Xu Zhiliang, Chen Nan, Kamocka Malgorzata M, Rosen Elliot D, Alber Mark
Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA.
J R Soc Interface. 2008 Jul 6;5(24):705-22. doi: 10.1098/rsif.2007.1202.
A two-dimensional multiscale model is introduced for studying formation of a thrombus (clot) in a blood vessel. It involves components for modelling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; and vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier-Stokes equations. The microscale interactions between the activated platelets, the platelets and fibrinogen and the platelets and vessel wall are described through an extended stochastic discrete cellular Potts model. The model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus, which is confirmed by the preliminary experimental data. We also make predictions about different stages in thrombus development, which can be tested experimentally and suggest specific experiments. Lastly, we demonstrate that the dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.
引入了一个二维多尺度模型来研究血管中血栓(凝块)的形成。它涉及用于模拟粘性、不可压缩血浆;未激活和激活的血小板;血细胞;激活化学物质;纤维蛋白原;以及血管壁及其相互作用的组件。血流的宏观动力学由连续介质纳维-斯托克斯方程描述。激活的血小板、血小板与纤维蛋白原以及血小板与血管壁之间的微观相互作用通过扩展的随机离散细胞Potts模型来描述。对该模型针对基本参数波动的稳健性进行了测试。模拟结果表明血栓内部结构不均匀的发展情况,这得到了初步实验数据的证实。我们还对血栓发展的不同阶段进行了预测,这些预测可以通过实验进行检验并提出具体实验。最后,我们证明在模拟中血栓大小对血流速度的依赖性与实验观察到的依赖性相近。