ORIGINAL ARTICLE

The augmented RIC model of the human respiratory system

Bill Diong Æ A. Rajagiri Æ M. Goldman ÆH. Nazeran

Received: 9 January 2008 / Accepted: 12 January 2009 / Published online: 31 January 2009

� International Federation for Medical and Biological Engineering 2009

Abstract This paper describes the augmented RIC model

of respiratory impedance and analyzes its parameter values

estimated—by a modified Newton method with least

squares criterion—from impulse oscillometry data. The

data were from asthmatic children, tested pre- and post-

bronchodilator, and from healthy adults and a second group

of adults with COPD. Our analyses show that the aug-

mented RIC model was 13.7–66.6% more accurate than the

extended RIC model at fitting these data, while its

parameter estimates were within previously reported ran-

ges, unlike the Mead1969, DuBois and Mead models,

which typically yielded compliance estimates exceeding

200 l/kPa. Additionally, the augmented RIC model’s Cp

parameter, representing peripheral airway compliance, is a

statistically significant discriminator between unconstricted

and constricted conditions (with p \ 0.001) occurring in

asthma and COPD. This corresponds well with current

medical understanding, so the augmented RIC model is

potentially useful for detection and treatment of airflow

obstruction.

Keywords Respiratory system impedance �Model parameter estimation � Impulse oscillometry �Asthma � COPD

1 Introduction

At the present time, lung function is most commonly

assessed by spirometry, which requires maximal coordi-

nated inspiratory and expiratory efforts by the subject,

making this test inappropriate for preschool children and

for older adults. However, early detection of childhood

asthma is crucial since, if left untreated, it can lead to

permanent damage of the airways leading to chronic

respiratory disability. As for older adults, asthma and

chronic obstructive pulmonary disease (COPD) can greatly

compromise their quality of life, and COPD is in fact the

fourth leading cause of death in the United States, recently

claiming about 119,000 lives each year.

In contrast to spirometry, respiratory function assessment

by the forced oscillation technique (FOT) [4, 13] requires

minimal, passive patient cooperation. Hence even preschool

children and older adults can provide valid measurements of

respiratory function for use in reliable detection or optimally

effective disease management, of obstructive respiratory

disease. One implementation of FOT for measuring respi-

ratory impedance is the impulse oscillometry system (IOS)

[13, 24, 28], which is a commercially available instrument

that applies 60–70 ms pulses of pressure at the subject’s

mouth as the respiratory system stimulus. The airflow

responses then lead to (after signal processing) frequency-

dependent impedance curves, that provide the most reliable,

reproducible, and appropriate method for demonstrating

reversible airflow obstruction in preschool (aged 2–5 years)

asthmatics [18]. These pressure-to-flow impedance curves

can also be correlated with the voltage-to-current imped-

ance of models containing electrical components that are

analogous to the mechanical resistances, inertances and

compliances in the respiratory system. Consequently,

parameter estimates for such respiratory system models

B. Diong (&) � A. Rajagiri

Department of Engineering, Texas Christian University,

Fort Worth, TX 76129, USA

e-mail: b.diong@tcu.edu

M. Goldman � H. Nazeran

Department of Electrical and Computer Engineering,

University of Texas at El Paso, El Paso, TX 79968, USA

123

Med Biol Eng Comput (2009) 47:395–404

DOI 10.1007/s11517-009-0443-2

[3–6, 12, 16, 19–22, 27] can then possibly serve as a com-

plementary quantitative means to detect, diagnose and treat

various respiratory diseases, including asthma and COPD.

In this paper, we expand on the initial results presented

in [20, 21], and also describe additional work. Specifically,

we examine the impedance-fitting performance of six

respiratory models, including the recently introduced aug-

mented RIC (aRIC) model, by estimating their parameters

from collected IOS data and then comparing the corre-

sponding estimation errors. We also present an analysis of

the estimated parameter values for the aRIC model aimed

at determining whether the model’s parameters are sensi-

tive to the presence of COPD in adults and/or to

bronchodilator intervention in asthmatic children.

