Multiscale Modeling &Simulation, Volume 18, Issue 4, Page 1489-1524, January 2020.
We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODEs) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes--Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical adenosine diphosphate hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool of primary and secondary hemostasis.

中文翻译：

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流动下血管外损伤中血小板聚集的数学模型

多尺度建模与仿真，第18卷，第4期，第1489-1524页，2020年1月。
我们提出了血管外损伤中流介导的基本止血的第一个数学模型，该模型可以跟踪从初始沉积到阻塞的过程。该模型由描述血小板聚集（粘附和内聚），依赖可溶性激动剂的血小板活化以及通过损伤的血流的常微分方程（ODE）系统组成。血小板聚集体的形成增加了流过伤口的阻力，这是使用斯托克斯-布林克曼方程式建模的。来自类似实验（微流体流动）和偏微分方程模型的数据为在血小板粘附，内聚和活化的ODE模型描述中使用的参数值提供了依据。该模型预测在一定流量和血小板激活条件下的损伤闭塞。测试剪切和激活速率影响的模拟导致延迟的咬合和聚集体异质性。这些结果证实了我们的假设，即流动介导的活化化学二磷酸腺苷稀释会阻碍聚集体的发展。这种新颖的建模框架可以扩展到包括更多的血小板激活机制以及凝血的生化反应的附加功能，从而产生对初次和二次止血的计算有效的高通量筛选工具。