Analysis of blood turbulent flow in carotid artery including the effects of mural thrombosis using finite element modeling

American Journal of Applied Sciences, Feb, 2009 by M. Arab-Ghanbari, M.M. Khani

INTRODUCTION

Arterial thrombosis can block blood flow to heart and brain tissues and cause a heart attack or stroke. Clinical studies confirm the link between thrombosis and atherosclerosis (1). Thrombus superimposed on ruptured atherosclerotic plaque is commonly found in autopsy studies of heart disease (2), (3), (4). Thrombosis is also associated with carotid artery plaque rupture in stroke and transient ischemic attack (5), (6), (7). Since the relationship between thrombosis and fluid mechanics is complex and numerous factors are involved in this issue, arterial thrombosis is the subject of intense study and speculation in biomechanics.

The process of thrombosis may be affected by a series of rheological and fluid dynamic parameters, including high rates of shear, areas of flow stagnation or recirculation and turbulence. In fact, Thrombosis is fundamentally linked to hemodynamics because blood transports cells and proteins to the thrombus and applies stress that may disrupt the thrombus. The convection of flow aggregates can be locally enhanced or diminished in arterial stenosis through localized regions of high shear, flow separation, recirculation, and reattachment (8). The role of hemodynamics in thrombogenesis has been investigated on natural and artificial surfaces (9), (10), (11), (12). In two other studies by the same author, a mechanistic approach based on simple classical fluid dynamic concepts has been adopted to quantify the hemodynamic forces acting on mural thrombi under both steady and pulsatile flow conditions (13), (14). Arterial thrombosis is also investigated via numerical studies. However, crucial limiting assumptions such as Reynolds number much less than that accrue in cardiovascular system diseases as well as deviates from realistic boundary condition because of considering a very small numerical solution region are made in these studies (10). Besides, several investigations have considered shear stress on the artery wall but there is no study that considers shear stress in flow domain where the most platelet activating process takes place.

Accurate modeling of arterial thrombosis has not been proposed yet and due to the importance of such modeling to get further insight into clinical aspects of thrombosis such modeling is extremely demanded. In this paper, for the first time, an axisymmetric model considering fluid-structure interactions (FSI) is introduced and numerically solved for common carotid artery with a thrombosis to perform flow and stress/strain analysis and investigate the probability of thrombus rupture which leads to embolization.

MATERIALS AND METHODS

Solid and Fluid Models: In order to investigate the effects of thrombosis on the artery hemodinamics and stress distribution of the artery wall, the model geometry is considered (Fig. 1). Due to the high shear rate, thrombosis in arteries is formed from platelets and does not contain red blood cells (15). Therefore, thrombus is assumed to have the same properties as platelets do and to be linear elastic, isotropic, incompressible and homogenous material. Young's modulus of 3 kPa and Poison's ratio of 0.48 is considered for thrombus (16). Equilibrium equations and boundary conditions for thrombus are:

[[sigma].sub.[ij.j].sup.s] = 0 (1)

[[sigma].sub.ij.sup.s].[n.sub.j][|.sub.outersolid] = [d.sup.f][|.sub.innersolid] (2)

[[sigma].sub.ij.sup.s].[n.sub.j][|.sub.outersolid] = 0 (3)

[[sigma].sub.ij.sup.s].[n.sub.j][|.sub.innersolid] = [[sigma].sub.ij.sup.f].[n.sub.j][|.sub.innersolid] (4)

where [d.sup.s], [d.sup.f], [[sigma].sub.ij.sup.s] are displacement and stress tensors for solid and fluid, respectively. Comma denotes the derivative with respect to the corresponding coordinate. The flow is assumed to be laminar, Newtonian, viscous and incompressible. The incompressible Navier-Stokes equations in Arbitrary Lagrangian-Eulerian (ALE) formulation are used as governing equations (18). This yields the following:

(([u - [u.sub.g]).[DELTA])u = [-[1/[rho]]][DELTA]P [upsilon][[DELTA].sup.2]u (5)

[[DELTA].u] = 0 (6)

u[|.sub.[y = 0]] = [u.sun.in] (7)

P[|.sub.[y = 17 cm]] = [P.sub.out] (8)

where u is flow velocity, [u.sub.g] is mesh velocity, p is pressure, [p.sub.in] is inlet pressures, [p.sub.out] is outlet pressures and [rho] is fluid density. We assumed three models with different thrombus heights (1.25, 1.75 and 1.8 mm respectively) and the fixed outlet pressure of 20 mmHg (17).

[FIGURE 1 OMITTED]

An axisymmetric model with fluid-structure interactions (FSI) is introduced and solved using the ADINA code (ADINA [TM], version 8.3, Automatic Dynamic Incremental Nonlinear Analysis, Watertown, MA). For thrombus, as shown in Fig. 2a, a rule-based mesh of 4470 axisymmetric rectangular solid elements of the plane strain type with 9 nodes in each element is used. It should be mentioned that are arranged so that the aspect ratios are less in elements which are under compression to prepare a more compression strength. This is done because in an ALE mesh, when deformation in compression direction is imposed to fluid elements, overlapping of solid and fluid elements will occur (18). Besides, due to large deformation of the compression site of the thrombus, larger elements are considered in this site. The mesh is also arranged to avoid distortion in solid elements due to tension or compression forces imposed from fluid domain on solid elements.