Reconstruction of cerebral hemodynamics with dynamic contrast-

enhanced time-resolved near-infrared measurements before and

during ischemia Jonathan T. Elliott*

a,b, Mamadou Diop

a,b, Laura B. Morrison

a, Ting-Yim Lee

a,b, Keith St.

Lawrencea,b

aImaging Division, Lawson Health Research Institute, 268 Grosvenor St., London, Canada N6A 4V2;

bDepartment of Medical Biophysics, Western University, 1151 Richmond St., London, Canada N6A 3K7

ABSTRACT

We present a dynamic contrast-enhanced near-infrared (DCE-NIR) technique that is capable of non-invasive

quantification of cerebral hemodynamics in adults. The challenge of removing extracerebral contamination is overcome

through the use of multi-distance time-resolved DCE-NIR combined with the kinetic deconvolution optical

reconstruction (KDOR) analytical method. As proof-of-principle, cerebral blood flow, cerebral blood volume and mean

transit time recovered with DCE-NIR are compared with CT perfusion values in an adult pig during normocapnia,

hypocapnia, and ischemia. Measurements of blood flow acquired with DCE-NIR were compared against concomitant

measurements using CT Perfusion.

Keywords: Near-infrared, time-resolved, dynamic contrast-enhanced, indocyanine green, deconvolution, reconstruction,

traumatic brain injury, neurointensive care

1. INTRODUCTION

Neurointensive care units (NCUs) are principally charged with the treatment and management of individuals presenting

with traumatic brain injury (TBI), subarachnoid hemorrhage (SAH) and ischemic stroke (IS). Complications that occur

during the recovery of neurotrauma patients often result in impaired cerebral blood flow (CBF) and lead to secondary

brain injury that is permanent or fatal. An important application of biomedical optics is the measurement of CBF at the

bedside, and dynamic contrast-enhanced (DCE) methods that employ time-resolved (TR) near-infrared (NIR) methods

have demonstrated promise [1]. However, to date, accurate optical reconstruction and subsequent kinetic analysis of

DCE information that is maximally sensitive to brain tissue has been elusive. First, the ill-posed nature of optical

reconstruction results in extracerebral layer (i.e., scalp, skull and CSF) contamination that propagates into kinetic

analysis, resulting in an underestimation of CBF [2]. Second, nonparametric kinetic analysis is typically performed for a

single region-of-interest with homogeneous dynamic properties, since it requires specific physiologically-derived

constraints for stability [3]. To overcome both these problems, we introduced the kinetic deconvolution optical

reconstruction (KDOR) method [4] and provided a theoretical basis for this approach. In this proceeding, we present the

first proof-of-principle animal experiment that suggests KDOR can accurately recover CBF, CBV and MTT in adult pigs

during normal and ischemic conditions. Measurements were compared with CT perfusion for validation.

2. THEORY

2.1 Dynamic contrast enhanced near-infrared measurements

The convolution theory of tracer kinetics provides the basis for the DCE-NIR methods presented in this proceedings [5],

and relates the time-dependent tissue concentration of dye, C(t), to the time-dependent arterial concentration of dye—

also known as the arterial input function—Ca(t), by the convolution:

,)()()(

0

t

a dutuCuFRtC (1)

where F is blood flow and R(t) is the impulse residue function, (i.e. the fraction of dye remaining in the tissue at time, t,

after an idealized bolus injection). It will be more convenient to define Eq. 1 as a discrete convolution formulated by the

matrix multiplication

Optical Tomography and Spectroscopy of Tissue X, edited by Bruce J. Tromberg, Arjun G. Yodh, Eva Marie Sevick-Muraca, Proc. of SPIE Vol. 8578, 85780A

