Mathematical Sciences: Mathematical Modeling and Computational Simulation of Platelet Aggregation in Large and Small Vessels

小行星9307643 研究人员扩展了早期的分析和计算工作的血小板聚集在小直径血管的微观尺度模型，并在大直径血管聚集的连续模型。 这两种模型都涉及血液的流体动力学和形成聚集体的力学和化学之间的相互作用。 对于微观尺度模型，该项目包括：1）完成将模拟扩展到三维所需的数值工具的开发; 2）探索和实施在高性能并行计算机上执行计算密集型三维计算的策略; 3）构建他的合作者J. Hubbell的实验流动室的计算模拟（Chemical Engineering，University of Texas），并将其模拟与Hubbell关于聚集体生长动力学的数据进行比较; 4）修改模型的涉及血小板对促聚集剂的响应和血小板-血小板凝聚效率的方面;以及5）探索模型的行为范围及其对参数变化的敏感性。 对于连续体模型，该项目要求：1）开发数值方法以研究允许应变依赖性聚集体破裂的模型形式; 2）开发将血小板与血管壁或人工心脏瓣膜的反应表面相互作用纳入该模型的技术;以及3）研究当聚集由整体流动中的外源刺激或通过与冠状动脉大小的血管的反应性壁接触而引发时模型的行为。 在后一种情况下，它是特别感兴趣的研究流动和血管几何形状之间的相互作用如何影响聚集体的形成。 血小板聚集体响应于血管损伤而在血管壁上形成;它们也是与血管疾病和使用心血管假体相关的危及生命的血凝块的主要成分。 该项目中进行的建模和模拟补充了传统的实验室实验。 它们提供了关于聚集反应各组成部分之间的动态相互作用的详细信息，这种信息在实验室中通常是无法获得的。 这些额外的信息将增加我们对聚集过程的物理和化学控制的了解。 这些研究也为聚集模型的进一步发展及其在临床上感兴趣的问题中的应用奠定了基础，包括流动和血管几何形状如何相互作用以影响天然血管（如冠状动脉）或假体装置（如血管移植物或人工心脏）内的聚集。 在这个项目中开发的数值工具也应该是有价值的，在解决广泛的生物流体动力学和工程问题。 ***

9307643 Fogelson The investigator extends earlier analytical and computational work on a microscopic-scale model of aggregation of blood platelets in small diameter blood vessels, and on a continuum model of aggregation in large diameter vessels. Both models involve interactions between the blood's fluid dynamics and the mechanics and chemistry of developing aggregates. For the microscopic-scale model, the project involves: 1) completing the development of the numerical tools needed to extend simulations to three dimensions; 2) exploring and implementing strategies for performing computationally intensive three-dimensional calculations on high-performance parallel computers; 3) constructing a computational analogue of the experimental flow chamber of his collaborator J. Hubbell (Chemical Engineering, University of Texas) and comparing simulations with it to Hubbell's data on the dynamics of aggregate growth; 4) modifying aspects of the model that concern a platelet's response to pro-aggregating agents and the efficiency of platelet-platelet cohesion; and 5) exploring the range of behavior of the model and its sensitivity to parameter variations. For the continuum model, the project requires: 1) developing numerical methods to study forms of the model that allow strain-dependent aggregate breakup; 2) developing techniques for incorporating into this model platelet interactions with the blood vessel's wall or the reactive surface of a prosthetic cardiac valve; and 3) studying the behavior of the model when aggregation is initiated by exogenous stimuli in bulk flow, or by contact with a reactive wall of a coronary-artery-sized vessel. In the latter context, it is of particular interest to study how the interaction between flow and vessel geometry affects aggregate formation. Platelet aggregates form on blood vessel walls in response to vascular injury; they are also major constituents of the life-threatening blood clots associated with vascular diseas e and with the use of cardiovascular prostheses. The modeling and simulations carried out in this project complement traditional laboratory experimentation. They provide detailed information, of a type that is generally not attainable in the laboratory, about the dynamic interactions among the components of the aggregation response. This additional information will increase our insight into the physical and chemical controls on the aggregation process. These studies also lay the foundations for further development of aggregation models and for their application to clinically interesting questions, including how flow and vessel geometry interact to influence aggregation within natural vessels, such as the coronary arteries, or prosthetic devices, such as vascular grafts or artificial hearts. The numerical tools developed in this project should also be valuable in solving a broad range of biofluid dynamics and engineering problems. ***