impedance of the lower arm arteries.

Table 1 Dimensions of the tube model according to anatomy

Segment 1 2 3 4 5 6 7

Length (mm) 68 61 56 63 63 63 46

Radius (mm) 4.03 3.64 3.14 2.82 2.66 2.50 2.36

Wall thickness (mm) 0.66 0.62 0.57 0.55 0.53 0.52 0.50

The dimensions of the segments are listed from proximal (segment 1)

to distal (segment 7). Actual anatomical data from Westerhof et al. (27).

31

Figure 1

WindkesselLoad

Tube system

B

A

Above, the tapered tube is shown with its Windkessel load (A). Below, the uniform tube (B) is drawn. For

clearness the radii are multiplied by 3.

Windkessel parameters are: peripheral resistance of the underarm (Rp = 56.3 103 g cm-4

s-1 or 42.3 mmHg ml-1 s), arterial compliance representing the combined elasticity of the

large vessels of the underarm (Cw = 7.26 10-6 cm4 s2 g-1 or 9.66 ml mmHg-1), (Westerhof

et al., 27, Stergiopulos et al., 24) and characteristic impedance, which is taken equal to

the characteristic impedance of the distal part of the brachial artery (Zc = 6.2 103 g cm-4

s-1 or 4.77 mmHg ml-1 s). Mathematica (Wolfram Research, Inc., Mathematica, Version

4.0, Champaign, IL) is used for the analysis. The model is linear allowing Fourier

analysis and treatment per frequency. First the Windkessel impedance is calculated as a

function of frequency. Then characteristic impedance of the last, most distal segment of

the tube system is calculated. The reflection coefficient G is then derived as

(1) G = (Zload – Zchar, tube)/(Zload + Zchar, tube).

Pressure and flow transfer from end to entrance of the segment are calculated from the

wave propagation coefficient g and the reflection coefficient G.

(2A) Pproximal = Pdistal(1 + Gdistal·e-2gz) ·egz/(1 + Gdistal)

(2B) Fproximal = Fdistal(1 – Gdistal·e-2gz) ·egz/(1 – Gdistal)

The impedance transfer is:

(3A) Zin, proximal/Zin, distal = (Pproximal / Fproximal)/(Pdistal / Fdistal)

(3B) = (1 – Gdistal)(1 + Gdistal·e-2gz) / (1 + Gdistal)(1 – Gdistal·e

-2gz)

Thus the impedance at the entrance of the last segment can now be calculated.

32

These calculations are repeated for all segments from distal to proximal end. The transfer

Pentrance /Pend is found by multiplication of the segmental transfers. Because the resistance

to mean flow in the tube system is negligible with respect to peripheral resistance (less

than 1%), the transfer function for mean pressure (zero Hz) equals 1, i.e., mean pressures

at the entrance and end are equal.

Using this model, the effects of changes in tube and in load (Windkessel) parameters on

the transfer function and blood pressure, were calculated. The tube parameters were:

(segment) length, radius, wall thickness, Young’s modulus, vessel wall viscosity, blood

density, blood viscosity and the Windkessel parameters (20). The changes in the

magnitude of the first peak and in the frequency at which the first peak of the transfer

function occurs were determined. These two variables were compared with those in the

reference condition.

With the transfer function of the entire tube system, the sensitivity of the aortic pressure

to changes in parameters was also calculated. Aortic pressure (“control” aortic pressure)

was taken from the extensive model by Stergiopulos et al. (24), and applied to the

entrance of the tube system, and the distal (brachial) pressure at the end of the last

segment is calculated using the reference parameters. This brachial pressure was then

taken as our standard brachial pressure to recalculate aortic pressure for variations in the

model parameters. The “reconstructed” aortic pressure was referenced against “control”

aortic pressure. Comparisons were done in terms of systolic, diastolic and pulse

pressures. Also the Root Mean Square Error (RMSE = ◊[S(Preconstructed – Pcontrol)2 / n],

where n is the number of data points) between “reconstructed” and “control” aortic

pressures was calculated to quantify the error in wave shape.

The magnitude and frequency of occurrence of the first peak of the transfer function and

systolic, diastolic and pulse pressures together with RMSE were called (output)

variables. The sensitivity of the variables to the parameters was calculated in terms of %

error: the percentage change in a variable for a change in a parameter. All parameters

were increased and decreased by 25%, which is a reasonable maximum of variation for

most parameters.

Uniform tube model

The next step was to investigate if a single uniform tube would be sufficient to describe

the transfer function (Figure 1B). To this end the geometrically correct system was

replaced with a uniform tube with a length of 420 mm, a radius of 3.5 mm, a wall

33

thickness of 0.65 mm and loaded with the control Windkessel, but with Zc matched to

the tube. Subsequently the Windkessel load was changed such that the reflection

coefficient was negligible and equal to one to determine the sensitivity to extreme load

changes, i.e. vasodilatation and vasoconstriction.

Figure 2

10.2 0.4 0.6 0.8

80

100

120

5 10 15 20

1

2

3

-1

-0.5

80

100

120

10.2 0.4 0.6 0.8Freq. [Hz]

Pre

ssure

[mm

Hg]

Gain

Phase

[rad]

Time [s]Time [s]

Transfer function of the tapered tube. Control brachial pressure is shown on the left. In the middle the gain

(top) and phase (bottom) of the transfer function are given as a function of frequency for control (fully drawn),

and for segment lengths increased by 25% (dashed) and decreased by 25% (dotted). Control aortic pressure is

shown on the right as a function of time for the control situation (fully drawn), and for segment length

increased and decreased (dashed and dotted).

Results

Tube model based on anatomy

The dimensions of the tube model according to anatomy are given in Table 1 and shown

in Figure 1. The control transfer function and the control aortic and brachial pressures

are shown in Figure 2. This brachial artery pressure is used to calculate the aortic

pressure when tube and load parameters are changed. Values of the vessel and the

Windkessel parameters in the control situation and the control output variables are listed

in Table 2. Parameters were increased and decreased by 25%. The changes of the

characteristic points of the transfer function, frequency and maximum value of the first

peak, and of the reconstructed aortic pressure, systolic, diastolic and pulse pressure, are

given in the Table 2 as percentages. Percentages are rounded to integer values,

percentages smaller than 0.5% are considered zero. Due to the smaller value of the pulse

pressure with respect to systolic and diastolic pressure, the percentages of variation in

34

the pulse pressure are largest. The difference between the reconstructed and control

aortic pressure in terms of wave shape is expressed as RMSE (mmHg). For similar

changes up and down of a parameter, output variables may change with unequal

magnitude. For instance, an increase in Rp has less effect than a decrease.

Table 2 Results of the sensitivity analysis

Parameter

control

value

Frequency

of peak

in TF

4.0 Hz

Magnitude

of peak

in TF

1.96

Aortic

Psystole

114 mmHg

Aortic

Pdiastole

78 mmHg

Aortic

PP

36 mmHg

RMSE

0 mmHg

incr decr incr decr incr decr incr decr incr decr incr decr

Segment

Length

(See

Table 1)

–15 30 8 –10 –3 2 1 0 –9 7 1.74 1.62

Radius (See

Table 1)

20 –25 25 –15 0 –1 0 0 0 –2 0.62 1.56

Wall

thickness

(See

Table 1)

5 –5 –5 7 1 –1 0 0 1 –3 0.40 0.63

Young’s

modulus

4 106

g cm-1s-2

5 –5 –6 9 1 –1 0 0 2 –4 0.54 0.81

Wall

Viscosity

(See text) 0 5 11 –10 –1 1 0 1 –4 3 0.59 0.73

Characteristic

Impedance

6.2 103

g cm-4 s-1

10 –5 –2 8 0 –1 0 0 1 –2 0.27 0.35

Peripheral

Compliance

7.3 10-6

cm4 s2 g-1

–5 10 –8 12 0 0 0 0 0 1 0.34 0.39

Peripheral

Resistance

56.3 103

g cm-4 s-1

0 5 0 –1 0 0 0 0 0 1 0.06 0.09

Blood

Density

1.05

g cm-3

–10 20 3 –4 –2 2 0 1 –5 4 0.96 1.06

Blood

viscosity

0.04

P

0 5 –2 2 0 0 0 0 0 0 0.12 0.13

Percent changes in the variables are given for 25% increase (incr) and decrease (decr) of the parameters.

Percentages are given as integer values, values smaller than 0.5% are considered zero. RMSEs are given in

mmHg. Control values of the parameters are given in the left column and control values of the output variables

are given in and top row.

35

Variations in diastolic pressure are negligible for almost all changes. Although most

physiological parameters in vivo change less than 25%, some, like peripheral resistance,

may change more than 25%. This was not considered further as this particular parameter

has very little influence (Table 2). A change of 25% in blood density is very unlikely.

Therefore it is mainly vessel size (diameter and length) that contributes to the transfer

function.

Uniform tube model

The uniform tube is shown in Figure 1B. For the control situation the transfer function is

given in the Figure 3. Peak magnitude of the transfer function is 2.25, at a frequency of

4.0 Hz. Aortic pressure was reconstructed by applying the transfer function on the basis

of a uniform tube to the brachial pressure. Relative differences are 1%, 0% and 3% for

systolic, diastolic and pulse pressure, respectively. RMSE is 2.06 mmHg.

Figure 3

5 10 15 20

1

2

3

Ga

in

-1

-0.5

Freq. [Hz]

Ph

ase

[ra

d]

Special attention was paid to the effect of the reflection coefficient. For this purpose,

Windkessel parameters were changed to two extremes, so that the reflection coefficient

takes on values of 0 (no reflection) and 1 (total reflection). For these situations new

control brachial pressures were calculated using the anatomical tube, so that the effects

of simplifying the transfer function is assessed on extreme wave shapes, and not the

combined effect of a changing transfer function and changing wave shapes.

Reconstructed aortic pressures were calculated from these brachial pressures using the

uniform tube. Peak frequency and magnitude can not be determined in these situations as

the maximum of the function approaches infinity as G approaches 1, and no maximum is

Transfer functions of the tube modelaccording to anatomy (fully drawn)and of the uniform tube (dotted).

36

present when G = 0. Nonetheless, the effect of these extreme peripheral changes is small.

For G = 0, the differences are –1%, 1% and –7% in systolic, diastolic and pulse pressure.

RMSE is 1.16 mmHg. In the case that G = 1, these differences become –1%, 0% and –

5%. RMSE is 1.98 mmHg.

Discussion This theoretical analysis shows that prediction of aortic pressure from brachial pressure

is mainly dependent on vessel size (length and diameter) and less dependent on other

parameters including wall elasticity. The uniform tube as simplification of the anatomy

also is acceptable and this outcome stresses that the tapering is only a minor factor as

well. From Figure 1 it is apparent, that the decrease in radius is quite small for this set of

arteries in which no major branches are present. Of note, in Figure 1 the radii were

multiplied by 3 to make the effect of decreasing size more appreciable. This implies that

the transfer function from brachial artery to aorta can be very simple, and can be based

on a lossless uniform tube. The tube parameters radius, wall thickness, segment length,

Young's modulus, blood density, blood viscosity, and wall viscosity, all contribute to the

time delay, an important overall property. The use of a uniform lossless tube allows for

analytical formulation of the transfer function and underpins the time shift method

(Stergiopulos et al., 23). The length, radius and elasticity are the main factors

contributing to the time delay and the importance of the time delay is in agreement with

what was reported before by Stergiopulos et al. (23). From those data we calculated that

for a 25% increase and 25% decrease in delay time the percentage changes for systolic

pressure (140 mmHg): 3% and 2%, diastolic pressure (67 mmHg): 1% and 0%, and

pulse pressure (73 mmHg) –7% and –5%. The advantage of using delay time is that it

can be determined, from for instance the ECG and non-invasively determined brachial

pressure. If the errors resulting from the introduction of a single uniform tube with

known delay time are regarded as acceptable this model can make it possible to

individualize a transfer function from delay information only.

The segment lengths used have been shown to be sufficiently short for the physiologic

frequency range; shorter lengths or more detailed tapering is not required (Westerhof

26).

37

The Windkessel parameters are of limited influence on the pressure transfer (Table 2).

We found that changes in peripheral resistance, which can vary over a wide range, had

only a small effect on systolic, diastolic and pulse pressure (Table 2). This in agreement

with earlier findings (2) that local administration of a vasoconstrictor (phenylephrine)

and vasodilator (sodium-nitroprusside) induced no measurable changes in differences

between brachial and finger artery pressure. Similarly, it was found that wave shape as

determined by photoplethysmography is not influenced by local infusion of vasoactive

drugs (6,19). In contrast, Karamanoglu et al. found (16) that the distal reflection

coefficient had major influence on mainly systolic pressure. Yet while we calculated our

results on basic parameters, Karamanoglu et al. simplified their model by using a

reflection coefficient at the distal site and varied this coefficient over a large range of

values. However, variation in peripheral resistance has a limited effect on the modulus of

the reflection coefficient. In Figure 4 the effect on G of a decrease by a factor 4 in Rp (4,

14) and an increase of a factor 4 (18) is shown. It is unlikely that such multiplication

factors would occur in resting conditions. The strong decrease in Rp results in a 30%

reduction of the first harmonic of G and the difference rapidly diminishes for higher

harmonics. The increase in peripheral resistance increases G even less (Figure 4). This is

also an explanation for the finding that increasing and decreasing a parameter may result

in unequal variation in the outcome variables. In conclusion, by assuming a great

influence of Rp on the reflection coefficient, Karamanoglu thus overrates the effect of Rp

on the transfer function. From this it may be inferred that, once the transfer function is

determined, vasodilation and vasoconstriction are not of great influence.

Figure 4

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Mo

du

lus

Frequency [Hz]

G as a function of frequency for Rp increased(dashed) and decreased (double dashed) by afactor 4. Increasing Rp hardly affects G.

38

Segers et al. investigated the possibility to individualize a transfer function based on

three segments. They found that model parameters were not related to heart rate, blood

pressure or age (22). Optimal reflection coefficients and characteristic impedances of the

segments of the model were determined. For convenience, segment lengths were kept

constant. Similar results could be obtained by adjusting segment length, but Segers et al.

consider it unlikely that this would have a major influence. However, from our study it

follows that path length is an important parameter.

It is interesting to note that the rather large changes in frequency and magnitude of the

peak in the TF that occur with changing radius, have little effect on the reconstruction of

pressure. From Table 2 it may be observed that the peak moves to a higher frequency

and a greater magnitude with increasing radius, and to a lower frequency and a smaller

magnitude with decreasing radius. The result of this combined change is that the first

three harmonics remain at their positions with changing radius, thus leaving the most

important part of the TF for pressure reconstruction intact.

The reflection coefficient G can be calculated from measured pressure and flow at the

distal site. When the uniform lossless tube is assumed, then the shift theorem (23) can be

applied and a transfer function for individual patients can be obtained. Then, since load

changes have little effect, this same transfer function can be used during interventions

such as vasodilation.

Most transfer functions described in the literature were obtained by averaging measured

transfers in groups of patients, or based on filters fitted to averaged transfers. Our

analysis shows that transfer functions can be beneficially obtained on the basis of actual

vascular parameters. A single uniform tube with a distal reflection coefficient is a good

approximation. This implies that the basic mathematical description of the transfer from

distal to proximal pressures is:

(4) Pproximal / Pdistal = (1 + Gdistal ·e-2jwDt) ·e jwDt /(1 + Gdistal),

as given by Stergiopulos et al. (23). This formula has two parameters and by determining

these parameters the transfer function can be personalized. Since the effect of the

reflection coefficient is small with respect to the effect of Dt, Gdistal can be set to a fixed

value. If Gdistal is set to 1, errors are somewhat larger but the formula further simplifies to:

(5) Pproximal / Pdistal = cos (wDt)

39

The main concern of this study was the investigation of the influence of arterial

parameters; therefore we did not evaluate the influence of heart rate or other cardiac

factors. Thus, we investigated the importance of physiological anatomical parameters on

a model describing the arteries between the brachiocephalic artery and the brachial

artery. This was done so that potential effects of major bifurcations would not obscure

our results. It is interesting to note however, that the transfer function from

brachiocephalic artery to brachial artery gives results similar to findings in the literature

for transfer functions from aorta to brachial, from aorta to radial, and even from carotid

to radial artery (8). Apparently, all these transfer functions are mainly determined by the

part between the branching from the aorta to the brachial artery. Using the data of

Lasance et al. (17) we calculated transfer functions from ascending aorta, aortic arch and

brachiocephalic artery to brachial artery (Figure 5). The results are very analogous for

the most important harmonics between 1 to 4 Hz (5). Particularly the transfer functions

from aortic arch and brachiocephalic artery to brachial artery are strikingly alike. The

short and wide aortic segments and the short and narrow segments of the underarm and

carotid artery contribute mostly to higher frequencies. Summarizing, the choice to

analyze model of the arteries between the brachiocephalic artery and the brachial artery

is not a major limitation of the study.

Figure 5

5

1

2

3

4

5 Archto brachial

frequency [Hz]

5

1

2

3

4

5

ga

in

Ascendensto brachial

5

1

2

3

4

5 Brachiocephalicto brachial

The gains of the TFs fromascending aorta, aortic arch andbrachiocephalic artery to brachialartery. Of the latter two, the first 5harmonics are super-imposable.The first TF peaks at a slightlylower frequency, as tube-length isgreater.

40

In conclusion, a simple uniform tube with known delay time, possibly measured, and an

estimate of the distal reflection coefficient are sufficient to obtain an accurate description

of pressure transfer from brachial artery to aorta.

Acknowledgments

We cordially thank Jan Paul Barends of the Lab for Physiology, ICaR-VU, VU University medical center, Amsterdam, The Netherlands for his inspiring help with the mathematics of in this study.

41

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1995;26:315-20.

3. Bos WJ, van Goudoever J, van Montfrans GA, van den Meiracker AH, Wesseling KH.


Circulation. 1996;94:1870-5.

4. Bottcher M, Madsen MM, Refsgaard J, Buus NH, Dorup I, Nielsen TT, Sorensen K.

Peripheral flow response to transient arterial forearm occlusion does not reflect myocardial

perfusion reserve. Circulation. 2001;27:103:1109-14.



pressure: validation of generalised transfer function. Circulation 1997;95:1827–1836.


Ritter JM, Anggard EE. Photoplethysmographic assessment of pulse wave reflection:

blunted response to endothelium-dependent beta2-adrenergic vasodilation in type II diabetes

mellitus. J Am Coll Cardiol. 1999;34:2007-14.



1999;46:698-706.



2004;17:1059-67. Review.



1996;14:243-50.


and pressure decrement. Cardiovasc Res 33: 698-705, 1997


Bos WJ. Finometer, finger pressure measurements with the possibility to reconstruct

brachial pressure. Blood Press Monit. 2003;8:27-30.


Bos WJ. Validation of the brachial pressure reconstruction of the Finometer. In preparation.

13. Hope SA, Tay DB, Meredith IT, Cameron JD: Use of arterial transfer functions for the

derivation of aortic waveform characteristics. J Hypertens 2003;21:1299 –1305.

42



surgery patients. Br J Anaesth. 2001;87:212-22.

15. Karamanoglu M, O’Rourke MF, Avolio AP, Kelly RP: An analysis of the relationship

between central aortic and peripheral upper limb pressure waves in man. Eur Heart J

1993;14:160–167.


multi-branched model of the human upper limb. Am J Physiol 1995;269:H1363–H1369.

17. Lasance HAJ, Wesseling KH, Ascoop CA: Peripheral pulse contour analysis in determining

stroke volume. Progress Report 5, Institute of Medical Physics, Utrecht, 1976.

18. Lundvall J, Edfeldt H. Very large range of baroreflex sympathetic control of vascular

resistance in human skeletal muscle and skin. J Appl Physiol. 1994;76:204-11.

19. Millasseau SC, Kelly RP, Ritter JM, Chowienczyk PJ. Determination of age-related

increases in large artery stiffness by digital pulse contour analysis. Clin Sci (Lond).

2002;103:371-7.

20. Nichols WW, O’Rourke MF. McDonald’s Blood Flow in Arteries,.4th ed. Edward Arnold,

London, 1998.

21. O’Rourke MF, Nichols WW. Use of arterial transfer function for the derivation of aortic

waveform characteristics (letter). J Hypertens 2003;21:2195–2199.

22. Segers P, Carlier S, Pasquet A, Rabben SI, Hellevik LR, Remme E, De Backer T, De Sutter

J, Thomas JD, Verdonck P. Individualizing the aorto-radial pressure transfer function:

feasibility of a model-based approach. Am J Physiol Heart Circ Physiol. 2000;279:H542-9.

23. Stergiopulos N, Westerhof BE, Westerhof N. Physical basis of pressure transfer from

periphery to aorta: a model-based study. Am J Physiol. 1998;274:H1386-92.

24. Stergiopulos N, Young DF, Rogge TR. Computer simulation of arterial flow with

applications to arterial and aortic stenoses. J Biomech. 1992;25:1477-88.




Hypertens. 2002;20:1981-6.

26. Westerhof N. Analog studies of human systemic arterial hemodynamics. PhD thesis,

University of Pennsylvania, Philadelphia PA, 1968.

27. Westerhof, N., Bosman, F., de Vries, C.J., Noordergraaf, A. Analog studies of the human

systemic arterial tree. J. Biomech. 2:121-143, 1969

28. Westerhof N, Noordergraaf A. Arterial viscoelasticity: a generalized model. Effect on input

impedance and wave travel in the systematic tree. J Biomech. 1970;3:357-79.

29. Womersley JR: The mathematical analysis of the arterial circulation in a state of oscillatory

motion. Technical Report Wade-TR. 56-614. Wright Air Development Center. Dayton, OH,

1957.

43

Chapter 3

Parameter adaptation to individualize

pressure reconstruction

Berend E Westerhof1, Ilja Guelen1, Wim J Stok2, Karel H Wesseling1,

Nico Westerhof3, Willem Jan W Bos4, Nikos Stergiopulos5,

Jos AE Spaan6

The use of transfer functions (TFs) to reconstruct central pressure from, preferably, non-

invasively obtained peripheral pressure, has received a great deal of attention in the

literature (see below). TFs allow the acquisition of aortic pressure and thereby give more

accurate information about the load on the heart and therefore should have better

prognostic value in the field of cardiovascular disease. Generalized functions, averaged

over groups of subjects, have been shown to provide sufficient improvement to

determine mean and diastolic aortic pressure within limits of accuracy as set by the

AAMI (1). Systolic pressure, being the most variable value, is somewhat more difficult

to derive correctly. Systolic and diastolic pressures are evidently of importance, but the

knowledge of the wave shape of aortic pressure allows for waveform analysis, i.e. the

calculation of the augmentation index (15), reflection index (19,20,28), and indexes of

cardiac oxygen supply and demand (30).

1 BMEYE, Amsterdam, The Netherlands

2 Dept of Physiology, Academic Medical Center, University of Amsterdam, The Netherlands

3 Lab for Physiology, ICaR-VU, VU University medical center, Amsterdam, The Netherlands

4 Dept of Internal Medicine, St Antonius Ziekenhuis, Nieuwegein, The Netherlands

5 Biomedical Engineering Laboratory, Swiss Federal Institute of Technology, Lausanne, Switzerland

6 Dept of Medical Physics, Academic Medical Center, University of Amsterdam, The Netherlands

44

Several approaches have been taken to acquire usable transfer functions, starting as early

as 1970 (3,5,7,9,13,14,16,21-25,27) including methods for calibration (2,3,10-12,29).

Recently, an extensive review of the literature was published (8). Compared to a

generalized TF, more exact results may be expected when a TF is individualized, i.e.

optimized for a particular subject. For instance, a TF can be made more accurate by

accounting for age (9) or sex (13). If extra measurements are performed details of an

individual TF might be obtained (14,25,26).

Earlier we found that the time delay between central and peripheral pressure is an

important parameter in the description of pressure transfer (25,26,31). As this time delay

can be non-invasively obtained, we set out to investigate whether this parameter could be

used to individualize the TF. We tested a simple mathematical TF in which time delay is

incorporated. We used a set of invasively determined brachial and aortic pressures to

explore the usefulness of the approach. We calculated remaining errors for the case in

which the parameters of the TF are optimized for each individual and for the case in

which the parameters are averaged values.

Methods

Measurements

Patients and methods have been described in the report by Lasance et al. (16). Pull-back

pressure recordings were made with a fluid filled catheter in ascending aorta, aortic arch,

descending aorta, brachiocephalic, subclavian, axillary and brachial artery. The data

were sampled at 100 Hz. For our main study we use ascending aortic pressure and

brachial pressure. Aortic and brachial pressure beats were selected so that mean pressure

and heart period were optimally matched. If no pair could be attained with a mean

pressure difference smaller than 9 mmHg and with a difference in heart period less than

90 ms, the beats were not used. With these restrictions, 50 pairs of beats remained of the

74 patients.

45

Pressure transformation analysis

Transfer function

The simple mathematical TF (25) that we use to test our hypothesis, based on a single

uniform tube, is:

(1) Pdistal / Pproximal = (1 + G) ·e -jwDt/ (1 + G ·e-2jwDt)

with G the reflection coefficient at the distal site, taken to be real (24), Dt the time delay

between the distal and proximal site, j the imaginary unit and w angular frequency. The

Fourier transformation of the brachial pressure wave divided by the TF gave the

“reconstructed pressure”. After inverse Fourier transformation the reconstructed pressure

was compared to the measured aortic pressure.

Calculations

First, systolic and diastolic pressures were determined of the aortic and brachial beats.

The Root Mean Square Error (RMSE), calculated with the measured aortic and

measured brachial beat shifted in time with respect to each other so that minimal errors

were obtained, described the difference in wave shape. Next, for each pair of pressures,

the optimal TF (equation 1) was found by iterative procedures. Optimal in this respect is

defined as giving minimal RMSE between aortic and reconstructed pressure. For each

pair of beats, optimal G and Dt were recorded together with the errors in systolic and

diastolic pressures and the RMSE. Subsequently four models were defined. In model 1,

optimal Dt and G for each individual were used. A simplified model requiring only

individualization of Dt while G was set at the group average was called model 2. Model 3

was a generalized TF with both Dt and G set at the group average. Finally, in model 4,

we set Dt to the average value and G to 1, representing total reflection. Augmentation

Index, AI, (15) was calculated from the results of the individualized TF (model 1) and

for the generalized TF (model 3) and compared to the AIs of the ascending aortic

pressure waves as another indication of the truthfulness of the reconstructed wave shape

Statistics

The RMSE and systolic, diastolic and pulse pressure after reconstruction with each of

the TFs were compared to measured aortic pressure, using a paired t-test. Differences

were assumed to be significant for P < 0.05.

46

Table 1

t-te

st

< 0

.001

0.

813

< 0

.001

Mod

el 4

Dt =

0.0

48

G =

1

123

± 18

70

± 9

53

± 13

4.9

± 1

.9

t-te

st

0.

009

0.

136

< 0

.001

Mod

el 3

Dt =

0.0

48

G =

0.6

122

± 19

69

± 9

53

± 13

4.4

± 2

.0

t-te

st

0.

060

0.

172

0.

001

Mod

el 2

Dt =

fit

G =

0.6

121

± 19

69

± 9

52

± 13

4.1

± 2

.0

t-te

st

0.

043

0.

176

0.

001

Rec

onst

ruct

ed

Mod

el 1

Dt =

fit

G =

fit

121

± 18

69

± 9

52

± 13

4.0

± 2

.0

t-te

st

< 0

.001

< 0

.001

< 0

.001

Bra

c

131

± 18

67

± 9

64

± 13

7.5

± 2

.1

Mea

sure

d

Asc

119

± 20

70

± 9

50

± 15

Aor

tic-,

Bra

chia

l- a

nd R

econ

stru

cted

pre

ssur

es

Sys

Dia

PP

RM

SE

Asc

is a

scen

ding

aor

tic p

ress

ure,

bra

c is

bra

chia

l pre

ssur

e. I

n th

e fu

rthe

r co

lum

ns, t

he v

alue

s of

the

reco

nstr

ucte

d pr

essu

res

afte

r

appl

icat

ion

of th

e T

F m

odel

s ar

e lis

ted

with

the

para

met

ers

give

n in

the

head

ing.

47

Results

For the 50 selected beat pairs the difference in mean pressure between brachial artery

and ascending aortic pressure measurements was – 0.4 ± 3.4 mmHg (range – 9 to 9

mmHg). Difference in interbeat interval (IBI) for these beats was – 3.4 ± 27 ms (range –

80 to 50 ms). In Figure 1 the averaged TF calculated form these beats is shown. For each

pair of beats the TF was determined using Fourier analysis, harmonics of each TF were

interpolated and resampled at 1 Hz before averaging. In Table 1, measured ascending

aortic pressure and brachial pressure are listed together with reconstructed pressure using

the four different TF models. Brachial pressure and each of the reconstructed pressures

are tested against aortic pressure. Best results are obtained using the TF with both Dt and

G individualized. Each step of generalization involves an increase in RMSE, which is

small, but statistically significant. Figure 2 shows the mathematical TFs for the

generalized case with and the Dt = 0.048 and G = 0.6 and 1, respectively.

Figure 1

- 2

- 4

- 6

- 8

- 10

5 10 15 20

1

2

3

4

5

frequency [Hz]

ga

inp

ha

se

[ra

dia

ns]

Transfer Function of ascendingaorta to brachial artery, obtainedin 50 patients. Top panel: amplitude of the gain,bottom panel: phase in radians.Errors are SEM.

