Assessment of peripheral tissue perfusion by optical dynamic
fluorescence imaging and nonlinear regression modeling

Yujung Kang*a, Jungsul Lee*a, Kihwan Kwonb, Chulhee Choia,c,dabDepartment of Bio and Brain Engineering, KAIST, Daejeon, Korea 305-751;

Department of Cardiology, College of Medicine, Ewha Womans University, Seoul,
Korea 158-710;cGraduate School of Medical Science and Engineering, KAIST, Daejeon, Korea 305-751;
d

KAIST Institute for the BioCentury, KAIST, Daejeon, Korea 305-751

Author for correspondence: Chulhee Choi, Department of Bio and Brain Engineering,
Graduate School of Medical Science and Engineering, and KI for the BioCentury, KAIST,
Daejeon 305-751, Korea. Fax: 82-42-869-4380; Tel: 82-42-869-4321; E-mail:cchoi@kaist.ac.kr*These authors contributed equally to this work.

ABSTRACTThe purpose of this study is to examine the peripheral tissue perfusion rates by time-series analysis of
distribution and elimination kinetics of a clinically proven NIR fluorescence probe, indocyanine green (ICG).
We developed a new method, dynamic ICG perfusion imaging technique to evaluate peripheral tissue perfusionthat employs planar imaging with a CCD digital imaging system and time-series analysis of the spatiotemporal
Photonic Therapeutics and Diagnostics VI, edited by N. Kollias, B. Choi, H. Zeng, R. S. Malek, B. J.-F. Wong, J. F. R. Ilgner,
K. W. Gregory, G. J. Tearney, L. Marcu, H. Hirschberg, S. J. Madsen, A. Mandelis, A. Mahadevan-Jansen, E. D. Jansen,
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dynamics (150s) of intravenously injected ICG by using nonlinear regression and differential evolution methods.
Six parameters (α, β, s, d, m; parameters which depend on an arterial input function (AIF) into a lower extremityand p; perfusion rates in the lower extremity) were estimated by the nonlinear regression modeling method. We
have confirmed the validity of our new method by applying the method to a normal control and a patient with
peripheral arterial occlusion disease (PAOD). PAOD patient showed a unique AIF curve pattern, which wascaused by collateral blood flow bypassing the occluded major artery. The lower extremity tissue perfusion rateof the PAOD patient was estimated as about 35% of those of normal values. These results indicate that ICG
perfusion imaging method is sensitive enough to diagnose PAOD and capable of diagnosing functional arterial
diseases.

Keyword: Indicator dilution curve, mathematical modeling, non-linear regression, differential evolution,
peripheral arterial occlusive disease, tissue perfusion, NIR fluorescence imaging.

1

INTRODUCTION

Although peripheral vascular disease (PVD) is prevalent in the primary care setting, it has also been
unrecognized and undertreated.1 Diagnostic methods presently used include the ankle brachial index (ABI),
Doppler ultrasonography, plethysmography, and angiography by X-ray or computed tomography (CT), all ofwhich have limitations.1, 2 Diagnostic modality to assess functional tissue perfusion will be ideal for the periodic
checkup, early diagnosis, and adequate treatment of PVD.
Indicator dilution methods have clinical and experimental potential as tools for measuring physiologicalcirculatory parameters such as tissue perfusion because they can be used to provide estimates of blood flow andvolumes of the intra and extravascular space.3-6 The techniques rely on an intravenous bolus administration of a
tracer at a specific site of the circulatory system, followed by frequent blood sampling or time-series imaging
noninvasively at a distal site. However, concentration-time profile contained re-circulatory information which
distorts the downslope of the observed curve. To analyze this recursive curve, various approaches such as

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extrapolation,5 deconvolution7 or partial differential equation (PDE)3 or fitting of the curve with gamma,8
lognormal9 and local density random walk probability distributions8, 10 have been studied. Even though thesemethods were suggested as novel approach for estimation of the pulmonary circulation,6 cardiac output
according to the systemic vascular resistance4, blood volume,3, 5 mean transit time,11 previous studies were notapplied for diagnosis of vascular diseases.
We have developed an ICG perfusion imaging method that employs intravenously injected near infrared (NIR)
contrast media, indocyanine green (ICG) and time-series planar NIR fluorescence imaging to assess perfusion in
the lower extremities based on the animal studies.12 Although, ICG perfusion imaging could be successfully
applied to the clinical trial,13 there were several differences in probe pharmacokinetics between the mouse andhuman. In this study, we present a novel modeling approach using nonlinear regression and differential
evolution method for measurement of tissue perfusion and arterial input function (AIF) in the human lower
extremity. Moreover, we have validated this modeling by applying the method to a normal control and a patientwith peripheral arterial occlusion disease (PAOD).

