Integrating Multiscale Modeling and in vivo Experiments for Studying Blood Clot Development

为了防止血管破裂后的血液流失，血液中的成分和血管壁迅速相互作用，形成血块（血栓），以限制出血。这种止血反应是快速和有调节的，因为过度和不适当的凝血会降低血流的通畅。虽然基因敲除小鼠提供了关于特定止血成分作用的定性结果，但数学和计算模型可以提示对止血至关重要的特定元素的阈值。确定这些阈值将有助于确定人群中的止血危险因素。这具有重要的生物医学意义。例如，深静脉血栓每年影响25万美国人，并导致2万人死亡，主要原因是血栓脱落的血块碎片导致肺栓塞。随着人口老龄化，发病率将会增加。开发准确的、定量的血栓形成模型，帮助我们了解血栓结构和稳定性的物理和生化过程，将有助于开发新的诊断方法和治疗策略。本提案的总体目标是开发三维多尺度数学模型和模拟血栓形成的计算工具包。这些模型将通过专门设计的实验来验证，以测试血栓发展、结构和稳定性的预测。此外，合理模型的发展将产生新的假设，这些假设可以在体内实验中得到验证。为了实现这一目标，Alber博士和徐博士（圣母大学）、Rosen博士（印第安纳大学医学院）和Jiang博士（洛斯阿拉莫斯国家实验室）之间形成了新的合作关系。为了将不同规模水平的血栓模型结合在一起，新的数学技术和计算方案将被开发出来，这些将包括随机分析、非线性分析和动力学理论的元素。新的方法将包括粗化方法、新的数值格式、数值解的误差估计以及用于长时间模拟所需的耦合离散和连续模型的并行化算法。数学和计算模型将把许多生物过程（血小板相互作用、凝血途径、血流动力学效应）纳入模拟，从而整合传统上单独研究的生物领域。

To prevent the loss of blood following a break in blood vessels, components in blood and vessel wall interact rapidly to form a blood clot (thrombus) to limit hemorrhage. This hemostatic response is rapid and regulated, since excessive and inappropriate clotting reduces the patency of blood flow. While knockout mice provide qualitative results about the role of particular hemostatic components, the mathematical and computational models can suggest threshold values of particular elements critical for hemostasis. Determining such thresholds will help identify hemostatic risk factors in human population. This has significant biomedical implications. For instance, deep vein thrombosis affects 250,000 Americans each year and leads to 20,000 deaths mainly from clot fragments that break off from the thrombus and cause pulmonary embolisms. The incidence will increase as the population ages. Developing accurate, quantitative models of thrombus formation that help us understand the physical and biochemical processes involved in clot structure and stability will contribute to the development of new diagnostic approaches and therapeutic strategies. The overall goal of this proposal is to develop three-dimensional multiscale mathematical models and a computational toolkit for simulating thrombus formation. These models will be validated with specifically designed experiments to test predictions of thrombus development, structure and stability. Moreover, the development of reasonable models will serve as a generator of new hypotheses that can be tested in experiments in vivo. To achieve this goal, a new collaboration has been formed between Dr. Alber and Dr. Xu (Notre Dame), Dr. Rosen (Indiana University Medical School) and Dr. Jiang (Los Alamos National Lab). To bring different scale levels of thrombus model together, new mathematical techniques and computational schemes will be developed and these will include elements of stochastic analysis, nonlinear analysis and kinetic theory. New methods will include coarsening methods, new numerical schemes, error estimates of numerical solutions as well as parallelization algorithms for the coupled discrete and continuous models needed for the long time simulations. The mathematical and computational models will incorporate many biological processes (platelet interactions, coagulation pathways, hemodynamic effects) into the simulation thus integrating biological fields that have traditionally been studied separately.