© 2013 SPIE · CCC code: 1605-7422/13/$18 · doi: 10.1117/12.2005128

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,

][

]3[

]2[

]1[

][000

]1[][

]2[]1[00

]2[][0

]2[1[][

]1[]2[]1[

0]1[]3[

00]2[]3[

]1[]2[

000]1[

ntFR

tFR

tFR

tFR

mtC

mtCmtC

mtCmtC

mtCmtC

tCmtCmtC

tCtCmtC

tCtC

tCtC

tCtC

tC

a

aa

aa

aa

aaa

aaa

aa

aa

aa

a

AF CRC (2)

where C is the [m x 1] tissue concentration vector, RF is the [n x 1] vector containing the F scaled R(t) function, and CA

is the [m x n] Toeplitz matrix constructed from Ca(t). Tracer kinetic methods in DCE optics [1,4,6], as well as DCE-CT

methods [3,7] use a constrained deconvolution method to solve Eq. 2 in a least squares sense; details on the

deconvolution constraints are provided elsewhere [3,4].

2.2 Optical reconstruction to recover regional concentration

In the traditional approach, region-of-interest analysis precedes deconvolution, whereby the tissue concentration in the jth

region, Cj(t) is reconstructed by solving the inverse of the forward problem [8] for each instant in time that the signal,

ΔSΩ, is characterized

,)10ln(1

RN

j

jJj CAS (3)

where Ω is the imaging domain, Aj is the Jacobian (calculated for the medium with bulk optical properties μj), which is

the transformation between the signal and Cj, the concentration of tracer in the jth

tissue region. The specific absorption,

ε, and ln(10) scale the Jacobian, which is typically determined for perturbations in μa. Again, it will be convenient to

express the forward problem in Eq. 3 as a matrix multiplication

][

]1[

]2[

]1[

],[]1,[

],1[]1,1[

],2[]1,2[

],1[]1,1[

qjC

qjC

jC

jC

qjpiAjpiA

qjpiAjpiA

qjiAjiA

qjiAjiA

CAS (4)

where S is the [p x 1] signal vector sampled over the imaging domain, C is the [q x 1] vector defining the region-specific

concentration, and A is the [j x q] Jacobian matrix scaled by ε∙ln(10), defining the sensitivity of the signal to

perturbations in each region caused by dye. The signal function domain can be defined for a finite set of spatial and/or

spectral coordinates depending on the configuration of the system. In DCE measurements, the signal can also be defined

for a set of temporal coordinates. Further dimensions can be specified, including "small" time, τ (i.e, time-bins or time-

gates), as is the case in time-resolved optical reconstruction [9]. As will be further discussed in subsection 2.4, statistical

moments can be used to collapse the time-resolved time-bin data into three components: attenuation (related to the

zeroth moment), mean time-of-flight (MTOF; related to the first centralized moment), and variance of time-of-flight

(VTOF; related to the second centralized moment). In the work presented in this proceedings paper, S will be defined on

the basis of three sets: source-detector position, ρ, time, t, and moment-order, k.

2.3 Kinetic deconvolution optical reconstruction (KDOR)

It has been noted that because of the diffuse nature of light in tissue, which is a highly scattering medium, the Jacobian

defined according to spatial, spectral and temporal coordinates contains a large amount of elements whose difference is

on the order of the signal noise (i.e., the Jacobian has a low effective rank) [4,8]. As a result, the least-squares solution to

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Eq. 4 is ill-posed, and must be stabilized using priors: hard and soft constraints based on a priori knowledge, or

mathematical constraints such as non-negativity. The choice of priors has a significant impact on reducing the loss-of-

information due to reconstruction, and common examples are anatomical priors [10] or spectral priors [11], which

constrain the solution in spatial and spectral dimensions, respectively. Until recently, priors acting temporally (i.e.,

employing equality and inequality constraints defined in the time domain), have been unexploited. In DCE-NIR

methods, however, the dye concentration in any region is a result of a bolus injection of dye introduced into the subject,

and therefore, can be defined using the convolution theorem of tracer kinetics. To mitigate the loss-of-information that

occurs during optical reconstruction and results in errors in subsequent kinetic analysis, we introduce the kinetic

deconvolution optical reconstruction (KDOR) approach. The KDOR approach combines these two steps into a signal

linear inversion, which can be constrained using the same temporally defined equality and inequality constraints

previously used in deconvolution. Additional constraints in spatial and spectral dimensions are also compatible with