48

Because RMSE data only give global information of the fits but no details on the wave

shape of the reconstructed aortic pressure wave, four examples are given in Figure 3. In

each case the generalized TF gives distinctly less accurate results compared to the

individualized TF. In the top panel, reconstructed pressure using the generalized TF has

no secondary rise in pressure, called pressure augmentation, while the pressure from the

individualized TF has. The second panel from the top, both reconstructed pressure show

an augmentation but the pressure reconstructed with the individualized TF has a closer

fit. In the third panel, the generalized TF does not damp but augments the oscillations

found in the brachial artery pressure. In the bottom panel, the pressure augmentation is

exaggerated by the generalized TF.

Figure 2

- 2

- 4

- 6

- 8

- 10

5 10 15 20

1

2

3

4

5

frequency [Hz]

ga

inp

ha

se

[ra

dia

ns]

For the AI we found average values of AIasc = 27 ± 15 for ascending aortic pressure;

AIRecInd = 30 ± 14 (NS) for the individualized model 1; AIRecGen = 25 ± 12 (P < 0.05) for

the generalized model 3. In the ascending aortic pressures, no AI was found in 2 cases;

using the individualized model no AI was found in 4 cases, while with the generalized

model this number was 7. Linear regression analysis gave the following descriptions:

Mathematical Transfer Functions. Top panel: amplitude of the gain,bottom panel: phase in radians. On thehorizontal axis: frequency in Hz. Thefully drawn line represents the TransferFunction with optimal parameters forthe group (t = 0.048 s, G = 0.6). Thedashed line is a Transfer Function withcomplete reflection (t = 0.048 s, G = 1).Phase of this Transfer Function isundetermined (“standing wave”).

49

AIRecInd = 0.88·AIasc + 5.4, R2 = 0.77

AIRecGen = 0.72·AIasc + 4.5, R2 = 0.52.

Figure 3

50

100

150

50

100

150

50

100

150

50

100

150

0.5 1.00 0.5 1.00 0.5 1.00

Time [s]

Pre

ssure

[mm

Hg]

Generalizedreconstruction

Individualizedreconstruction

Brachial

Four examples in which the individualized Transfer Functions gives better results than the generalized Transfer

Function. Left, brachial pressures, middle, ascending aortic pressure (drawn) with reconstructed pressure

(dashed) using the generalized Transfer Function. Right, again ascending aortic pressure (drawn) with

reconstructed pressure (dotted) using the individualized Transfer Functions.

50

Discussion We investigated whether individualization of a simple mathematical TF would result in

better estimation of central pressure values and in a better-predicted wave shape. We

found that the wave shape with the individualized TF is better than with the generalized

one; this improvement is significant, but limited. The parameters of the simple TF, Dt

and G, travel time of the pressure wave and reflection coefficient at the end of the

transmission line, respectively, can be measured. Travel time could be measured

performing simultaneous pressure measurements at the sites between which the TF is

defined, and G by measuring pressure and flow at the peripheral site. In the present study

we did not perform these extra measurements but analyzed a set of aortic and brachial

pressures to investigate if the approach would be fruitful. Therefore, we calculated

individual Dt and G from the actual measurements. We then analyzed the results from

each of four different TFs. As expected, the smallest RMSE was found when individual

TFs were used, i.e. with individual Dt and G. When G was fixed to an average value,

RMSE showed a statistically significant increase. Also fixing Dt to an average value

again resulted in a larger RMSE. We found travel time to be the most important

parameter; G was less influential on the results. Comparing the generalized TF with Dt =

0.048 and G = 0.6 (Figure 2) to the measured data of Figure 1, it can be seen that the first

4 harmonics are closely approximated by the TF generated by procedure which

minimizes RMSE, at the cost of higher frequencies. The harmonic at 5 Hz is amply

overestimated by the mathematical TF. Thus, the first four harmonics are the most

important for accurate pressure reconstruction. This explains why the TF with G = 1

gives acceptable results; Figure 2 demonstrates that for the first four harmonics the

difference between both mathematical TFs is negligible.

The AI of the reconstructed pressure using the individualized TF was not significantly

different from the AI of measured ascending aortic pressure, while the AI of the

generalized pressure was. The coefficient of determination was higher in the

individualized model. This is corroborates the findings in RMSE reported above.

51

Figure 4 gives a further underpinning of the importance of delay as a model parameter.

As our set of measurements included brachiocephalic, subclavian, axillary artery, we

calculated TFs between those sites and brachial artery as well. From the Figure it is

apparent that with shorter length of the intermediate arteries, the peak in the TF moves to

higher frequencies. When the mathematical TF was fitted to the first four harmonics,

delays of 0.043s, 0.037s and 0.025s were found, respectively.

Figure 4

5 10 15 20

1

2

3

4

5

gain

Brachiocephalic to brachial

5 10 15 20

1

2

3

4

5

gain

Subclavian to brachial

5 10 15 20

1

2

3

4

5

frequency [Hz]

gain

Axillary to brachial

Transfer functions from brachiocephalic, subclavian andaxillary artery to brachial artery.With shortening of travel time, thepeak moves to a higher frequency.Mathematical Transfer Functions(no error bars) were fitted to thefirst 4 harmonics.

52

Sugimachi et al. (26) took our earlier work (25) as a basis for further research as well.

They used the distal Windkessel load of their model to determine flow and use wave

separation and the shift theorem (25) with individualized time delay to reconstruct

central pressure. They also concluded this delay is the key parameter to individualize the

TF and that Windkessel parameters are of limited importance. However, they were not

able to improve reconstruction with individualization, which was probably due to the

rather small study group and the relative uniformity of the subjects.

Obviously, for the method to be useful in practice, the extra measurements should be

non-invasive and convenient. As G was found to be of less importance than Dt, the latter

should preferably be measured. One option is to simultaneous measurement of brachial

and axillary artery pressure by applanation tonometry and determining the delay. Echo-

or impedance cardiography could also be considered for the required central information.

Another possibility is to use the delay between the R-top in the ECG and the upstroke in

peripheral pressure, although the preejection period remains an uncertain factor.

Sugimachi et al. (26) further suggest the use of carotid and radial pulse recordings or the

use of the second heart sound and the dicrotic notch of the distal pulse.

The finding that a generalized TF can be used to accurately reconstruct central pressures

corresponds to findings in literature (5,8,14), which, however, have been questioned as

well (13,17). One could summarize that in individual cases a generalized TF might not

be adequate, for group averages however the results can be very good. Thus, inter-

individual differences may be a problem, but intra-individual differences have been

shown to be smaller (5). This could imply that one individualization procedure may be

sufficient, allowing following a subject over a longer period of time (11,29).

It has also been noticed that the peripheral pressure (4) or photoplethysmographic wave

shape (6,18) changes little during local infusion of vasoactive drugs, thus confirming the

conclusion that the TF is quite insensitive to changes in G (31). On the other hand,

systemic infusion of these vasoactive substances has much greater effect on difference

between central and peripheral wave shape (4,6,18). This may result from to the change

in mean systemic pressure: for instance, an increase in mean pressure will decrease

arterial compliance and thus increase wave speed. This will decrease Dt and thus modify

one of the most sensitive parameters describing the TF. Therefore, although

individualization of TF may have only a minor effect in the present study, the method

may prove useful in protocols involving systemic infusion of vasoactive drugs.

53

For higher frequencies, our generalized TF in Figure 1 differs somewhat from the

original TF as given by Lasance et al. (16). One reason is that, in the original study, pairs

of 2 successive aortic as well as 2 successive brachial beats were selected for analysis,

while we used single beats, so that a meaningful RMSE could be calculated. Another

obvious reason is that the study populations differ in size. We discarded pairs of beats

with too large differences in mean pressure and heart period. Mean pressure will fall due

to resistance in the arteries. However, resistance of the larger arteries like the brachial

artery is usually quite small and a pressure drop of 10 mmHg in mean pressure not likely

to occur. Since the measurements were not recorded simultaneously, we wanted to

exclude beats in which mean pressure did not remain stable between measurements. A

similar reasoning holds for IBI. Nonetheless, the first few harmonics of both TFs are

remarkably close.

Limitations

In this study we determined the optimal time delay from the actual measurements of

ascending aortic and brachial pressure. In a practical application, the time delay should

be determined from other measurements as the central pressure will not be available.

However, here we wanted to investigate the feasibility of the procedure before further

effort was put into developing a method to establish a time delay.

Another limitation of the study is that the generalized TF is based on the measurements

of central and distal pressure, in other words, the learning population and the study

population are the same. Therefore the results are optimal for this group and the same TF

would perform less well in a random population.

54

Future developments

A time delay might be conveniently obtained from a time difference between ECG and

distal pressure. A formula would have to be developed to predict travel time from this

delay by correcting for the time between R-top and ejection. Whether this method would

give delays of sufficient accuracy remains to be determined.

Acknowledgments

We cordially thank Jan Paul Barends of the Lab for Physiology, ICaR-VU, VU University medical center,

Amsterdam, The Netherlands for his inspiring help with the mathematics of in this study.

55

References

1. American national standard for electronic or automated sphygmomanometers. AAMI SP 10-

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1–25.





3. Bos WJ, van Goudoever J, van Montfrans GA, van den Meiracker AH, Wesseling KH.


Circulation. 1996;94:1870-5.



1995;26:315-20.



pressure: validation of generalized transfer function. Circulation 1997;95:1827-1836.


Ritter JM, Anggard EE. Photoplethysmographic assessment of pulse wave reflection: blunted

response to endothelium-dependent beta2-adrenergic vasodilation in type II diabetes mellitus.

J Am Coll Cardiol. 1999;34:2007-14.



1999;46:698-706



2004;17:1059-67. Review.



1996;14:243-50.


and pressure decrement. Cardiovasc Res 33: 698-705, 1997






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13. Hope SA, Tay DB, Meredith IT, Cameron JD: Use of arterial transfer functions for the

derivation of aortic waveform characteristics. J Hypertens 2003;21:1299 –1305.


multi-branched model of the human upper limb. Am J Physiol 1995;269:H1363–H1369.

15. Kelly R, Hayward C, Avolio A, O'Rourke M. Noninvasive determination of age-related

changes in the human arterial pulse. Circulation. 1989;80:1652-9.



17. Lehmann ED. Estimation of central aortic pressure waveform by mathematical transformation

of radial tonometry pressure data. Letter. Circulation. 1998;98:186-7.

18. Millasseau SC, Kelly RP, Ritter JM, Chowienczyk PJ. Determination of age-related increases

in large artery stiffness by digital pulse contour analysis. Clin Sci (Lond). 2002;103:371-7.

19. Murgo JP. Westerhof N. Giolma JP. Altobelli SA. Aortic input impedance in normal man:

relationship to pressure wave forms. Circulation. 1980;62:105-16.

20. Nichols WW, O’Rourke MF: McDonald’s Blood Flow in Arteries,.4th ed. Edward Arnold,

London, 1998.

21. O’Rourke MF: Influence of ventricular ejection on the relationship between central aortic and

brachial pressure pulse in man. Cardiovasc Res 1970;4:291–300.

22. O’Rourke MF, Nichols WW: Use of arterial transfer function for the derivation of aortic

waveform characteristics (letter). J Hypertens 2003;21:2195–2199.

23. Pauca AL, O’Rourke MF, Kon ND: Prospective evaluation of a method for estimating

ascending aortic pressure from the radial artery pressure waveform. Hypertension

2001;38:932–937.

24. Segers P, Carlier S, Pasquet A, Rabben SI, Hellevik LR, Remme E, De Backer T, De Sutter J,

Thomas JD, Verdonck P. Individualizing the aorto-radial pressure transfer function:

feasibility of a model-based approach. Am J Physiol Heart Circ Physiol. 2000

Aug;279(2):H542-9.



26. Sugimachi M, Shishido T, Miyatake K, Sunagawa K. A new model-based method of

reconstructing central aortic pressure from peripheral arterial pressure. Jpn J Physiol.

2001;51:217-22.

27. Stok WJ, Westerhof BE, Blum V, Karemaker JM. Changes in finger-aortic pressure transfer

function during and after incremental bicycle exercise. Submitted.

28. Westerhof BE, Guelen I, Westerhof N, Karemaker JM, Avolio A. Quantification of wave

reflection in the human aorta from pressure alone. This Thesis. Submitted.




Hypertens. 2002;20:1981-6.

57

30. Westerhof BE, van Montfrans GA, Guelen I, Wesseling KH, Spaan JA, Parati G, Westerhof

N, Karemaker JM, van Lieshout JJ, Bos WJ. Variations in cardiac oxygen supply and demand

in hypertensive subjects after rising. This Thesis.

31. Westerhof BE, Guelen I, Stok WJ, Wesseling KH, Spaan JA, Westerhof N, Bos WJ,

Stergiopulos N. Sensitivity of pressure transfer to arterial parameters. This Thesis.

59

Chapter 4

Quantification of wave reflection in the

human aorta from pressure alone

Berend E. Westerhof1, Ilja Guelen1, Nico Westerhof2,

John M. Karemaker3, Alberto Avolio4

Wave reflections affect the pressure and flow wave in the proximal aorta (1) and their

contribution depends on their magnitude and time of return. When the reflected wave

arrives in systole it augments pressure. This augmentation is greater when the heart is

hypertrophied. In heart failure wave reflections affect the flow wave negatively, thereby

reducing stroke volume and cardiac output (2–4).

One way to estimate the amount of reflection is by waveform analysis in which aortic

pressure is separated into its forward and backward components (1,5,6). The magnitudes

of the backward (reflected) wave and the forward wave allow for the estimation of the

amount of reflection. This waveform analysis requires measurement of both pressure and

flow waves and derivation of characteristic impedance. A method that requires the

measurement of pressure only is computation of the Augmentation Index, AI (7,8). AI

gives reproducible results (9,10) and is in use in clinical settings (11–14). However, AI

is determined by both the magnitude and timing of the reflected wave. This is evident

from Figure 1, panel A. In this figure the original pressure wave is separated into its

forward and backward components and then reassembled for different delays of the same

backward wave. AI is clearly influenced by the time of return of the reflected wave.

1 BMEYE, Amsterdam, The Netherlands 2 Physiology, ICaR-VU, VU University medical center, Amsterdam, The Netherlands 3 Physiology, Academic Medical Center, University of Amsterdam, The Netherlands 4 Graduate School of Biomedical Engineering, University of New South Wales, Sydney Australia

60

Panel B gives two examples in which AI suggests no wave reflection (left) or a reflected

wave that is larger than the forward wave (right). Thus the magnitude of wave reflection

cannot be quantified from AI. This may explain why the AI may not be a good measure

of central pulsatile load in patients with congestive heart failure (15).

Figure 1

50

mm

Hg

50

0m

l/s

Pmeasured

Pforward

Pbackward

P-41 ms

Pmeasured

P+41 ms

P+123 ms

PP�P

A

B

1 s

1 s 1 s

50

mm

Hg

In this study we investigate a new method to calculate pressure wave reflection in the

human proximal aorta based on measured pressure alone and derive an index to quantify

reflection independent of the time of return of the reflected wave. We assume a

triangular shape of the flow wave based on the timing features of the aortic pressure.

This is a reasonable assumption in view of the ascending aortic flow patterns obtained by

a variety of flow measurement techniques (6). Subsequently, separation of the pressure

wave into its forward and backward components is carried out using the measured

The Augmentation Index depends not only

on the magnitude but also on the time of

return of the reflected wave. In panel A, on

the left, the measured pressure, flow, and the

derived forward and backward pressure

waves are shown. On the right the pressure

waves obtained by summation of the

forward and backward waves are shown

when the backward wave is shifted in time.

Thus, with the same magnitude of the

reflected wave, but different times of return,

the wave shape, the Pulse Pressure, PP, and,

consequently, the Augmentation Index (AI),

∆P/PP, are different. AIs from top to bottom

were 0.20, 0.21, 0.13 and undefined,

respectively, while Reflection Index (RI, see

text) was 0.35. Panel B gives two examples

in which AI gives erring results. On the left,

the backward wave returns when the

forward wave is already falling. AI was

found to be 0.03 while the RI was 0.33. On

the right, the forward wave is still rising

when the backward wave returns, resulting

in an AI of 0.59, suggesting that the

backward wave is larger than the forward

wave. RI in this case was 0.44.

61

pressure and the triangular flow wave. The results will be compared to the actual results

obtained using the measured flow wave in the aorta. The Augmentation Index will also

be assessed.

Methods

(Abbreviations are listed after the References)

Simultaneous measurements of pressure and flow velocity, Pm and Fm, in the human

ascending aorta recorded for previous studies were used. Twelve healthy subjects were

catheterized for various clinical indications. Five healthy subjects of these twelve were

kindly provided through personal communications with Dr Rubal. Data of six subjects

were taken from the publications of Murgo et al. (5,15–18), including base line

conditions, exercise and Valsalva maneuvers. One subject performing a Mueller

maneuver was analyzed (18). In 5 patients pressure and flow velocity were measured

directly following a selective coronary angiographic procedure to evaluate ischemic

heart disease and were kindly provided by Dr. Blum (20). In this group of 17 humans the

total number of analyzed beats including the maneuvers was 26. All participants gave

informed consent and the respective institutional review committees approved the

studies.

Figure 2

-10

50

100

150

0.4 0.8

Pre

ssu

re(m

mH

g)

Flo

wve

locity

(cm

/s)

Time (s)

Principle of method. The flow is

approximated by a triangle. End-

diastole and the incisura (second

vertical line) of the measured pressure

wave determine the start and end of the

triangle. The peak is set at the inflection

point (first vertical line) or at 30% of

ejection time (arrow). The inflection

point is determined by standard method.

Calibration of flow is not required (see

text).

62

A catheter equipped with a micromanometer and an electromagnetic flow velocity

sensor was used for the measurements (Millar Instruments, Houston, Texas). All signals

were sampled at a rate of 100 Hz.

The method to construct a flow wave makes use of the notion that the flow wave can be

approximated by a triangular shape during ejection. The duration and the time of peak

flow of this triangle can be derived from the pressure wave shape as follows (Figure 2).

The time of end-diastolic aortic pressure is the time of valve opening and the start of

ejection. The incisura gives the time of valve closure and the end of ejection. These

times determine the ejection time and thus the base of the triangle. In a first analysis the

time of the peak of the triangle is set at the time of the inflection point of the measured

pressure wave in systole. The inflection point is derived using higher order derivatives of

pressure as previously described (7,8). In a second analysis on the same subjects the

maximum of the triangular flow was set at 30% of the ejection time, the average found

from the flow measurements (see results). This was done in order to test the condition

when an inflection point in the pressure wave cannot be explicitly identified.

The triangular flow with the peak time set at the inflection point of the measured

pressure was called FtIP, and the flow with the peak time fixed at 30% of the ejection

time was called Ft30.

In the calculations of forward, Pf, and backward pressure, Pb, the following equations are

used (5):

Pf(t) = (P(t) + Zc·F(t))/2

and

Pb(t) = (P(t) – Zc·F(t))/2

The P(t) in this case is the measured pressure wave and F(t) is either the measured flow

wave or the constructed flow wave with a triangular shape. Zc is the characteristic

impedance of the proximal aorta. The total input impedance P/F was calculated in the

frequency domain and the characteristic impedance was derived from the averaged value

of the 4th to 7th harmonic of the input impedance modulus (6). Zc was determined for all

three flow wave shapes.

63

From the above equations it can be seen that the product Zc·F appears in the calculation

of the forward and backward waves. Zc is a ratio of pressure and flow, P/F (explicitly, Zc

= Pf/Ff = – Pb/Fb). Thus by multiplication of Zc and F the amplitude of flow is eliminated

and Zc·F is independent of the flow calibration. When flow is twice as large, Zc is twice

as small but the product remains the same. A similar reasoning holds whether flow

velocity or volume flow is used in the calculations. Thus calibration of the flow wave is

not required, the shape is of importance only, and so stroke volume does not have to be

determined. In the remaining text flow velocity will simply be called flow.

Using the above equations we calculated forward and backward pressure waves on the

basis of the measured pressure, Pm, in combination with the measured flow, Fm, and each

of the two triangular flows, FtIP and Ft30. The amplitudes of the forward waves obtained

by the triangular flows, |PftIP| and |Pf

t30|, were compared with the amplitude of the

forward pressure wave derived from the measured flow |Pfmf|. Similarly the backward

waves |PbtIP| and |Pb

t30| were compared to |Pbmf|.

The accuracy of the shapes of the forward and backward pressure waves were

determined by calculating the Root Mean Square Error (RMSE) between the waves

derived from triangular and measured flow waves.

The Reflection Index, RI, was defined as:

RI = |Pb|/(|Pf|+|Pb|).

The RIs derived from the measured flow, and from the two triangular flows, are called

RImf, RItIP and RIt30, respectively. Because the reflection index is a ratio of two pressures

calibration of pressure is not required.

The RI was calculated instead of the Reflection Magnitude defined as RM= |Pb|/|Pf|, to

facilitate comparison with the augmentation index. We calculated the Augmentation

Index, AI, as the augmentation of the pressure, ∆P, divided by pulse pressure, PP. See

Figure 1.

All derivations were carried out in a set of 26 simultaneous aortic pressure and flow

pairs recorded in the group of 17 subjects. Data are presented as mean ± standard

deviation. Repeated Measures Analysis of Variance was used to investigate differences

between derivations based on measured flow, both triangular flows and augmentation

64

index. Cases in which no inflection point was found and thus FtIP and AI could not be

determined were excluded from testing. Distributions were normal and a parametric test

was used. Differences were assumed to be significant if P < 0.05. Regressions of RItIP

and RIt30 and AI on RImf were calculated and plotted for all available data points.

Regression of RIt30 on RImf was also calculated using all heartbeats excluding those that

had no inflection point.

To investigate the influence of convexity and concavity of the flow wave on the

reflection index we approximated the most extreme cases of convexity and concavity in

our study population by using a trapezoidal flow and compared it to the results from

triangular flow.

Results

Median age of the subjects was 50 years, ranging from 29 to 57 years. Excluding

exercise and Valsalva maneuvers, systolic and diastolic pressures were 126 ± 17, 75 ± 10

mmHg (mean ± SD) and heart rate was 69 ± 6 bpm. Ejection time and the time of the

inflection point in pressure were 0.31 ± 0.03 and 0.10 ± 0.03 seconds, respectively. Thus

the ratio of time of inflection point to ejection period was 32 ± 9%. The ratio of time of

peak flow to ejection period was 30 ± 5%.

Figure 3

0.4 0.80

50

100

150

Pre

ssure

(mm

Hg)

Time (s)

Pmeasured

Pforward

Pbackward

Example of a measured pressure andforward and backward waves whencalculated from measured flow (boldlines) and calculated from triangularflow, FtIP (thin lines).

65

Figure 3 shows an example of the measured pressure wave and the calculated forward

and backward pressure waves using measured flow, bold lines, and triangular flow based

on the inflection point in the pressure wave, thin lines.

Table 1 shows the averaged amplitudes of the forward and backward waves based on al

three methods.

Table 1

Amplitudes of the forward and backward waves and the values of the Reflection Index and

Augmentation Index over 21 determinations in 17 humans.

Mean ± SD ANOVA Range of differences

min max

|Pfmf| 33.2 ± 7.3

|PftIP| 35.0 ± 6.4 NS -6.4 8.0

|Pft30| 33.4 ± 7.0 NS -10.8 4.5

|Pbmf| 23.4 ± 7.2

|PbtIP| 22.5 ± 6.4 P < 0.05 -3.3 2.7

|Pbt30| 21.7 ± 6.9 P < 0.001 -4.5 1.2

RImf 0.41 ± 0.04

RItIP 0.39 ± 0.05 NS -0.06 0.02

RIt30 0.39 ± 0.04 NS -0.07 0.03

AI 0.34 ± 0.16 P < 0.01 (range: 0.02 to 0.59)

The |P| are the amplitudes of the pressure waves in mmHg, RI is Reflection Index, and AI Augmentation Index.

The subscripts f and b indicate forward and backward waves. The superscripts mf, tIP, t30 give results that are

based on the wave analysis using measured pressure, together with measured flow, triangular flow with peak

time at inflection point of pressure and triangular flow where peak time is set at 30% of ejection time,

respectively. Parametric ANOVA testing was used. The range of differences gives smallest and largest

deviation from reference, but in the case of AI it gives the range of all AI determinations.

The average amplitudes of the forward waves PftIP and Pf

t30 are not different from the

reference. The average amplitudes of the backward waves PbtIP and Pb

t30 are different

from the reference. This difference, however, is quite small, namely 0.9 mmHg for PbtIP

and 1.8 mmHg for Pbt30. The average Reflection Index and Augmentation Index are also

66

presented in Table 1. Only AI differs from RImf. AI also has a larger variance, while RItIP

and RIt30 do not (F-test).

Table 2 gives the RMSErrors of the forward and backward waves when using a

triangular flow compared with the actual forward and backward waves.

Table 2

RMSErrors of the forward and backward waves over 21 determinations in 17

humans.

RMSError Mean ± SD Range

min max

PftIP 1.83 ± 0.68 0.90 3.69

Pft30 1.79 ± 0.99 0.63 5.07

PbtIP 1.83 ± 0.68 0.90 3.69

Pbt30 1.79 ± 0.99 0.63 5.07

Errors in mmHg. For identification of the parameters see table 1.

Figure 4 shows the relations between the RI derived from the measured pressure and

flow and the RI calculated from the measured pressure and triangular flows (A and B).

The relation for the triangular flow based on the inflection point in pressure can be

described by: RItIP = 0.86 RImf + 0.03 (R2 = 0.73, n = 21). For the relation between the

triangular flow with its maximum set at 30% of ejection time, we found RIt30 = 0.84 RImf

+ 0.04 (R2 = 0.88, n = 26). In Figure 4C the relation between the Augmentation Index

and the Reflection Index based on measured pressure and flow is shown, described by

AI = 2.62 RImf – 0.74 (R2 = 0.57, n = 21). Both intercept and slope contribute to the

model, whereas in the regressions of RItIP and RIt30 on RImf the intercepts do not

contribute. The range of the AI is much larger than that of the RI. In 5 cases no inflection

point was found in the pressure and thus panels A and C of Figure 4 show 21 data points

while panel B shows all 26 points. When the 5 points in which no inflection point could

be determined are excluded, the relation between RIt30 and RImf becomes RIt30 = 0.77

RImf + 0.06 (R2 = 0.67, n=21). The data is also presented as a Bland-Altman plot in

Figure 5. Note that the AI is too low for small RI and too high for large RI.

67

Figure 4

RItIP

0.2

0.4

0.6

RIm

f

RIt30

0.6

0.4

0.2 0

00

.20

.40

.6

RIm

f

AI0.6

0.4

0.2 0

00

.20

.40

.6

RIm

f

AB

C

RI

=0

.86

xR

I+

0.0

3tIP

mf

R=

0.7

32

0.6

0.4

0.2 0

0

RI

=0

.84

xR

I+

0.0

4t3

0m

f

R=

0.8

82

AI

=2

.62

xR

I-

0.7

4m

f

R=

0.5

72

Rel

atio

n be

twee

n R

efle

ctio

n In

dex

calc

ulat

ed f

rom

mea

sure

d pr

essu

re a

nd m

easu

red

flow

on

the

hori

zont

al a

xes,

RIm

f and

, on

the

vert

ical

axe

s, c

alcu

late

d fr

om p

ress

ure

and

tria

ngul

ar f

low

s, R

ItIP (

A, n

= 2

1) a

nd R

It30 (B

, n =

26)

,

and

also

the

Aug

men

tatio

n In

dex

(C, n

= 2

1).

68

Figure 5

AB

C

00

.20

.40

.6

-0

.2

-0

.4

0.2

0.4

0.0

-0

.2

0.2

-0

.4

0.4

0.0

-0

.2

0.2

-0

.4

0.4

0.0

00

.20

.40

.60

0.2

0.4

0.6

RIRItIPmf

-

(RItI

P+

RI

)/2

mf

(RIt3

0+

RI

)/2

mf

(AI

+R

I)/

2m

f

RIRIt30mf

-

AIRI -mf

Bla

nd-A

ltman

plo

t of

Ref

lect

ion

Indi

ces

(A, n

= 2

1 an

d B

, n =

26)

and

Aug

men

tatio

n In

dex

(C, n

= 2

1). D

ashe

d lin

es

are

aver

ages

; dot

ted

lines

are

95

% c

onfi

denc

e in

terv

als.

69

While RItIP and RIt30 are comparable with the measured reflection index, RImf, AI is not

proportional to the RImf.

Figure 6

0.2 0.4 0.6 0.80.2 0.4 0.6 0.8

150

100

50

0.2 0.4 0.6 0.8

Measured flowTriangular flowTrapezoid flow

0.2 0.4 0.6 0.8

200

400

600

800

1000

Flo

w(m

l/s)

Pre

ssu

re(m

mH

g)

Time (s)Time (s) The two most extreme cases of convexity (left) and concavity (right) of

the flow wave shape. A trapezoidal flow approximates the measured flow

and gives better estimates of RI. See text for calculated RIs. The

triangular flow can be based on measured pressure, but a trapezoidal flow

wave cannot.

Figure 6 shows the extreme cases of convex and concave flow in our study population.

