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Research Papers

# Numerical Analysis of the Cooling Effect of Blood Over Inflamed Atherosclerotic Plaque

[+] Author and Article Information
Taehong Kim

Department of Mechanical Engineering, Texas A&M University, MS 3123, College Station, TX 77843-3123taehong-kim@tamu.edu

Obdulia Ley1

Department of Mechanical Engineering, Texas A&M University, MS 3123, College Station, TX 77843-3123oley@tamu.edu

1

Corresponding author.

J Biomech Eng 130(3), 031013 (Apr 30, 2008) (11 pages) doi:10.1115/1.2913236 History: Received April 09, 2007; Revised October 08, 2007; Published April 30, 2008

## Abstract

Atherosclerotic plaques with high likelihood of rupture often show local temperature increase with respect to the surrounding arterial wall temperature. In this work, atherosclerotic plaque temperature was numerically determined during the different levels of blood flow reduction produced by the introduction of catheters at the vessel lumen. The temperature was calculated by solving the energy equation and the Navier–Stokes equations in 2D idealized arterial models. Arterial wall temperature depends on three basic factors: metabolic activity of the inflammatory cells embedded in the plaque, heat convection due to luminal blood flow, and heat conduction through the arterial wall and plaque. The calculations performed serve to simulate transient blood flow reduction produced by the presence of thermography catheters used to measure arterial wall temperature. The calculations estimate the spatial and temporal alterations in the cooling effect of blood flow and plaque temperature during the measurement process. The mathematical model developed provides a tool for analyzing the contribution of factors known to affect heat transfer at the plaque surface. Blood flow reduction leads to a nonuniform temperature increase ranging from $0.1°Cto0.25°Celsius$ in the plaque/lumen interface of the arterial geometries considered in this study. The temperature variation as well as the Nusselt number calculated along the plaque surface strongly depended on the arterial geometry and distribution of inflammatory cells. The calculations indicate that the minimum required time to obtain a steady temperature profile after arterial occlusion is $6s$. It was seen that in arteries with geometries involving bends, the temperature profiles appear asymmetrical and lean toward the downstream edge of the plaque.

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## Figures

Figure 5

Streamlines (left) and temperature contours (right) around an inflamed plaque located in the bending artery shown in Fig. 2. The lines correspond to times (a) t=2.4s and (b) 2.8s during the normal cycles. The dimensions of plaque used are lmp=1500, dmp=50, dp=540, and lf=50μm.

Figure 6

Streamlines (left) and temperature contours (right) around an inflamed plaque located in the bending artery shown in Fig. 2. The lines correspond to times (a) t=5.4s and (b) 5.8s after blood flow occlusion to 5% of normal cycles. The dimensions of plaque used are lmp=1500, dmp=50, dp=540, and lf=50μm.

Figure 7

Transient temperature distribution at the plaque/lumen interface for the stenotic straight artery. The temperature variation is produced by the reduction in the mean blood flow velocity as indicated in Fig. 4. The times presented are 0.1–0.8s offset into each cycle, which correspond to t=C.1s, C.4s, C.6s and C.8s, where C indicates the cardiac cycles considered (C=3, 4, 5, and 6).

Figure 8

Transient temperature distribution at the plaque/lumen interface for the bending artery. The temperature variation is produced by the reduction in the mean blood flow velocity as indicated in Fig. 4. The times presented are 0.1–0.8s offset into each cycle, which correspond to t=C.1s, C.4s, C.6s and C.8s, where C indicates the cardiac cycles considered (C=3, 4, 5, and 6).

Figure 9

Nusselt number variation along the plaque/lumen interface for the stenotic straight artery calculated during Cycles 3–6

Figure 13

Relationship between average peak velocity and maximum temperature difference at the plaque/lumen interface. Steady flow is considered in the bending artery shown in Fig. 2. The dimensions of plaque used are lmp=1500, dmp=50, dp=540, and lf=50μm The solid line corresponds to filled curve by using linear least squares procedure.

Figure 1

Classification of AWT methods available in clinical practice

Figure 2

Arterial geometry for (a) straight stenotic artery and (b) bending artery. The dimensions presented are shown in millimeters.

Figure 3

Plaque geometry and dimensions. dw is the arterial wall thickness, dp is the plaque thickness, dmp is the macrophage rich layer thickness, and lf is the thickness of the fibrous cap. lp and lmp represent the extension or length of the plaque and the macrophage layer in the longitudinal direction, respectively. The location xi=x∕lp of eight observation points is presented. Point A corresponds to the front of the plaque (xA=0.3), Point C presents a point at xC=0.5, Point E is defined at xE=0.7, and Point H is the ending point of the plaque (xH=1).

Figure 4

Pulsatile flow wave form used at the inlet of (a) the straight stenotic artery (49) and (b) the bending artery (34). The flow velocities are reduced with three different flow stages: (1) a normal in pulsatile blood flow (Cycles 1–3), (2) a rapid reduction in inlet velocity to 50% (Cycle 4), and (3) a significant occlusion of blood flow to 10% and 5% of its normal value (Cycles 5 and 6).

Figure 10

Nusselt number variation along the plaque/lumen interface for the bending artery calculated during Cycles 3–6

Figure 11

Time variation of temperature calculated at different points along the plaque/lumen interface for the stenotic straight artery. The inlet velocity profile for this arterial geometry is given in Fig. 4, and the points where the temperature is recorded correspond to Points A–H indicated in Fig. 3.

Figure 12

Time variation of temperature calculated at different points along the plaque/lumen interface for a bending artery. The inlet velocity profile for this arterial geometry is given in Fig. 4, and the points where the temperature is recorded correspond to Points A–H indicated in Fig. 3.

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