2 Methods

2.1 Respiratory impedance models

Various electric circuit models with lumped parameter

components representing the respiratory system’s resis-

tances (R—typically in units of cmH2O/l/s or kPa/l/s),

inertances (I—units of cmH2O/l/s2 or kPa/l/s2) and com-

pliances (C—units of l/cmH2O or l/kPa), have been studied

over the years. The simplest are the well-known series RC

and RIC (see Fig. 1a) models, while some work has also

been done on the DuBois model (Fig. 1e) [4, 12]. In [22],

the RC and RIC models together with a 7-element Mead

model (Fig. 1f) were studied with respect to newborn

infants’ respiratory impedance as measured by FOT. In [5,

6], a 5-element respiratory system model (Fig. 1d—based

upon a simplified lung model proposed by Mead [16] and

designated in this paper as the Mead1969 model) was

compared to the RIC and DuBois models using impedance

data obtained with pseudorandom noise forced oscillation

from normal subjects and COPD patients. Note that these

models of impedance are all based upon a time-corre-

spondence between an imposed pressure (at the mouth) and

the resulting response of air flow, which satisfies a linear

ordinary differential equation. This is in contrast to respi-

ratory system models of the pressure–flow relationship

with respect to time that satisfy nonlinear ordinary differ-

ential equations, such as [10] and [29]. Moreover, these

stimulus-response models are also fundamentally different

from the structural types modeling air (and particle) flow

through the respiratory system, e.g., using computational

fluid dynamics [2].

The extended RIC (eRIC) model (Fig. 1b) was recently

introduced in [27] and then analyzed in [3] to reveal its

advantages as well as its shortcomings. The drawbacks of

this model then prompted the proposal of the aRIC model

(Fig. 1c) in [20]. Since the aRIC model is a relatively new

model and the focus of this paper, it will be the only one of

the above-mentioned models described in detail here.

The aRIC model was proposed as an augmentation of

the eRIC model, which has components representing large

airway resistance R, large airway inertance I, peripheral

airway resistance Rp and peripheral airway compliance Cp

[3, 27] (see Fig. 1b). The additional element Ce in the aRIC

model (see Fig. 1c), represents extrathoracic compliance

due mainly to upper airways shunt effects. Alternatively,

the aRIC model can be regarded as a simplification of the

7-element Mead model (with its lung compliance Cl and

chest wall compliance Cw parts ignored): justification for

doing so is provided in a later section. Although previously

given in [20], for completeness, we show the aRIC model’s

input impedance, as a function of frequency f (in Hz) as

IR C IcRc

R2 C2

C1

(a) RIC model (d) Mead1969 model

IR

Rp

C R

Rt Ct

CI

I t

(b) Extended RIC model (e) DuBois model

IR

Ce

Rp

Cp

Rp C l

Cb

Ce

CwIRc

(c) Augmented RIC model (f) Mead model

Fig. 1 Electric circuit models of respiratory system impedance

Z fð Þ ¼A RAþ Rp

� �

A 1� x2ICeð Þ þ x2R2pCpCe

� �h i2

þ xCe RAþ Rp

� �� �2

þ jx IA� R2

pCp

� �A 1� x2ICeð Þ þ x2R2

pCpCe

h i� xCe RAþ Rp

� �2

A 1� x2ICeð Þ þ x2R2pCpCe

h i2

þ xCe RAþ Rp

� �� �2

ð1Þ

396 Med Biol Eng Comput (2009) 47:395–404

123

where A = 1 ? (xRpCp)2 is used to simplify the

impedance expression, radian frequency x = 2pf and

j =ffiffiffiffiffiffiffi�1p

: Note that the real part of this complex func-

tion is known as the resistive impedance ZR whereas the

imaginary part (multiplying j) is known as the reactive

impedance ZX.