On the left, the measured pressure and convex flow give a reflection index of 0.33, with

a triangle this is 0.28 and with the trapezoid 0.33 is found. In the case of concavity, on

70

the right in Figure 6, measured pressure and flow give 0.49, with a triangle this is 0.44,

with the trapezoid 0.48 is found.

Discussion We found that from aortic pressure measurement alone and an assumed triangular flow

wave derived from the timing features of the pressure wave, an accurate estimate of the

Reflection Index can be obtained. The amplitudes of the forward waves calculated from

the triangular flows are not significantly different from those calculated from measured

pressure and flow, but the amplitudes of the backward waves derived from triangular

flows are different. The comparison of |PbtIP| and |Pb

t30| with |Pbmf|, however, shows that

the differences are small, particularly the difference between |PbtIP| and |Pb

mf|.

The Reflection Index derived from the triangular flow Ft30, with maximal flow at 30% of

ejection, shows the strongest correlation, panel B in Figure 4. This correlation, however,

is based on more data, including very low values occurring during Valsalva maneuvers

and during one of the exercise recordings. In these data no inflection point was found

and therefore RItIP and AI could not be determined. When these five points are also

excluded from the analysis of RIt30, the correlation between RIt30 and RImf becomes

weaker than the correlation between RItIP and RImf. Thus the use of the inflection point in

the pressure wave is preferred to determine the flow wave shape but in case an inflection

point cannot be found in the pressure wave, the 30% value of ejection time for the peak

time still gives useful results. In all situations in which an Augmentation Index can be

determined, the Reflection Index using the flow wave based on the inflection point can

be calculated as well.

We defined Reflection Index as the ratio |Pb|/(|Pf|+|Pb|). Wave reflection is usually

quantified as the ratio |Pb|/|Pf|, which we here call RM for reflection magnitude. The RI is

conceptually comparable with the Augmentation Index because both give a similar ratio.

For the RI the backward wave, |Pb|, with respect to the summed waves, |Pb| + |Pf|, is

derived. For the AI the secondary pressure increase, related to the backward wave, with

respect to total wave (pulse pressure) is calculated. The summation of the amplitudes |Pb|

+ |Pf| is well defined because timing is excluded from the calculation. In AI the pulse

pressure is the summation of the wave shapes, i.e., Pb(t) + Pf(t) and this sum depends on

timing as discussed above (Figure 1). The RM and RI as used in the present study can be

converted into each other without loss of information:

71

RM = RI / (1 – RI), and RI = RM / (1 + RM).

When the Reflection Magnitude, RM, is calculated as RM = |Pb| / |Pf|, average values are

0.70 ± 0.13, 0.64 ± 0.12 and 0.64 ± 0.11 for RMmf, RMtIP and RMt30, respectively. Both

RMtIP and RMt30 are significantly different from RMmf .The regressions are RMtIP = 0.79

RMmf + 0.08 (R2 = 0.72, n = 21) and RMt30 = 0.73 RMmf + 0.13 (R2 = 0.65, n = 21).

These regressions are comparable to those found earlier for the regressions of RItIP and

RIt30 on RImf with exclusion of the data without an inflection point.

We found that the AI varies over a much larger range than the Reflection Index (Figure

4C). From the Bland-Altman plot (Figure 5), we see that both RItIP and RIt30 give results

comparable to the measured reflection index, RImf. However, AI is not proportional to

the RImf as can also be seen from Figure 4C in which the regression line has an intercept

different from zero. This results from the contribution to wave shapes of incident and

reflected waves and on the timing of the reflected wave as can be seen from Figure 1.

Even when a reflected wave of similar amplitude returns, the time of reflection has a

strong effect on the AI. When the reflected wave returns in diastole (right bottom curve

in panel A of Figure 1) the AI does not give a good estimate of the amount of reflection.

By using the information contained in the flow wave, even in the simplified form of a

triangle, wave analysis can be carried out and the forward and backward pressure waves

can be obtained. From the amplitudes of these waves Reflection Index and Reflection

Magnitude can be calculated, without the confounding effects of timing.

The triangular flow, using the assumption that its time of maximum is 30% of the

ejection time, is based on average data. To obtain some insight into the errors, we

calculated the Reflection Index as a function of peak time, while the ejection period and

heart rate were kept constant. We found that the percentage error in RI was about half

the percentage error in peak time. Thus, a 10% error in time of peak flow results in a 5%

error in RI.

The wave shape of pressure and flow depend on the pump function of the heart and the

arterial load. In a strong heart, which approximates a flow source, the flow wave will be

convex. In a weak heart, which approaches a pressure source, the flow wave will be

scalloped or concave (2). We found that convexity of the flow wave shape leads to

overestimation and concavity leads to underestimation of the reflection index. We have

calculated the reflection index for the most extreme cases of convexity and concavity

using a triangular flow and a trapezoidal flow. The trapezoidal flow can accurately

72

mimic convexity or concavity (Figure 6). This better approximation of the flow wave

results in better estimations of the reflection index with errors of 2% and 0%

respectively. Using a triangular flow these errors were 15% and 10%. However, these

examples are chosen at the extreme of the range of aortic flows. In practice we do not

have the information to construct a trapezoidal flow wave shape.

The characteristic impedance derived from triangular flow wave is close to that one

derived from measured pressure and flow. The relations between characteristic

impedance calculated from measured pressure and flow, and from the triangular flows,

FtIP and Ft30, are given by the following correlation coefficients: R2 = 0.86 for FtIP and R2

= 0.89 for Ft30. Thus there is good relation between the characteristic impedances. We

also found that a factor 2 change is Zc results in about 16% error in RI. This is a

substantial change and any real changes in Zc would be much smaller than that.

The use of the 30% of ejection time allows the calculation of the Reflection Index even

if an inflection point in the systolic pressure wave is not apparent. Thus, our method

allows comparison of the Reflection Index in young and old subjects. However, by using

an average value of 30% of ejection time, individual differences are not accounted for.

The use of the inflection point of pressure allows for the estimation a peak time for an

individual patient. The calculations to find peak flow from the timing features of the

pressure waves, the separation of the waves, and the subsequent calculation of the

Reflection Index are straightforward and can be automated, allowing for Reflection

Index to be routinely obtained.

As shown in the methods section flow calibration is not required. Moreover, when the

Reflection Index is calculated, calibration of the pressure is not required either. This

implies that derivation of the Reflection Index has the same advantage as the derivation

of the AI, namely that calibration is not necessary.

Limitations

The triangular wave shape that is assumed for the flow is an approximation that may

differ from the actual flow wave shape. In the present study however, this approximation

gave results close to those obtained with high fidelity measured flows even during the

Valsalva maneuver and exercise. We therefore believe that the approximation of flow

with a triangular shape to calculate RI is a useful one and we showed that the results can

give potentially more detailed information on wave reflection than AI.

73

Perspectives

We suggest that the calculations to quantify wave reflection can also be performed using

the carotid pressure wave as a surrogate for the aortic pressure. In this study we have

shown that the RI does not depend on the calibration of pressure. Therefore the pressure

can be obtained non-invasively, as, for instance, by applanation tonometry. The entire

derivation then may be based on the noninvasive measurement of the pressure wave

shape only. For instance, the effects of pharmacological interventions on the timing of

the reflected wave (21) could be studied without measurement of aortic flow. Also,

accurate estimation of the amount of reflection as a function of age in large

epidemiological studies is considerably more practical when flow measurement is not

required (22). When the calculations are automated, the derivation of the Reflection

Index would be as easy as the derivation of the Augmentation Index with improved

quantitative information on the magnitude of wave reflection.

Acknowledgements

We cordially thank Dr Viktor Blum, and the Cardiology Service, Brooke Army Medical Center, Fort Sam Houston, TX 78234 (Dr Bernard J. Rubal), for allowing us to use their data.

74

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2. Westerhof N, O'Rourke MF. Haemodynamic basis for the development of left ventricular

failure in systolic hypertension and for its logical therapy. J Hypertens. 1995;13:943-52.

3. O’Rourke, MF. Mechanism of a hypertensive response to exercise. J Am Coll Cardiol. 2004;

44:1527 (Letter).

4. WK Laskey and WG Kussmaul. Arterial wave reflection in heart failure. Circulation.

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5. Murgo JP, Westerhof N, Giolma JP, Altobelli SA. Manipulation of ascending aortic pressure

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122-132.

6. Nichols WW, O’Rourke MF. Vascular impedance. In: McDonald’s Blood Flow in Arteries.

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7. Kelly R, Hayward C, Avolio A, O'Rourke M. Noninvasive determination of age-related

changes in the human arterial pulse. Circulation. 1989;80:1652-9.

8. Takazawa K, Tanaka N, Takeda K, Kurosu F, Ibukiyama C. Underestimation of vasodilator

effects of nitroglycerin by upper limb blood pressure. Hypertension. 1995;26:520-3.

9. Wilkinson IB, Fuchs SA, Jansen IM, Spratt JC, Murray GD, Cockcroft JR, Webb DJ.

Reproducibility of pulse wave velocity and augmentation index measured by pulse wave

analysis. J Hypertens. 1998;16:2079-84.

10. Papaioannou TG, Stamatelopoulos KS, Gialafos E, Vlachopoulos C, Karatzis E, Nanas J,

Lekakis J. Monitoring of arterial stiffness indices by applanation tonometry and pulse wave

analysis: reproducibility at low blood pressures. J Clin Monit Comput. 2004;18:137-44.

11. London GM, Pannier B, Guerin AP, Marchais SJ, Safar ME, Cuche JL. Cardiac hypertrophy,

aortic compliance, peripheral resistance, and wave reflection in end-stage renal disease.

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12. Asmar RG, London GM, O'Rourke ME, Safar ME; REASON Project Coordinators and

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13. Kelly RP, Millasseau SC, Ritter JM, Chowienczyk PJ. Vasoactive drugs influence aortic

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14. Hayashi T, Nakayama Y, Tsumura K, Yoshimaru K, Ueda H. Reflection in the arterial system

and the risk of coronary heart disease. Am J Hypertens. 2002;15:405-9.

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15. Mitchell GF, Tardif JC, Arnold JM, Marchiori G, O'Brien TX, Dunlap ME, Pfeffer MA.

Pulsatile hemodynamics in congestive heart failure. Hypertension. 2001;38:1433-9.

16. Murgo JP. Westerhof N. Giolma JP. Altobelli SA. Aortic input impedance in normal man:

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17. Murgo JP. Westerhof N. Input impedance of the pulmonary arterial system in normal man.

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18. Murgo JP. Westerhof N. Giolma JP. Altobelli SA. Effects of exercise on aortic input

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76

List of abbreviations

AI Augmentation Index calculated as pressure augmentation divided by

pulse pressure, ∆P/PP

Fm measured flow wave

FtIP triangular flow wave with maximum flow at the time of the inflection

point in the pressure wave

Ft30 triangular flow wave with maximum flow at the time of 30% of

ejection time determined from the pressure wave

∆P pressure augmentation, the extra rise in pressure after an inflection

point

PP pulse pressure

Pm measured pressure wave

Pf(t) forward or incident pressure wave as a function of time

Pb(t) backward or reflected pressure wave as a function of time

Pfmf, Pb

mf forward, backward pressure wave determined using measured flow

PftIP, Pb

tIP forward, backward pressure wave determined using FtIP

Pft30, Pb

t30 forward, backward pressure wave determined using Ft30

|Pf| amplitude of Pf

|Pb| amplitude of Pb

RI Reflection Index calculated as |Pb|/(|Pf|+|Pb|)

RM Reflection Magnitude calculated as |Pb|/|Pf|

RImf, RMmf RI and RM calculated from measured pressure and measured flow

RItIP, RMtIP RI and RM calculated from measured pressure and FtIP

RIt30, RMt30 RI and RM calculated from measured pressure and Ft30

Zc characteristic impedance

77

Chapter 5

Variations in cardiac oxygen supply and

demand in hypertensive subjects after rising

Berend E Westerhof1, Gert A van Montfrans2, Ilja Guelen1;

Karel H Wesseling1, Jos AE Spaan3, Gianfranco Parati4, Nico Westerhof5,

John M Karemaker6, Johannes J van Lieshout2,

Willem Jan W Bos7

The increased risk of sudden cardiac death soon after awakening suggests mechanisms

that are particularly likely to occur during this time. Specifically, the increase in heart

rate and blood pressure early in the morning increases cardiac oxygen demand and has

been associated with morning excess of acute myocardial infarction (1–3). We

hypothesized that in hypertensive subjects this early morning increase in heart rate and

blood pressure also affects the oxygen supply potential, further compromising the

relationship between cardiac oxygen supply and demand. To test our hypothesis we

analyzed a group of hypertensive patients; a group of normotensive volunteers served as

reference.

1 BMEYE, Amsterdam, The Netherlands 2 Dept of Internal Medicine, Academic Medical Center, University of Amsterdam, The Netherlands 3 Dept of Medical Physics, Academic Medical Center, University of Amsterdam, The Netherlands 4 II Cardiology Unit, S. Luca Hospital, University of Milano-Bicocca and Istituto Auxologico, Milano Italy 5 Lab for Physiology, ICaR-VU, VU University medical center, Amsterdam, The Netherlands 6 Dept of Physiology, Academic Medical Center, University of Amsterdam, The Netherlands 7 Dept of Internal Medicine, St Antonius Ziekenhuis, Nieuwegein, The Netherlands

78

Pulse wave analysis was performed to determine parameters which were shown to

correlate to cardiac oxygen supply potential, cardiac oxygen demand, and the supply -

demand ratio. The effects of diurnal variations in blood pressure and heart rate on

indices estimating cardiac oxygen supply potential and cardiac oxygen demand were

studied. We used previously recorded 24-hour continuous intra-arterial and finger

arterial blood pressure measurements in 14 hypertensive patients and 8 healthy

normotensive volunteers (4). Reconstructed aortic pressure was used for all calculations.

Methods Subjects

For a detailed description we refer to our original report (4). In short, 14 hypertensive

patients, aged 20–60 years, and 8 normotensive volunteers, aged 19–32 years, were

studied. In the hypertensive group 11 patients were male, in the normotensives group all

participants were male. The hypertensives had discontinued their medication two weeks

prior to the measurements. All subjects gave written informed consent and the respective

review committees approved the protocol (4).

Measurements

Brachial Artery Pressure (BAP) was measured intra-arterially at the non-dominant arm

with the Oxford Medilog Mark II system and ambulatory finger arterial pressure was

obtained from the dominant arm using the Portapres device (4). Measurements were

performed from 1 PM until 1 PM the next day. Apart from free in-hospital activities, all

subjects performed the following activities at preset times: siesta (2:00 – 3:30 PM),

cycling at 50 W (4:45 – 5:15 PM), sleep (10 PM – 6 AM), and two walks outside the

hospital (10:00 – 10:30 AM, 11:00 – 11:30 AM).

Data analysis

Blood pressure was A/D converted with a sampling rate of 100 Hz. Beat to beat values

of systolic, mean and diastolic BAP (corrected for zero drift) and Heart Rate (HR) were

calculated. Episodes with artifacts were rejected. Aortic pressure waves were

reconstructed from invasive brachial and noninvasive finger artery pressures using a

generalized transfer function (5–14). The transfer function compensates for the

physiological wave transformation of pressure waves traveling towards the periphery.

79

Diastolic Time Fraction (DTF, the ratio of duration of diastole and heart period) was

calculated to assess the oxygen supply potential, since a decrease in DTF is directly

related to coronary blood flow if the vasodilatory reserve is exhausted (15,16). Rate-

Pressure Product (RPP, systolic pressure times heart rate), was calculated to assess

cardiac oxygen demand (17,18). The supply - demand ratio (19–22) was assessed by the

ratio of the diastolic area (Adia, in mmHg·s) and systolic area (Asys, in mmHg·s) under the

pressure curve.

Statistics

Thirty-minute averages were calculated for all parameters. The effect of rising was

evaluated by comparing equal periods before (01:00 – 06:00, night) and after rising

(08:00 – 13:00, morning). Results were expressed as mean ± SD in tables and as mean ±

SEM in figures. Night vs. morning values and hypertensives vs. normotensives were

compared by paired t-tests. Linear regression analysis was performed over the 48 half-

hour averages to analyze the relationship between parameters and HR.

Figure 1

75

100

150

75

100

150

Pre

ssure

(mm

Hg)

time (hours) time (hours)

HR

(BP

M)

50

100100

50

Normotensives Hypertensives

18 24 6 12 18 24 6 12

Nig

ht

Morn

ing

Nig

ht

Morn

ing

Left, Normotensives, right, Hypertensives. Systolic, mean and diastolic aortic pressure in top panel, Heart Rate

(HR) in second panel. Dotted vertical lines demarcate Night and Morning periods; bars over the time scale

indicate the activities listed in the Methods section (siesta, cycling, sleeping and two walks). The change in

blood pressure and heart in the morning is slower in the hypertensives.

80

Results Diurnal variations in blood pressure and heart rate are depicted in Figure 1. In the

hypertensive subjects, systolic, mean and diastolic blood pressure and heart rate were

higher during the night (Table 1, right panel), with oxygen supply parameter DTF as

well as supply - demand ratio (Adia / Asys) lower and with demand parameter RPP higher.

In the morning, blood pressure and HR increased (Table 1, lower panel, Figure 1) in both

groups. Pressures were higher in hypertensives but HR was comparable. DTF decreased

as did the supply - demand ratio while RPP increased (Table 1, Figure 2). Supply

potential and the supply - demand became equivalent for normotensive and hypertensive

subjects. RPP remained higher in the hypertensive group.

Figure 2

1

1.5

2

A/A

dia

sys

1

1.5

2

RP

P(m

mH

G·B

PM

)

5 000

10 000

15 000

5 000

10 000

15 000

DT

F(%

)

50

75


50

75

18 24 6 12 18 24 6 12

Nig

ht

Mo

rnin

g

Nig

ht

Mo

rnin

g

time (hours) time (hours) Same layout as Figure 1. Parameter of cardiac oxygen supply potential, Diastolic Time Fraction (DTF) in the

top panel, in the middle panel the supply - demand ratio Adia / Asys, and the parameter of cardiac oxygen

demand, Rate Pressure Product (RPP), in the bottom panel. The change in the parameters in the morning is

slower in the hypertensives.

81

DTF and Adia / Asys decreased with HR, RPP increased (Table 2). The early morning

increase in HR (BPM) in the hypertensive subjects (from 67 ± 3 to 89 ± 5 BPM; 33%)

was smaller than in the normotensives (from 53 ± 2 to 82 ± 11 BPM; 55%). The smaller

HR increase limited the untoward changes in cardiac oxygen parameters.

The results based on non-invasive finger arterial pressure and those of brachial intra-

arterial pressure, both reconstructed to aortic pressure, lead to the same outcomes of the

tests given in Table 1.

Table 1 Hemodynamic parameters and cardiac oxygen indices.


Night Mean SD Mean SD P,

HT vs. NT

Psys 96 2 124 3 <0.001

Pdia 61 2 79 2 <0.001

Pmean 77 2 99 2 <0.001

HR 53 2 67 3 <0.001

DTF 67.5 0.9 64.0 0.9 <0.001

Adia/Asys 1.79 0.07 1.52 0.06 <0.001

RPP 5100 260 8400 410 <0.001

Morning Mean SD

P,

morning

vs. night

Mean SD

P,

morning

vs. night

P,

HT vs. NT

Psys 115 4 <0.001 136 3 <0.001 <0.001

Pdia 76 4 <0.001 92 3 <0.001 <0.001

Pmean 94 4 <0.001 112 2 <0.001 <0.001

HR 82 11 <0.001 89 5 <0.001 0.054

DTF 58.9 3.6 <0.001 58.3 1.1 <0.001 0.613

Adia/Asys 1.27 0.22 <0.001 1.20 0.06 <0.001 0.303

RPP 9200 1300 <0.001 11900 930 <0.001 <0.001

Night averages (top) and morning averages (bottom) for normotensives (left) and hypertensives (right). In the

right column, Hypertensives (HT) are tested versus Normotensives (NT). In the lower half of the Table the

morning averages are tested versus night. Psys, Pdia and Pmean are systolic, diastolic and mean aortic pressure

(mmHg), HR is heart rate in beats per minute (BPM), DTF is diastolic time fraction (%), RPP is Rate Pressure

Product (mmHg·BPM), Adia / Asys is de ratio of diastolic and systolic areas (mmHg·s), respectively, under the

aortic pressure curve.

82

Discussion We studied diurnal variations in blood pressure, heart rate, and of parameters estimating

cardiac oxygen supply potential and oxygen demand, in both hypertensive and

normotensive subjects. The new findings of this study are that in hypertensive subjects

the diurnal variation in cardiac oxygen supply parameters and in the supply - demand

ratio is smaller, and that soon after awakening an increase in cardiac oxygen demand is

accompanied by a concomitant reduction in supply potential.

Table 2 Linear regressions on Heart Rate


Regression R2 Regression R2

DTF – 0.30 x HR + 84 0.97 – 0.23 x HR + 79 0.94

Adia/Asys – 0.018 x HR + 2.77 0.96 – 0.013 x HR + 2.38 0.91

RPP 130 x HR – 1730 0.97 150 x HR – 1300 0.85

Regressions of parameters for cardiac oxygen supply potential and cardiac oxygen demand on Heart Rate

(HR). For explanation of the quantities refer to Table 1.

Methodological considerations

Oxygen supply - demand parameters were calculated from aortic pressure waves

reconstructed from invasive brachial artery pressure and non-invasive finger arterial

pressure recordings, using transfer functions (11–14). Transfer functions compensate for

the physiological wave transformation of pressure waves traveling towards the

periphery. The transfer functions mainly correct for the amplification of the systolic

pressure (11–14). The use of a transfer function therefore mainly affects calculation of

RPP. Generalized waveform filters in the upper limb show little inter-individual

variation at low frequencies (7–11), which are of importance for the calculation of mean

and diastolic pressure, and thus for calculation of DTF. Therefore, the inaccuracies

introduced by the use of a transfer function have no major effect on the estimates of

cardiac oxygen supply potential.

83

The measurements of cardiac oxygen supply potential and oxygen demand in groups of

normotensives and hypertensives were indirect. Continuous ambulatory coronary flow

measurement to validate the suggested reduction in coronary perfusion in patients with

coronary heart disease is as yet not feasible. Simultaneous oxygen supply - demand

parameters from continuous blood pressure together with ST-segment depression in

patients known with coronary heart disease, might, in part, answer the question whether

ischemia correlates best with changes in oxygen supply vs. demand parameters.

Diurnal hemodynamic variations

Major changes in parameters occurred after rising, i.e. at the time that the peak in

ischaemic events is usually observed (23,24). In healthy subjects subendocardial

perfusion is hampered if the Adia / Asys ratio falls below 0.4 to 0.6 (22,25). The ratios

observed in this study, in which no strenuous exercise was performed, remained well

above this limit in all subjects. However, this limit is not fixed but may increase under

circumstances where the vasodilatory reserve is exhausted, e.g. in case of coronary

artery stenosis. Thus the magnitude of the observed changes in Adia / Asys ratio per se

does not reflect early morning myocardial ischemia in healthy subjects, but may explain

occurrence of coronary ischemia in those subjects who suffer from coronary artery

disease. In hypertensives (26) as well as in myocardial hypertrophy (27), coronary flow

reserve is less. Therefore, oxygen supply parameters are better indicators of

subendocardial ischemia in hypertensives than in normotensives. The diurnal variation in

the cardiac oxygen supply potential parameters and in the Adia / Asys ratio in the

hypertensive subjects was smaller, a phenomenon not described before. Of interest, the

finding that oxygen supply - demand parameters as derived from invasive pressure was

tracked by a non-invasive arterial pressure determination allows to study these supply

and demand parameters in a non-invasive manner.

Cardiac Oxygen Supply Potential

As soon as coronary vasodilatory reserve is exhausted, e.g. related to the presence of a

stenosis, subendocardial and mid-myocardial perfusion become dependent directly on

diastolic pressure and time (15,16,20–22). Usually, reduced supply is associated with

coronary vasospasm or atherosclerosis (1). The present study demonstrates that

hemodynamic changes may equally affect DTF as parameter of cardiac oxygen supply

potential in the morning.

84

A reduction in DTF can be attributed to an increase in HR primarily by shortening of

diastole. In healthy subjects a decrease in perfusion pressure or time is compensated for

by coronary vasodilation (22) rendering the decrease in the oxygen supply potential

parameter of importance mainly in patients with coronary stenosis. To the best of our

knowledge the supply parameter, in contrast to the demand parameters has never been

associated with cardiac ischemic events in the morning (24). Pepine (28) mentions the

beneficial effects of beta-blockers on cardiac oxygen supply because of the prolongation

of diastolic time, but not in relation to circadian rhythms and cardiac oxygen supply.

Cardiac Oxygen Demand

Diurnal variations in the balance between cardiac oxygen supply and demand have

traditionally been attributed to changes in oxygen demand due to physical activity

(1,2,29,30). The close correlation between an increase in HR and subsequent

development of coronary ischemia is considered to reflect this increase in oxygen

demand (31,32). The observed increase in RPP after rising, which results from an

increase in both systolic blood pressure and heart rate, is in agreement with the

hypothesis that the morning increase in ischemic events may be caused by an increase in

cardiac oxygen demand.

Hypertensives versus normotensives

Hypertensive subjects appear to be at risk for ischemic events due to larger oxygen

demand (33,34) during night as well as in the morning. During the morning period, the

oxygen supply potential of the hypertensives vs. normotensives did not differ, possibly

related to a damped HR response to rising. In contrast, during the night oxygen supply

potential was lower in hypertensives. This may play a role hitherto overlooked in

nocturnal ischemia (35–37)

85

Conclusion

We observed a decrease in cardiac oxygen supply potential parameters and the ratio Adia

/ Asys after rising in healthy subjects and in hypertensive patients. Traditionally an

increased cardiac oxygen demand has been considered as the factor reducing the oxygen

supply - demand balance. However, we observed that the supply - demand balance may

change detrimentally by a reduction of the oxygen supply potential as well. The smaller

increase in HR in our hypertensive group limits a further deterioration of oxygen

parameters.

86

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89

Chapter 6

Time-domain cross-correlation baroreflex

sensitivity:

performance on the Eurobavar data set

Berend E. Westerhof1, Janneke Gisolf2, Wim J. Stok2,

Karel H. Wesseling1, John M. Karemaker2

See editorial commentary in Appendix

Baroreflex sensitivity (BRS) is now a prognostic factor in cardiology (1–3). It is the

amount of response in heart beat interval to a change in blood pressure, expressed in

ms/mmHg. A blood pressure increment must lead to an increment in interval within 3 or

4 s, and similarly a blood pressure decrement must lead to an interval decrement within 3

or 4 s, for the changes to be considered to be baroreflex action.

Since the concept was proposed in 1969 (4), a number of methods has been developed

for the assessment of BRS, some using a circulatory challenge such as injections of

vasoconstrictor or vasodilator agents (4), neck suction (5) or a change from supine to

standing (6,7), and some using spontaneous blood pressure and interval variability,

studied in the time domain (8–10) or in the frequency domain (9,11). These various

methods produce somewhat different numerical values (12), although results obtained on

the same data set show acceptable correlation (3).

1 TNO TPD Biomedical Instrumentation, Amsterdam, The Netherlands 2 Dept of Physiology, Academic Medical Center, University of Amsterdam, The Netherlands

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Before the cross-correlation method described below, we developed a sequential method

(sBRS) based on and comparable to the well-known method of Di Rienzo et al. (8).

During the development of that technique, when spontaneous fluctuations in pressure

and interval were plotted against each other, we often noticed open Lissajous loops,

which indicated that allowance should be made for a delay between pressure and

interval, as was suggested at an early stage by Karemaker (13). As the amount of delay

for each patient and patient state is not known in advance, we decided to compute BRS

as a cross-correlation function of blood pressure and pulse interval and call this method

cross-correlation baroreflex sensitivity, or xBRS.

Recently, the European Society of Hypertension working group on baroreflex and

cardiovascular variability, in which 11 centres participate, has produced a

comprehensive database which is available for the testing and comparison of methods

(3). We tested the xBRS method on that data set, comparing the results obtained by

xBRS using our local Amsterdam sequence and spectral algorithms with the 21 results

obtained with various methods returned by the 11 centres participating in EUROBAVAR

(3).

Methods The xBRS, sBRS and spectral methods described below we will refer to as Amsterdam

‘local’ methods and results, to distinguish them from those in the EUROBAVAR study.

The EUROBAVAR data set

The EUROBAVAR data set consists of 10–12 min recordings obtained in 21 patients (four

men and 17 women) who were monitored non-invasively with a Finapres 2300

(Ohmeda, Louisville, Colorado, USA) and a Cardiocap II (Datex Engstrom, Helsinki,

Finland) in both the supine (henceforth referred to as ‘lying’) and the standing positions.

Their ages ranged from 20 to 68 years. One patient had diabetes with evident cardiac

autonomic neuropathy, one was a recent recipient of a heart transplant, one had diabetes

without cardiac neuropathy, eight were normotensive patients, one had hypertension,

two had hypertension that was treated, two had hypercholesterolaemia that was treated,

one woman was pregnant in her first term, and four were healthy volunteers. (For further

details see Laude et al. (3).)

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The EUROBAVAR data set is available from the internet as beat-to-beat systolic and

interval values. A set (a) consists of 16 files from eight patients, identified as a001l for

lying and a001s for standing, and so on. A set (b) consists of 30 files identified as b001l

and b001s and so on; these were from 13 new patients and two copied from the previous

(a) set to test repeatability.

