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TECHNICAL PAPERS: Fluids/Heat/Transport

Multiphysics Simulation of Blood Flow and LDL Transport in a Porohyperelastic Arterial Wall Model

[+] Author and Article Information
Nobuko Koshiba

Graduate School of Frontier Sciences, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japankoshiba@sml.k.u-tokyo.ac.jp

Joji Ando

Graduate School of Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Xian Chen

Division of Digital Patient, Digital Medicine Initiative, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8582, Japan

Toshiaki Hisada

Graduate School of Frontier Sciences, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

J Biomech Eng 129(3), 374-385 (Nov 11, 2006) (12 pages) doi:10.1115/1.2720914 History: Received April 09, 2006; Revised November 11, 2006

Atherosclerosis localizes at a bend and∕or bifurcation of an artery, and low density lipoproteins (LDL) accumulate in the intima. Hemodynamic factors are known to affect this localization and LDL accumulation, but the details of the process remain unknown. It is thought that the LDL concentration will be affected by the filtration flow, and that the velocity of this flow will be affected by deformation of the arterial wall. Thus, a coupled model of a blood flow and a deformable arterial wall with filtration flow would be invaluable for simulation of the flow field and concentration field in sequence. However, this type of highly coupled interaction analysis has not yet been attempted. Therefore, we performed a coupled analysis of an artery with multiple bends in sequence. First, based on the theory of porous media, we modeled a deformable arterial wall using a porohyperelastic model (PHEM) that was able to express both the filtration flow and the viscoelastic behavior of the living tissue, and simulated a blood flow field in the arterial lumen, a filtration flow field and a displacement field in the arterial wall using a fluid-structure interaction (FSI) program code by the finite element method (FEM). Next, based on the obtained results, we further simulated LDL transport using a mass transfer analysis code by the FEM. We analyzed the PHEM in comparison with a rigid model. For the blood flow, stagnation was observed downward of the bends. The direction of the filtration flow was only from the lumen to the wall for the rigid model, while filtration flows from both the wall to the lumen and the lumen to the wall were observed for the PHEM. The LDL concentration was high at the lumen∕wall interface for both the PHEM and rigid model, and reached its maximum value at the stagnation area. For the PHEM, the maximum LDL concentration in the wall in the radial direction was observed at the position of 3% wall thickness from the lumen∕wall interface, while for the rigid model, it was observed just at the lumen∕wall interface. In addition, the peak LDL accumulation area of the PHEM moved about according to the pulsatile flow. These results demonstrate that the blood flow, arterial wall deformation, and filtration flow all affect the LDL concentration, and that LDL accumulation is due to stagnation and the presence of filtration flow. Thus, FSI analysis is indispensable.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Normalized computational LDL wall concentration profiles of a straight vessel after 30min. The top three cases are the results of Stangeby and Ethier (21), while the lower three cases are from the present study. The X-axis position of 0 indicates the lumen∕wall interface, while the X-axis position of 1 indicates the media∕adventitia interface. p is the transmural pressure and K is the endothelial permeability to LDL. Our obtained LDL concentration profiles are identical to those of Stangeby and Ethier (21).

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Figure 2

Mesh model of the artery and the inlet and outlet profiles. (a) A finite element mesh model of an artery with multiple bends used in the computational analysis based on Wada and Karino (18). Bend-B is an acute bend, while bend-A and bend-C are milder bends. (b) Inlet velocity (solid line, left scale) and outlet pressure (dashed line, right scale) profiles for 1 pulse after Berne (43).

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Figure 3

Blood flow patterns for pulsatile flow in the PHEM (upper panels) and rigid model (lower panels) when the pulsatile flow reaches its peak. (a, c) Entire patterns. (b, d) Detailed flow patterns downward of bend-B. The diameter of the PHEM is stretched by the increased pulsatile pressure. For both models, backflow is observed downward of bend-B and stagnation is observed downward of bend-A.

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Figure 7

LDL concentration profiles in the radial direction of the lumen and wall at the white spot at the time point of 0.25s in a pulse when the concentration of LDL reaches its peak. (a, b) Pulsatile flow. (c, d) Steady flow. (a, c) Lumen. (b, d) Wall. The X-axis positions of −0.3, 0, and 1 indicate the position of 30% of the luminal radius from the lumen∕wall interface, the lumen∕wall interface, and the media∕adventitia interface, respectively. The LDL concentration in the lumen increases sharply near the wall, and the LDL concentration profile in the wall is a U-shape. For pulsatile flow in the PHEM, the highest LDL concentration in the wall is observed at the position of 3% wall thickness from the lumen∕wall interface where stagnation of the filtration flow exists.

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Figure 4

Distributions (time profiles) of the resultant filtration velocities in the wall during the whole pulse cycle. The position of the measured area is downward of bend-B, as illustrated in (g). (a, b, e, f) PHEM. (c, d, g, h) Rigid model. (a–d) Pulsatile flow. (e–h) Steady flow. In (a), (c), (e), and (g), the numbers 1–7 designate different parts of the wall, as illustrated below the panels. Note that the velocity scale of the PHEM for pulsatile flow differs from the others. In (b), the red area indicates that the filtration velocity is over 8×10−5mm∕s, while the dark blue area indicates that the filtration velocity ranges from 0to−25×10−5mm∕s. The filtration velocity at point 1 in the PHEM is extremely high at the moment when the blood pressure reaches its peak, and is approximately 15-fold higher than that in the rigid model. Backflow and stagnation (dark blue area) are observed for pulsatile flow in the PHEM (a, b).

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Figure 5

Profiles of the blood pressure (dotted-dashed line), transmural pressure (dashed line), radial stress (thin line), and sum of the transmural pressure and radial stress (thick line) during a pulse in the wall at the same position as in Fig. 4 (white spot in Fig. 4). (a, c) PHEM. (b, d) Rigid model. (a, b) Pulsatile flow. (c, d) Steady flow. Values on the Y-axis denote tensile stresses. Points 1, 2, and 5 are located at the middle of each layer in the wall, as illustrated in the lower right of each panel. It should be noted that in the rigid model, the profile of the blood pressure overlaps with that of the sum of the transmural pressure and radial stress. For pulsatile flow in the PHEM, the radial stress and sum of the transmural pressure and radial stress vary in phase with the blood pressure, while the transmural pressure varies out of phase with the blood pressure. For pulsatile flow in the rigid model, the transmural pressure, radial stress, and sum of the transmural pressure and radial stress vary in phase with the blood pressure.

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Figure 6

Distributions of LDL concentrations at the time point of 0.25s in a pulse when the LDL concentration reaches its peak. The LDL concentrations at the lumen∕wall interface in the lumen (a–d), at the lumen∕wall interface in the wall (e–h), and at the second layer finite elements of the wall (i–l) are shown. (a, e, i) Pulsatile flow in the PHEM. (b, f, j) Pulsatile flow in the rigid model. (c, g, k) Steady flow in the PHEM. (d, h, l) Steady flow in the rigid model. In the lumen, the highest LDL concentration in the PHEM is higher than that in the rigid model. Furthermore, for pulsatile flow in the PHEM, the LDL concentration downward of bend-A is higher than that downward of bend-B. In the wall, the LDL concentration is higher at the second layer than at the lumen∕wall interface for pulsatile flow in the PHEM, but highest at the lumen∕wall interface for the other three cases.

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