2.2 Model parameter estimation

Estimating a model’s parameters is similar in concept to

curve-fitting. Therefore, it is necessary to first select a

suitable error criterion E that is to be minimized [1]. For

this study, the least squares (LS) criterion

E ¼X

f¼5;10;15;20;25;35

f½ZRðf Þ�ZR;estðf Þ�2

þ ½ZXðf Þ � ZX;estðf Þ�2g ð2Þ

was used to minimize the sum of the squared errors

between the measured IOS ZR and ZX data samples at 5, 10,

15, 20, 25 and 35 Hz, and the estimated resistive (ZR,est)

and reactive (ZX,est) impedance values at the corresponding

frequencies. The LS criterion was chosen for this work due

to its commonplace use, its relation with other system

identification algorithms [9, 23], and its availability in

different software packages.

Note that the frequencies used in this study are consis-

tent with those reported in other IOS studies [7, 14].

Oscillation frequencies lower than about 4–5 Hz, are

‘contaminated’ by harmonics of the subject’s spontaneous

breathing frequency. Moreover, such low frequencies may

also excite the nonlinear visco-elastic properties of lung

tissue [25]. At the other extreme, oscillation frequencies

higher than about 35 Hz are increasingly affected by shunt

properties of the upper airways. These six frequencies yield

twelve data values, which are more than the minimum

number of values required for proper estimation of the 7 or

fewer parameters in the considered models.

A linear LS algorithm and a nonlinear LS algorithm

were used to estimate the parameters of the various respi-

ratory models. The MATLAB� lsqlin (linear LS) function

was used for the RIC model, whereas the MATLAB lsq-

nonlin (nonlinear LS) function was necessary for the other

models because of the nonlinear dependence of their

impedance functions on the parameters. Both of these

algorithms are based upon the interior-reflective form of

Newton’s method; the most significant difference between

them being that in the nonlinear case, the converged-upon

solution of parameter estimates may be only locally min-

imal instead of globally minimal, as is guaranteed in the

linear case. To ameliorate this problem, a procedure was

used whereby each estimation run began with an initial

guess, i.e., a parameter estimate vector produced by a

random number generator that’s appropriately weighted.

Random initial guesses ranging uniformly from 0 to 5, 0 to

0.5 and 0 to 0.05 were used for the values of resistances,

capacitances and inductances, respectively. This was

repeated at least 40 times per model for each set of test data

to find parameter estimates minimizing the error function

(2), with the program stopping each time when the error

value E changed by less than a factor of 10-9 from one

iteration to the next. This LS error value thereby provides

an overall measure of the ‘goodness of fit’ to the given test

data for each model and was used on results for both

normal subjects and patients with lung disease to assess the

degree of applicability of a given model (on average) to

both healthy and ill persons.

2.3 IOS measurements and data

Measurements during normal resting breathing for 30–50 s

were obtained in children with a previous diagnosis of

asthma [18] pre- and post-bronchodilation, in a group of

normal healthy adults with no known respiratory disease,

and in a group of adults with known COPD of varying

severity. While breathing on the mouthpiece (with a nose-

clip to seal the nares), the IOS [28] applied pulses of

pressure at the mouthpiece every 200 ms. After 30–50 s,

the test was completed, and the subject rested for approx-

imately 1 min prior to the next test: these measurements

were made 3–6 times. For the asthmatic children, the entire

set of measurements was repeated 15 min after inhaling a

standard medical bronchodilator (to open up their con-

stricted airways). The experimental records were made

after approval by the Institutional Review Board of the

University of Texas at El Paso.

2.3.1 Children

Data were collected from 37 asthmatic children (2–5 years

old, 12–31 kg, 0.88–1.17 m in height) in El Paso, TX.

These children were selected by willingness of their par-

ents to agree to our use of IOS measurements for research

purposes. We included 127 pre-bronchodilator tests (81 in

females), and 135 post-bronchodilator tests (86 in females).

Multiple tests were performed on each child to ensure

reliability of test values after excluding those tests with

artefacts (airflow leak, swallowing, etc.). Between 1 and 13

tests per child formed each data set (one set with con-

stricted airways and one after bronchodilation). The

standard deviation of multiple measurements within a child

(before, or after, bronchodilator) was 10–15%.