KDOR, providing a robust means of extracting regional kinetic information from a set of optical measurements. The

formulation of KDOR, combining Eq. 2 and 4, is given by

,**

FBRS (5)

where the block matrix B is the Kronecker product, ACA , and represents the transformation between S*, the signal

vector and RF*, the blood-flow scaled impulse residue function vector. It should be noted that S

* is a column vector

obtained by stacking the signal vectors, S acquired at all timepoints, t; similarly, RF* is a column vector obtained by

stacking all RF vectors defined for each region, j. The quantification of blood flow is achieved by optimizing

HRGRSBR FFF **

2

**and subject to min

FR (6)

where G and H are inequality and equality matrices that contain the specific physiologically-derived constraints

employed in DCE deconvolution methods [3].

In the work presented here, the signal was defined according to source-detector distance, moment order, and time,

respectively: ρ={6 mm, 20 mm, 30 mm, 40 mm}, k = {0, 1, 2}, and t = {0 s, 0.4 s, 0.8 s ... 320 s}.

2.4 Statistical moments of time-resolved data

The analysis of time-resolved data using the statistical moments of the distributions of time-of-flight has been previously

discussed in great depth [1, 12]. Briefly, time-resolved measurements acquired on the surface of the head, N(τ), represent

the convolution between some tissue response function and the instrument response function (IRF), and the effect of the

IRF is significant. Furthermore, the large amount of data, usually measured for about 1024 timebins, is difficult to

manage. It has been proposed that three normalized statistical moments―attenuation, A, mean time-of-flight, <t>, and

variance, V―contain the principle components of N(τ), and are given by

)ln( 0mA (7a)

2

1

m

mt (7b)

2

0

1

2

1

m

m

m

mV (7c)

where ,),()(2

1t

t

k

k dtNtm and t1 and t2 are temporal integration limits. Furthermore, the changes in these moments

(i.e., ΔA, Δ<t>, ΔV) are insensitive to the IRF. Several studies have demonstrated that ΔV is more sensitive to brain

tissue than lower-order moments when measurements are collected on the surface of the head [1]. A perturbation in

optical properties in the jth region of tissue results in a change in the kth moment according to the moment's sensitivity

factor, which is equivalent to the concept of the Jacobian in the previous section. Sensitivity factors for the three

moments—mean partial pathlength (MPP), mean time-of-flight sensitivity factor (MTSF) and variance sensitivity factor

(VSF)—were computed by Monte Carlo simulations according to the methods described in Ref. [12].

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CO

3. MATERIALS AND METHODS

3.1 Data acquisition and processing

Time-resolved data were collected using an in-house developed multi-channel time-resolved system which has been

previously described [13]. Briefly, a picosecond diode laser light source (LDH-P-C-810, PicoQuant, Germany) emitting

at 802 nm was used. Light pulses, repeated at a rate of 80 MHz, were guided to the subject with a 1.5-m long multimode

fiber and directed onto the scalp at a single position. Photons exiting the scalp were collected by four optodes configured

linearly at distances of 6, 20, 30, and 40 mm from the source, which in turn guided the collected light through bandpass

filters (FEB800-10, Thorlabs, NJ) to four photomultiplier tubes (PMT). Photon count rates of about 1% the repetition

rate were maintained to collect sufficient signal while minimizing dead-time effects.

To perform DCE TR-NIR acquisition, a time-of-flight histogram, N(τ), was collected every 0.4 seconds for a total of 320

seconds; 12.8 s of data was collected before the bolus injection of ICG, with the remaining data acquired during passage

of dye. This was performed simultaneously in all four channels. In addition, the arterial input function, Ca(t), was

acquired using a pulse dye densitometer (Nihon-Koden, Japan). Moment analysis was performed following the

acquisition of data using the method highlighted in Section 2.4 and in Ref. 12. These data were stored for subsequent

analysis in MATLAB (MathWorks, MA).

