Leiderman Karin, Fogelson Aaron L
Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, USA.
Math Med Biol. 2011 Mar;28(1):47-84. doi: 10.1093/imammb/dqq005. Epub 2010 May 3.
The body's response to vascular injury involves two intertwined processes: platelet aggregation and coagulation. Platelet aggregation is a predominantly physical process, whereby platelets clump together, and coagulation is a cascade of biochemical enzyme reactions. Thrombin, the major product of coagulation, directly couples the biochemical system to platelet aggregation by activating platelets and by cleaving fibrinogen into fibrin monomers that polymerize to form a mesh that stabilizes platelet aggregates. Together, the fibrin mesh and the platelet aggregates comprise a thrombus that can grow to occlusive diameters. Transport of coagulation proteins and platelets to and from an injury is controlled largely by the dynamics of the blood flow. To explore how blood flow affects the growth of thrombi and how the growing masses, in turn, feed back and affect the flow, we have developed the first spatial-temporal mathematical model of platelet aggregation and blood coagulation under flow that includes detailed descriptions of coagulation biochemistry, chemical activation and deposition of blood platelets, as well as the two-way interaction between the fluid dynamics and the growing platelet mass. We present this model and use it to explain what underlies the threshold behaviour of the coagulation system's production of thrombin and to show how wall shear rate and near-wall enhanced platelet concentrations affect the development of growing thrombi. By accounting for the porous nature of the thrombus, we also demonstrate how advective and diffusive transport to and within the thrombus affects its growth at different stages and spatial locations.
血小板聚集和凝血。血小板聚集主要是一个物理过程，即血小板聚集在一起，而凝血是一系列生化酶反应。凝血的主要产物凝血酶通过激活血小板并将纤维蛋白原裂解为纤维蛋白单体，使纤维蛋白单体聚合成网状结构以稳定血小板聚集体，从而将生化系统与血小板聚集直接联系起来。纤维蛋白网和血小板聚集体共同构成血栓，血栓可生长至阻塞血管直径。凝血蛋白和血小板往返于损伤部位的运输在很大程度上受血流动力学控制。为了探究血流如何影响血栓的生长，以及生长的血栓如何反过来反馈并影响血流，我们开发了首个在血流状态下血小板聚集和血液凝固的时空数学模型，该模型详细描述了凝血生物化学、血小板的化学激活和沉积，以及流体动力学与生长的血小板团块之间的双向相互作用。我们展示这个模型，并利用它来解释凝血系统产生凝血酶的阈值行为的潜在机制，以及壁面切应力和近壁处血小板浓度增加如何影响生长血栓的发展。通过考虑血栓的多孔性质，我们还展示了血栓内外的平流和扩散运输如何在不同阶段和空间位置影响其生长。