IOS test data were obtained with the child seated in a

comfortable chair, and the mouthpiece adjusted so that the

head and neck were in the neutral posture. The IOS

Med Biol Eng Comput (2009) 47:395–404 397

123

deadspace (mouthpiece, filter, and three-way chamber to

direct airflow) was approximately 60 ml. IOS data from

each test consisted of ZR and ZX values at 5, 10, 15, 20, 25

and 35 Hz, a total of 12 values per test.

2.3.2 Adults

The first set of 25 IOS measurements was obtained from

ten adults with COPD who agreed to their test results being

used for research purposes. All ten adults had a known

history of COPD for several years, and were on various

medications, including different kinds of bronchodilators.

They were 54–79 years of age (mean 66, SD 7.4), 1.60–

1.80 m in height (mean 1.74 m, SD 5.6 cm), 54.5–95.9 kg

in weight (mean 79.0 kg, SD 11.5 kg). Four test results

were from 1 female and 21 were from 9 males with 2–3 test

results per male adult. The second IOS dataset of 33 test

results was obtained from ten adults with no identifiable

respiratory disease, who had previously agreed to undergo

IOS testing for purely research purposes and were paid a

nominal sum to reimburse transportation/parking expenses.

Nine test results were from 3 females and 24 were from

7 males, 24–67 years of age (mean 43.6, SD 14), 1.73–

1.83 m in height (mean 1.77 m, SD 3.6 cm), weighing

50.0–100.9 kg (mean 77.7 kg, SD 14.9 kg) with 1–6 test

results per adult after excluding results with artefacts.

Again, IOS data consisted of ZR and ZX values at 5, 10, 15,

20, 25 and 35 Hz.

3 Results

There was convergence of the various model parameter

estimation programs from all initial values, although the

converged-on solution of the nonlinear LS algorithm

depended on the specific set of initial values. Also as

expected, the larger the number of model parameters being

estimated, the greater the proportion of non-globally min-

imum solutions and the longer the computing time to

convergence. The set of parameter estimates corresponding

to the smallest LS error was selected as the best fit to the

measured impedance data.

Table 1 shows the least square errors in ZR and ZX of all

models for a representative pre-bronchodilator test result

from one child, and the corresponding total LS errors. For

this test (illustrative of all results), estimation error of the

Table 1 Estimation errors for one pre-bronchodilator test result from

one asthmatic child

Model ZR LS error ZX LS error Z LS error

RIC 0.1329 0.0352 0.1681

eRIC 0.0223 0.0057 0.0280

aRIC 0.0125 0.0026 0.0151

Mead1969 0.0202 0.0026 0.0228

DuBois 0.0127 0.0019 0.0146

Mead 0.0074 0.0036 0.0110

5 15 25 350.5

0.6

0.7

0.8

0.9

1

ZR (

kPa/

l/s)

IOS dataRICExt RICAug RIC

5 15 25 35-0.6

-0.4

-0.2

0

0.2

0.4

ZX (

kPa/

l/s)

Frequency (Hz)

IOS dataRICExt RICAug RIC

5 15 25 350.5

0.6

0.7

0.8

0.9

1

ZR (

kPa/

l/s)

IOS dataMead1969DuBoisMead

5 15 25 35-0.6

-0.4

-0.2

0

0.2

0.4

ZX (

kPa/

l/s)

Frequency (Hz)

IOS dataMead1969DuBoisMead

(a) (b)

Fig. 2 Impedance plots of IOS

data and model estimates for the

same patient as Table 1 (a) RIC,

extended RIC and augmented

RIC models (b) Mead1969,

DuBois and Mead models

398 Med Biol Eng Comput (2009) 47:395–404

123

RIC model is significantly higher than the other models’,

while the 7-element Mead model yields the lowest total error.

As an illustrative example, the measured and estimated

respiratory impedances of this child are graphed in Fig. 2a

(RIC, eRIC and aRIC) and Fig. 2b (Mead1969, DuBois and

7-element Mead): these are shown in groups of three

models for ease of recognition. The upper graph is ZR

versus frequency; the lower graph is ZX versus frequency.