In addition to DCE-NIR measurements, computed tomography (CT) anatomical images and CT perfusion measurements

were acquired using LightSpeed QXi scanner (GE Healthcare, WI). Dynamic CT data was acquired during bolus

injection of iodine-based contrast (1.0 mL/kg of 300-Isovue) at a rate of 1 mL/s. CT data was used as anatomical

information in the Monte Carlo simulations. In addition, to confirming the ischemic injury, CT perfusion was used to

determine CBF, CBV and MTT in a region-of-interest approximating the region interrogated by the NIR light for

validation of DCE-NIR measurements.

3.2 Monte Carlo simulations

Monte Carlo simulations were computed to determine the sensitivity factors for moments k = {0, 1, 2} at source-detector

distances ρ = {6 mm, 20 mm, 30 mm, 40 mm} using the Monte Carlo eXtreme (MCX) algorithm [15]. First, the subject-

specific anatomical CT volume was segmented into the following regions: air, scalp tissue, skull, brain tissue, and probe

holder (which was constructed with flexible rubber). For the purpose of this work, segmentation was performed

manually; however, automatic segmentation should be achievable with a multi-region graph cut method [16], and is

currently being investigated. Figure 1 shows the CT image and segmented binary image used in the MC simulation.

Figure 1. (A) An anatomical CT slice used in manual segmentation to define (B) the binary volume, and (C) a CT perfusion

blood flow map showing the large ischemic region (white arrow).

Typically, a set of optical properties are selected based on published values for specific tissue-types. For example,

typical optical properties are given for scalp, skull, CSF, and brain tissue [14], but can vary widely. Alternatively, we

populated a library of simulated TPSF functions, Nmc(τ), for a range of scalp and skull absorption and scattering

coefficients: μa1,2 = [0.02, 0.04] and μs1,2′= [0.63, 1.17]. The experimentally measured temporal point spread function,

TPSFexp, for the short source-detector distance (6 mm) was used as the ground truth in the following optimization

)()()(min exp uTPSFuIRFuNmc

(8)

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A1

0.8 -

0.6 -

0.4 -

0.2 -

-Baseline

Hypocapnia

Ischemia

0 Fi I

0 20 40

Time (s)

60 80

6

where μ = {μa,1, μa,2, μs,1, μs,2}, and u is the subset of t corresponding to the time-bins which fall between the point on the

curve left of the peak that is 50% of the maximum, and the point on right of the peak that is 20% of the maximum. In

this way, a set of optical properties are recovered that produce simulated TPSFs corresponding to the experimentally

measured TPSFs. Following the selection of appropriate optical properties, the sensitivity functions corresponding to the

three moments and defined for two tissue regions—brain and an extracerebral layer (ECL) comprised of both scalp and

skull—are determined.

3.3 Animal experiments

All animal experiments were conducted following the guidelines of the Canadian Council on Animal Care (CCAC) and

approved by the animal use subcommittee at Western University. A Duroc-cross pig was acquired from a local supplier

on the morning of the experiment. Following induction with 1.75-3% isoflurane, the animal was tracheotomized and

mechanically ventilated on oxygen / medical air. A rubber probe holder was placed on the head and fixed in place with

tissue glue, and three surgical incisions were made, one each on the caudial, rostral and lateral sides of the probe holder,

so that only the segment medial to the holder was left intact. This was done to reduce the blood flow in the scalp, which

is much higher in the pig due to high vascularization of the thick temporalis muscles originating at the temperoparietal

region of the head [1].

Following the scalp surgery, the animal was given a 1-hr stabilization period before the start of the validation

experiment. DCE-NIR and CT perfusion measurements were made for each of three physiological conditions: baseline,

hypocapnia, and ischemia. A DCE NIR measurement consisted of collecting multi-channel TR NIR data from the

surface of the head during the bolus injection of ICG (0.1 mg/kg, Cardiogreen, Signa-Aldrich, St. Louis, MO), and

simultaneously acquiring the Ca(t) by dye densitometry. The CT perfusion measurement was performed following the

DCE-NIR measurement. Hypocapnia was achieved by increasing the respiration rate on the ventilator, resulting in the

overexpiration of CO2 and subsequent increase in CBF as a compensatory mechanism. Ischemia was achieved by

drilling a burr hole through the scalp and scull just lateral to the probe holder at the half way point, and infusing

endothelin-1 (ET-1), a potent vasoconstrictor, directly into the cortical tissue via a 30-Ga needle angled towards the

midline. The objective was to cause widespread ischemia across the hemisphere beneath the probe holder, as shown in

Figure 1C.