Cross-correlation baroreflex sensitivity

The xBRS method differs from the original (8) time-domain sequential method in that it

observes blood pressure and heart interval variability over a fixed time period rather than

over a variable number of beats. Cross-correlation and regression between systolic blood

pressure and interbeat interval (IBI) are computed over 10 s sliding windows, a time-

span sufficient to accommodate fully a 10 s variability in rhythm, or several cycles at

ventilatory frequencies. The method thus may observe two or more slopes

simultaneously. Often, the interval variability is delayed with respect to systolic pressure

variability. Steptoe and Vögele (14) found a 0-, 1- or 2-beat delay to be adequate in

young men. Delays in the baroreflex, however, are measured in seconds of time, not

beats (15). We therefore programmed delays in the pulse interval series to compensate

for physiological delays by applying time shifts of 0–5 s to interval, thereby correlating

current pressure with later interval values. A 5 s delay should suffice for sympathetically

mediated reflexes on pulse interval.

Systolic pressure and heart interval series were taken from the EUROBAVAR files. Beat

events were spaced on the time axis by distances equal to heart interval. Cubic splines

were fitted to the blood pressure and interval event series and the splines were resampled

at 1 Hz. For each window, the correlation coefficient was computed six times. The first

computation was for zero delay and was executed between the first 10 pressure and

interval value pairs (t = 1–10 s). The next computation was for a delay of 1 s and was

carried out between the same 10 pressures, but with interval values at t = 2–11 s.

Computations continued until the 10 pressure values (t = 1–10 s) were correlated with

interval values at t = 6–15 s. The cross-correlation with the greatest value was selected,

and the corresponding regression slope was taken as a determination of BRS, provided it

was positive and its probability of being a random regression was less than 1% (P <

0.01). When these conditions were not met, there was no result for this time segment.

The accepted regression slope was divided by the correlation coefficient to obtain a

slope fitting pressure and interval variability simultaneously (16); this was done because

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the pressure and the interval values are both disturbed by random variability in excess of

that explained by baroreflex variability. The corresponding delay was recorded as best

delay τ. There were no thresholds for pressure or interval changes within a segment.

The timing point of a valid xBRS was the middle position of the pressure and possibly

time-shifted interval windows. A simulated spike of short duration demonstrates timing

in Figure 1. Such short events cause clusters of BRS detection, 1 s apart. In the software,

such clusters are detected as contiguous values not more than 1.5 s apart; the BRS values

in a cluster are averaged and timed at the cluster mid-position, thus indicating the joint

event. Spiked events are rare, however, and approximately sinusoidal events of limited

duration are more probable. These may also cause clusters. Values within clusters were

usually not as stable as in the simulation example, but were seen to vary over a 2 : 1

range in amplitude. The results presented are based on individual determinations, not on

clusters. With each new determination, the window was advanced 1 s, cumulative means

and ranges were updated, and histograms were formed of xBRS and best delay τ, for

inspection.

Figure 1

Simulated pressure and interval plots to demonstrate timing. The upper line is systolic blood pressure (SYS,

mmHg).; the lower line is interval (IBI, ms). x, Time of a cross-correlation determination of baroreflex

sensitivity (BRS, ms/mmHg); .tniopdim retsulc ,

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Sequential baroreflex sensitivity

For comparison, we include results obtained with the sBRS method, programmed

previously in consultation with Di Rienzo and colleagues (8). This method detects

sequences of beats with simultaneously increasing or decreasing pressure and interval. A

minimum of three sequential beats (three intervals, four R-waves) is required, and a

pulse interval delay of 0 is taken – that is, systolic pressure falls within the R–R interval

considered. The method requires a systolic pressure variation of at least 2.5 mmHg over

the beats in the sequence, but has no threshold for interval. The estimate is accepted

when correlation is significant at P = 0.05.

At the occurrence of the next beat, the direction of the changes in interval and pressure

are compared with those of the previous beats. If directions are the same, then

correlation and regression are again computed over the longer sequence and evaluated

for significance. This leads to clusters of sBRS values similar to the clusters that the

xBRS method produces. Our results are based on the individual values.

Spectral method

Our spectral method computes baroreflex sensitivity as the transfer gain of the cross-

spectra between pressure and interval. Their coherence is usually high in the 10 s rhythm

band taken from 0.06 to 0.15 Hz and at ventilatory frequencies in the spectra between

0.15 and 0.5 Hz. Spectral estimates of the entire recording were computed with in-house

developed software (Graphical User Interface For Fourier Transform), providing an

easy-to-use interface on top of proven Matlab signal analysis procedures. Signals were

detrended and a von Hann window (17) applied. A discrete Fourier transform was used

that needed no interpolation or zero padding. Triangular spectral smoothing was set at a

width of 10 for this study, in view of the 10 min duration of the records. Spectral density,

coherence, pressure–interval transfer gain and phase plots are shown on a computer

screen and in addition a cursor allows manual selection of bands in which coherence and

spectral power are high. An output program lists the resultant data and all the choices

made for later analysis.

Statistics

Histograms of xBRS values per patient file most often conformed to a log-normal

distribution. For log-normally distributed variables, the geometric average is a better

estimate of central tendency than the arithmetic average. To obtain the geometric

94

average, we took the logarithm of the numbers, computed their arithmetic average, and

exponentiated the resultant mean. The numbers were required to be positive or the

logarithm could not be taken. BRS values were positive. Values of xBRS best delay τ

were averaged arithmetically per patient file, as were values for sBRS. In addition, the

distributions of best delay τ per patient file were pooled separately for the lying and

standing positions and compared using the χ2 test (16). Multiple regression was used in

an attempt to correlate xBRS to patient parameters, to explain variability between

patients.

When grouped data were compared, non-parametric statistics were used. To maintain

comparability with the results of the EUROBAVAR study, we present the pooled

arithmetic mean, SD and range. For goodness of fit to a distribution, we used the

Kolmogorov–Smirnov one-sample test. For correlation, we used Spearman rank

correlation. For significance of differences we used the Mann–Whitney U-test or the

Wilcoxon matched pair signed ranks test where appropriate.

Results

Duplicates

The duplicate files were b014 and b015. They gave results identical to their twins (a003

and a008) with our local methods. Identical results were expected, because no manual

selection of data was made and the same algorithms were applied to the same data files.

In the case of the overall statistics, we removed these duplicates, 21 patients and 42

records thus remaining (3).

Distribution types

The Kolmogorov–Smirnov test on xBRS rejected 25 (12 lying and 13 standing) files as

normally distributed (P = 0.05). The same test rejected no lying and one standing

distribution as log-normal. The xBRS distribution for patient a002s was not accepted as

either normal or log-normal. The assumption of log-normal distributions, therefore, was

acceptable in 41 of the 42 cases, and the assumption of normal xBRS distributions per

file must be rejected. For sBRS, similarly, normality was rejected 12 times, accepted 23

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times and undecided seven times because of a very small number of values. Log-

normality was rejected in no case and undecided eight times. The assumption of log-

normal sBRS distributions per file was the safer one, but the picture was less clear.

For grouped data, neither the normal nor the log-normal distribution hypothesis was

rejected for any method (xBRS, sequential or spectral), and arithmetic averages were

taken.

Table 1

Number of estimates and variance for sequential (sBRS) and cross-correlation (xBRS) baroreflex

sensitivity

Number of estimations Variance

sBRS xBRS sBRSa xBRS

Lying (n = 20) (n = 21) (n = 18) (n = 18)

mean 50 185 83 39

SD 63 84 129 53

range 2–174 18–418 0–545 4–179

Standing (n = 21) (n = 21) (n = 18) (n = 18)

mean 76 214 23 12

SD 78 106 34 17

range 1–279 11–423 1–139 0–71

a Data from patients for whom there was no value for sBRS variance have been removed.

Ability to provide baroreflex sensitivity estimates

The xBRS method provided BRS values for all patient files of both sets (Table 1). The

smallest number of determinations was 11 on patient b010 in the standing position. The

sBRS method did not provide a result for patient a003 in the lying position (note that the

number in the sample for sBRS was 20, not 21); for patients b005 and b010 in the

standing position, only a single sBRS value was obtained; on both records for patient

b004, and for patients b005l and b013l, only two sBRS values were obtained over the

entire 11 min patient record. sBRS produced fewer than 22 determinations for 22 of the

42 patient records, or fewer than two per minute. The number of xBRS estimates was

three times greater on average than for sBRS. The average period of time between xBRS

estimates was 3.0 s; between sBRS estimates it was 7.7 s. A total of 0.2% of xBRS

values were obtained at intervals longer than 60 s, compared with 1.8% of sBRS values,

not including the three patients in whom no or only single estimates were obtained.

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Excluding both patients with impaired baroreflexes, xBRS provided 20 values per

minute, sBRS just six. With the spectral methods, occasionally, we had to accept bands

without significant coherence.

Table 2

Baroreflex sensitivity assessed by various methods

EUROBAVAR Local

sequential

spectral-

LF

spectral-

HF sBRS TG-LF TG-HF xBRS

Lying (n = 6a) (n = 6a) (n = 4a) (n = 20) (n = 21) (n = 21) (n = 21)

mean 16.2 11.2 16.9 13.4 9.5 14.6 12.4

SD 9.8 10.7 12.3 12.1

range 2.1-46 0.2-51 1.5-54 2.0-60

Standing (n = 20a) (n = 21) (n = 21) (n = 21) (n = 21)

mean 6.7 6.8 5.2 5.9 6.2

SD 3.9 3.8 4.3 3.9

range 1.2–15.7 0.1–14.7 0.4–16.6 0.8–16.3

Ratio L/S (n = 6a) (n = 6a) (n = 4a) (n = 20) (n = 21) (n = 21) (n = 21)

mean 2.10 1.70 2.63 2.01 1.87 2.68 1.96

SD 0.97 1.02 1.43 0.92

range 0.80–4.54 0.70–3.82 0.85–6.31 0.85–4.20

LF, HF, Low- and high-frequency; sBRS, sequential baroreflex sensitivity; TG, spectral transfer gain; xBRS,

cross-correlation baroreflex sensitivity. n, Number of patients having at least one BRS estimate, or a number of

procedures of that type returned by participating centres. EUROBAVAR pools the estimates obtained with the

various techniques for the standing position because they differed little. Values for SD and range are between

patients.

Lying and standing baroreflex sensitivity values

Table 2 provides a comparison between the EUROBAVAR results averaged over the

various centres and techniques, results from our local sequential and spectral techniques,

and those from the new xBRS method. Values for the lying and standing positions and

their ratio (which is also considered an important statistic) are listed separately. Note that

the number in the sample is 20 for sBRS in the lying position, because no value was

obtained for patient record a003l. There was a clear difference between results for lying

and standing, with lying values for baroreflex sensitivity approximately two times

greater than standing values for all techniques. The SD and range for the local

techniques are for the group of 21 patients. The greater value for xBRS SD in the lying

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position is accounted for by patient b013l, treated separately below (Outlier patient). The

differences between the xBRS and sBRS methods were small and not significant (U-

test), and rank correlation at 0.95 (Spearman) was highly significant (P < 0.0001).

Within-patient variance in baroreflex sensitivity

The within-patient stability of BRS values was analysed by computing the variance (SD

squared) for each method. In three cases, no sBRS variance was available because no, or

only a single, BRS value was obtained; the results from these patients were removed

from the averages of both methods. Table 1 gives the variances. For xBRS, the average

variance per patient file and position was approximately 50% of that for sBRS. The

variance ratio became 2.2 when the lying and standing data for each method were

combined. All differences were significant (Wilcoxon at P = 0.0001).

The coefficient of variation (SD in % of the mean per patient record) was on average

41% for xBRS (range 19–62%) and 52% for sBRS (range 3–96%); in both cases it was

nearly proportional to the BRS – that is, large and small values of sensitivity had

approximately the same percentage scatter.

Ability to detect baroreflex impairment

The smallest BRS values were obtained for patients b005 and b010 in both positions,

with lying values greater than those for standing (Table 3). The value was also small in

the case of patient a005, but only for the standing position. In these patients, xBRS

yielded values similar to those from sBRS, but the xBRS method gave more values per

patient file.

Table 3

Sequential (sBRS) and cross-correlation (xBRS) baroreflex sensitivity in patients with impaired

baroreflex

sBRS xBRS

File Value n Value n

b005s 1.2 1 0.8 ± 0.3 46

b005l 2.1 ± 0.6 2 2.3 ± 0.8 82

b010s 2.5 1 1.3 ± 0.4 11

b010l 2.2 ± 0.7 3 2.0 ± 1.8 18

Values are mean ± SD. n, Number of values obtained per record. Note that the number of sBRS estimates was

so small that it was not always possible to establish a value for SD.

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Figure 2 shows a plot of systolic pressure and interbeat interval of the patient who had

recently received a heart transplant. There was a gradual down-drift of the interval,

possibly as a result of increases in circulating (nor)adrenaline after standing up. The

interval oscillations looked like noise; enlarged, they were almost sinusoidal in the

rhythm of ventilation at one oscillation per 3 or 4 s, and the enlarged systolic oscillations

seemed to be synchronous. Thus the xBRS algorithm produced an occasional value, and

so did sBRS, even though fluctuations probably had a non-baroreflex origin (18).

Figure 2

Recording in the heart transplant patient in the standing position. Upper trace: systolic blood pressure (SYS,

mmHg); lower trace: interbeat interval (IBI, ms). Sequential baroreflex sensitivity (∆, ms/mmHg), cross-

correlation baroreflex sensitivity (x, ms/mmHg), and xBRS cluster (s 066 si elacs emit lluf ehT .dekram era (

(11 min). An sBRS value occurs near t = 40 s reading 2.5 ms/mmHg; xBRS is 1.31 ms/mmHg (SD 0.4

ms/mmHg) averaged over 11 estimates. To show details of variability, the period marked by a thick bar on the

time axis between 450 and 490 s is also shown enlarged: x 4.4 with respect to the time, x 4 with respect to the

IBI and x 2 with respect to the pressure.

Outlier patient

In the (b) set files there was one patient (b013) with a very high value for xBRS in the

lying position: 59.7 ms/mmHg (SD 13.3 ms/mmHg). The sBRS value was 45.5

ms/mmHg, the spectral low-frequency transfer gain value 51.2 ms/mmHg and the

spectral high-frequency transfer gain value 54.0 ms/mmHg. For the standing position,

values were more normal. Figure 3 shows 20 s (two windows wide) sections of the

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records for both positions. For the lying position, the mean of the pressure range per

xBRS determination was 3.93 mmHg and that of the interval range was 236 ms, a very

high ratio. It can thus be argued that the high xBRS value is not unreasonable.

Figure 3

Section of the standing (left) and the lying (right) recordings in patient b013, who had the highest BRS values

in the group. The bold line is pressure; the thin line is interval. x, Time of a cross-correlation determination of

baroreflex sensitivity (BRS, ms/mmHg); ,IBI ;(gHmm) erusserp doolb cilotsys ,SYS .tniopdim retsulc ,

interbeat interval (ms). Both diagrams have the same vertical scales, with the common pressure scale at the left

and the interval scale at the far right. In this figure, standing BRS is about 20 ms/mmHg, and lying BRS ranges

between 45 and 70 ms/mmHg.

Correlations between methods

To compute correlation coefficients, first the data for patient a003, for whom there was

no sBRS value for the lying position, were removed. In Table 4, we present the non-

parametric (Spearman) rank coefficients, ranking being insensitive to the very high value

of patient b013. xBRS had the greatest correlation with sBRS; next best was xBRS on

spectral high-frequency transfer gain value, and finally xBRS on spectral low-frequency

transfer gain value. The significance of these correlations (P = 0.0001) was very high.

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Table 4

Spearman rank correlation between local methods of estimating baroreflex sensitivity

Lying sBRS TG-LF TG-HF

TG-LF 0.783***

TG-HF 0.912*** 0.689

xBRS 0.931*** 0.808*** 0.901***

Standing

TG-LF 0.442

TG-HF 0.916*** 0.442

xBRS 0.884*** 0.697 0.853***

Combined

TG-LF 0.711***

TG-HF 0.938*** 0.598***

xBRS 0.943*** 0.764*** 0.903***

sBRS, sequential and baroreflex sensitivity; TG-LF, TG-HF, low- and high-frequency spectral transfer gains;

xBRS, cross-correlation baroreflex sensitivity. All correlations are significant at P < 0.05; ***significant at P <

0.0001.

Correlations and differences between lying and standing results

The coefficient of determination R2 (Table 5) was the same for both positions, implying

that lying and standing xBRS were determined with the same precision, even though the

pressure and interval ranges differed according to position. xBRS values (Table 2) were

correlated at P = 0.0004, meaning that a patient with a high or low sensitivity in the

standing position has a high or low sensitivity when lying down. Best delay τ was

similarly correlated at P = 0.0002, meaning that a patient with a short or long delay in

the standing position had a short or long delay when lying down. The paired difference

for xBRS (lying – standing) was 6.14 ms/mmHg (SD 9.3 ms/mmHg) and was significant

(P = 0.0001). The paired difference for τ (lying – standing) was –102 ms and was not

significant.

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Table 5

Miscellaneous parameters detected by cross-correlation baroreflex sensitivity

τ (s) R2 ∆p (mmHg) ∆I (ms)

Lying

mean 1.45 0.71 8.7 93

SD 0.02 3.1 53

range 0.51–2.63 0.68–0.75 4.0–15.8 10–237

Standing

mean 1.55 0.72 13.5 81

SD 0.03 4.1 45

range 0.86–2.87 0.64–0.78 5.6–19.0 5–215

For each patient record: τ, best delay; ∆p, systolic blood pressure range; ∆I, interval range.

Although the mean difference between τ for both body positions was not significant, the

cumulative distributions of τ showed a clear shift towards greater values for the standing

position (Figure 4). Comparing these distributions by computing χ2, the difference was

highly significant (P < 0.0001).

Figure 4

Distributions of best delay τ for lying and standing positions pooled for all patients. Light, lying; dark,

standing. With the change from lying to standing, a shift towards greater values of τ is apparent.

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Regression of cross-correlation baroreflex sensitivity upon interval, delay and age

The between-patient SD for xBRS in the lying position was almost as great as the mean;

for the standing position it was about two-thirds of the mean (Table 2). Was this just

estimation error or was it patient specific? It appeared that 73% of the scatter in xBRS

values between patients and positions could be explained for by variations in interval,

delay and patient age. The multiple regressions of xBRS on these parameters were:

x = –18.2 + 0 0616I – 4.82τ + 0.431A (lying)

x = –7.8 + 0 0299I – 1.56τ + 0.158A (standing)

x = –14.1 + 0 0509I – 3.77τ + 0.323A (combined)

where x is the xBRS geometric mean value per patient, I is the mean interval, τ is best

delay and A is patient age. Regressions on pressure were not significant. The regression

on τ and the strong lying–standing correlation (see paragraph above) suggest that best

delay τ with the xBRS method was more than simply a methodological parameter with

which to obtain greatest correlation, but also had physiological significance. Clearly and

significantly, xBRS decreased with shorter interbeat interval (greater heart rate), with

longer delay and with greater patient age.

Figure 5

Scatter plot of cross-correlation baroreflex sensitivity (xBRS, ms/mmHg) against the three local BRS

estimates. x, Lying position; refsnart lartceps ycneuqerf-hgih dna -wol ,FH-GT ,FL-GT ;seulav gnidnats ,

gains (ms/mmHg). The line of identity is drawn in each plot.

103

Scatter plots

With xBRS plotted against the three other local results (Figure 5) the scattergrams

appeared to be similar, but they differed in detail. For the lying position, xBRS tended

towards lower values than sBRS and spectral high-frequency transfer gain. The plot of

xBRS against low-frequency transfer gain had a wider scatter in the lower range of

values than that of xBRS against the other methods.

Discussion This study has shown that the xBRS method produced results comparable to those

achieved with pre-existing time-domain and spectral methods (3). On average, xBRS

determinations of baroreflex sensitivity were approximately equally close to those

obtained with sBRS and with local spectral low-frequency and high-frequency transfer

gain. The number of determinations per minute of time was high for all patients except

the one who had a recent heart transplant. xBRS was sensitive to fluctuations in the low-

frequency and high-frequency bands. This is shown clearly in Figure 3, which shows

values for 10 s rhythm (left panel) and ventilatory frequency fluctuations (right panel)

corresponding roughly to their low-frequency transfer gain and high-frequency transfer

gain values. xBRS values were highly significantly correlated between the lying and

standing positions within patients, and more than 70% of the variance between patients

was explained by interbeat interval, best delay τ and patient age.

With clinical interest in baroreflex sensitivity mounting, it is important to have reliable,

simple to use, well researched methods for BRS computation. The time-honoured

sequential method (8) is such a method giving accurate results (19). The cross-

correlation method proposed in this study gave smaller within-patient scatter and a

greater number of values per minute than the sBRS method. It removed uncertainty as to

the number of beats of interval delay that should be implemented in common sequential

methods by computing regression for all reasonable delays. Thresholds were avoided, to

improve frequency of detection in patients with impaired baroreflexes. Nevertheless, the

method provided results comparable to and correlated with those obtained with

sequential BRS in the EUROBAVAR data set. The effects of algorithmic differences

between the sBRS and xBRS methods are that:

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(1) within-patient variance is reduced using a fixed 10 s wide window, which allows

computation of complete oscillations, not just their slopes;

(2) improved correlation and increased number of detections follow from a search for

greatest cross-correlation by varying the time delay between pressure and interval;

(3) application to young and old patients, in the supine, standing or head-up tilted

position, or under any other influence that may alter the delay between pressure and

interval, is possible by the automatic selection of best delay τ;

(4) a better estimator of central tendency on the within-patient log-normally distributed

values is provided by geometric averaging, which is traditionally not used with the

common sequential techniques;

(5) detection reliability is increased by a low P value (P = 0.01, compared with P =

0.05 for most sequential implementations);

(6) determination of BRS in patients with low baroreflex sensitivity is facilitated by the

absence of thresholds for pressure and interval variation (range).

Time-domain sequential BRS methods can pinpoint the instant of activity of the

baroreflex better than frequency domain methods, but only when a large number of

determinations is available. The xBRS method, on average, produced three times as

many values as our implementation of the sequential method, sBRS, and the

determinations were more uniformly distributed over time. The advantage of a high

number of determinations per minute is evident when a statistically reliable BRS

estimate is to be obtained in a stationary patient in the smallest possible period of time. It

is also obvious when tracking changes in BRS in non-stationary patients, for example

during tilt and mental or physical exercise procedures. When patients are monitored in

the supine position, the low number of sBRS determinations (fewer than two per minute

in 12 of the 21 patients) in the EUROBAVAR data set seems problematic. xBRS had such

a low frequency of determination only in the heart transplant patient.

As was shown by Laude et al. (3) in their Figure 1, common sequential determinations

seemed to have greater difficulty than spectral techniques in providing (the low) values

in the two autonomically impaired patients. The six centres that returned sequential data

had estimates for only 14 of the 24 patients. xBRS produced the low values reliably in

both cases and both body positions. One could argue that the failure to provide data in

these cases of low to zero BRS is actually correct, as we know that a baroreflex is absent

or ineffective. Leaving an observer with no data, however, could have other

implications. For example, in patients under atropine, the vagal reflex is suppressed but a

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sympathetic reflex may still be present. This reflex has a longer delay and for that reason

may be overlooked by the common fixed-delay sequential technique, whereas an

algorithm that searches for best delay might provide useful data values, as do spectral

methods that compute rather than assume the phase shift between pressure and interval

and therefore are also successful in such difficult cases.

The scatter in the values of individual BRS determinations with both time-domain

methods was substantial and is puzzling. Within-patient variance for xBRS is 50% that

of sBRS, a statistically significant improvement. Is it likely that, with improved

methodology, the scatter would be reduced to zero? Probably not. The present scatter

was proportional to baroreflex sensitivity and proportionality was closer for xBRS,

which had lower within-patient variance. This suggests a physiological cause for part of

the within-patient scatter. Blood pressure and R–R interval variability are known to

show ‘one-over-f ’ behaviour – that is, spectral intensity increases with decreasing

frequency (20). It is thus not surprising that BRS was not constant even in stationary

patients, and it is questionable whether averaging over progressively longer periods

would provide a true value of BRS. A certain amount of scatter observed in BRS values,

in addition to variability caused by mental and physical exercise, day–night difference,

and body position change, should be regarded as an essential aspect of baroreflex blood

pressure control.

Best delay τ varies per determination within a patient record and its mean value per

patient differs between patients. For the lying position, delays of 0 s occur most

frequently, whereas for the standing position a 1 s delay occurs most often (Figure 4).

This finding casts doubt on any fixed delay of 0 or 1 beat in common sequential BRS

methods, and supports the findings of Steptoe and Vögele (14). The automatic selection

of a best delay removes an uncertainty of those sequential methods that have a fixed 0 or

1 beat delay that may be less suitable in certain patient conditions.

Frequency-domain methods distinguish between low-frequency (partly sympathetic) and

high-frequency (vagal) baroreflex activity, whereas time-domain methods would require

a filter stage preceding the BRS computation to achieve the same distinction. A

limitation of the xBRS method in its present form is that it does not discriminate

between oscillations in ventilatory and 10 s rhythm bands. In a recent review (21),

Eckberg concluded that ventilatory pressure and interval variability had little to do with

baroreflex action, because there is a common cause: the human respiratory gate. This

limitation might not be too serious in practice if it is argued that respiratory gating

106

suppresses the baroreflex to a degree depending on ventilatory rate, and is therefore

responsible for the lower BRS values found in exercise. BRS determinations on

spontaneous fluctuations are, indeed, highly correlated between both spectral bands and

between spectral and time-domain estimates, and produce similar values. However, there

is no guarantee that such correlation and similarity would be maintained under all

circumstances met clinically.

In conclusion, the proposed time-domain, cross-correlation computation of BRS (xBRS)

yielded values for BRS to spontaneous systolic pressure and interval variability that were

close to those achieved with earlier methods, including those for the lying to standing

ratio. The values tended to show less scatter within patients compared with those

obtained from the sequential method. xBRS is able to deal with situations in which

changes in interval lag behind pressure changes – in the elderly, at high heart rates, or

when the baroreflex tends towards sympathetic – because it searches for best delay.

Statistically unbiased estimates of central tendency on the log-normal distributions of

xBRS values result from geometric averaging. Time resolution is good, with 20 xBRS

determinations per minute on average. In autonomically impaired patients with low

interval variability and thus baroreflex sensitivity, the absence of thresholds for pressure

and interval changes is probably responsible for the ability of the method to provide

acceptable results.

Disclosures

BE Westerhof was in part supported by a research grant of FMS The Netherlands for this investigation.

J Gisolf was supported by a grant from Space Research Organization Netherlands (SRON), Project MG-052.

107

References

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2. La Rovere MT, Specchia G, Mortara A, Schwartz PJ. Baroreflex sensitivity, clinical

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253:H680–H689.

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baroreceptor reflex by blood pressure monitoring in unanesthetized cats. Am J Physiol Heart

Circ Physiol 1988; 254:H377–H383.

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baroreceptor reflex sensitivity by means of spectral analysis. Hypertension 1987; 10:538–543.

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13. Karemaker JM. Vagal effects of the baroreflex on heart rate [PhD thesis]. Amsterdam:

University of Amsterdam; 1980.

108

14. Steptoe A, Vögele C. Cardiac baroreflex function during postural change assessed using non-

invasive spontaneous sequence analysis in young men. Cardiovasc Res 1990; 24:627–632.

15. Borst C, Karemaker JM. Time delays in the human baroreceptor reflex. J Autonom Nerv Syst

1983; 9:399–409.

16. Snedecor GW, Cochran WG. Statistical methods. 6th ed. Ames, Iowa: The Iowa State

University Press; 1967.

17. Hamming RW. Digital filters. New York: Prentice-Hall; 1977.

18. Bernardi L, Valenti C, Wdowczyck-Szulc J, Frey AW, Rinaldi M, Spadacini G, Passino C,

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20. Castiglioni P, Parati G, Omboni S, Mancia G, Imholz BPM, Wesseling KH, Di Rienzo M.

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21. Eckberg DL. The human respiratory gate. J Physiol 2003; 548:339–352.

109

Chapter 7

Dynamics of baroreflex sensitivity during

postural stress

BE Westerhof1, J Gisolf2, JM Karemaker2, KH Wesseling1,

NH Secher3, JJ van Lieshout4

Information on human cardiovascular function can be obtained from oscillations in

arterial pressure and R–R intervals. These oscillations and their relationships can be

studied by a physiological perturbation like postural stress that profoundly affects

autonomic neural outflow (9). Postural circulatory stress elicits baroreflex unloading

leading to reduced parasympathetic and increased sympathetic outflow to the sinus node

and an increase in sympathetic vasomotor outflow and total peripheral resistance to

maintain blood pressure. The cardiac baroreflex (BRS) can be quantified by time domain

sequential methods (1,7) and frequency domain analysis (5,29). Algorithms based on

spectral analysis generally require steady state and an observation window of preferably

several minutes unless sophisticated methodologies are applied (19). Time domain

sequential algorithms require not more than a few heartbeats to obtain BRS. A possible

disadvantage is that only a small number of values becomes available per minute and

with such methods a transient within that time frame might not be well described.