ZR and ZX of the estimated RIC model impedance shown in

Fig. 2a have the worst fit to IOS measurements: in partic-

ular, the RIC model’s ZR is independent of frequency,

whereas measured ZR shows considerable frequency

dependence.

Mean LS estimation errors (for ZR, ZX and Z) of the six

models for children’s data are detailed in Table 2, along

with standard deviation of LS errors in each model’s esti-

mation of Z. Table 3 presents the same information for the

two sets of adult data.

4 Discussion

4.1 Relationship of augmented RIC model to other

models

The aRIC model has an additional element Ce, compared

to the eRIC model, to model extrathoracic compliance

corresponding to upper airways shunt effects, which are

known to increase ZR at higher frequencies [13, 17, 24]

and can be observed in a significant proportion of IOS

measurements. Such an increase in ZR cannot occur with

the eRIC model [3]; so this characteristic accounts for its

poorer performance when such an increase in measured

ZR exists. Improvements in mean Z LS errors of the

aRIC model compared to the eRIC model are 14.36%,

13.71%, 66.58% and 50.92%, for children, pre- and post-

bronchodilator, and for COPD and normal adults,

respectively.

A less desirable consequence of this additional compo-

nent is that larger Ce values increasingly impair the

previously derived [3] simple, elegant (approximate) rela-

tionship between low-frequency dependence of resistive

impedance, ZR(5) - ZR(fres), and low-frequency reactance

ZX(5), which may be viewed as a consequence of periph-

eral airway compliance acting in parallel with peripheral

airway resistance. However, as with the eRIC model, the

aRIC model’s ZR(0) value equals R ? Rp, a fact that can be

used for parameter approximation purposes via data

extrapolation.

Note that the aRIC model can alternatively be viewed as

a simplification of the Mead model (with Cl, Cw equal to

infinity, thereby making them equivalent to short-circuits).

Thus it is not surprising that error performance of the RIC,

eRIC, aRIC and Mead models are ranked as they are.

Table 2 Mean estimation errors for asthmatic children: pre- and post-bronchodilation (n: number of tests)

Model

Pre-bronchodilation (n = 127) Post-bronchodilation (n = 135)

Mean ZR

LS error

Mean ZX

LS error

Mean ZLS error

Z LS

error SD

Mean ZR

LS error

Mean ZX

LS error

Mean ZLS error

Z LS

error SD

RIC 0.18962 0.04673 0.23635 0.22795 0.04256 0.01330 0.05586 0.05454

eRIC 0.02472 0.01330 0.03802 0.02733 0.00822 0.00643 0.01466 0.01437

aRIC 0.02010 0.01246 0.03256 0.02219 0.00674 0.00591 0.01265 0.01158

Mead1969 0.01532 0.00683 0.02215 0.02447 0.00338 0.00345 0.00682 0.00558

DuBois 0.00913 0.00528 0.01441 0.01405 0.00259 0.00254 0.00513 0.00391

Mead 0.00789 0.00705 0.01493 0.01501 0.00210 0.00293 0.00503 0.00368

Table 3 Mean estimation errors for adults: COPD and normal (n: number of tests)

Model

COPD (n = 25) Normal (n = 33)

Mean ZR

LS error

Mean ZX

LS error

Mean ZLS error

Z LS

error SD

Mean ZR

LS error

Mean ZX

LS error

Mean ZLS error

Z LS

error SD

RIC 0.02368 0.00379 0.02747 0.02868 0.00240 0.00059 0.00299 0.00155

eRIC 0.00111 0.00290 0.00401 0.00279 0.00169 0.00102 0.00271 0.00178

aRIC 0.00064 0.00070 0.00134 0.00087 0.00027 0.00036 0.00064 0.00062

Mead1969 0.00095 0.00059 0.00154 0.00092 0.00170 0.00028 0.00198 0.00197

DuBois 0.00060 0.00051 0.00111 0.00073 0.00065 0.00024 0.00089 0.00070

Mead 0.00037 0.00057 0.00095 0.00065 0.00023 0.00035 0.00057 0.00063

Med Biol Eng Comput (2009) 47:395–404 399

123

4.2 Comparing the models

4.2.1 Children

4.2.1.1 Pre-bronchodilation The mean LS estimation

modeling errors in Table 2 shows that the DuBois model

yielded the best fit (on average) followed closely by the

Mead model and the Mead1969 model. The proposed aRIC

model performed slightly worse than the Mead1969 model

but slightly better than the eRIC model, while the RIC

model provided the worst fit.

