论文标题
耦合随机差分反应扩散系统，用于血管生成
A coupled stochastic differential reaction-diffusion system for angiogenesis
论文作者
论文摘要
在有界结构域中分析了非线性混合型方程的早期阶段的耦合系统。该系统由随机微分方程组成，这些方程描述了由于趋化性，Durotaxis和随机运动，描述了尖端和茎的内皮细胞位置的运动；细胞外流体，基底膜和纤维蛋白基质的体积分数的普通微分方程；以及参与血管生成过程的几种蛋白质浓度的反应扩散方程。随机微分方程的漂移项涉及体积分数和浓度的梯度，并且反应扩散方程中的扩散率非局部取决于体积分数，从而使系统高度非线性。通过使用定点参数和Hölder规律性理论证明了该系统独特解决方案的存在。两个空间维度的数值实验说明了血管形成的开始。
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk endothelial cells, due to chemotaxis, durotaxis, and random motion; ordinary differential equations for the volume fractions of the extracellular fluid, basement membrane, and fibrin matrix; and reaction-diffusion equations for the concentrations of several proteins involved in the angiogenesis process. The drift terms of the stochastic differential equations involve the gradients of the volume fractions and the concentrations, and the diffusivities in the reaction-diffusion equations depend nonlocally on the volume fractions, making the system highly nonlinear. The existence of a unique solution to this system is proved by using fixed-point arguments and Hölder regularity theory. Numerical experiments in two space dimensions illustrate the onset of formation of vessels.