1 BMEYE, Amsterdam, The Netherlands

2 Dept of Physiology, Academic Medical Center, University of Amsterdam The Netherlands

3 Dept of Anesthesia, Rigshospitalet, University of Copenhagen, Denmark.

4 Dept of Internal Medicine, Academic Medical Center, University of Amsterdam The Netherlands

110

Recently (35) the response to head up tilt was investigated with a time domain method.

The method, however, gave sparse results, requiring fitting of Legendre functions to

outline the response. A new sequential BRS method (34,13,14) requires only a 10 sec

window and generates values at a much higher rate than earlier methods, close to one

value per two seconds. Additionally, the method provides information about the delay

between changes in systolic blood pressure (SBP) and interbeat interval (IBI), called τ.

Earlier we found that BRS decreases from the supine to the standing position and that τ

increases (34).

Figure 1

30° 70° 90°0°–20°

360 360 720 360 720 360 720 360

Time (s)

720

50

100

150

50

100

1

2

10

20

30

Pre

ssu

re(m

mH

g)

HR

(BP

M)

TP

R(M

U)

xB

RS

(ms/m

mH

g)

0

Hemodynamic data: systolic, mean and diastolic blood pressure, heart rate (HR), total peripheral resistance

(TPR) and xBRS. Moving averages with 12 s window.

111

Considering that during passive head-up tilt muscle sympathetic nerve activity increases

linearly with the sine of the tilt angle, reflecting the body axis component of gravity

(9,16), we determined time- and frequency domain BRS function during graded

progressive orthostatic stress. Orthostatic stress was expressed as sin(α), in which α

corresponds to the angle of body position, representing the vertical component of the

fluid column on which the gravitational forces are exerted. α was increased stepwise

from –20º to 90º. We traced the alterations in BRS and analyzed the dynamic changes in

distribution of the time-domain determined IBI to SBP delay τ. The hypothesis tested

was that with increasing postural stress, BRS becomes attenuated by a reduction in its

vagal component with a shift in τ towards higher values, corresponding with a shift to

increased sympathetic efferent stimulation.

Methods

We studied ten healthy volunteers (22-39 yr, 9 males). They were non-smokers, had

normal physical fitness without sports training, had no history of orthostatic fainting and

used no medication. Informed consent had been obtained from all participants and the

study was approved by the ethics committee of Copenhagen (KF01-120/96) and

performed in accordance with the guidelines laid down in the Declaration of Helsinki.

After instrumentation the subjects rested in the 0º position for 30 min. Participants were

subjected to a standing (90º) and tilt protocol including 20 degrees head-down tilt (–20º)

and 30 and 70 degrees head-up tilt (30º and 70º) preceded and followed by a period of

supine rest (0º). The –20º, 30º and 90º lasted 10 min, 70º lasted 60 min but was

interrupted earlier when presyncopal symptoms and signs occurred, or at the request of

the test subject. A period of at least 6 min 70º was recorded in all cases.

112

Figure 2

360 720

10

20

30

40

50

360 720

10

20

30

40

50

360 720

10

20

30

40

50

360 720

10

20

30

40

50

360 720

10

20

30

40

50

360 720

10

20

30

40

50

360 720

10

20

30

40

50

xB

RS

(ms/m

mH

g)

time (s) time (s)

xB

RS

(ms/m

mH

g)

xB

RS

(ms/m

mH

g)

xB

RS

(ms/m

mH

g)

0°

0°

0°

0°

0°

0°

0°

30° 30°

–20°

70° 70°

90° 90°

xBRS baroreflex sensitivity results of one participant. Each dot represents a BRS result. Drawn horizontal lines

represent period averages. Geometric running averages trace the transients. Note the overshoot in BRS after

tilt-back from 70º and in 0º position after 90º.

113

Instrumentation and data processing

Noninvasive finger pressure was recorded with a TNO Finapres Model 5 and sampled at

100 Hz. The TNO Beatfast software was used to reconstruct brachial pressure form

finger pressure (3,15,33) and to determine beat-to-beat parameters. Interbeat interval,

systolic, diastolic and mean arterial pressure were analyzed as well as parameters

determined from arterial pressure using a model (17,32) which calculates stroke volume,

cardiac output and total peripheral resistance (Figure 1). Systolic blood pressure (SBP)

and interbeat interval (IBI) were used for subsequent analysis with baroreflex sensitivity

software (34,13,14).

Period selection

Sections of 6 min before and 6 min after each change in α were selected for analysis.

Starting from –20º, this resulted in 7 transients (Figure 2). Periods before and after tilt

were compared to determine the difference in BRS and τ distribution. To quantify the

dynamic BRS response to a change in tilt angle, the 6 min periods following a transient

were subdivided in 120 s sections for statistical evaluation. Running averages were

calculated using a 120 s window for plotting.

BRS was related to –20º and 0º (Figure 2, top right panel) and to 30º, 70º and 90º using

periods following an increase in α (Figure 2, left panels). Periods immediately following

an increase in α were used as opposed to the periods just prior to a decrease, to exclude

the effects of fainting.

Fainters and non-fainters

Three of the ten participants experienced presyncopal symptoms or requested to be tilted

back during the 70º period as well as during the 90º period. BRS, τ distribution and

hemodynamic parameters of these three fainters were compared to the non-fainters.

114

Figure 3

360 720

10

20

30

40

50

360 720

10

20

30

40

50

360 720

10

20

30

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360 720

10

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360 720

10

20

30

40

50

360 720

10

20

30

40

50

360 720

10

20

30

40

50

xB

RS

(ms/m

mH

g)

time (s) time (s)

xB

RS

(ms/m

mH

g)

xB

RS

(ms/m

mH

g)

xB

RS

(ms/m

mH

g)

0°

0°

0°

0°

0°

0°

0°

30° 30°

–20°

70° 70°

90° 90°

Running averages of xBRS baroreflex sensitivity results of all participants and group average (heavy line).

115

Baroreflex sensitivity

For time-domain analysis of BRS the cross-correlation method was used (34,13,14).

Beat-to-beat SBP and IBI data are fitted with cubic spline functions and resampled at 1 s

intervals. The cross-correlation between ten-second series of SBP and IBI samples are

computed for delays τ in IBI of 0 to 5 s. The combination with the τ giving the highest

cross-correlation is selected if significant at P = 0.05. The regression slope is recorded as

one xBRS value together with the τ. Subsequently, the process is repeated for series of

SBP and IBI samples 1 s later. Theoretically, one xBRS value can be obtained each

second. This technique produces approximately three times as many BRS values as

existing sequential techniques and with a reduced scatter between subsequent values

(34).

For frequency analysis, beat-to-beat SBP and IBI time series were detrended and

Hanning windowed. Power spectral density and transfer gain of the cross-spectra of SBP

and IBI (5,29) were computed using discrete Fourier transform (6). The ten-second-

rhythm band from 0.06 to 0.15 Hz, called “s10”, and the respiratory band from 0.15 to

0.5 Hz, called “Resp” were selected; transfer gain and phase were computed for

coherence > 0.5.

Statistics

Distributions of xBRS values are best described as log-normal (34); therefore, geometric

averages were used. Within-subject differences were tested with the Mann Whitney u-

test. Differences in BRS and hemodynamic parameters were evaluated for the group by

parametric repeated measures ANOVA. BRS values before and after a change in α were

compared and BRS values representing each α were compared separately to investigate

BRS values as a function of sin(α). Histograms of the distributions of τ were plotted and

compared by the chi2 test after normalizing of data. The number of estimations in the

chi2 test was set to the group average number of estimations for each period.

116

Results

With increasing α, diastolic (76 to 89 mmHg) and mean pressure (96 to 106 mmHg) and

systemic vascular resistance (1.2 to 1.4 mmHg·s/ml) increased (Figure 1), while IBI (1.1

to 0.75 s) and stroke volume (95 to 61 ml) decreased.

Table 1

Effects of axis of body angle αααα on time domain and frequency domain baroreflex sensitivity.

Angle of body axis

–20º 0º 30º 70º 90º

xBRS, ms/mmHg 22.3 ± 5.1 ‡ 18.6 ± 5.0 13.6 ± 5.7 * 8.7 ± 3.7 †‡ 9.2 ± 4.3 †‡

N 168 ± 73 189 ± 52 212 ± 67 269 ± 45 †‡ 272 ± 64 †‡

Gs10, ms/mmHg 18.6 ± 9.7 (5) 17.1 ± 8.6 (8) 10.9 ± 4.5 (8) 7.5 ± 3.1 (10) * 7.6 ± 2.9 (9) *

Gresp, ms/mmHg 28.1 ± 10.9 (6) 24.3 ± 14.3 (10) 18.6 ± 9.6 (8) 7.8 ± 6.2 (6) * 9.6 ± 6.0 (6)

Ps10, degrees – 60 ± 38 (5) – 42 ± 16 (8) – 49 ± 15 (8) – 51 ± 11 (10) – 47 ± 11 (9)

Presp, degrees – 22 ± 22 (6) – 6 ± 35 (10) – 31 ± 26 (8) – 46 ± 36 (6) – 47 ± 35 (6)

Values are means ± SD; xBRS, cross-correlation baroreflex sensitivity; N, number of xBRS results; Gs10,

transfer gain in the 10s band; Gresp, transfer gain in the respiratory band; Ps10, transfer phase in the 10s band;

Presp, transfer phase in the respiratory band. Between brackets (n) the number of results available from spectral

analysis. * P < 0.05 vs. 0º; † P < 0.001 vs. 0º; ‡ P < 0.05 vs. 30º

Time domain

xBRS during transients in α is given in Figures 2 and 3. In one case tilt back from 70º

was not available in the data, in another case the transient from 90º to 0º was not

available. For the total of 68 tilt transients, in 63 cases (93%) BRS had altered in the 6

min following a change in α and this difference was present in 78% after 1 min and in

85% after 2 min. BRS was significantly different between the 30º, 70º and 90º in all but

one subjects. BRS at –20º was not significantly different from 0º, and at 70º not different

from 90º. The averaged values of BRS for each α are given in Table 1. Averaged BRS

related to α (xBRS = –10.1·sin(α) + 18.7; r2 = 0.99, Figure 4).

117

The number of xBRS results increased with tilt angle (Table 1). Expressing the number

of xBRS results per minute gives 28 ± 12, 31 ± 9, 35 ± 11, 45 ± 8, 45 ± 11 for α

increasing from –20º to 90º.

Figure 4

0

10

20

30

-0.5 0 0.5 1

xB

RS

(ms/m

mH

g)

xBRS = 10.1 sin ( ) + 18.7

r = 0.99

–2

α

sin ( )α

0

10

20

30

-0.5 0tra

nsfe

rg

ain

(ms/m

mH

g) G = 14.9 sin + 24.0

r = 0.97

resp – ( )α

2

– ( )

r = 0.98

α

2

G = 8.9 sin + 16.1s10

sin ( )α

0.5 1

-60

-40

-20

0

tra

nsfe

rp

ha

se

(de

gre

es)

P = 40.9 sin 7.5

r = 0.99

resp – ( ) –α

2

P = 7.0 sin 43.0

r = 0.59

s10 – –( )α

2

-0.5 0 0.5 1

xBRS baroreflex sensitivity and spectral gain and phase as a function of the tilt angle. Data are mean ± SEM.

Note that in the regressions of phase on the sine of tilt angle the –20º periods are excluded.

Distribution of ττττ

The distribution of delays between SBP and IBI determined from the strongest cross-

correlation also related to α (Figure 5). With increase the distribution moved toward

more τ of 1s and less τ of 0s; –20º was not significantly different from 0º, and 70º not

significantly different from 90º.

118

Figure 5

20

40

1 2 3 4 5

60

0

τ (s)

dis

trib

utio

n(%

)

30°

70°

90°

0°

–20°

Distributions of delays (cubic spline fit). X-axis: delay τ (s) corresponding to the best cross correlation between

blood pressure and interbeat interval variations. Y-axis: the percentage of incidence. In 0º and –20º the 0s τ

dominates while in 30º the 1s τ is more frequent. In 70º and 90º the 1s τ dominates even more.

Frequency domain

Spectral gain and phase for 10 s band and respiratory band are given in Table 1 and in

Figure 4. xBRS and spectral gain were tightly correlated for both the 10s band (Gs10 =

0.88 xBRS – 0.40; r2 = 0.98) and respiratory band (Gresp = 1.48 xBRS – 3.65; r2 = 0.97).

The phase in the respiratory band tended to lower values (P = 0.07) for higher αs,

corresponding to the xBRS determined shift in τ (Figure 5)

Transients

The rate of change in BRS depended on the change in α and was asymmetrical for an

increase vs. a decrease (Figure 3). From 70º to tilt back and from 90º to 0º there was a

BRS overshoot (P < 0.05).

Figure 6 shows the changes in τ distributions vs. response time to an increase in α. At

30º the τ distribution shifted towards a modest dominance of 1s τ. At 70º, 1s τ

progressively increased, while in 90º the 1s τ immediately dominated.

119

Figure 6

40

Dis

trib

utio

n(%

)

20

00

2

4

1

3

5

4 - 6 min

2 - 4 min

0 - 2 min

40

20

00

2

4

1

3

5

4 - 6 min

2 - 4 min

0 - 2 min

Dis

trib

utio

n(%

)

40

20

00

2

4

1

3

5

4 - 6 min

2 - 4 min

0 - 2 min

τ (s)

Dis

trib

utio

n(%

)

τ (s)

τ (s)

30°

70°

90°

Distribution of delay τ over time after the change from 0º to 30º, to 70º and to 90º. In 30º τ of 0s and 1s are

equally distributed, then there is a slight increase of 1s τs. In 70º 1s τ progressively increase. In 90º the

distribution immediately shifts to mainly 1s τ and this situation is maintained throughout the analyzed period.

120

Fainters versus non-fainters

In the frequency domain, gain for fainters versus non-fainters tended to be lower in 70º

(5 ± 4 vs. 9 ± 2, P = 0.08 and 4 ± 1 vs. 12 ± 6, P = 0.08 for Gs10 and Gresp, respectively)

and was comparable for other αs (P > 0.1). In the fainters, during 70º the phase Ps10 was

lower (–62 ± 6 vs. –46 ± 9, P = 0.03) and the phase Presp tended to be lower (–70 ± 29 vs.

–21 ± 24, P = 0.09). xBRS in fainters tended towards lower values (70º: 6 ± 4 vs. 10 ± 3,

P = 0.09, 90º: 6 ± 1 vs. 11 ± 5, P = 0.1). At 70º and 90º the τ distribution in fainters vs.

non-fainters had shifted more to 1s τ (P < 0.05, Figure 7) within 2 min.

Figure 7

1 2 3 4 5

20

40

60

80Fainters

01 2 3 4 5

20

40

60

80Non fainters

0

τ (s)

dis

trib

ution

(%)

30°

70°

90°

0°

–20°

30°

70°

90°

0°

–20°

τ (s) Distribution of delay τ in fainters (right panel) vs. non-fainters (left panel), same axes as in Figure 4, after the

change from 0º to 30º, 0º to 70º and 0º to 90. The fainters have more delays of 1s. Note that the distributions of

–20º and 0º of the fainters is similar to the distribution at 30º of the non-fainters.

Discussion

The main findings of this study were that 1) during gravitational stress the sensitivity of

the cardiac baroreflex obtained from time domain decreases linearly with the sine of the

angle of the vertical body axis, and 2) the dynamic baroreflex adaptation to a

physiological perturbation like postural stress occurs rapidly, i.e. within one minute in

the majority of subjects.

121

The autonomic regulatory systems controlling blood pressure responses to postural stress

include the cardiopulmonary, aortic, and carotid baroreflexes and vestibular inputs. The

posture induced carotid baroreceptor unloading evokes an increase in efferent

sympathetic vasoconstrictor activity as well as parasympathetic withdrawal that leads to

a reduction in interbeat interval. A drop in carotid distending pressure and a change in

pulsatile receptor stretching by the reduced stroke volume are among the proposed

stimuli that together constitute the changing carotid baroreceptor input during a change

in body position (10).

Figure 8

0.2

0.4

0.6

0.8

1.0

5

10

15

20

25

50 100 150 200

pressure (mmHg)

Affere

ntactivity

(a.u

.)

xB

RS

(ms/m

mH

g)

Normalized baroreceptor afferent activity is shown as a function of mean pressure (triangles). An arc tan

function is fitted to the data. The derivative, peaking at 100 mmHg, is a measure of baroreflex sensitivity. The

baroreflex sensitivity curve is fitted to the measured xBRS data (boxes) of Table 1 by assuming that the

distance between baroreceptors and heart level is 25 cm, resulting in a pressure drop of 19 mmHg between 0º

and 90º position.

The derivative of normalized baroreceptor afferent activity (31) represents a measure of

BRS as a function of pressure (Figure 8). As an example, the derivative of baroreceptor

afferent activity provides a satisfactory description the xBRS data (Table 1) with the

xBRS value for –20º set equal to 100 mmHg arterial pressure at the carotid sinus and the

vertical distance to the heart level at 25 cm. Then, in the 0º position, carotid sinus

pressure is 94 mmHg, to reduce to 75 mmHg in the 90º position, assuming mean arterial

pressure at heart level constant and neglecting an influence of the aortic baroreceptors.

This suggestion of graded baroreceptor unloading with an increasing angle of body axis

is not at variance with data presented by Pawelczyk and Raven (27). They found that a

reduction in central venous pressure by lower body negative pressure augmented BRS

122

and concluded that the inhibitory influence of pressure or volume sensitive

cardiopulmonary receptors was removed by central hypovolemia. Of note, in that study

the subjects remained supine and gravitational unloading of the carotid baroreceptors did

not play a role. However, in tilt studies using pulsed neck suction and pressure (11,12)

protocols to determine BRS, no decrease (4) or an increase in the cardiac baroreflex is

found (23), while in studies using sequential BRS methods, a decline in sensitivity in

reaction to tilt is established (18,20,25,30). The discrepancy between the findings with

sequential (1,7) methods, using spontaneous variations in blood pressure and heart rate

on the one hand, and the neck cuff stimulation on the other, has received little attention.

Data from experiments gauging the separate arterial and cardiopulmonary baroreflex

gains suggest that the arterial component remains equivalent during tilt while the

cardiopulmonary contribution decreases (21). Neck suction obviously assesses only the

arterial component and thus would remain equal with tilt, corroborating this finding.

However, these observations challenge the suggestion that the unloading of the carotid

baroreceptors is involved, in which case BRS is expected to be reduced as shown in this

report. During dynamic exercise with increasing workload, BRS as determined statically

by pulsed neck suction and pressure, and dynamically by transfer function gain and time

domain sequence analysis was demonstrated to provide similar information (24). This is

compatible with a movement along the right leg of the baroreflex sensitivity curve

(Figure 8) with increasing mean arterial pressure (24).

The finding that cardiac baroreflex sensitivity decreased linearly with the sine of the

angle of the vertical body axis complements the observation by Iwase et al. (16) that

muscle sympathetic nerve activity increases linearly with the sine of the angle during

passive head-up tilt. The shift towards longer delays between systolic blood pressure and

interbeat interval supports the suggestion that the decrease of BRS is a result of the vagal

withdrawal associated with larger postural stress. The linear relationship between angle

of body axis and cardiac baroreflex as found in this study does not reveal direct

information on its vagal vs. sympathetic constituents.

The distribution of the delay between variations in blood pressure and interbeat interval

may provide additional insight in the performance of the sequential methods for

baroreflex sensitivity assessment. We found that the distribution of delays shifted

towards longer delays with increasing tilt angle. The observed reduction in BP to IBI

delays of 0s suggests acute withdrawal of the fast efferent parasympathetic branch to the

sinus node. Using a different approach to assess cardiac vagal tone in humans, Julu et al.

(18) found a decrease as well.

123

As an opposing view the shift in τ distribution may be interpreted as an effect of

increasing HR. For low HRs the effect of efferent vagal activity on heart rate becomes

apparent within the same beat (2). It was shown that the vagal effect on HR can be

described by 0s delay when IBI is greater than 775 ms (28), or HR lower than 77 BPM.

For higher heart rates the effect of efferent vagal activity becomes apparent only in the

next beat expressed as 1s delay. Thus, at higher heart rates the decrease of 0s delay in

itself is therefore no proof reduced vagal activation. However, with the body axis at 30º

the average interval was 969 ms, corresponding to 62 BPM, allowing to attribute the

shift in the delay distribution to a decrease in vagal tone.

An increase in peripheral resistance during graded tilt up conforms to increased

sympathetic vasomotor tone. Similarly, forearm vascular resistance (4) and muscle

sympathetic nerve activity (25) as indication of sympathetic efferents are found to

increase with tilt. Postural stress is a complex physiological intervention with

baroreceptor unloading that may provoke both parallel and reciprocal changes of vagal

and sympathetic nerve activity (9). Evidently the issue whether sympathetic and vagal

nerve activities change reciprocally remains unsettled as long as knowledge on changing

cardiac vagal neural traffic is lacking. We do consider that tracking of dynamic changes

in BRS together with changes in the distribution of heart rate to blood pressure delays as

obtained from time domain analysis has the potential to reveal information on the vagal

contribution.

In the subjects who presented with presyncopal signs during 70º and 90º the faster and

more pronounced shift towards longer delays with increasing tilt angle was already

apparent in the first two minutes of 70º and 90º, compatible with early sympathetic

activation.

The increasing number of xBRS data with tilt can be explained in several ways. It could

be interpreted as the effect of increased baroreflex effectiveness (8), proposed as a

complimentary measure of baroreflex function, or as less effective suppression of

oscillations due to decreased baroreflex sensitivity with mathematically a larger number

of correlations. The finding that the number of baroreflex results decreased substantially

with the prescribed significance level of the SBP-IBI regression slope of the xBRS

method, but values for baroreflex sensitivity remained unaffected (Table 2), indicates

that the number of results is method-dependent, but baroreflex sensitivity level is not.

124

Table 2

Baroreflex sensitivity and number of results as a function of P value required for the xBRS result to be

accepted.

P – level of the xBRS method

P0.05 P0.01 P0.005 P0.001

xBRS (ms/mmHg) 14.5 ± 4.7 14.9 ± 4.9 15.2 ± 5.2 15.9 ± 7.2

N 222 ± 60 153 ± 65 * 127 ± 64 *† 79 ± 56 *†‡

N/min 37 ± 10 26 ± 11 * 21 ± 11 *† 13 ± 9 *†‡

Values are means ± SD over all tilt angles; xBRS, cross-correlation baroreflex sensitivity; N, number of xBRS

results. * P < 0.001 vs. P0.05; † P < 0.001 vs. P0.01; ‡ P < 0.001 vs. P0.005

In summary, in healthy subjects the sensitivity of the cardiac baroreflex obtained from

time domain decreases linearly with the sine of the angle of the vertical body axis and

the dynamic baroreflex adaptation to a physiological perturbation like postural stress

occurs rapidly. The shift towards longer delays between blood pressure and interbeat

interval variations with increasing body axis angle suggests that the decrease of BRS

with tilt results from reduced vagal activity and increased sympathetic cardiac tone.

Disclosures

BE Westerhof was in part supported by a research grant of FMS The Netherlands for this investigation.

J Gisolf was supported by a grant from Space Research Organization Netherlands (SRON), Project MG-052.

125

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129

Chapter 8

Variable day/night bias in 24-h non-invasive

finger pressure against intrabrachial artery

pressure is removed by waveform filtering

and level correction

Berend E. Westerhof1, Ilja Guelen1, Gianfranco Parati2,

Antonella Groppelli2, Gert A. van Montfrans3, Wouter Wieling3,

Karel H. Wesseling1, Willem Jan W. Bos4

In previous studies we showed (1,2) that non-invasive arterial finger pressure (FAP) and

intrabrachial pressures (BAP) differ systematically. The frequency transfer function from

brachial to finger arteries has a resonance near 8 Hz. In addition, the finger diastolic and

mean pressures may be some 8–10 mmHg less than brachial values. By application of a

generalized waveform filter, the 8 Hz resonance can be compensated by an 8 Hz anti-

resonance, and near-brachial waveforms can be derived from FAP waveforms (3). The

subsequent application of a generalized regression-type equation with the filtered finger

systolic and diastolic pressures as independent variables restores the BAP values, on

average (1,2). This brachial reconstruction technique was developed on a database of

short, steady-state sections of individual waveforms available from previous studies, and

the results were correct for the population concerned.

1 TNO TPD Biomedical Instrumentation, Amsterdam, The Netherlands 2 Ospedale SanLuca, Milano, Italy 3 Academic Medical Center, Amsterdam, The Netherlands 4 St Antonius Hospital, Nieuwegein, The Netherlands

130

Later, we demonstrated that waveform filtering also improved the tracking of changes in

(systolic) pressure and baroreflex sensitivity during states of vasodilatation from bicycle

ergometer exercise and vasoconstriction from graded phenylephrine infusion (3),

situations for which tracking of BAP by FAP was considered inadequate (4,5). This was

the first result showing that waveform filtering not only improves resting blood

pressures, but is also effective in correcting the response of an individual person’s FAP

to changes in circulatory state.

In a previous study (6) we demonstrated the ability of non-invasive continuous

ambulatory FAP recording with Portapres to track BAP with limited bias and acceptable

precision, but that the important day-to-night blood pressure dip (7) was overestimated

in the finger. We therefore decided to evaluate the effectiveness of the combined

waveform filtering and level correction techniques on 24-h recordings of FAP and BAP,

with particular interest in the changes in bias between day and night.

Methods

Participants

We recorded non-invasive FAP and BAP continuously during 24 h in eight

normotensive volunteers and 16 patients with hypertension. Details of the patients and

measurements have been published previously (6). Briefly, the volunteers were aged 19–

32 years and the patients were aged 20–60 years. The patients had discontinued their

antihypertensive medication 2 weeks before they were studied. FAP was measured on

the dominant (right) arm using a TNO Model 1 Portapres device. BAP was recorded in

the brachial artery of the non-dominant arm with the Oxford Medilog Mark II, but the

pressure signal was recorded on a separate channel of the Portapres, guaranteeing

synchronous recording. Because we measured BAP and FAP on contralateral arms, we

required that the average of six simultaneous left- and right-arm auscultatory systolic and

diastolic pressures should agree to within 5 mmHg. Hydrostatic height differences

between the finger and the Oxford pressure transducer were also recorded and

continuously subtracted from the FAP waveform. Measurements were started at 1300 h

and lasted until 1300 h on the following day. A standardized activities procedure was

strictly adhered to, as follows. Siesta: 1400–1530 h; cycling at 50 W: 1645–1715 h;

sleep: 2200–0600 h; outside walk: 1000–1030 h and 1100–1130 h. In the remaining

131

periods, the participants were free to move in the hospital. The study procedure was

approved by the ethics committees of both hospitals and informed consent was obtained

from each participant.

Analysis

In the case of some participants, not all periods of interest were successfully recorded,

because of various instrumental failures (6). Two patients of whom we had no

sufficiently complete recordings were excluded from the present study, thus eight

volunteers and 14 patients remained. In the results, the number of included participants

is given for each period. A generalized waveform filter was applied to the FAP records

to remove the near 8 Hz resonance (3) and level correction was applied to the waveform

filtered FAPs as previously described (1,2). In addition to the continuous FAP and BAP

signals, we thus had a third signal channel named ‘reconstructed BAP’ (reBAP).

Original FAP, reBAP and original BAP waves were analyzed for beats. Those beats that

were simultaneously present were compared after artifacts had been rejected, in exactly

the same way (using the original files) as in the previous study (6). In the 22 participants,

90% of the beats were simultaneously available. Finally, level differences were obtained

per beat for systolic, diastolic and mean pressures, as the difference between original

FAP and BAP values and between reBAP and BAP values.

Statistics

Mean values and standard deviations (SD) were calculated for each individual for the

entire 24-h period, for each 30 min and for the following specific periods: daytime,

siesta, sleep, cycling and walking. Next, the mean values were pooled for the group of

the eight volunteers, for the 14 patients, and for all 22 participants. This was permissible,

in view of the strict scheduling of the specific activities and rest periods during the 24-h

period. Averages for specific periods were not always available for each individual,

because of artifacts, so for each period we specify the number of participants involved.

When the mean values and SD of the pressure differences are calculated in this way, bias

and precision statistics are obtained. The principal differences were original FAP minus

BAP (FAP – BAP) and reBAP minus BAP (reBAP – BAP), which were tested for the

significance of their bias from zero using the t-test. Significance was assumed at P <

0.05.

132

Figure 1

40

mm

Hg

sie

sta

160

120

80

18 24 6 12

FAP and BAP Syst. Dias. Mean

nig

ht

wa

lk2

wa

lk1

cyclin

g

–20

0

20

40

18 24 6 12

ReBAP BAP Syst.–

18 24 6 12

Time (h)

ReBAP BAP Dias.–

–20

0

20

40

18 24 6 12

FAP – BAP Dias.