4. RESULTS AND DISCUSSION

A representative example of attenuation and variance curves at baseline, hypocapnia, and ischemia conditions is shown

in Figure 2. The attenuation curves exhibit very little difference in shape when acquired under the three conditions,

except for a slight difference in the washout of dye under hypocapnia. When examining the change in variance curves,

there is a significant shape difference between the ischemia curve compared with the other two curves. Note that under

the first two conditions, the variance curve contains a significant fast component that arrives earlier than the attenuation

signal, which is slow and persistent. This fast component is abolished under the ischemia condition, which affects only

the blood flow in the brain tissue. This suggests that the variance curve is maximally sensitive to changes occurring in

the brain.

Figure 2. (A) The attenuation and variance collected at p = 30 mm during the three conditions, and (B) the variance signal

from the same measurements.

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80

60

40

20

0

Baseline

Hypocapnia

Ischemia

0 10 20 30 40

Time (s)

B0.08

0.06

0.04

0.02

0 20 40

Time (s)

60 80

The KDOR method was used to analyze the entire data set, collected at four distances and defined for the three statistical

moments. The recovered flow-scaled impulse residue functions are depicted in Figure 3A, and show clear differences in

height for the three conditions. Note that the maximum of these curves is equal to blood flow.

Figure 3. (A) The impulse residue functions recovered with KDOR from the entire dataset, for the three conditions and (B)

the corresponding brain dye concentration curves recovered by the algorithm.

The recovered brain tissue concentration curves are depicted in Figure 3B for the three conditions. Note that for the first

two conditions, the first pass of the dye decreases to about 15% of the maximum before recirculation causes a transient

fluctuations. This shape is characteristic of brain dye curves under non-ischemic conditions, confirmed by measurements

in piglets [17], directly on the brain of adult pigs [1] and in CT region-of-interest curves. The recovered curve under

ischemia shows a reduction in the amount of dye delivered to the brain tissue, and has slightly slower kinetics suggesting

that flow has been reduced. Quantitative comparisons were made under these three conditions with CT perfusion

measurements calculated for appropriate regions-of-interest. These values are summarized in Table 1. In all cases, the

DCE NIR and CT measurements are in good agreement; however, DCE NIR measurements exhibit slightly smaller

blood volumes than CT perfusion.

Table 1. The DCE NIR and CT perfusion recovered hemodynamic values for the three conditions.

Baseline Hypocapnia Ischemia

DCE NIR CT DCE NIR CT DCE NIR CT

CBF (mL min-1

100g-1

) 75.0 70.1 61.5 62.9 27.2 38.1

CBV (mL 100g-1

) 3.74 5.38 3.13 4.38 3.33 4.41

MTT (sec) 2.99 4.61 3.06 4.18 7.33 6.93

Previously, we have demonstrated that the moments-based approach can be used to measure the change in blood flow

through the kinetic analysis of the variance signal. The limitation of the previous approach was that only a relative blood

flow index was obtained and, unless another modality is used for calibration, quantitative values of blood flow are not

produced. This could potentially limit the clinical use of the technique, since in order to guide medical interventions, a

CBF threshold is most likely needed. By combining the methodology of previous moments-based techniques with the

recently published KDOR method, we present a straightforward means of overcoming the signal contamination typical

in adult subjects to recover quantitative values of CBF. Additional experiments will be performed as a validation study

to demonstrate the precision and accuracy of the DCE-NIR method. Furthermore, we will optimize the KDOR algorithm

and create a fully automatic workflow capable of incorporating CT and DCE NIR data and producing CBF values in

near real-time, which will be made available on our group website.

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5. CONCLUSIONS

The results of this proof-of-principle experiment suggest that the KDOR method combined with DCE-NIR

measurements is capable of accurately quantifying CBF, CBV and MTT in the adult. This technique is completely

compatible with clinical use in the NCU.

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