2

METHODS and MATHEMATICAL MODELING

2.1 Subjects
All protocol, survey, and consent forms were approved by the Institutional Review Board of Ewha Womans
University Mokdong Hospital. Written informed consent was obtained from subjects. A 61-year old woman was
recruited as healthy subject who was non-smoker and manifested no symptoms of lower extremities. A 70-year
old man with mild claudication was recruited as a patient with PAOD. He had also diagnosed with type 2
diabetes mellitus 4 years ago. His blood glucose level was higher (168 mg/dl) than healthy subject (87 mg/dl),
and he has been treated with glimepiride without insulin therapy. To evaluate the time-series ICG perfusion
imaging as a reliable tool for diagnosis of PAOD, we performed also CT-angiography and ABI.

2.2 Diagnosis of PAOD
2.2.1 NIR Fluorescence Imaging

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An ICG fluorescence imaging system for lower extremities has been developed by Vieworks Corporation(Seongnam, Gyeonggi-do, Korea).13 This imaging system employed a CCD digital camera with a 830nm bandpass filter and 760nm light emitting diode arrays. After remaining supine for 5–10 min, 30 serial images (748 ×
518 pixels) of both feet were taken at 5-s intervals for 200 s immediately after an intravenous bolus injection of
ICG (0.16 mg/kg) for obtaining indicator dilution of ICG fluorescence. This ICG dilution curve was translated
into quantitative tissue perfusion and AIF using followed mathematical modeling.

2.2.2 CT-Angiography
CT angiography was performed with a 16-MDCT scanner (SOMATOM Sensation; Siemens Medical Solutions,
Erlangen, Germany). An 18-gauge catheter was placed into the antecubital vein, and 120 ml of nonionic contrast
material (Iohexol, Omnipaque 300, Nycomed; Amersham, Princeton, UK) was injected at 4 ml/s. CT scans wereobtained from above the iliac bifurcation to the feet. Postprocessing for CT angiography resulted in images
rotated over 360° for the aortoiliac, femoropopliteal, and tibial arteries using commercially available cardiac
reconstruction software (Syngo, version A50A; Siemens Medical Solutions).

2.2.3 ABI
After remaining supine for 5–10 min, blood pressures were recorded in both brachial arteries and in the dorsalis
pedis and posterior tibial arteries (VasoGuard P84; SciMed Ltd., Bristol, UK). The ABI was calculated for eachleg by dividing the highest ankle systolic pressure by the highest brachial systolic pressure.

2.3 Model Based Analysis of the ICG Dilution Curve
2.3.1 Non Linear Regression Model.
To translate the ICG dilution curve into quantitative tissue perfusion in lower extremity, perfusion rate (%/min)
was defined as the fraction of blood exchanged in the vascular volume of the region of interest (ROI) per minute.
We assumed that blood volume through the vasculature in the ROI is time invariant during the imaging,
therefore, volumetric inflow and outflow were thought to be the same as the previous report.12 ROI usuallycontained several hundred pixels which are unit that we can get the ICG dilution curve from. Therefore,

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representative average ICG dilution curve from the ROI is used for evaluating the perfusion rate of the ROI. In
the ROI, arterial input function (AIF) of blood has been described as a linear combination of Gaussian functions
because the ICG dilution curves registered from the carotid artery5, iliac artery6 and large peripheral artery3show two major peaks which indicates first and second circulation.
exp

k

(1)

where r is number of observable circulatory peak, we used 2 for r to consider up to second recirculation. α
determines sharpness of the first peak, s determines broadening of the second peak from the first one and β is thetime-to-peak (sec) in the first peak after appearance of the first fluorescence signal. Parameter m is interval (sec)of time-to-peak between first and second peak, and d is height ratio of the second to first peak (Figure 1).
The change of ICG concentration of the ROI can be described using Fick’s law:change of the concentration
I ROI

inflow· AIF

outflow· IROI(2)

where IROI is ICG fluorescence intensity observed in the ROI. Because we assume that the ICG concentration in
the ROI is homogenous, the ICG concentration of the outflow is the same as that of the ROI. p represents
perfusion rate of the ROI. By solving Equation 2 with Laplace transformation, we get IROI as a convolution of
AIF and exponential decay as follows using Equation 3:
IROI tIROI t

exp

t

exp

t

d exp

AIF t
αs

(3)
β

km

(4)

By introducing Equation 1 into Equation 3, exact form of IROI could be derived as in Equation 4. t indicates timeafter onset of the fluorescence signal in the ROI.