–20

0

20

40

18 24 6 12

–20

0

20

40 FAP BAP Syst.–

sie

sta

ReBAP and BAP Syst. Dias. Mean

18 24 6 12

40

80

120

160

nig

ht

cyclin

g

wa

lk2

wa

lk1

mm

Hg

mm

Hg

Time (h)

Continuous systolic (Syst.), diastolic (Dias.) and mean blood pressures averaged per 30 min and pooled for the

group of 22 participants in the study for whom the full 24-h signal data were available. Measurements started

at 1300 h and continued until 1300 h on the following day. Periods of scheduled and exactly timed activities

are indicated on the time axis. Continuous lines, intrabrachial artery pressures (BAP); dashed lines, non-

invasive finger artery pressures (FAP); dotted lines, reconstructed brachial artery pressures (reBAP). The lower

panels show the individual pressure differences before (left) and after (right) brachial reconstruction. To show

tracking ability, the individual mean bias has been removed.

133

Results

The left upper panel of Figure 1 presents the 30-min mean values for the systolic,

diastolic and mean values of FAP and BAP, pooled for the entire group. Bias was clearly

smallest for systolic pressure. For all three pressures, FAP showed a greater dip than

BAP during siesta and at night. Exercise in the forms of cycling and walking caused

FAP values to increase more than those for BAP. The right upper panel compares the

same pressures, but original FAP values are replaced by reBAP. Differences are reduced,

and the larger dips in FAP during siesta and at night have disappeared. The lower panels

show the individual hourly pressure differences before (left) and after (right) brachial

reconstruction.

Table 1

Differences between original 24-h finger arterial pressure (FAP) or reconstructed brachial artery

pressure (reBAP) and intrabrachial artery pressure (BAP)

Systolic

(mmHg)

Diastolic

(mmHg)

Mean

(mmHg)

FinAP – BAP

Volunteers (n = 8)

Patients (n = 14)

All (n = 22)

5 ± 10

–1 ± 10

1 ± 10

–7 ± 7 *

–9 ± 7 *

–8 ± 7 *

–9 ± 8 *

–11 ± 8 *

–10 ± 8 *

reBAP – BAP

Volunteers (n = 8)

Patients (n = 14)

All (n = 22)

3 ± 10

–1 ± 11

1 ± 11

1 ± 7

–4 ± 6 *

–2 ± 7

1 ± 7

–3 ± 7

–2 ± 7

Differences expressed as mean ± SD. * Significant difference from zero (P = 0.05); all other differences, NS.

Table 1 presents the 24-h statistics after averaging over the volunteers (n = 8), the

patients (n = 14), and the entire group. Whereas the diastolic and mean differences for

the three groups before reconstruction (FAP – BAP) were significantly different from

zero, after reconstruction (reBAP – BAP) they were not, except for diastolic pressure in

the patient group. Note that, although bias decreased to statistically insignificant

amounts, precision as expressed by the SD of the data was not improved by the

reconstruction. The reconstruction technique functioned nearly equally well in

normotensive and hypertensive individuals.

134

Table 2

Nocturnal pressure dip (night - day) differences in intrabrachial (BAP), finger (FinAP) and

reconstructed brachial (reBAP) artery pressures

Systolic

(mmHg)

Diastolic

(mmHg)

Mean

(mmHg)

BAP

Volunteers (n = 8)

Patients (n = 13)

All (n = 21)

–20 ± 6

–20 ± 9

–20 ± 8

–10 ± 4

–15 ± 7

–13 ± 6

–13 ± 4

–16 ± 7

–15 ± 5

FinAP

Volunteers (n = 8)

Patients (n = 13)

All (n = 21)

–27 ± 9 *

–28 ± 12 *

–28 ± 11 *

–14 ± 8

–19 ± 10

–17 ± 10 *

–17 ± 7

–20 ± 11 *

–19 ± 10 *

reBAP

Volunteers (n = 8)

Patients (n = 13)

All (n = 21)

–20 ± 7

–18 ± 10

–19 ± 9

–12 ± 5

–15 ± 8

–14 ± 7

–15 ± 6

–16 ± 9

–15 ± 7

Differences expressed as mean ± SD. * Significant difference from BAP (P = 0.05); all other differences, NS.

Table 2 shows that nocturnal arterial pressure dipping is significantly enhanced in the

FAP values: by 8, 4 and 4 mmHg for systolic, diastolic and mean values, respectively,

all participants taken together. These differences reduced to less than 1 mmHg after

reconstruction, or by a clear factor of 4, disregarding the sign of the bias. Variability

estimates also improved.

Figure 2 illustrates the reduction in FAP/BAP bias after reconstruction, displayed for the

24-h period and per scheduled activity. During the day, the night, the siesta and during

cycling, bias reduced to negligible values after reconstruction. Only during walking was

diastolic bias significantly positive.

135

Figure 2

-20

0

20 *

*****

Fin - BAP reBAP - BAP

-20

0

20

*

24 hn = 22

dayn = 22

nightn = 21

siesn = 21

cycln = 20

walkn = 17

-30

0

10

******

-20

20

-20

0

20

-30

0

10

0

SB

P(m

mH

g)

DB

P(m

mH

g)

MB

P(m

mH

g)

24 hn = 22

dayn = 22

nightn = 21

siesn = 21

cycln = 20

walkn = 17

Bias and precision of original finger artery pressure (FAP: left panel) and reconstructed brachial artery pressure

(reBAP: right panel) against intrabrachial artery pressure (BAP) pooled for the group and averaged over the

24-h period (24h), the day period (day), the night period (night), the siesta (sies), 50 W bicycle exercise (cycl),

and two 30-min periods of outside walk (walk). n, number of participants with sufficient recording time

available for a realistic average. *Significant difference from zero (P < 0.05).

136

Discussion

The present results show clear benefits of generalized waveform reconstruction on bias,

and slighter benefits on precision, against BAPs. Remarkably, the greater biases during

siesta and night automatically received the required greater correction. This finding was

not necessarily to be expected, as the reconstruction algorithms were developed for a

population cross-section on short (30 s) sections of waveform data for individuals in

almost identical, resting circulatory states. The findings of the present study suggest that

the same reconstruction algorithms can be applied in individuals, over time, to improve

the tracking of BAP changes by non-invasive FAP measurement over a period of 24 h.

Causes of waveform distortion and pressure gradient

FAP pulse waveform distortion and reductions in FAP values are caused by the pulse

wave transmission effects present in the arm arteries between brachial and finger

measurement sites, and by a pressure gradient that develops as a result of flow in the

rather narrow peripheral arteries of the forearm and hand. As shown in the left panel of

Figure 1, the pressure gradient appeared to increase when the participant was inactive

during siesta and night, and to decrease during the scheduled moderate activities of 50 W

cycling and walking. This seems, at first sight, unexpected. It is, however, well known

that peripheral vasoconstriction occurs in the arteries of the arm during non-arm exercise

(8), which might have caused a decrease in forearm flow and thus a decrease in flow-

related pressure gradient. The level correction formula largely accounts for this effect on

the basis of the relative values of systolic and diastolic FAP, but not completely so, as

the residual differences in Figures 1 and 2 suggest.

Bias and precision

The bias was almost completely removed by waveform reconstruction. After

reconstruction, it was well within the limit of 5 mmHg, as required by the Association

for the Advancement of Medical Instrumentation (AAMI) protocol (9). The precision

was only marginally improved. After reconstruction, the precision for mean and diastolic

pressure, but not for systolic pressure, was within the 8 mmHg required by the AAMI

protocol. Systolic values are more affected by motion artifacts, shifts in finger height

with respect to heart level, and systolic overshoot, damping and limited bandwidth of the

137

catheter–manometer systems used to obtain the reference pressure (10). Furthermore, the

generalized waveform filter used in the brachial waveform reconstruction is based on a

population average, and is possibly suboptimal in individual cases. Although the effects

of suboptimal behavior are reportedly small (11), they are expected to affect systolic

values when blood pressure and heart rate are quite variable, such as during a 24-h

recording. However, we did not observe such deviant behavior of systolic pressure

values.

Night–day differences

The nocturnal decline in blood pressure (7), or its absence, has become the subject of

many studies (12). FAPs measured with Portapres tend to exaggerate the nocturnal blood

pressure dip but, for this group of patients, the reconstruction technique restored the

correct BAP changes, to within 2 mmHg for all pressures (Table 2). The suggested cause

for changes in blood pressure gradient has been changes in forearm flow. It should be

realized, however, that changes in flow can only cause changes in the pressure gradient

if arterial diameter and thus small artery resistance remain constant. It has been shown

(13) that localized intra-arm arterial application of sodium nitroprusside, which probably

relaxes both arterial and arteriolar vasomotor tone, does not affect the BAP-to-FAP

gradient. However, during the night, when arteriolar peripheral tone relaxes and arterial

diameter decreases subsequent to reductions in arterial distending pressure, an increased

pressure gradient can be expected, and was indeed observed (Figure 1, left panel).

Application of the methodology

We have developed three ways to improve the relationship between FAP and BAP. Two

methods, generalized waveform filtering and generalized level correction, were applied

in the present study; the third is an individual level calibration (2). The first method,

waveform filtering, reshapes the non-invasive FAP waveform to near-brachial contours,

with pulse pressure amplitude reduced to brachial values. The second, level correction,

reduces bias between FAP and BAP recordings in a manner correct for a population, and

even reduces bias variability in individuals during a 24-h period. However, precision

does not improve after generalized level correction. The third way to improve the

FAP/BAP relationship – level correction with a return-to-flow brachial systolic pressure

estimate – improves both bias and precision, but requires an additional measurement

with extra hardware. It is important to note that the first two methods, waveform filtering

and level correction, can be applied retrospectively, by means of computer software, to

138

previously recorded FAPs, without further effort. That these generalized methods also

reduce bias variability during the day suggests that an individual calibration needs to be

performed only once during the day. The observation that waveform filtering and level

correction are less perfect during the activity of walking outside the hospital should be

taken as cautionary in this context.

Conclusion

We conclude that reconstruction of BAP from non-invasive FAP strongly reduces the

FAP/BAP bias over a period of 24 h, and improves tracking of nocturnal blood pressure

changes for all three blood pressure levels.

139

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7. O’Brien E, Sheridan J, O’Malley K. Dippers and non-dippers. Lancet 1988; 2:397.

8. Rowel LB, Brengelmann GL, Blackmon JR, Bruce RA, Murray JA. Disparities between

aortic and peripheral pulse pressures induced by upright exercise and vasomotor changes in

man. Circulation 1968;37:954–964.

9. American national standard for electronic or automated sphygmomanometers. AAMI SP 10-

1987. Arlington VA: Association for the Advancement of Medical Instrumentation; 1987. pp.

1–25.

10. Gardner RM. Direct blood pressure measurement – dynamic response requirements.

Anesthesiology 1981; 54:227–236.

11. Chen CH, Nevo E, Fetics B, Pak PH, Yin FCP, Maugham WL, Kass DA. Estimation of


pressure; validation of generalized transfer function. Circulation 1997; 95:1827–1836.

12. Staessen JA, Thijs L, Fagard R, O’Brien ET, Clement D, de Leeuw PW, Mancia G, for the

Systolic Hypertension in Europe Trial Investigators. Predicting cardiovascular risk using

conventional vs ambulatory blood pressure in older patients with systolic hypertension. JAMA

1999;282:539–546.

13. Bos WJW, van den Meiracker AH, Wesseling KH, Schalekamp MADH. Effect of regional

and systemic changes in vasomotor tone on finger pressure amplification. Hypertension 1995;

26:315–320.

141

Chapter 9

Non-invasive blood pressure measurement in

relation to a variety of basic and clinical

applications

In the past years while the studies described in this Dissertation were in progress, I

contributed to a series of other investigations in which my role was to develop methods

or apply techniques for a variety of research projects. These were mostly based on

clinical questions, a few of which could be answered by application of the theories and

techniques developed in this thesis, others by different methods not mentioned in the

preceding Chapters. The present Chapter gives an overview of these studies, providing

additional demonstrations of usefulness of non-invasive blood pressure measurements.

Pressure transfer analyses

Physical basis of pressure transfer from periphery to aorta (1)

We proposed a new method to derive aortic pressure from peripheral pressure and

velocity by using a time domain approach. Peripheral pressure was separated into its

forward and backward components by waveform analysis, and these components were

then shifted with a delay time, which was the ratio of distance and wave speed, and

added again to reconstruct aortic pressure. We tested the method on a distributed model

of the human systemic arterial tree. From carotid and brachial artery pressure and

velocity, aortic systolic and diastolic pressure could be predicted within 0.3 and 0.1

mmHg and 0.4 and 1.0 mmHg, respectively. The central aortic pressure wave shape was

also predicted accurately from carotid and brachial pressure and velocity (root mean

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square error: 1.07 and 1.56 mmHg, respectively). The pressure transfer function depends

on the reflection coefficient at the site of peripheral measurement and the delay time. A

50% decrease in arterial compliance had a considerable effect on reconstructed pressure

when the control transfer function was used. A 70% decrease in arm resistance did not

affect the reconstructed pressure. The transfer function thus depends on wave speed but

has little dependence on vasoactive state. We conclude that central aortic pressure and

the transfer function can be derived from peripheral pressure and velocity.

The findings of this study gave the impetus for the research described in Chapters 2 & 3.

Finger pressure measurements with the possibility to reconstruct brachial pressure (2)

In this study, the objective was to evaluate three methods developed for the

reconstruction of brachial pressure from non-invasive finger arterial.

Finger arterial pressure (FinAP) may differ from intra-brachial pressure (BAP). First,

pulse shape differences can be removed by applying a generalized waveform filter. Next,

pressure level differences can be corrected by a generalized level correction equation

using filtered systolic and diastolic levels. Finally, a level calibration, which uses an

additional return-to-flow (RTF) systolic pressure measurement on the ipsilateral upper

arm, can be used for an individual calibration of the reconstructed brachial pressure.

These methods were validated in 37 subjects, aged 41 to 83 years after a cardiac

catheterization procedure. Intra-brachial and FinAP pressures were recorded

simultaneously. FinAP pressures were compared after application of waveform filtering

and level correction (flcAP), and after an additional RTF calibration (reBAP). FinAP

systolic, diastolic and mean pressures for the group differed from BAP by –9.7 ± 13.0, –

11.6 ± 8.0 and –16.3 ± 7.9 mmHg (mean ± SD) respectively. After waveform filtering

and level correction, flcAP differed by –1.1 ± 10.7, –0.2 ± 6.8 and –1.5 ± 6.6 mmHg.

After individual calibration, reBAP differed by 3.1 ± 7.6, 4.0 ± 5.6 and 2.7 ± 4.7 mmHg.

We conclude that reconstruction of BAP from FinAP with waveform filtering and level

correction reduces the pressure differences, with an individual RTF calibration to well

within AAMI requirements.

Changes in finger-aortic pressure transfer function with incremental bicycle exercise (3)

Non-invasive finger blood pressure recording has become a surrogate for central blood

pressure under widely varying circumstances. We calculated finger-aorta transfer

functions using the AutoRegressive-eXogenous (ARX) model method in 7 cardiac

patients during rest, incremental bicycle exercise and post-exercise. Finger pressure was

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measured non-invasively using Finapres and aortic pressure using a catheter-tip

manometer. When using the individual transfer functions, developed during rest, for

reconstruction of aortic pressure (rAortic) during all workloads, systolic pressure was

increasingly underestimated, with a large variation between subjects: +4.0 to –18.1

mmHg. In most subjects diastolic pressure (DBP) was overestimated: –3.9 to +5.5

mmHg. In all cases wave distortion was present. Post-exercise, the error in systolic

rAortic only slowly declined and diastolic pressure was overestimated in all subjects.

During rest, the transfer function gain had a minimum between 3.65 and 4.85 Hz (Fmin).

During exercise this minimum shifted to frequencies between 4.95 and 7.15 Hz at the

maximum workload, with no change in gain. Post-exercise, gain in most subjects shifted

to values closer to unity, while Fmin did not return to resting values. Within each subject

aorta-Finapres delay was linearly related to mean pressure (MAP). During exercise, both

delay and heart rate (HR) were linearly related to Fmin. During rest and exercise, Fmin

could be predicted by the linear model:

Fmin = 0.07*(MAP–DBP)+0.019*HR–0.013*delay+2.71 with R2 = 0.89.

We conclude that during exercise a general transfer function gives an unreliable

reconstruction of aortic pressure. Prediction of transfer functions parameters may be

possible, which could improve both reconstructed systolic and diastolic pressure as well

as wave shape.

Hemodynamic analyses

Total arterial inertance as the fourth element of the Windkessel model (4)

In earlier studies it was found that the three-element Windkessel, although an almost

perfect load for isolated heart studies, does not lead to accurate estimates of total arterial

compliance. To overcome this problem, we introduce an inertial term in parallel with the

characteristic impedance. In seven dogs we found that ascending aortic pressure could be

predicted better from aortic flow by using the four-element Windkessel than by using the

three-element Windkessel: the root-mean-square errors and the Akaike information

criterion and Schwarz criterion were smaller for the four-element Windkessel. The three-

element Windkessel overestimated total arterial compliance compared with the values

derived from the area method and the pulse pressure method (P = 0.0047, paired t-test),

whereas the four-element Windkessel compliance estimates were not different (P =

0.81). The characteristic impedance was underestimated using the three-element

Windkessel, whereas the four-element Windkessel estimation differed marginally from

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the averaged impedance modulus at high frequencies (P = 0.0017 and 0.031,

respectively). When applied to the human, the four-element Windkessel also was more

accurate in these same aspects. Using a distributed model of the systemic arterial tree,

we found that the inertial term results from the proper summation of all local inertial

terms, and we call it total arterial inertance. We conclude that the four-element

Windkessel, with all its elements having a hemodynamic meaning, is superior to the

three-element Windkessel as a lumped-parameter model of the entire systemic tree or as

a model for parameter estimation of vascular properties.

Left ventricular wall stress normalization in chronic pressure-overloaded heart (5)

It is generally accepted that the left ventricle (LV) hypertrophies (LVH) to normalize

systolic wall stress (σs) in chronic pressure overload. However, LV filling pressure (Pv)

may be elevated as well, supporting the alternative hypothesis of end-diastolic wall

stress (σd) normalization in LVH. We used an LV time-varying elastance model coupled

to an arterial four-element lumped-parameter model to study ventricular-arterial

interaction in hypertension-induced LVH. We assessed model parameters for

normotensive controls and applied arterial changes as observed in hypertensive patients

with LVH (resistance +40%, compliance –25%) and assumed 1) no cardiac adaptation,

2) normalization of σs by LVH, and 3) normalization of σs by LVH and increase in Pv,

such that σd is normalized as well. In patients, systolic and diastolic blood pressures

increase by ~40%, cardiac output (CO) is constant, and wall thickness increases by 30–

55%. In scenarios 1 and 2, blood pressure increased by only 10% while CO dropped by

20%. In scenario 2, LV wall thickness increased by only 10%. The predictions of

scenario 3 were in qualitative and quantitative agreement with in vivo human data. LVH

thus contributes to the elevated blood pressure in hypertension, and cardiac adaptations

include an increase in Pv, normalization of σs, and preservation of CO in the presence of

an impaired diastolic function.

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Pulse wave analyses

Beta-blocking therapy in patients with the Marfan syndrome and entire aortic

replacement (6)

In non-operated patients with Marfan’s syndrome, use of β-adrenergic blocking therapy

has been shown to reduce the rate of aortic dilation and the development of aortic

dissection. However, its efficacy after entire aortic replacement is unknown. The aim of

this study was to describe the influence of (nearly) entire aortic replacement and β-

blocking therapy on blood pressure and wave reflections in Marfan patients.

Four Marfan patients (mean age 316 ± 3 years) and 8 age matched control subjects were

studied. Blood pressure and wave reflections (reflection coefficient and augmentation

index) were studied by means of magnetic resonance imaging, continuous non-invasive

blood pressure measurements and applanation tonometry. Patients were studied with

atenolol, labetalol and without β-blocking therapy.

In Marfan patients, aortic systolic pressure (129 ± 13 vs. 114 ± 10 mmHg), pulse

pressure (58 ± 13 vs. 40 ± 5 mmHg), wave speed (11 ± 3 vs. 4 ± 0.4 m s-1) and reflection

coefficient (65 ± 22 vs. 41 ± 5%) were significantly increased compared to controls.

There was no difference in aortic pressure between various medications in Marfan

patients (atenolol 129/76 mmHg, labetalol 121/75 mmHg and without β-blocking

therapy 129/71 mmHg). Higher reflection coefficients were seen in patients with

atenolol compared to discontinued medication (73 ± 18 vs. 65 ± 22%), and also the

augmentation index was higher with atenolol compared to labetalol and discontinued

medication (24 ± 22 vs. 17 ± 17 vs. 22 ± 22%, respectively).

Our results describe increased pulse pressure, systolic pressure, wave speed and wave

reflections in four Marfan patients after entire aortic replacement. The use of atenolol or

labetalol did not decrease aortic pressure and with atenolol increased wave reflections

were observed. Therefore, the beneficial effect of atenolol in these patients is doubtful.

Aortic pressure-area relation in Marfan patients with and without β blocking agents (7)

Our objective was to investigate the heterogeneous response to β blockade in patients

with Marfan syndrome by non-invasive assessment of the aortic pressure–area curve.

Twenty-five patients with the Marfan syndrome who used β-blocking agents (aged 29 ±

10 years; 20 men, five women), seven without β blockade (34 ± 14 years; five men, two

women), and 10 controls (29 ± 5 years; seven men, three women) underwent magnetic

146

resonance imaging and non-invasive continuous blood pressure measurement. Pressure–

area curves were constructed at the level of the descending thoracic aorta. A transition

point was defined as the pressure at which the pressure–area relation deviated from its

elastic (linear) to the collagen (exponential) course.

In six patients (five with and one without β blockade), a transition point in the pressure–

area curve was observed, indicating that the load bearing component was not only elastin

but also collagen. In the remaining 26 Marfan patients and in the control subjects a linear

pressure–area relation was observed.

This new non-invasive method to derive aortic pressure–area curves showed that most

patients with Marfan syndrome have a similar pressure–area curve to controls with

similar blood pressures. Five patients on β blockade showed a transition point in the

pressure–area curve which could play a crucial role in the heterogeneous response to β

blocker treatment in Marfan patients. Patients with a transition point at low blood

pressures may not benefit from β blocking agents.

The mean pressure is not calculated adequately by adding 1/3 of the pulse pressure to

the diastolic pressure (8)

The mean arterial pressure at the upper arm is traditionally calculated by adding 1/3 of

the pulse pressure to the diastolic pressure. We tested the validity of this formula in

previously recorded intra-brachial pressure and Riva-Rocci / Korotkoff blood pressure

measurements in 57 subjects (study A) and 24-hour intra-arterial recordings in 22

subjects (study B). In study A the intra-arterially measured mean pressure was found at

39.5 ± 2.5 % of the pulse-pressure above the diastolic pressure. Mean pressure was

higher than at the expected 33.3 % of the pulse-pressure in all individuals. Mean

pressure calculated with the traditional 1/3 rule underestimated the actual mean pressure

by 4.9 ± 5.3 mmHg (P < 0.01). The error was similar for calculations based on Riva-

Rocci-Korotkoff-measurements. In study B we showed activity related variations in the

relative level of the mean pressure; this level increased by 1.8 ± 1.4 % (P < 0.01) during

sleep, and decreased by 0.5 ± 0.9 % during walking (P < 0.05) and by 0.8 ± 1.3 % during

cycling (P < 0.01). Results were not related to age, blood pressure, pulse-pressure or

heart rate. We propose an improved formula to calculate the mean pressure at the upper

arm. Adding 0.4 times the pulse-pressure to the diastolic pressure reduces the error in

calculating the mean pressure from –4.9 ± 5.3 mmHg (P < 0.01) to 0.4 ± 5.1 mmHg

(n.s.).

147

In conclusion, the mean pressure at the upper arm is underestimated when calculated

with the traditional formula of adding 1/3 of the pulse pressure to the diastolic pressure.

This underestimation can be overcome by adding 0.4 times the pulse pressure to the

diastolic pressure.

Baroreflex sensitivity analysis

Sublingual nitroglycerin used in routine tilt testing provokes a cardiac output-mediated

vasovagal response (9)

We set out to determine the effect of sublingual nitroglycerin (NTG), as used during

routine tilt testing in patients with unexplained syncope, on hemodynamic characteristics

and baroreflex control of heart rate (HR) and systemic vascular resistance (SVR).

Nitroglycerin is used in tilt testing to elicit a vasovagal response. It is known to induce

venous dilation and enhance pooling. Also, NTG is lipophilic and readily passes cell

membranes, and animal studies suggest a sympatho-inhibitory effect of NTG on

circulatory control.

Routine tilt testing was conducted in 39 patients with suspected vasovagal syncope (age

36 ± 16 years, 18 females). Patients were otherwise healthy and free of medication.

Before a loss of consciousness set in, oncoming syncope was cut short by tilt-back or

counter-maneuvers. Finger arterial pressure was monitored continuously (Finapres). Left

ventricular stroke volume (SV) was computed from the pressure pulsations using a

model. Spontaneous baroreflex control of HR was estimated in the time and frequency

domains.

During tilt testing, 22 patients developed presyncope. After NTG administration but

before presyncope, SV and cardiac output (CO) decreased (P < 0.001), whereas SVR

and HR increased (P < 0.001) in all patients. Arterial pressure was initially maintained.

Baroreflex sensitivity decreased after NTG. On Cox regression analysis, the occurrence

of a vasovagal response was related to a drop in SV after NTG (hazard ratio 0.86, P =

0.005).

The cardiovascular response to NTG is similar in vasovagal and non-vasovagal patients,

but more pronounced in those with tilt-positive results. The NTG-facilitated presyncope

appears to be CO-mediated, and there is no evidence of NTG-induced sympathetic

inhibition.

148

References







function during and after incremental bicycle exercise. Submitted.

4. Stergiopulos N, Westerhof BE, Westerhof N. Total arterial inertance as the fourth element of

the Windkessel model. Am J Physiol. 1999;276:H81-8.

5. Segers P, Stergiopulos N, Schreuder JJ, Westerhof BE, Westerhof N. Left ventricular wall

stress normalization in chronic pressure-overloaded heart: a mathematical model study. Am J

Physiol Heart Circ Physiol. 2000;279:H1120-7.

6. Meijboom LJ, Westerhof BE, Nollen GJ, Spaan JA, de Mol BA, Jacobs MJ, Mulder BJ. Beta-

blocking therapy in patients with the Marfan syndrome and entire aortic replacement. Eur J

Cardiothorac Surg. 2004;26:901-6.




8. Bos WJW, Vincent HH, Westerhof BE, van Montfrans GA. The mean pressure is not

calculated adequately by adding 1/3 of the pulse pressure to the diastolic pressure. Submitted.




149

Chapter 10

Summary and Conclusions

The binding theme of the preceding chapters can be summarized as a pursuit of better

diagnostics and earlier recognition of warning signs in cardiovascular disease. Early

recognition demands accurate non-invasive measurements and reliable methods of

analysis. As shown in this Dissertation, continuous recording of the full pressure wave

shape is indispensable for any detailed analysis going beyond determination of systolic

and diastolic pressure. Non-invasive finger arterial pressure has all the required features.

Some small steps have been taken, testing techniques and proposing approaches, but still

there is a long way to go. Studies in large populations of patients are to prove the clinical

value of these models and methods.

The purpose of this summary chapter is to give an overview of studies that contributed to

obtaining information from the non-invasive measurement of finger arterial pressure,

and emphasize the understanding derived from them.

Pressure transfer analyses

Transfer functions, allowing the derivation of aortic pressures from peripheral pressures,

are frequently used to obtain better insight into processes involving the interaction

between arterial load and the heart. Generalized transfer functions give useful results,

especially in larger study populations. However, more detailed information might be

obtained by individualization of the transfer function, i.e. made optimal for an

individual.

150

Sensitivity of pressure transfer to arterial parameters

Applying transfer functions to pressure measurements requires insight into the variability

within and between individuals. We therefore investigated the quantitative contribution

of all local arterial, blood and distal load properties to the pressure transfer function from

aorta to brachial artery (Chapter 2). This theoretical analysis of the pressure transfer

started out with anatomical data on vessel dimensions, including relative geometric

taper, Young’s modulus, wall viscosity, blood viscosity and blood density. A three-

element Windkessel represented the load to the model of the vessel. The sensitivity

analysis was performed in terms of frequency and magnitude of the peak in the transfer

function and in terms of systolic and diastolic aortic pressure. The percent change of

these variables for a 25% alteration of each of the model parameters was calculated. The

Root Mean Square Error (RMSE) described the inaccuracy in wave shape. Sensitivity

was less than 3% for systolic and diastolic pressure and RMSE less than 1.8mmHg.

Vessel length and diameter had the greatest influence. From these data we concluded

that the intra-individual variability was small.

To investigate to which extent the tapering of the vessel influences the transfer function,

a single uniform tube was modeled. This simplification introduced only small errors in

systolic and diastolic pressures (1% and 0%). Wave shape was less well described

(RMSE 2.06 mmHg). When the reflection coefficient G was changed to zero or to unity

still reasonable results were obtained, showing that vasodilation and vasoconstriction

have little effect on the transfer function.

We conclude that vessel length and diameter are the most important parameters

determining pressure transfer. Because of this we may conclude that delay time is the

main determinant. Vasodilation and constriction have little effect. Thus, a simple

uniform tube with known delay time, possibly measured, and an estimate of the distal

reflection coefficient are sufficient to obtain an accurate description of pressure transfer.