Since many different initial guesses were used in esti-

mating the parameters of these models and the ‘optimal’

results were consistent, the LS errors obtained are very

likely to be the global minima. Hence, it is significant to

note that the Mead model typically yielded unphysiologic

values of Cl and Cw, corresponding to lung compliance and

chest wall compliance, respectively, (although values for

other components were physiologic)—many being several

orders of magnitude larger than previously published and

widely-accepted value of 2 l/kPa for Cl and also for Cw

[26]. Similarly, the DuBois model also yielded unphysio-

logic values of tissue compliance Ct (values for other

components were physiologic)—many being several orders

of magnitude larger than 1.0 l/kPa for Ct (combination of

lung tissue and chest wall values) [4]. The Mead1969

model also yielded unphysiologic values of C2 (corre-

sponding to aggregated lung and chest wall compliance)

much larger than 1.0 l/kPa [4]. While these published

values are for normal adults, it is reasonable to expect the

values for normal children to be of the same order of

magnitude and actually lower. Using two orders of mag-

nitude larger than published, accepted values as the

arbitrary threshold between physiologic and unphysiologic,

Table 4 shows the percentage of compliance estimates

obtained that were unphysiologically large.

In contrast, all of the parameter estimates obtained for

the aRIC model were within the expected ranges of phys-

iological values for the subjects studied. The tendencies of

the Mead and DuBois models to overestimate compliances

from IOS data was previously established in [3, 20, 21], but

this is the first documentation that the Mead1969 model

also may yield unphysiologic values (of C2, from IOS

data).

4.2.1.2 Post-bronchodilation Table 2 reveals that the

Mead model yielded the best overall fit followed closely by

the DuBois model and the Mead1969 model. The perfor-

mance of the aRIC model and the other models remained in

the same order as for pre-bronchodilator data. Again, some

estimated values for C2 (Mead1969), Cl and Cw (Mead),

and Ct (DuBois) were unphysiologic (see Table 4), while

the aRIC model yielded physiological estimates.

We believe the Mead1969, DuBois and 7-element Mead

models produced grossly unphysiologic values for certain

compliances because of the small volume displacements

(less than 10 ml) produced by the IOS as compared to

volume displacements at least an order of magnitude larger

under which the Mead1969, DuBois and Mead models had

usually been studied. We suggest that there is an insuffi-

cient stimulus from IOS to provoke a measureable response

typically from the lung and/or chest wall.

It is also worth noting again that the DuBois model

yielded a better fit (on average) than the Mead model for

the set of pre-bronchodilation test data. While the DuBois

model is not a simplification (by short-circuiting or open-

circuiting of components) of the Mead model, which would

require its modeling error to be worse than the Mead

model, it does have less components than the Mead. This

implies that the DuBois model contains a component—not

found in the Mead model—which is significant in model-

ing the pre-bronchodilation data for asthmatic children;

that component may be It, lung tissue inertance.

4.2.2 Adults

4.2.2.1 COPD Table 3 shows that the RIC model had the

largest error in estimating Z while the smallest error was

achieved by the Mead model, followed by the DuBois

model. The aRIC model had slightly smaller error than the

Mead1969 model. However, the Mead1969 and the Mead

models again yielded unphysiologic values for the com-

pliances C2, and Cl and Cw, respectively, for some subjects

(see Table 4).

