Thermal Analysis of Blood Flow Alterations in Human Hand and Foot Based on Vascular-Porous Media Model

Abstract

Microvascular and Macrovascular diseases are serious complications of diabetic mellitus, which significantly affect the life quality of diabetic patients. Quantitative description of the relationship between temperature and blood flow is considerably important for non-invasive detection of blood vessel structural and functional lesions. In this study, thermal analysis has been employed to predict blood flow alterations in a foot and a cubic skin model successively by using a discrete vessel-porous media model and further compared the blood flows in 31 diabetic patients. The tissue is regarded as porous media whose liquid phase represents the blood flow in capillaries and solid phase refers to the tissue part. Discrete vascular segments composed of arteries, arterioles, veins, and venules were embedded in the foot model. In the foot thermal analysis, the temperature distributions with different inlet vascular stenosis were simulated. The local temperature area sensitive to the reduction of perfusion was obtained under different inlet blood flow conditions. The discrete vascular-porous media model was further applied in the assessment of the skin blood flow by coupling the measured skin temperatures of diabetic patients and an inverse method. In comparison with the estimated blood flows among the diabetic patients, delayed blood flow regulation was found in some of diabetic patients, implying that there may be some vascular disorders in these patients. The conclusion confirms the one in our previous experiment on diabetic rats. Most of the patients predicted to be with vascular disorders were diagnosed as vascular complication in clinical settings as well, suggesting the potential applications of the vascular-porous media model in health management of diabetic patients.

Keywords: blood flow estimation; diabetic foot; porous media model; thermal analysis; vascular disorder.

FIGURE 1

(A) Display of the SPAS sensor and (B) its temperature measurement process during fixed at a hand.

FIGURE 2

(A) Three-dimensional cubic tissue model with voxel meshes and (B) its bottom view.

FIGURE 3

Structure of arteries (red) and veins (blue) (A) at the initial state and after (B) 100 iterations, (C) 500 iterations, and (D) 2,000 iterations of the RRT algorithm.

FIGURE 4

Temperature distribution of (A) model surface with no input heating power; (B) internal tissue and vessel temperature distribution with no extra heating power; (C) model surface temperature under heating and (D) internal tissue and vessel temperature under heating.

FIGURE 5

Temperature distribution of a foot from (A) dorsal, (B) side, and (C) plantar view.

FIGURE 6

Dorsal view of the blood flow in arteries when stenosis occurs in (A) anterior tibial artery, (B) posterior tibial artery, and (C) peroneal artery, respectively.

FIGURE 7

Temperature distribution of the foot model when stenosis occurs in (A–C) anterior tibial artery occlusion, (D–F) posterior tibial artery, and (G–I) peroneal artery.

FIGURE 8

Measured temperature curves by the SPAS for a healthy person and a diabetic patient.

FIGURE 9

Fitted curves to express the relationships of the blood flow, ambient temperature, and skin temperature in the (A) recovery and (B) heating phase.

FIGURE 10

Average blood flow rate of healthy subjects during rest, heating, and recovery phases.

FIGURE 11

Average blood flow rate of diabetic patients in three groups (A) DM1–DM3, (B) DM4–DM9, and (C) DM10–DM15 during resting, heating, and recovery phases.

FIGURE 12

Artery element number and average temperature error along with the increment of iteration steps in the RRT algorithm.