2.3.2 Differential Evolution
To estimate parameters α, β, d, m, p, and s in Equation 4, we used differential evolution which had beensuccessfully applied for the evolutionary optimization method over continuous spaces.14, 15 Briefly, each vectorof parameters in initial parameter population is uniformly distributed in predefined range of parameters.
Differential evolution generates new parameter vectors by adding a weighted difference vector between two

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population members to a third member. In this study, evolution constraint of each generation is the maximum
root-mean-square-deviation (RMSD) between experimentally observed average representative ICG dilution
curve and numerically estimated ICG dilution curve (IROI(t)) with parameters of each member in population of
the immediate previous generation. If the resulting vector yields a smaller RMSD than a constraint, the newly
generated vector will replace the vector. If RMSD from population is no smaller than that from the previous
generation, evolution terminates. The parameters from last generation are applied to obtain both AIF and
perfusion rate of ROI. Imaging processing and data analysis were performed using Visual C++ (version 4.0;
Microsoft, Redmond, WA, USA).

3

RESULTS

3.1 Diagnostic Results of the CT angiography and ABI
A healthy subject had normal ABI values, 1.08 on the left side and 1.03 on the right side and showed noabnormality in the lower extremity CT angiography (Figure 3A). In contrast, the patient with PAOD had
abnormal ABI values, 0.7 on the left side and non-detectable level on the right side. CT-angiography of lower
extremity revealed occlusion at right external iliac artery, proximal and mid-portion of superficial femoral arteryand left proximal superficial femoral artery with well-developed collateral vessels on left and right superficial
femoral arteries and also multiple calcifications on the right and left major arteries as bright white lumps (Figure
4A).

3.1 Estimation of the Tissue Perfusion Based on the Non-Linear Regression Modeling
For measurement of the perfusion rate, ROI was obtained in and around toenails where both arterial inflow
through major arteries and circulation through capillaries could be represented strongly compared to the otherregions of foot where venous circulation was represented dominantly from. Therefore ICG dilution curves inand around toenails showed shorter time-to-peak and higher maximal intensity than ones in the other regions.
The average representative ICG dilution curves from feet of the healthy subject showed rapid time-to-peaks ofaround 10 sec after onset time of fluorescence signal and precipitous down-slope (Figure 2). In contrast, theProc. of SPIE Vol. 7548 75483L-6
Downloaded From: http://proceedings.spiedigitallibrary.org/ on 11/06/2012 Terms of Use: http://spiedl.org/termsaverage representative ICG dilution curves from feet of the PAOD patient showed remarkably delayed time-topeaks of around 45 to 75 sec after onset time of fluorescence signal and no down-slope within 150 sec after
onset time. Because the difference of the ICG dilution curve is dependent on tissue perfusion,12, 13, 16 based on
the Equation 4, ICG dilution curves were translated into the quantitative perfusion rates and AIFs (Figure 3B, C
and 4B, C). The feet perfusion rates of the healthy subject were 51.4 and 64.2 %/min and the perfusion rates of
the PAOD patient were 21.3 and 17.7 %/min, which are about 27 to 41 % of the normal perfusion rates.
Estimated AIF of the healthy subject showed separate two peaks with average 96.5 sec interval (m) and 0.1
intensity ratio of the second peak to the first peak (d). In contrast, two peaks in the estimated AIF of the PAOD
patient were not separated over time which showed m as average 13.52 sec and d as 1.0. In the estimated AIFs, α,
sharpness of the first peaks of the healthy subject were 11.8 and 12.5 from Lt. and Rt., respectively which weresimilar or relatively small compared to the those of PAOD patient (22.1 and 11.7) and β, the time-to-peaks offirst peak of the healthy subject (11.8 and 12.3 sec) was relatively short compared to β of PAOD patient (22.1
and 13.7 sec).