Table 4 Percentage of compliance estimates that were unphysiologically large

Mead1969

C2 [ 100 l/kPa (%)

DuBois

Ct [ 100 l/kPa (%)

Mead

Cl [ 200 l/kPa (%)

Mead

Cw [ 200 l/kPa (%)

Children (pre-BD) 17.32 13.39 66.93 27.56

Children (post-BD) 15.56 12.59 50.37 32.59

Adults (COPD) 28.00 0 96 36

Adults (normal) 39.39 3.03 96.97 57.58

400 Med Biol Eng Comput (2009) 47:395–404

123

4.2.2.2 Normal Table 3 also shows that the mean LS

errors of Z for normal adults are in the same order as for

the COPD patients except that the aRIC model and the

DuBois model have switched places, and the aRIC model

has the second lowest error. Notably, the percentage

difference between the RIC model and the other models is

significantly reduced due to a huge drop in this model’s

mean estimation error from its value for the group of

COPD patients. This observation correlates with the

widely-accepted notion that the ZR for healthy humans is

essentially independent of frequency; but diseases that

cause ZR to become frequency-dependent are poorly-

modeled by the RIC model, as illustrated by Fig. 2a.

Again, unphysiologic values were obtained in the

Mead1969, DuBois and Mead models for compliances C2,

Ct, and Cl and Cw, respectively, for some subjects (see

Table 4).

In contrast to the results in children, the DuBois model

has only one unreasonable value for Ct out of 58 adult test

results, so that the choice of the aRIC model as ‘best’ for

adult IOS data is less clear cut.

4.3 Reference values and statistical differences

of augmented RIC model parameters

4.3.1 Children

Parameter estimates of the aRIC model were analyzed

further to determine if they could discriminate between

asthmatic children’s pre- and post-bronchodilation states.

Since previous studies have established that reference

values for normal respiratory impedance in children are

strongly correlated to subject height [17], Fig. 3 shows

scatter plots of the aRIC model’s parameters (for pre- and

post-bronchodilation) versus height. Trend lines—based on

linear regression using a least squares error criterion—for

those estimates corresponding to the post-bronchodilation

data (to be used as a rough approximation of ‘normal

children’ data) are also superimposed on these plots. Trend

line equations are displayed for each of these parameters as

functions of height (H).

In [17], clinical values of ZR (denoted Rrs in that paper)

for most of the reviewed studies on healthy children start at

about 1.2 kPa/l/s (for various frequencies between 4 and

8 Hz) for height = 90 cm and decrease to about 0.35 kPa/

l/s for height = 175 cm. In comparison, linear regression

values from Fig. 3 for children’s post-bronchodilation

R = 0.79 kPa/l/s and Rp = 1.4 kPa/l/s, which are the main

components of ZR, for height = 90 cm, and decrease to

R = 0.42 kPa/L/s and Rp = 0.8 kPa/L/s for height =

115 cm. Hence the aRIC model’s estimates of R and Rp

correspond reasonably well to the clinical reference values

of Rrs for normal children given in [17].

Fig. 3 Estimated value of augmented RIC model parameter versus

child’s height

Med Biol Eng Comput (2009) 47:395–404 401

123

To assess the aRIC model’s ability to discriminate

between pre-and post-bronchodilation states, we applied

the Student’s t test to each of the five parameters. Pre-

bronchodilation Cp (peripheral airway compliance) is sta-

tistically significantly different from post-bronchodilation

Cp (p = 6 9 10-24). For R, Rp, I and Ce, p = 9 9 10-5,

8 9 10-5, 3 9 10-5 and 2 9 10-2, respectively. This

association of the asthmatic state (pre-bronchodilation)

with reduced peripheral airway capacitance is consistent

with current medical interpretation of the significance of

inflamed small peripheral airways, and concomitant

implied increase in their resistance and decrease in their

compliance, in the pathology of asthma [15].

4.3.2 Adults

Parameter estimates of the aRIC model for normal adults

and those with COPD were also plotted versus height (see

Fig. 4). Linear trend lines for the normal adults’ estimates

are also superimposed on these plots and trend line equa-

tions are displayed for each of these parameters as

functions of height (H).

