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Research Papers

# Lumped Parameter Thermal Model for the Study of Vascular Reactivity in the Fingertip

[+] Author and Article Information
O. Ley, C. Deshpande, B. Prapamcham

Texas A&M University, College Station, TX 77843-3123

M. Naghavi

Endothelix, Houston, TX 77054

J Biomech Eng 130(3), 031012 (Apr 30, 2008) (13 pages) doi:10.1115/1.2913233 History: Received February 23, 2007; Revised November 12, 2007; Published April 30, 2008

## Abstract

Vascular reactivity (VR) denotes changes in volumetric blood flow in response to arterial occlusion. Current techniques to study VR rely on monitoring blood flow parameters and serve to predict the risk of future cardiovascular complications. Because tissue temperature is directly impacted by blood flow, a simplified thermal model was developed to study the alterations in fingertip temperature during arterial occlusion and subsequent reperfusion (hyperemia). This work shows that fingertip temperature variation during VR test can be used as a cost-effective alternative to blood perfusion monitoring. The model developed introduces a function to approximate the temporal alterations in blood volume during VR tests. Parametric studies are performed to analyze the effects of blood perfusion alterations, as well as any environmental contribution to fingertip temperature. Experiments were performed on eight healthy volunteers to study the thermal effect of $3min$ of arterial occlusion and subsequent reperfusion (hyperemia). Fingertip temperature and heat flux were measured at the occluded and control fingers, and the finger blood perfusion was determined using venous occlusion plethysmography (VOP). The model was able to phenomenologically reproduce the experimental measurements. Significant variability was observed in the starting fingertip temperature and heat flux measurements among subjects. Difficulty in achieving thermal equilibration was observed, which indicates the important effect of initial temperature and thermal trend (i.e., vasoconstriction, vasodilatation, and oscillations).

###### FIGURES IN THIS ARTICLE
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Copyright © 2008 by American Society of Mechanical Engineers
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## Figures

Figure 5

(a) Alteration in blood perfusion response due to variation in the time needed to reach the maximum hyperemic flow tdw. (b) Temperature alterations calculated using the zero order model in response to variation in tdw. The remaining parameters take the values indicated in Table 2. The plots are shown after arterial occlusion is released (t>3min).

Figure 13

Comparison of finger temperature measured during DTM with the temperature measured when DTM and HVOP are performed simultaneously for Subjects 1, 3, 4, and 8. The temperature plot is normalized using the average baseline temperature before the start of occlusion. A drop in finger temperature can be observed when DTM and HVOP are simultaneously performed.

Figure 1

(a) DTM during and after arterial occlusion; the infrared thermographs indicate temperature changes during the procedure. (b) Parameters measured with a DTM device (VENDYS™). The blue line shows temperature of the control finger. (c) A schematic example of desired and undesired VRs (45-46,95).

Figure 2

Model for blood perfusion during hyperemia. Stage 1 corresponds to vessel occlusion, and starts with base line value (ωbo). Occlusion lasts during a time tocc, and blood volume exponentially falls during this stage. Stage II or reperfusion has two components: hyperemia and return to normal value.

Figure 3

(a) Alteration in blood perfusion response due to variation in the magnitude of the hyperemic response expressed in terms of coefficient β; (b) Temperature alterations calculated using the mathematical model and the variations in the β coefficient. The remaining parameters take the values indicated in Table 2. The plots are shown after arterial occlusion is released (t>3min).

Figure 4

(a) Alteration in blood perfusion response due to variation in τh. (b) Temperature alterations calculated using the mathematical model and the variations in τh. The remaining parameters take the values indicated in Table 2. The plots are shown after arterial occlusion is released (t>3min).

Figure 6

Effect of variation in the heat transfer coefficient hair over the fingertip temperature during DTM test calculated using the mathematical model. The remaining parameters take the values indicated in Table 2.

Figure 7

Effect of variation in ambient temperature Tair over the fingertip temperature during DTM test, calculated using the mathematical model. The remaining parameters take the values indicated in Table 2.

Figure 8

Effect of variation in body temperature TA over the fingertip temperature calculated using the zero order model during vascular reactivity tests. The remaining parameters take the values indicated in Table 2. The plots are shown after arterial occlusion is released (t>3min).

Figure 9

Variation on the fingertip temperature during the VR test due to alterations in the initial temperature Ti. Calculations performed using the mathematical model and maintaining the remaining parameters constant as indicated in Table 2.

Figure 10

Temporal changes in cuff inflation pressure during arterial occlusion (200mmHg) and venous occlusion (60mmHg) performed during hyperemic VOP or dynamic measurement or hyperemic perfusion during experiments performed in healthy subjects. Each inflation provides an average measurement of the perfusion during the inflation time.

Figure 11

Plots indicating percentile change in strain gauge length per unit time (minute) x(t) in the finger after arterial occlusion, changes measured using VOP on different subjects. Values for the exponential fit are given in Table 5.

Figure 12

Comparison of measured and calculated finger temperature changes during DTM for Subjects 1, 3, 4, and 8. Calculations correspond to solutions using the zero order model using the temporal variations in blood perfusion during Stage IIB or hyperemia measured experimentally using VOP. In these plots, the maximum and minimum temperatures are calculated using the upper and lower values of the concerned parameters.

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