论文标题
迈向数学模型，用于缩放动脉中血液的固化和破裂
Towards a Mathematical Model for the Solidification and Rupture of Blood in Stenosed Arteries
论文作者
论文摘要
在本文中，我们提出了一种数学和数值模型，用于血液固化及其在狭窄的动脉中的破裂。血流与动脉壁中现有狭窄之间的相互作用被建模为三维流体结构相互作用问题。假定血液是一种非牛顿不可压缩的流体，其依赖性粘度遵守修饰的carreau模型，而流动动力学则由Navier-Stokes方程描述。而动脉壁被认为是一种超弹性材料，其位移满足准静态平衡方程。使用FreeFem ++在二维结构域上使用FreeFem ++进行数值模拟。我们研究了血液粘度，其速度和最大剪切应力的行为。从数值结果中，已经确定了血液再循环区域。此外，在流动方向狭窄之后，已经直接观察到了高粘度和低速的血液。该区域可能对应于血液积累，然后对应于固化区，该区域会受到血流剪切应力和动脉壁变形施加的力。因此，该区域被认为会破裂，然后释放出导致小动脉阻塞的血凝块。
In this paper, we present a mathematical and numerical model for blood solidification and its rupture in stenosed arteries. The interaction between the blood flow and an existing stenosis in the arterial wall is modeled as a three dimensional fluid-structure interaction problem. The blood is assumed to be a non-Newtonian incompressible fluid with a time-dependent viscosity that obeys a modified Carreau's model and the flow dynamics is described by the Navier-Stokes equations. Whereas, the arterial wall is considered a hyperelastic material whose displacement satisfies the quasi-static equilibrium equations. Numerical simulations are performed using FreeFem++ on a two dimensional domain. We investigate the behavior of the viscosity of blood, its speed and the maximum shear stress. From the numerical results, blood recirculation zones have been identified. Moreover, a zone of the blood of high viscosity and low speed has been observed directly after the stenosis in the flow direction. This zone may correspond to a blood accumulation and then solidification zone that is subjected to shear stress by the blood flow and to forces exerted by the artery wall deformation. Therefore, this zone is thought to break and then to release a blood clot that leads to the occlusion of small arterioles.
