Fogelson Aaron L, Nelson Anna C, Zapata-Allegro Cheryl, Keener James P
Departments of Mathematics and Biomedical Engineering, University of Utah, Salt Lake City, UT (http://www.math.utah.edu/~fogelson).
Department of Mathematics, University of Utah, Salt Lake City, UT.
SIAM J Appl Math. 2022;82(1):267-293. doi: 10.1137/21m1401024. Epub 2022 Jan 27.
In [Fogelson and Keener, , 81 (2010), 051922], we introduced a kinetic model of fibrin polymerization during blood clotting that captured salient experimental observations about how the gel branching structure depends on the conditions under which the polymerization occurs. Our analysis there used a moment-based approach that is valid only before the finite time blow-up that indicates formation of a gel. Here, we extend our analyses of the model to include both pre-gel and post-gel dynamics using the PDE-based framework we introduced in [Fogelson and Keener, ., 75 (2015), pp. 1346-1368]. We also extend the model to include spatial heterogeneity and spatial transport processes. Studies of the behavior of the model reveal different spatial-temporal dynamics as the time scales of the key processes of branch formation, monomer introduction, and diffusion are varied.
在[《Fogelson和Keener,,81(2010),051922》]中,我们介绍了一种血液凝固过程中纤维蛋白聚合的动力学模型,该模型捕捉了关于凝胶分支结构如何依赖于聚合发生条件的显著实验观察结果。我们在那里的分析使用了一种基于矩的方法,该方法仅在表明凝胶形成的有限时间爆破之前有效。在这里,我们使用我们在[《Fogelson和Keener,,75(2015),第1346 - 1368页》]中引入的基于偏微分方程的框架,将模型分析扩展到包括凝胶前和凝胶后动力学。我们还扩展了模型以包括空间异质性和空间传输过程。对模型行为的研究揭示了随着分支形成、单体引入和扩散等关键过程的时间尺度变化而产生的不同时空动力学。