Weller Frédéric Frank
Department of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 293, Heidelberg, Germany.
J Math Biol. 2010 Dec;61(6):805-18. doi: 10.1007/s00285-009-0324-1. Epub 2010 Jan 7.
Recently, neglect of either shear stress, surface saturation, or thrombus growth in mathematical models of platelet deposition has been identified as leading cause of inability to match experimental evidence. While the consideration of shear stress is necessary to obtain at least some qualitative agreement, purely shear-dependent approaches yield notable quantitative discrepancies. In a previous paper, the author demonstrated that surface saturation significantly improves model predictions. However, discrepancies still persist when thrombus growth is neglected. Therefore, the present work develops a free boundary problem which takes this into account. Numerical simulations are performed using the level set method. The results agree well with measurements in stagnation point flow and tubular expansions, which demonstrates the coupling of flow, platelet adhesion, and aggregate growth in primary hemostasis.
最近，在血小板沉积的数学模型中，对剪切应力、表面饱和度或血栓生长的忽视已被确定为无法与实验证据相匹配的主要原因。虽然考虑剪切应力对于至少获得一些定性一致性是必要的，但纯粹依赖剪切的方法会产生显著的定量差异。在之前的一篇论文中，作者证明表面饱和度显著改善了模型预测。然而，当忽略血栓生长时，差异仍然存在。因此，本研究提出了一个考虑到这一点的自由边界问题。使用水平集方法进行了数值模拟。结果与驻点流和管状扩张中的测量结果吻合良好，这证明了在初级止血过程中流动、血小板粘附和聚集体生长之间的耦合。