In [17], clinical average values of ZR (Rrs) were reported

for healthy adult females as 0.31 kPa/l/s and for healthy

adult males as 0.25 kPa/l/s. In comparison, linear regres-

sion values from Fig. 4 for aRIC model parameters R =

0.21 kPa/l/s and Rp = 0.20 kPa/l/s for height = 173 cm,

and change to R = 0.18 kPa/l/s and Rp = 0.30 kPa/l/s for

height = 183 cm in our mixed population of adult males

and females. Hence the aRIC model’s estimates of R and

Rp correspond reasonably well to clinical reference values

of Rrs for normal adults [17].

We again applied the Student’s t test to each of the five

aRIC parameters. Normal adult Cp is statistically signifi-

cantly greater than Cp in adults with COPD (p = 2 9

10-11) while for R, Rp, I and Ce, p = 5 9 10-3, 1 9 10-4,

2 9 10-8 and 1 9 10-3, respectively.

4.4 Additional clinical relevance of augmented

RIC model’s parameters

Inhaled bronchodilator medication causes a decrease in

aRIC Rp and a concomitant increase in Cp. These model

parameters have significant relevance to the primary IOS

data and its physiological interpretation. Previously,

Grimby et al. [8] and Kjelgaard et al. [11] showed that

respiratory resistance decreases as oscillation frequency

increases in humans with small airway dysfunction

(SAD), most prominently between 3 and 9 Hz. In addi-

tion, frequency reactance ZX(5) is abnormally increased in

magnitude and is sensitive to inhaled bronchodilator

medication in children with asthma [14]. IOS data in both

Fig. 4 Estimated value of augmented RIC model parameter versus

adult’s height

402 Med Biol Eng Comput (2009) 47:395–404

123

children and adults manifest a very close association

between low-frequency dependence of resistive imped-

ance, ZR(5) - ZR(15), and ZX(5). Thus, IOS data with

increased frequency dependence of resistance and

increased magnitude of ZX(5) are commonly interpreted as

indicating SAD. In the subjects studied for this paper,

aRIC Rp and Cp are increased and decreased, respectively,

in both adults and children (pre-bronchodilation) with

SAD. Changes in Rp and Cp after bronchodilator in

children (and differences in Rp and Cp between COPD

and normal adults) are consistent with decreased SAD

after bronchodilation (and the difference between SAD

and health in adults). Thus, while we recognize that the

aRIC model must represent an oversimplified ‘respiratory

system structure’, nevertheless its parameters as calcu-

lated from IOS data reflect changes consistent with known

physiological changes resulting from obstructive airway

disease and with their modification by appropriate

treatment.

5 Conclusions

This paper has described the estimation of component

parameter values for the recently introduced aRIC model,

from IOS measurements of ill and healthy children and

adults. The ability of this model’s impedance to fit mea-

sured IOS data was compared to that of 5 other well-known

models using a LS criterion. While 3 of these other models

yielded less error (on average) than the aRIC model, the

same 3 models also typically yielded unphysiologic values

of greater than 200 l/kPa for at least one of their compli-

ance components. Hence, the aRIC model, with the next

lowest estimation error and its consistently physiologic

parameter estimates, appears to be the most useful model at

present for IOS-based computer-aided detection and treat-

ment of airflow obstruction as commonly occurs in asthma

and COPD.

Furthermore, the aRIC model’s parameter Cp, repre-

senting peripheral airway compliance, provides statistically

significant discrimination between abnormal airway func-

tion and less abnormal (or normal) airway function in

children and adults. This finding corresponds well with

current medical understanding of the pathologies of asthma

and COPD, and will be of use in the detection and/or

treatment of these disorders.

Acknowledgments This project was supported by grant number

S11 ES013339 from the US National Institute of Environmental

Health Sciences (NIEHS), NIH. Its contents are solely the responsi-

bility of the authors and do not necessarily represent the official views

of the NIEHS, NIH. The help of Dr. Roger Menendez, Allergy &

Asthma Center of El Paso, TX, with the children’s IOS data is also

gratefully acknowledged.

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