Journal Article

Grow with the flow: a spatial–temporal model of platelet deposition and blood coagulation under flow

Karin Leiderman and Aaron L. Fogelson

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 28, issue 1, pages 47-84
Published in print March 2011 | ISSN: 1477-8599
Published online May 2010 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/dqq005
Grow with the flow: a spatial–temporal model of platelet deposition and blood coagulation under flow

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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.

Keywords: thrombosis; mathematical model

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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