4

DISCUSSIONS

We have previously developed a novel ICG perfusion imaging method that employs the intravenous injection of
ICG dye, time-series planar imaging with a CCD digital imaging system, and analysis of ICG dilution curveusing mathematical modeling.12, 13 In this study, we further demonstrated the advantage of the novel modelingapproach with nonlinear regression and differential evolution methods for clinical application of ICG perfusion
imaging.
Although methods for measuring functional tissue perfusion in the peripheral tissue are required for validationof our novel imaging method, there is no comparable method for measuring functional tissue perfusion
especially in the peripheral tissues. Therefore, we compared the perfusion rates and AIFs evaluated fromvolunteers with lower extremity CT-angiography and ABI which revealed large arterial occlusions. The
perfusion rates showed positive correlation with lower extremity CT-angiogram and ABI, even though more
extensive clinical data are still needed.

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The ABI test is known to be highly sensitive and specific for diagnosing PAOD in patients with severe arterial
stenosis; however, it is also known to be unreliable on patients with arterial calcification which results in less or
incompressible arteries.1, 17 Because the stiff arteries produce falsely elevated ankle pressure, false negative
results are often found in patients with diabetes mellitus, renal failure or heavy smoker.18-20 In this study, ABI
value even was not detected on the right side of the PAOD patient with multiple calcification in lower
extremities. On the other hand, the perfusion rate of this foot was quantitatively estimated by the ICG perfusion
imaging. Therefore, we believe that the ICG perfusion imaging can diagnose the perfusion rate in the foot evenwith stiff arteries due to the calcification and therefore it can be applied to patients with diabetes mellitus as well
as PAOD.
AIF as well as perfusion rate is evaluated simultaneously from the ICG dilution curve. To express recirculation
pattern, AIF has been modeled to have two peaks within 150 sec after onset of ICG fluorescence signal in the
ROI. Because the plasma ICG is rapidly eliminated with a half-life of about 3-4 min by enterohepatic route,21 if
the second peak was due to the recirculation, the intensity ratio of second to first peak should be remarkably
smaller and there should be enough interval time between two peaks. In the estimated AIF, second peak in thehealthy subject could represent recirculation; however, in PAOD patient, the second peak might be supposed asanother blood flow through collaterals because of high intensity ratio and too small interval to be considered tobe recirculation. CT-angiogram also shows well-developed collaterals to support this idea. These remarkabledifferences of the AIFs between a healthy and a PAOD patient might provide information about functional tissue
perfusion along with perfusion rate, especially in the case of the patient with chronic occlusive disease andgradual collateralization. Nonetheless, the large-scale clinical studies are necessary to get a conviction of thisresult.

5

CONCLUSIONSICG perfusion imaging has multiple advantages such as superior sensitivity,12 cost-effectiveness and minimal
invasiveness. Even though this study enrolled only two subjects for validation of novel mathematical modeling,
the results clearly suggest that the ICG perfusion imaging based on this novel modeling could be reliable

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method for diagnosis of PAOD.

ACKNOWLEDGEMENT

This work was supported by the Korea Healthcare Technology R&D Project (A091258), Ministry for Health,Welfare and Family Affairs of the Republic of Korea.

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Figure 1. Diagram of the AIF and parameters. The typical AIF into the ROI has two peaks.

Figure 2. Representative ICG dilution curve. The solid and dotted lines indicate ICG dilution curve of the healthy subject
and the patient with PAOD, respectively. X-axis represents time after ICG injection.

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Figure 3. A 61-year-old healthy subject. A. lower extremity CT-angiography. B, C. X- and y-axis indicate time after
onset of ICG fluorescence signal from the ROI and ICG fluorescence intensity (FI), respectively. Red line indicates ICG
dilution curve obtained from real data while the modeled curve fitted to the real ICG dilution curve by differential evolution
is indicated as black line. Estimated AIF shows typical separated two peaks (green line). Summed kinetics of the two peaks
is indicated by blue line from the Left (B) and Right (C) foot. The number within the graph shows perfusion rate. Red andblack line show ICG FI value amplified as 3-fold to visualize well. Green and blue line overlap completely because two
peaks are separated perfectly.

Figure 4. A 70-year-old patient with PAOD. A. lower extremity CT-angiography. Arrows indicate arterial occlusive regions.
B, C. X- and y-axis indicate time after onset of ICG fluorescence signal from the ROI and ICG fluorescence intensity (FI),respectively. ICG dilution curve (red line), curve fitted to the ICG dilution curve by differential evolution (Black line), andestimated AIF (green line), summed kinetics of the two peaks (blue line) from the Left (B) and Right (C) foot. The number
within the graph indicates perfusion rate.

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