Parameter adaptation to individualize pressure reconstruction

Based on the parameter analysis presented above, we hypothesized that the transfer

function could be individualized by a representative time delay. Chapter 3 describes a

study in a group of 50 patients: measured ascending aortic pressure was 119 ± 20 / 70 ±

9 mmHg, (mean ± SD, systolic / diastolic) and intra-arterially measured brachial

pressure was 131 ± 18 / 67 ± 9 mmHg. The Root Mean Square Error, RMSE, as measure

of difference in wave shape was 7.5 ± 2.1 mmHg. When individual transfer functions

were used with optimized delay, reconstructed pressure was 121 ± 19 / 69 ± 9 mmHg

and RMSE reduced to 4.1 ± 2.0 mmHg. Using a generalized transfer function with a

151

population-averaged delay, reconstructed pressure was 122 ± 19 / 69 ± 9 mmHg and

RMSE was 4.4 ± 2.0 mmHg. Details of the wave shape that were reproduced by the

individualized transfer function were lost with the generalized transfer function. Thus,

with the extra information of time delay, we were able to obtain a transfer function that

was optimal for the individual, giving better results than a generalized transfer function.

Hemodynamic analyses

Hemodynamic analysis is a broad denominator. In this thesis we investigated two

phenomena, both related to central blood pressure and both determinants of cardiac

performance. The first is the reflection index in Chapter 4, the second is the cardiac

oxygen supply and demand ratio in Chapter 5.

Quantification of wave reflection in the human aorta from pressure alone

Wave reflections are apparent from the proximal aortic pressure signal when a secondary

systolic rise in pressure is found. Since reflection may increase systolic pressure it is an

important factor to consider when studying systolic hypertension.

A frequently used measure of wave reflection is the Augmentation Index (AI), the ratio

of the secondary rise in pressure and pulse pressure. However, this index has the

weakness that it only can discern a reflection when the secondary rise in pressure is

detectable. The timing of the reflected wave may be such that the secondary rise in

pressure is not quantifiable.

A more accurate measure is the reflection index (RI), obtainable after separation of

pressure in its forward and reflected components, so-called waveform analysis.

However, this requires measurement of aortic flow, often not readily available. We

therefore explored the possibility of replacing the unknown flow by an artificial

triangular wave. Flow duration was set to ejection time; peak flow at the inflection point

of pressure, FtIP and, for a second analysis, at 30% of ejection time, Ft30. Wave separation

then gave forward, Pf, and backward, Pb, pressure waves. RI was defined as:

RI = |Pb| / (|Pf| + |Pb|).

Twelve healthy subjects, including interventions such as exercise and Valsalva

maneuvers, and 5 patients with ischemic heart disease were analyzed. RIs using FtIP and

Ft30 were compared with RImf using measured flow, Fm, recorded with a Millar catheter

with high fidelity pressure and velocity sensors at the tip. RImf = 0.41 ± 0.05, (mean ±

152

SD, n = 21), RItIP, RIt30 and AI are 0.39 ± 0.05, 0.39 ± 0.04, 0.34 ± 0.16, respectively, AI

significantly different with a larger scatter.

Relations are: RItIP = 0.86 RImf + 0.03 (R2 = 0.73, n = 21), RIt30 = 0.84 RImf + 0.04 (R2 =

0.88, n = 26) and AI = 2.62 RImf – 0.74 (R2 = 0.57, n = 21).

We conclude that RI can be determined from aortic pressure alone, even when AI cannot

be obtained.

Variations in cardiac oxygen supply and demand in hypertensive subjects after rising

The increase in heart rate and blood pressure soon after awakening increases cardiac

oxygen demand, which has been associated with morning excess of acute myocardial

infarction. Oxygen demand is elevated in hypertensive subjects and we tested the

hypothesis that in hypertensive subjects this early morning increase in heart rate and

blood pressure also affects the oxygen supply potential. Since it is the ratio between

supply and demand that determines whether subendocardial ischemia may occur, we

considered this an important question.

Aortic pressure was reconstructed from 24-hour intra-brachial and finger pressure

recordings in 14 hypertensive patients and in 8 normotensive subjects as reference.

Supply was assessed by Diastolic Time Fraction (DTF), demand by Rate-Pressure

Product (RPP) and supply/demand ratio by Adia/Asys with Adia and Asys diastolic and

systolic area under the aortic pressure curve. In the morning, blood pressure and heart

rate (HR) increased in both groups. HR increased 33% in hypertensives and 55% in

normotensives to become similar in the morning. DTF and Adia/Asys ratio decreased in

both groups (P < 0.001), while demand increased in both groups (P < 0.001). Parameters

correlated closely with HR (R2 ~ 0.9). Compared to normotensives, hypertensive subjects

had lower supply as well as lower supply/demand ratio, and a higher demand (P < 0.001)

during the night that persisted (P < 0.001) during the morning.

The data suggest that in hypertensive vs. normotensive subjects the cardiac oxygen

demand around awakening becomes elevated. The morning imbalance in supply and

demand is related not only to increased demand but to decreased supply as well. The

deterioration of the balance between supply and demand appears limited by a smaller

morning rise in HR in hypertensives.

153

Baroreflex sensitivity analyses

Baroreflex sensitivity analysis is widely used to obtain insight in the functioning of the

autonomic system in health and disease. A method rapidly giving reliable information on

baroreflex sensitivity is a sought after tool.

Time-domain cross-correlation baroreflex sensitivity: Performance on the EUROBAVAR

data set

To test a new method (xBRS) for time domain baroreflex sensitivity (BRS) computation

on spontaneous blood pressure and heart interval variability we used the EUROBAVAR

data set which is available from the internet1. This set is especially compiled for

evaluation and comparison of methods determining baroreflex sensitivity (see

Appendix).

In Chapter 6, the xBRS method was put to use on the 42 records in the EUROBAVAR data

set, obtained on 21 patients in lying and standing position. One patient had a recent heart

transplant and one was diabetic with evident cardiac autonomic neuropathy. xBRS

computes correlation between beat to beat pressure and interval, resampled at 1 Hz, in a

sliding 10 s window, with delays of 0 to 5 s for interval. The delay with the highest

positive correlation is selected and, when significant at P = 0.01, slope (ms/mmHg) and

delay (s) are recorded as one xBRS value. Each second of the recording is the start of a

new computation. Non-parametric tests are used.

Lying, xBRS yields 12.4 versus EUROBAVAR sequential 16.2 ms/mmHg, standing 6.2

versus 6.7 ms/mmHg, lying to stand ratio 1.96 versus 2.10. xBRS gave results on all

files, 20 values per minute on average at a lower within patient variance. Best xBRS

delays were 0, 1, and 2 s, and delay increased 100 ms in stand position. xBRS gave

results on the diabetic and the heart transplant patient, while other methods were unable

to do so.

The xBRS method should be considered for experimental and clinical use since xBRS

yields values strongly correlated with and close to EUROBAVAR averages, yields more

values per minute, has lower within patient variance, and measures baroreflex delay.

1 http://www.cbi.dongnocchi.it/glossary/eurobavar.html

154

Dynamics of baroreflex sensitivity during postural stress

Postural stress requires immediate autonomic nervous action to maintain blood pressure.

This can be explored by determining continuous time domain baroreflex sensitivity

(BRS) during stepwise changes in angles of body axis (α). Our hypothesis was that with

increasing postural stress, BRS becomes reduced by a reduction in its vagal component

(Chapter 7).

In 10 healthy young volunteers α included 20 degrees head-down tilt (–20º), supine (0º),

30 and 70 degrees head-up tilt (30º, 70º) and free standing (90º). Non-invasive blood

pressure recordings were analyzed over 6 min periods before and after each change in α.

BRS was determined by frequency-domain analysis and with xBRS, a high-resolution

time-domain method additionally providing the time delay τ between systolic blood

pressure and interbeat interval variations.

On average, between 28 (–20º) to 45 (90º) xBRS estimates per minute became available

for analysis. Following a change in α, xBRS altered in the first minute in 78% of the

cases and in 93% within 6 minutes. With increasing tilt angle, decrease in BRS was

described as

BRS = –10.1·sin(α) + 18.7; R2 = 0.99,

with good correlation between xBRS and cross-spectral gain (R2 = 0.98 for the low-

frequency band and R2 = 0.97 for the high-frequency band. The time delay τ shifted

towards higher values and correspondingly the phase in the spectral analysis tended to

become more negative.

In conclusion, with progressive orthostatic stress, time- and frequency-domain

baroreflex sensitivity declined linearly with the sine of α. The increase in delay τ at

higher levels of orthostatic stress appears to correspond with decreased vagal and

increased sympathetic cardiac tone.

Diurnal blood pressure analyses

The circadian blood pressure pattern and the day-night differences in blood pressure give

more accurate prognostic values than office blood pressure measurements and better

insight in blood pressure regulation.

155

Variable day/night bias in 24-hour non-invasive finger pressure against intra-brachial

artery pressure is removed by waveform filtering and level correction

The nocturnal blood pressure dip is overestimated by finger blood pressure, since it

shows a negative bias against intra-brachial artery pressure and the bias is greater during

the night. We have available a methodology to reconstruct brachial from finger artery

blood pressure by waveform filtering (transfer function) and generalized level (bias)

correction that reduces the bias for short term blood pressure records. We wanted to

investigate (Chapter 8) if this methodology also decreases the extra bias during the night

thereby yielding a better estimate of the nocturnal dip.

Twenty-four-hour finger (FinAP) and intra-brachial (BAP) blood pressure recordings

were simultaneously obtained in 8 healthy normotensive volunteers and 14 hypertensive

patients (aged 19 to 60 y), during standardized scheduled activities. The data were

analyzed off-line, applying the brachial reconstruction technique (reBAP) consisting of a

waveform filter and level correction. Simultaneous beats yielded systolic, diastolic and

mean pressures, which were averaged per half hour, per day, per night, per activity, over

the 24-hour period, and for volunteers and patients, separately.

Over the full 24 hours FinAP systolic, diastolic and mean pressures for the total group

differed +1 ± 10, –8 ± 7, and –10 ± 8 mmHg (mean ± SD), respectively, from BAP.

Similarly, reBAP differed +1 ± 11, –2 ± 7, and –2 ± 7 mmHg. BAP dipped 20 ± 8, 13 ±

6, and 15 ± 6 mmHg during the night. These dips were overestimated +8, +4, and +4

mmHg by FinAP but not by reBAP: –1, +1, and +1 mmHg. The volunteer and the

patient groups showed slight differences in results, which were not statistically

significant.

The generalized reconstruction technique to obtain near-brachial pressure from

noninvasive finger pressure almost completely removes bias over the full 24-hour day-

night period and allows accurate tracking of diurnal changes for systolic, diastolic and

mean pressures.

156

Concluding remarks

Starting on a time scale of milliseconds, we investigated a physiological model of

pressure transfer, concluding that the time delay between proximal and distal pressure is

an important measurable parameter for individualization of a pressure transfer function.

Next, we tested this finding on a set of measurements, demonstrating that a simple

transfer function could be improved by incorporating the time delay, thus facilitating

more accurate assessment of central pressures, the pressure that matters to the heart and

hence important for diagnostics. Also on a small time scale, we proposed a method to

calculate the reflection index from pressure alone, improving on the established method

of augmentation index calculation. Augmentation index is widely used as a simple

measure of arterial stiffness, which is in its turn an important marker for cardiovascular

morbidity and mortality.

Moving to a time scale of seconds, we analyzed parameters for cardiac oxygen supply

potential and cardiac oxygen demand. Not only oxygen demand increases after rising,

which is an accepted concept, but supply potential decreases, providing new insight in

the balance between supply and demand, perhaps giving an indication for use of

medication. A new method to calculate baroreflex sensitivity was established to give

values comparable to findings with other methods, but at a higher rate, allowing

assessment of baroreflex sensitivity in a shorter time span. The higher time resolution

also facilitates detailed analysis of changes in baroreflex sensitivity. We consecutively

analyzed the baroreflex sensitivity during orthostatic stress, discovering a tight relation

between baroreflex sensitivity and the tilt angle. We also showed that the new method

gives an indication of the sympatho-vagal balance. Finally, on a time scale of 24 hours,

we demonstrated a method to improve brachial artery pressure tracking by finger arterial

pressure measurements, so that dipper and non-dippers can be reliably distinguished

from non-invasive pressures.

We demonstrated in these studies that the non-invasive assessment of blood pressure can

be performed reliably and that it can help in increasing our understanding of blood

pressure control as well as in early detection of disease and effect of treatment.

157

Appendix

Assessing arterial baroreflex control of heart

rate: new perspectives

Gianfranco Parati1,2, J. Philip Saul3 and Paolo Castiglioni4

Editorial commentary to Chapter 6

The arterial baroreflex is a key mechanism involved in blood pressure homeostasis (1)

and its impairment is a characteristic feature of a number of cardiovascular diseases (1–

6). There is evidence that a deranged baroreflex control of heart rate may carry an

adverse prognosis in cardiac patients (7,8), while interventions that improve the

sensitivity of the heart rate baroreflex (BRS), such as physical training (9–11) or β-

adrenergic receptor blockade (12), may reduce the risk of cardiovascular events.

For several years, the conventional approach to BRS assessment has been based on the

application of laboratory tests only (1,13). However, in the 1980s, innovative methods

for the assessment of this parameter were described, based on the time or frequency

domain analysis of spontaneous blood pressure fluctuations coupled with reflex changes

in R–R interval (also termed heart interval) (13–19). Because all these newer techniques

evaluate arterial baroreflex function by considering the reflex heart rate effects of blood

pressure changes in the absence of external stimulations on the cardiovascular system,

the estimates of BRS yielded were defined as ‘spontaneous’ (13,20).

1 Department of Clinical Medicine, Prevention and Applied Biotechnologies, University of Milano-Bicocca, Milan, Italy 2 Cardiology II, S. Luca Hospital, IRCCS, Istituto Auxologico Italiano, Milan, Italy 3 South Carolina Children’s Heart Center, Medical University of South Carolina, Charleston, South Carolina, USA 4 Centro di Bioingegneria FDG, IRCCS Fondazione Don C. Gnocchi ONLUS, Milano, Italy

158

In this issue of the journal, a further contribution to this field is provided by Westerhof et

al. (21), who propose a new approach to the assessment of spontaneous baroreflex

function.

Why assess spontaneous baroreflex function?

The available methods for the assessment of spontaneous BRS all share a number of

common features. First, these techniques do not require any external intervention on the

cardiovascular system, thus preventing undesirable interferences with the autonomic

function patterns explored. Second, they can be used not only to assess BRS in

standardized laboratory conditions, but also to investigate the dynamic features of

baroreflex modulation of heart rate over time in daily life (17,19,22–25). Third, arterial

baroreflex control of heart rate is explored around the baroreflex ‘set point’, excluding

the portions of the sigmoidal baroreceptor stimulus–response curve approaching

threshold and saturation (14,20). The information on arterial baroreflex function

obtained appears to be complementary to that provided by the application of

conventional laboratory tests, based on either the injection of vasoactive drugs (26) or on

the manipulation of carotid baroreceptors through a neck chamber device (27–30), which

may explore arterial baroreflex function through a full-range, although artificial,

stimulation of arterial baroreceptors. Following the first introduction of methods for

spontaneous BRS assessment almost 20 years ago, a number of studies have supported

the pathophysiological and clinical relevance of the information on baroreflex function

that they provide (13,19,22,31–35), although the ability of ‘spontaneous’ BRS

assessment to offer new insights into neural cardiovascular regulation over and above the

solid evidence provided by classic laboratory tests has stimulated a lively debate (36–

38).

Available methods to explore spontaneous baroreflex function

Each of the several methods proposed to estimate BRS from the spontaneous variability

of blood pressure and heart rate is based on a specific physiological hypothesis and

makes use of different techniques of signal analysis (Table 1). These differences may

sometimes provide quantitatively different BRS estimates. The sequence method

(15,18,19) can be seen as the natural extension of the traditional drug-injection technique

applied to the analysis of spontaneous variability. It can be classified as a time-domain

method because it is based on the identification of specific patterns in the time series of

systolic pressure and heart interval. The technique scans the beat-to-beat series of

159

systolic pressure to identify a ‘sequence’ (i.e. a series of heart beats) in which a

monotonic increase (or decrease) of systolic pressure is followed, after a delay of zero,

one or two beats, by a monotonic increase (or decrease) of heart interval. The technique

assumes that the progressive changes of heart interval following the monotonic changes

of systolic pressure reflect the buffering action of the baroreflex. The slope of the

regression line between heart interval and systolic pressure values within the sequence is

taken as an estimate of BRS. The new xBRS estimator presented in this issue of the

journal by Westerhof et al. (21) may be classified into the family of time-domain

methods too. Similarly to the sequence method, BRS is obtained as the slope of the

regression line between values of systolic pressure and heart interval. However, these

values do not belong to a sequence, but to a 10-s window of data where the heart-interval

values are delayed by applying a time-shift that maximizes the cross-correlation.

Table 1. Methods for spontaneous baroreflex sensitivity (BRS) assessment

Short Name Type References

Sequence technique Time domain (13, 18, 19)

xBRS Time domain (21)

αLF, αHF Frequency domain (17)

HLF and HHF Frequency domain (16)

ak Mathematical models (14)

Hts Mathematical models (40)

ARMA Mathematical models (41)

XAR Mathematical models (42)

ARXAR Mathematical models (43)

Z-coefficient Statistical methods (48)

BRS, baroreflex sensitivity; xBRS, cross-correlation BRS; αHF, alpha coefficient in the high frequency band

(0.15–0.50 Hz); αLF, alpha coefficient in the low frequency band (0.04–0.14 Hz); HHF, HLF, modulus of the

transfer function between changes in systolic blood pressure and changes in heart interval; ak, BRS gain for

mathematical models; Hts, gain of SBP-heart interval transfer function; ARMA, AutoRegressing Moving

Average (model); XAR, eXogenous (model) with AutoRegressive input; ARXAR, bivariate AutoRegressive

(model) with eXogenous input.

A completely different approach is followed by the frequency domain methods. Spectral

analysis shows that spontaneous fluctuations of systolic pressure and heart interval tend

to be linearly correlated at the respiratory frequency (high frequency, HF, band) and

around 0.1 Hz (low frequency, LF, band). The alpha method (17) assumes that this

160

correlation is due to baroreflex cardiovascular control. Estimates of BRS are obtained by

computing the root-squared ratio between heart-interval and systolic pressure powers

calculated in the LF band (αLF) or in the HF band (αHF), provided that the coherence

between systolic pressure and heart interval (an index of their linear correlation) is

sufficiently high. The transfer function method (16) assumes that the heart interval is the

noisy output of a linear system in which systolic pressure is the input. BRS is then

estimated as the modulus of the transfer function, H, of this system. This is achieved by

computing the modulus of the cross-spectrum between systolic pressure and heart

interval, divided by the systolic pressure spectrum. The transfer function is usually

evaluated separately in the LF and HF frequency bands, obtaining two distinct estimates

of BRS: HLF and HHF. Also the recently proposed trigonometric method (39) belongs to

the class of frequency domain methods, because it estimates BRS by means of a

decomposition of blood pressure and heart-rate variabilities in periodic components.

Another approach for estimating BRS is based on the description of spontaneous blood

pressure and heart rate variability by means of a mathematical model of circulation. The

model coefficients are tuned to fit the experimental data (13). The proposed models

differ in terms of their complexity and modelling strategies, including, as possible

examples, dynamic adjustment models (40), autoregressive-moving average (ARMA)

models (41), exogenous models with autoregressive input, XAR (42), and bivariate

autoregressive models with two exogenous inputs ARXAR (43). Once the model has

been identified, BRS is derived from the model parameters.

Mathematical models for BRS assessment have been proposed to take into account the

complex relationship between blood pressure and heart interval. An increase or decrease

in blood pressure may result in an increase or decrease in heart interval. This process,

known as negative feedback, is an attempt to return blood pressure to its original value.

The other arm of this negative feedback control system, which closes the loop, is the

transmission of the heart interval change into a change in blood pressure, which can be

thought of as feedforward. For the baroreflex, the feedback gain which is the estimated

BRS, has been generally termed α-gain, while the feedforward has been termed β-gain

by some investigators (44). However, most baroreflex quantification techniques are

based on the assumption that the feedforward response is inconsequential, quantifying

only the feedback relation between blood pressure and heart interval. Models that

account for only the effect of blood pressure on heart interval are bivariate open loop and

unidirectional, while those that also consider the effect of heart interval on blood

pressure are bivariate closed loop and bidirectional. Finally, closed loop models that

161

account for other variables in addition to blood pressure and heart interval can be

considered multivariate. The inclusion of respiration in the baroreflex model is the most

common application of a multivariate model.

A multivariate closed-loop bidirectional model that includes as many parameters as

possible will clearly be the most accurate, because it is able to reduce the variance of the

BRS estimates due to factors other than blood pressure and heart interval. However, such

models are also limited by their complexity and the necessity of measuring multiple

parameters during spontaneous operation. Thus, most models focus on the use of only

blood pressure and heart interval. Finally, the issue of causality in computing the BRS

must be addressed. Causal models take into account the physiological timing

relationships between the parameters in the model, assuming that current values of a

parameter are dependent on past values of both itself and of the other parameters that

influence it. Non-causal models do not impose such timing relationships, effectively

assuming causality does not exist or is unimportant. Most spectral methods do not

include causality, but a variety of methods do include feedback causality, including the

sequence method, the xBRS proposed by Westerhof et al. (21) and most bivariate

autoregressive techniques (44–47).

Finally, an alternative way to quantify BRS is to statistically assess the probability to

find an association between values of systolic blood pressure and heart interval. The

statistical level of coupling is quantified by the Z-index, which is a function of two

variables: systolic pressure and heart interval. Z may range between –1 and +1: negative

values indicate exclusion, positive values indicate a link between the two variables. BRS

is derived from the shape of the Z-surface on the systolic pressure–heart interval plane

(48) (Table 1).

How to select the proper method for spontaneous BRS assessment

Given such a wide variety of different BRS estimators, there is a need to define the

criteria for the selection of the most appropriate method in a given experimental or

clinical setting. Indeed, the choice of the most appropriate technique depends on the

nature of the experiment, and it is often determined by stationarity level and length of the

signals, by the experimental protocol and by the characteristics of the subjects under

evaluation.

162

Stationarity

Most frequency domain methods and methods based on black-box modelling require the

stationarity of blood pressure and heart rate time series (i.e. they require the probability

distributions of the time series values to be independent of time translations). By

contrast, this is not a prerequisite for the Z-analysis or for the sequence technique, the

latter estimating BRS at the time of a clear non-stationarity of the recorded signals, such

as a blood pressure ramp.

Length of the signals

Theoretically, the method that requires the shortest segment of data to provide a single

BRS estimation is the sequence technique. An estimate can be obtained by only four

heart beats if they are characterized by a sequence-like progressive change in blood

pressure and heart interval. However, in practice, baroreflex sequences occur randomly

in blood-pressure and heart-rate time series, and signal lengths of the order of minutes

are therefore required to obtain reliable BRS estimates. The xBRS method described in

this issue of the journal (21) is characterized by very good performances in terms of the

minimal signal length required to obtain BRS estimates. Compared to the sequence

technique, the shortest segment of data needed to compute a BRS estimate is slightly

longer (15 s). However, the probability to obtain a BRS quantification from this short

segment is much higher compared to the sequence technique, and reliable BRS estimates

can be derived from shorter recordings. Frequency domain methods and black-box

models require longer segments of data to compute power spectra with the required

frequency resolution, or to reliably identify the model parameters. Z-analysis, which

implies the need to calculate conditional probabilities of events, also requires much

longer recordings.

Differentiation of BRS estimates

If there is an interest in assessing the BRS separately during a rise and a fall in blood

pressure, then the obvious method is the sequence technique, which can provide separate

estimates for increasing and decreasing blood pressure ramps, corresponding to arterial

baroreceptor stimulation and deactivation, respectively. By contrast, if a separate

estimation of the ‘vagal’ and ‘sympathetic’ contribution to BRS values is desired,

frequency-domain methods appear to be preferable.

163

Estimation of very low BRS

Generally, the various techniques make use of thresholds to limit the interference of

noise, and to ensure sufficiently reliable estimates. For example, with the sequence

technique, estimates of BRS can be obtained only from sequences of beats in which the

absolute changes between consecutive systolic pressure values or heart-interval values

are greater than a given threshold. Similarly, α and transfer function techniques estimate

BRS only if the squared coherence modulus between systolic pressure and heart interval

is greater than a pre-defined threshold. However, this means that, because of these

thresholds, a given technique may be unable to provide estimates in subjects with very

low BRS (e.g. in patients with autonomic failure). In this regard, the xBRS technique

presented by Westerhof et al. (21) appears to score sufficiently well because it is able to

provide reliable BRS estimates even in subjects with very low BRS values.

Improving the assessment of BRS: the contribution of the method by Westerhof et

al.

When quantifying the short-term relationship between arterial pressure and inter-beat

interval, it is important to consider that this relationship may not invariably represent the

physiology of the heart rate baroreflex because there are many systems other than the

baroreflex (e.g. respiration) that influence both blood pressure and heart interval on a

beat-to-beat basis. Theoretically, unless all of these systems are accounted for, or

controlled, the quantified baroreflex relationship is likely to be biased, and to have

reduced accuracy, regardless of the technique used for its quantification. Other

limitations of the available methods for spontaneous BRS assessment include within

subject variance of the BRS values, restriction to a fixed time delay from blood pressure

to heart interval changes, inability to detect low BRS values due to threshold issues, and

the availability of only a small number of BRS values in many instances. The xBRS

model described by Westerhof et al. (21) is aimed at addressing some of the above

problems. Conceptually, the xBRS model is simply a more complicated version of a

sequence model, using a variety of computation rules to address some of the limitations

of previous sequence and spectral methods. The authors do demonstrate that their model

addresses these limitations by reducing BRS estimate variance, providing more BRS

values and more accurately including timing effects. However, even this bivariate

method of blood pressure and heart interval interaction cannot be regarded as using a

complete model that is closed loop and causal, such as the autoregressive techniques that

have been previously described (39–47).

164

Finally, it has to be acknowledged that the new method proposed by Westerhof et al.

(21) has not yet been validated in studies making use of experimentally-induced

baroreflex dysfunction (e.g. through surgical baroreceptor denervation or

pharmacological blockade). However, it has been tested on the systolic blood pressure

and heart interval time series of a European dataset collected in the frame of the

activities of the Working Group on Blood Pressure and Heart Rate Variability of the

European Society of Hypertension. This dataset represents the first step of a

‘EuroBAVAR’ (European BAroreflex VARiability) Project that originally focused on

the technical comparison between different methods for assessing spontaneous BRS

(49), and which is now also used to tune and validate new approaches proposed for this

analysis, as in the case of the xBRS model by Westerhof et al. (21).

However, besides its technical validation, the actual clinical relevance of this new index,

with respect to the other available BRS estimates, now needs to be assessed in

longitudinal outcome studies.

165

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Background

The company BMEYE located in the AMC in Amsterdam (formerly the TNO

Biomedical Instrumentation research unit) has a long tradition of research in the area of

non-invasive hemodynamic measurements. The BMEYE core technology includes

continuous, non-invasive finger arterial pressure measurement, which has found its way

to the market in several medical devices, best known the Finapres (1-47), the Portapres

(48-55) and the Finometer (42,43). Continuous blood pressure measurement in space

research depends solely on the specially developed BMEYE finger arterial pressure

measurement devices (40,46).

BMEYE has worked on continuous model-based cardiac output calculation from

pressure, resulting in the Wesseling pulse contour method (56,57) and the Modelflow

method (58-66), using an elegant three-element Windkessel model.

Another long-standing interest is in blood pressure control and baroreflex, resulting in

elaborate models of the circulation (57,67,69,72). A recently developed method to

determine baroreflex sensitivity (73) is currently resulting in several publications (74-76)

offering new insights in this field.

Cooperation with clinical partners has always been very important. Newly developed

methods require new research for validation; new research may require new methods.

New applications of the BMEYE methodology also result in interesting new research.

To mention but a few: the analysis of non-invasive pressure wave shape to detect pre-

symptomatic signs of orthostatic intolerance during head-up tilt (82), plethysmography

of the finger pulse as a non-invasive method for predicting drug-induced changes in left

ventricular preload (77) and continuous non-invasive hemodynamic monitoring to

optimize atrioventricular delay settings of pacemakers in cardiac resynchronization

therapy (86).

170

Algorithms that can be applied to non-invasive pressure recordings to determine cardiac

preload on basis of systolic pressure variation (78) or pulse pressure variation (84) are

also interesting. Ventricular filling pressures has also been associated to heart rate

recovery after exercise in patients with suspected coronary artery disease (85). Several

studies suggest a relation between pulse pressure and endothelial dysfunction (80), pulse

pressure and coronary vasomotor dysfunction (83) or pulsatility and coronary artery

disease (79). Reactive hyperemia in the finger has been suggested to non-invasively

identify coronary atherosclerosis (81).

With the trend towards continuous non-invasive patient monitoring we feel that finger

blood pressure measurement will become the basis for many new systems for diagnostic

purposes, assessment of key risk factors and monitoring of acute vital signs in daily

clinical patient care.

171

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179

Samenvatting

Het gemeenschappelijke thema van voorafgaande Hoofdstukken kan omschreven

worden als een zoektocht naar betere diagnostiek en vroegere detectie van

waarschuwingstekens bij cardiovasculaire ziektes. Vroege herkenning van zulke tekens

vereist nauwkeurige niet-bloedige metingen en betrouwbare analyse methoden. Zoals

aangetoond in deze dissertatie, is de continue registratie van de gehele drukcurve

onmisbaar voor onderzoek dat verder gaat dan het bepalen van systolische en

diastolische bloeddruk. Niet-invasieve vingerbloeddruk meting heeft al de benodigde

eigenschappen. Enkele kleine stappen zijn gezet op het aangegeven pad, enkele nieuwe

technieken zijn getest en aanpakken voorgesteld, maar er is nog een lange weg te gaan.

Studies in grote groepen patiënten zijn nodig om de klinische relevantie aan te tonen van

de modellen en methodes.

Het doel van deze Samenvatting is om een overzicht te geven van de studies die

bijdragen aan het verkrijgen van informatie uit niet-invasieve arteriële vingerbloeddruk

en om het verkregen begrip te benadrukken.

Analyse van drukoverdracht

Overdrachtsfuncties maken het mogelijk om aortadrukken te reconstrueren vanuit

perifeer gemeten drukken en worden regelmatig gebruikt om beter inzicht te krijgen in

processen die de interactie tussen het hart en de vaten betreffen. Gegeneraliseerde

overdrachtsfuncties geven bruikbare resultaten, vooral bij onderzoek in grotere

studiepopulaties. Echter, meer gedetailleerde informatie zou verkregen kunnen worden

wanneer de overdrachtsfunctie geïndividualiseerd zou worden.

180

Gevoeligheidsanalyse van overdrachtsfuncties voor arteriële parameters

Het toepassen van overdrachtsfuncties op drukmetingen vereist kennis van de

variabiliteit in- en tussen individuen. Om die variabiliteit te onderzoeken (Hoofdstuk 2)

hebben we de kwantitatieve bijdrage van alle locale arteriële-, bloed- en distale

belastingsparameters aan de overdrachtsfunctie van de arteria brachialis naar de aorta

bestudeerd (Hoofdstuk 2). Deze theoretische analyse van de overdrachtsfunctie ging uit

van anatomische gegevens van vaatafmetingen, inclusief taps toelopen, Young’s

modulus, wand viscositeit en bloed viscositeit en dichtheid. Een drie-elementen

Windketel representeerde de belasting van de buis. De gevoeligheidsanalyse werd

beschreven in termen van frequentie en hoogte van de piek in de overdrachtsfunctie en in

termen van systolische en diastolische druk. De percentuele verandering van deze

variabelen voor een verandering van 25% in elk van parameters werd uitgerekend en de

Root Mean Square Error (RMSE) werd gebruikt om de onnauwkeurigheid in de

golfvorm te beschrijven.

De gevoeligheid was minder dan 3% voor systolische en diastolische druk en de RMSE

was kleiner dan 1.8 mmHg. Hieruit concluderen we dat de verschillen binnen een

individu weinig zullen variëren. Vaatlengte en diameter zijn de parameters met de

grootste invloed op de overdrachtsfunctie. Daar deze parameters belangrijk bijdragen

aan de looptijd van de drukgolf, kan geconcludeerd worden dat de vertraging tussen

perifere en central druk bepalend is voor de overdrachtsfunctie. Veranderingen in de

drie-elementen Windketel belasting bleken weinig effect te hebben, dus vasodilatie and

vasoconstrictie zijn van weinig invloed. Een simpele mathematische beschrijving van de

overdrachtsfunctie die is te optimaliseren voor een individuele patiënt door looptijd te

bepalen zou dus een goede beschrijving van de overdrachtsfunctie kunnen geven.

Aanpassing van parameters om de drukoverdrachtsfunctie te individualiseren

Uitgaande van de bovenstaande bevindingen hebben we onderzocht (Hoofdstuk 3) of de

drukoverdrachtsfunctie geïndividualiseerd zou kunnen worden door middel van een

representatieve looptijd van de drukgolf. Hoofdstuk 3 beschrijft een studie in een groep

van 50 patiënten: gemeten druk in de aorta ascendens was 119 ± 20 / 70 ± 9 mmHg,

(gemiddeld ± SD, systolisch / diastolisch) en intra-arterieel gemeten brachialisdruk was

131 ± 18 / 67 ± 9 mmHg. De Root Mean Square Error, RMSE, als maat voor verschil in

golfvorm was 7.5 ± 2.1 mmHg. Wanneer de overdrachtsfuncties met de beste schatting

voor de looptijd werden gebruikt, werd voor de gereconstrueerde aortadruk 121 ± 19 / 69

± 9 mmHg gevonden en de RMSE nam af tot 4.1 ± 2.0 mmHg. Een gegeneraliseerde

overdrachtsfunctie met de groepsgemiddelde looptijd gaf 122 ± 19 / 69 ± 9 mmHg en

181

een RMSE van 4.4 ± 2.0 mmHg. Details van de golfvorm werden beter weergegeven

door de geïndividualiseerde overdrachtsfunctie Dus, door de extra informatie verkregen

uit de looptijd kunnen we een overdrachtsfunctie bepalen die optimaal is voor een

individuele patiënt en die betere resultaten geeft dan de gegeneraliseerde

overdrachtsfunctie.

Hemodynamische analyses

Hemodynamische analyse is een wijd begrip. In dit proefschrift hebben we een aantal

verschijnselen onderzocht gerelateerd aan centrale bloeddruk en bepalend voor

hartfunctie. Een eerste, de reflectie-index, is beschreven in Hoofdstuk 4; een volgende,

zuurstof vraag en aanbod, is beschreven in Hoofdstuk 5.

Kwantificering van golfreflectie in de menselijke aorta op basis van alleen druk

Polsgolf reflecties zijn herkenbaar in de druk in de proximale aorta wanneer een

secundaire toename in de druk zichtbaar is. Reflecties kunnen de systolische druk

verhogen en worden beschouwd als een factor van belang in de studies van systolische

hypertensie. Een veel gebruikte maat van polsgolf reflectie is de Augmentatie Index

(AI), de verhouding van de secundaire stijging ten opzichte van de polsdruk. Een

tekortkoming van deze methode is dat alleen een schatting polsgolf reflectie verkregen

word wanneer een tweede stijging waarneembaar is. Het tijdstip waarop de

gereflecteerde golf terugkomt kan zo zijn dat de secundaire stijging niet te kwantificeren

is.

Een nauwkeuriger maat van polsgolf reflectie is de Reflectie Index (RI), die te berekenen

is na splitsing van de druk in zijn voorwaartse en gereflecteerde golf, zogenaamde

polsgolf analyse. Deze methode heeft echter ook de gemeten bloedstroom of

stroomsnelheid in de aorta nodig, die vaak niet beschikbaar is. We hebben daarom de

mogelijkheid onderzocht (Hoofdstuk 4) om de onbekende stroom te vervangen door een

kunstmatige, driehoekvormige stroom. Voor de tijdsduur van de stroom werd de

ejectietijd genomen, maximale stroom werd gelegd op het tijdstip van het optreden van

de secundaire drukstijging, beide bepaald uit de aortadruk. Deze stroom noemden we

FtIP. Voor een tweede analyses werd de maximale stroom op 30% ejectietijd gelegd, deze

stroom noemden we Ft30. Splitsing gaf dan voorwaartse (P forward, Pf), en

teruggekaatste (of terugwaartse, P backward, Pb), druk golven. RI werd gedefinieerd als:

RI = |Pb| / (|Pf| + |Pb|).

182

Twaalf gezonde proefpersonen werden geanalyseerd, aantal ingrepen werd uitgevoerd

waaronder inspanning en Valsalva manoever. Ook werden 5 patiënten met ischeamische

hartziekte onderzocht. RI’s bepaald met FtIP en Ft30 werden vergeleken met RImf, bepaald

met gemeten stroom, Fm, opgenomen met een Millar katheter met high fidelity druk- en

stroomopnemers aan de tip. RImf = 0.41 ± 0.05, (gemiddelde ± SD, n = 21), RItIP, RIt30 en

AI waren 0.39 ± 0.05, 0.39 ± 0.04, 0.34 ± 0.16, respectievelijk. AI was verschillend met

een grotere spreiding. De verbanden konden beschreven worden als: RItIP = 0.86 RImf +

0.03 (R2 = 0.73, n = 21), RIt30 = 0.84 RImf + 0.04 (R2 = 0.88, n = 26) en AI = 2.62 RImf –

0.74 (R2 = 0.57, n = 21). We concluderen hieruit dat de RI bepaald kan worden uit

aortadruk alleen, zelfs wanneer de AI niet vastgesteld kan worden.

Variaties in cardiale zuurstof vraag en aanbod in hypertensieve patiënten na opstaan

De toename in hartfrequentie en bloeddruk vlak na het wakker worden doet de vraag

naar zuurstof van het hart toenemen. Dit is in verband gebracht met de overmaat aan

acute hartinfarcten in de ochtend. De zuurstofvraag in hypertensieve patiënten is

verhoogd, en we onderzochten de hypothese dat toename in hartfrequentie en bloeddruk

in de ochtend ook het zuurstof aanbod aan het hart beïnvloedt (Hoofdstuk 5). We achtten

dit een belangrijke vraag omdat de verhouding tussen aanbod en vraag bepaalt of

ischaemie optreedt.

Aortadruk werd gereconstrueerd uit 24-uursmetingen van intra-arteriële brachialis- en uit

vingerbloeddrukregistraties in 14 hypertensieve patiënten en 8 gezonde vrijwilligers als

referentie. Zuurstof aanbod werd geschat met de diastolische tijdsfractie (Diastolic Time

Fraction, DTF), vraag werd geschat met vermenigvuldiging van hartfrequentie en druk

(Rate-Pressure Product, RPP) en aanbod/vraag ratio met Adia/Asys waarin Adia en Asys het

diastolische and systolische oppervlak onder de aortadrukcurve zijn.

In de ochtend namen hartfrequentie (heart rate, HR) en bloeddruk toe in beide groepen.

HR nam 33% toe in de hypertensieven and 55% in de normotensieven om op hetzelfde

niveau uit te komen in de morgen. DTF en de Adia/Asys ratio namen in beide groepen af

(P < 0.001), terwijl RPP toenam in beide groepen (P < 0.001). De parameters

vertoonden een sterk verband met HR (R2 ~ 0.9). Vergeleken met de normotensieven

hadden de hypertensieven een lager aanbod en een lagere aanbod/vraag ratio gedurende

de nacht. Ook hadden de hypertensieven een hogere vraag (P < 0.001), die in de ochtend

doorzette (P < 0.001).

Deze gegevens suggereren dat, vergeleken met de normotensieven, de zuurstofvraag van

het hart toeneemt. De onbalans tussen aanbod en vraag wordt niet alleen veroorzaakt

door toegenomen vraag maar ook door afgenomen aanbod. De verslechtering in de

183

aanbod / vraag ratio lijkt beperkt te worden door de kleinere toename van HR in de

ochtend bij de hypertensieven.

Baroreflex gevoeligheidsanalyses

Baroreflex gevoeligheidsanalyse wordt algemeen toegepast om inzicht te krijgen in het

functioneren van het autonome systeem in ziekte en gezondheid. Een methode die snel

betrouwbare informatie geeft over baroreflex gevoeligheid is een gezocht stuk

gereedschap.

Tijddomein kruiscorrelatie baroreflex gevoeligheidsanalyse: uitkomsten op de

EUROBAVAR data set

Om een nieuwe methode (xBRS) voor de bepaling van baroreflex gevoeligheid (BRS)

op basis van spontane variatie in bloeddruk en hartperiode te testen, gebruikten we de

EUROBAVAR data set die op het internet1 te vinden is. Deze set is speciaal samengesteld

voor het evalueren en vergelijken van methodes voor het bepalen van baroreflex

gevoeligheid.

In Hoofdstuk 6 werd de xBRS methode ingezet op de 42 registraties van de the

EUROBAVAR data set, verkregen van 21 patiënten in liggende en staande positie. Een

patiënt had recent een transplantatiehart ontvangen, een was diabetisch met cardiale

autonome neuropathie. xBRS berekent de correlatie tussen slag-op-slag druk en

hartperiode gegevens, herbemonsterd op 1 Hz, in een schuivend raam, met een

vertraging van 0 tot 5 s in hartperiode. De vertraging met de grootste positieve correlatie

wordt geselecteerd en, indien significant met at P = 0.01, worden de helling (ms/mmHg)

en de vertraging (s) opgeslagen als een BRS bepaling.

Voor onderzoek van de resultaten werden niet-parametrische tests gebruikt.

Voor de liggende positie gaf xBRS 12.4 tegen EUROBAVAR sequential 16.2 ms/mmHg,

voor staan 6.2 tegen 6.7 ms/mmHg, liggen/staan ratio 1.96 tegen 2.10. xBRS gaf

uitkomsten op alle files, 20 waardes per minuut gemiddeld en met een lagere intra-

individuele variantie. Beste xBRS vertragingen waren 0, 1, en 2 s, en de vertraging nam

100 ms toe in staande positie. xBRS gaf ook uitkomsten bij de diabeticus en

harttransplantatie-patiënt terwijl de andere methoden dat niet deden.

De xBRS methode zou in overweging kunnen worden genomen voor experimentele en

klinische toepassing, omdat de xBRS methode uitkomsten geeft die strek correleren met

1 http://www.cbi.dongnocchi.it/glossary/eurobavar.html

184

en dicht uitkomen bij uitkomsten van de EUROBAVAR gemiddelden, meer waardes per

minuut geeft, kleinere lagere intra-individuele variantie heeft en bovendien een maat

voor de baroreflex vertraging geeft.

Dynamica van de baroreflex gevoeligheid gedurende houdingsafhankelijke belasting

Houdingsafhankelijke belasting vereist onmiddellijk autonome neurale activiteit om de

bloeddruk op peil te houden. Een en ander kan onderzocht worden door continue

baroreflex gevoeligheidsanalyse (BRS) in het tijddomein bij stapsgewijze veranderingen

in de hoek van de lichaamsas (α). De hypothese was dat met toegenomen

houdingsafhankelijke belasting de BRS afneemt door een afname in zijn vagale

component (Hoofdstuk 7).

In 10 gezonde jonge vrijwilligers werd α gevarieerd tussen 20 graden head-down tilt (–

20º), supine (0º), 30 and 70 graden head-up tilt (30º, 70º) and vrij staan (90º). Niet-

invasieve bloeddrukken werden geanalyseerd gedurende periodes van 6 min voor- en na

een verandering in α. BRS werd bepaald spectraalanalyse en met xBRS, een tijdsdomein

methode met hoge resolutie en die bovendien de tijdsvertraging τ tussen systolische

bloeddruk- en hartperiodevariaties geeft.

Gemiddeld kwamen tussen de 28 (–20º) en 45 (90º) xBRS bepalingen per minuut

beschikbaar voor analyse. Na een verandering in α veranderde xBRS in de eerste minuut

in 78% van de gevallen en in 93% van de gevallen binnen 6 minuten. Met toenemende

tilhoek, kon de verandering in BRS als volgt beschreven worden:

BRS = –10.1·sin(α) + 18.7; R2 = 0.99,

met een goede correlatie tussen xBRS en cross-spectral gain (R2 = 0.98 en R2 = 0.97

voor de geanalyseerde lage- en de hoge frequentieband.

De tijdsvertraging τ verschoof naar langere waardes, de fase vertoonde een neiging om

negatiever te worden.

Concluderend, met toenemende houdingsafhankelijke belasting namen de tijd- en

frequentie domein bepaalde baroreflex gevoeligheid lineair af met sin(α). De toename in

τ bij grotere houdingsafhankelijke belasting lijkt verband te houden met afgenomen

vagale en toegenomen sympathische cardiale toon.

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24-uurs bloeddrukanalyse

Het circadiane bloeddrukpatroon en de dag-nacht verschillen hebben betere

voorspellende waarde dan spreekkamer bloeddrukmetingen en geven beter inzicht in de

bloeddrukregeling.

Variabele dag/nacht afwijking in 24-uurs niet-invasieve vingerbloeddruk tegen intra-

arteriële brachialis bloeddruk wordt verkleind door golfvorm filteren en niveau-

correctie

De nachtelijke bloeddruk afname wordt overschat door de vingerbloeddruk, daar deze

een negatieve afwijking heeft ten opzichte van intra-arteriële brachialisbloeddruk die

groter wordt gedurende de nacht. We hebben een methode om brachialis bloeddruk te

reconstrueren vanuit arteriële vingerbloeddruk door middel van golfvorm-filteren

(overdrachtsfunctie) en een gegeneraliseerde niveau-correctie die de afwijking verkleint

voor korte bloeddrukregistraties. We wilden onderzoeken (Hoofdstuk 8) of deze

methodologie ook de extra afwijking in de nacht vermindert en zo een betere schatting

mogelijk maakt van de nachtelijke bloeddrukafname (dip). Vierentwintig-uurs

registraties van vinger (Finger Arterial Pressre, FinAP) en van intra-arteriële

brachialisbloeddruk (Brachial Artery Pressure, BAP) werden simultaan opgenomen 8

gezonde, normotensieve vrijwilligers en in 14 hypertensieve patiënten (leeftijd 19 tot 60

jaar), onder gestandaardiseerde activiteiten. Deze data werden off-line geanalyseerd, met

gebruikmaking van de reconstructietechniek (reconstructed Brachial Artery Pressure,

reBAP) bestaande uit golfvorm-filteren en niveau-correctie. Gelijktijdige slagen gaven

systolische, diastolische en gemiddelde drukken, die gemiddeld werden per half uur, per

dag, per nacht, per activiteit en over de gehele 24 uur, en voor vrijwilligers en patiënten

apart.

Over de gehele 24 uur verschilde de FinAP systolische, diastolische en gemiddelde druk

voor de gehele groep +1 ± 10, –8 ± 7, and –10 ± 8 mmHg (gemiddelde ± SD),

respectievelijk, van BAP. reBAP verschilde +1 ± 11, –2 ± 7, en –2 ± 7 mmHg. BAP nam

20 ± 8, 13 ± 6, and 15 ± 6 mmHg af gedurende de nacht. Deze afnamen werden

overschat door FinAP: +8, +4, and +4 mmHg maar niet door reBAP: –1, +1, and +1

mmHg. De resultaten van de vrijwilliger en de patiënten vertoonden kleine verschillen,

die niet statistisch significant waren.

De gegeneraliseerde reconstructietechniek voor het verkrijgen van brachialis bloeddruk

uit niet-invasieve vingerbloeddruk verwijdert de afwijking over de 24 uur bijna volledig

en laat nauwkeurig volgen van dag-nacht veranderingen toe voor systolische,

diastolische en gemiddelde bloeddrukken.

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Conclusies

Beginnend op en tijdsschaal van milliseconden, onderzochten we een fysiologisch

correct model van drukoverdracht en kwamen tot de conclusie dat de tijdsvertraging

tussen de proximale en distale druk een belangrijke meetbare grootheid is waarmee de

drukoverdrachtsfunctie geïndividualiseerd kan worden.

Vervolgens toetsten we deze bevinding op een set meetgegevens waarmee we

aantoonden dat een simpele beschrijving van de drukoverdracht verbeterd kon worden

door de looptijd in te voeren, zodoende een meer nauwkeurige bepaling van de aorta

bloeddruk mogelijk makend. De centrale aorta bloeddruk is de bloeddruk die het hart als

belasting ervaart en dus van belang in diagnose.

Evenzeer op een kleine tijdsschaal, stelden we een methode voor om de reflectie index te

berekenen uit alleen de bloeddruk, dus zonder gebruik te maken van de bloedstroom.

Deze methode betekent een verbetering ten opzichte van de gevestigde Augmentatie

Index berekening. De Augmentatie Index wordt veelvuldig gebruikt als een simpele

maat van vaatwandstijfheid, die op zijn beurt weer een indicator is voor cardiovasculaire

morbiditeit en mortaliteit.

Naar een tijdsschaal van seconden gaand, analyseerden we parameters van cardiale

zuurstof vraag en aanbod. Niet alleen neemt de cardiale zuurstof vraag toe in de ochtend

na het wakker worden, wat een geaccepteerd concept is, maar ook neemt het cardiale

zuurstof aanbod af, wat vernieuwde inzichten geeft in de veranderingen in de balans

tussen vraag en aanbod en mogelijk een aanwijzingen inhoudt voor de toepassing van

medicatie.

Ook werd een nieuwe methode voor de bepaling van baroreflex gevoeligheid

ontwikkeld, die uitkomsten geeft die goed vergelijkbaar zijn met die van bestaande

methode maar met hogere frequentie, zodat veranderingen in de baroreflex gevoeligheid

in een kortere tijd vastgesteld kunnen worden.

Vervolgens analyseerden we met deze methode de baroreflex gevoeligheid tijdens

houdingsafhankelijke belasting en vonden een nauwe correlatie tussen baroreflex

gevoeligheid en hoek in de lichaamsas. Ook lieten we zien dat de nieuwe methode een

indicatie geeft van de sympatho-vagale balans.

Ten slotte, op een tijdsschaal van 24 uur, toonden we een methode om het volgen van de

brachialisdruk vanuit de vingerbloeddruk te verbeteren, zodat dippers en non-dippers

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(zie Introductie, sectie Blood pressure measurements in hypertension) betrouwbaar

onderscheiden kunnen worden met niet-invasieve drukmetingen.

We hebben aangetoond in deze studies dat niet-invasieve bepaling van bloeddruk

betrouwbaar toegepast kan worden en dat het kan helpen om in ons begrip van

bloeddrukregeling als ook in vroege opsporing van ziekte en bij effecten van medicatie.

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Dankwoord

Het dankwoord is het laatste, maar ook het belangrijkste hoofdstuk van een proefschrift. Niet alleen omdat een proefschrift met de medewerking van velen tot stand komt, maar vooral omdat het dankwoord vaak het enige hoofdstuk is dat wordt gelezen. Allereerst wil ik mijn promotores Karel Wesseling en Jos Spaan noemen. Karel, met jou is het allemaal begonnen. Ik wil je bedanken voor jouw uitnodiging om bij je te komen promoveren en voor de leuke tijd die we hebben gehad met het samen werken aan interessant onderzoek. Ik denk met veel plezier terug aan de bezoekjes aan Den Haag. Jos, met jou is alles nu afgerond. Ik wil je bedanken voor de steun bij de laatste loodjes. Jouw heldere blik is mij veel waard geweest. Mijn copromotor John Karemaker wil ik bedanken voor zijn bijdrage op allerlei vlak over de jaren heen. John, hoewel je pas sinds kort officieel mijn copromotor bent, ben je het eigenlijk altijd geweest. Ik ben blij dat ik van je enorme kennis heb kunnen leren, zelfs in een uitgebreide cursus, en ik ben dankbaar voor al de tijd die je voor me hebt vrijgemaakt. Beste collega’s van bmeye, ik wil jullie bedanken dat jullie me de gelegenheid hebben gegeven om te promoveren, ook in de veranderende omstandigheden. Beste Ilja, we hebben straks heel wat artikelen samen. Nog een paar erbij? Beste Gertrude, dank je wel voor jouw geweldige inbreng in dit proefschrift. Jos, ik heb er veel vertrouwen in dat we Het Gaan Maken. Jeroen, dank je wel voor alle hulp en steun. Hans, dank je wel voor de goede sfeer die je binnenbrengt. Olaf, nu jij! Dank je voor de leerzame discussies. Ben en Bob: leuk dat jullie weer terug zijn! Beste Peter en Gijs, dank jullie wel voor de steun in de TNO-tijd. De leden van de commissie ben ik erg erkentelijk voor de tijd en aandacht die zij hebben besteed aan de beoordeling van dit proefschrift. Beste Willem Jan, dank je wel voor jouw intensieve mentorschap de eerste jaren. Ik heb dat wel gemist na je vertrek. Jouw betrokkenheid en inzet is ongeëvenaard.

190

Dear Nikos, it was in Lausanne that I got my introduction in the field of hemodynamics and where I learned how much fun research is. It was through the work on the 4-element Windkessel that I got into contact with Karel. Thank you. Beste Wouter, ik heb me altijd welkom gevoeld in jouw onderzoeksgroep: dank je wel. Beste Han, jij hebt, met je onstuitbare enthousiasme, een geweldige bijdrage geleverd aan dit proefschrift, dank je wel. Beste Gert, dank je wel voor jouw kennis en geestige verhalen. Beste Janneke, dank je wel voor de leuke samenwerking. Jammer dat je zo snel klaar was met je promotie. Had een voorbeeld aan mij genomen. Beste Wim, we hebben een paar goede papers en ik hoop dat we nog meer kunnen doen samen. Beste Gijs, Lilian, Maarten en Barbara, de onderzoeken die we samen hebben uitgevoerd gingen niet van een leien dakje, maar we hebben wel veel plezier gehad en alles is uiteindelijk goed gekomen. Op naar de volgende onderzoeken! Dear Alberto, it was fun working around the clock on our paper, writing you at night and reading your reaction from Australia the next morning. Dear Gianfranco, thank you for the nice cooperation; let’s keep up the good work! Beste Jeroen (van Goudoever) en Jeroen (van den Wijngaard), dank jullie wel voor het kritisch lezen van mijn proefschrift. Dear Gabriela, thank you for being my soul mate and (para)nymph. Beste Claas, dank je wel voor je broederschap en voor het zijn van mijn paranymph. Lieve Pa en Ma, dank voor uw interesse door de jaren heen en uw vertrouwen. Lieve Opperoma, dank u wel voor uw optimisme en vrolijkheid. Lieve paps en mams, zonder jullie was het niet gelukt: jullie steun, zowel wetenschappelijk als organisatorisch, heeft erg veel voor me betekend. Als de hoeveelheid dank in verhouding zou staan tot het aantal regels in het dankwoord dan zouden er een paar pagina’s toegevoegd moeten worden. Lieve Marleen, Marten en Rosa, jullie hebben veel geduld gehad en ik ben erg dankbaar dat jullie me de gelegenheid hebben gegeven om dit proefschrift af te maken. Woorden en ook weer pagina’s schieten tekort.

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Overview of studies

1. Bos WJ, Vincent HH, Westerhof BE, van Montfrans GA. The mean pressure is not calculated

adequately by adding 1/3 of the pulse pressure to the diastolic pressure. Submitted.











Cardiothorac Surg. 2004;26:901-6.




7. Segers P, Stergiopulos N, Schreuder JJ, Westerhof BE, Westerhof N. Left ventricular wall

stress normalization in chronic pressure-overloaded heart: a mathematical model study. Am J

Physiol Heart Circ Physiol. 2000;279:H1120-7.



9. Stergiopulos N, Westerhof BE, Westerhof N. Total arterial inertance as the fourth element of

the windkessel model. Am J Physiol. 1999;276:H81-8.


function during and after incremental bicycle exercise. Provisionally accepted.

11. Van Os-Bossagh P, Kosterman LM, Hop WC, Westerhof BE, de Bakker JV, Drogendijk AC,

Van Duyl WA. Micromotions of bladder wall in chronic pelvic pain (CPP): a pilot study. Int

Urogynecol J Pelvic Floor Dysfunct. 2001;12:89-96.

12. Westerhof BE, Gisolf J, Karemaker JM, Wesseling KH, Secher NH, van Lieshout JJ.

Dynamics of baroreflex sensitivity during postural stress. Provisionally accepted.

192

13. Westerhof BE, Gisolf J, Stok WJ, Wesseling KH, and Karemaker JM. Time-domain cross-


22: 1371-1380, 2004.




Hypertens. 2002;20:1981-6.

15. Westerhof BE, Guelen I, Stok WJ, Wesseling KH, Spaan JA, Westerhof N, Bos WJ,

Stergiopulos N. Sensitivity of pressure transfer to arterial parameters. Ready for submission.

16. Westerhof BE, Guelen I, Stok WJ, Wesseling KH, Westerhof N, Bos WJ, Stergiopulos N,

Spaan JA. Parameter adaptation to individualize pressure transfer. Ready for submission.

17. Westerhof BE, Guelen I, Westerhof N, Karemaker JM, Avolio A. Quantification of wave

reflection in the human aorta from pressure alone. Under review.

18. Westerhof BE, van Montfrans GA, Guelen I, Wesseling KH, Spaan JA, Parati G, Westerhof

N, Karemaker JM, van Lieshout JJ, Bos WJ. Variations in cardiac oxygen supply and demand

in hypertensive subjects after rising. Ready for submission.

19. van den Wijngaard JP, Westerhof BE, Faber DJ, Westerhof N, van Gemert MJ. Transmission

line model for abnormal umbilical artery doppler flow velocity in twin-twin transfusion

syndrome. In preparation.

Berend E. Westerhof

Blood pressure analysis on tim

e scales from seconds to days B

erend E. Westerhof

Blood pressure analysison time scales from seconds to days

UitnodigingVoor het bijwonen van de openbare

verdediging van het proefschrift:

Blood pressure analysis on time scales

from seconds to days

van

Berend E. Westerhof

Op dinsdag 13 December 2005

om 12.00 uur

In de Aula van de Universiteit van Amsterdam, Oude Lutherse Kerk,

Singel 411 (hoek Spui)te Amsterdam

Receptie ter plaatsena afloop van de promotie

Berend E. WesterhofM. van Borsselenlaan 361181 DA Amstelveen

Tel: 020 6432746

Paranimfen:

Gabriela Montorzi-ThorellTel: +41 22 7430384

[email protected]

Claas WesterhofTel: 010 4258645

[email protected]

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