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Mathematical Medicine and Biology Advance Access originally published online on October 3, 2006
Mathematical Medicine and Biology 2007 24(1):111-130; doi:10.1093/imammb/dql022
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Fibrin gel formation in a shear flow

Robert D. Guy**,1, Aaron L. Fogelson***,2 and James P. Keener****,2

1 Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, USA, 2 Departments of Mathematics and Bioengineering, University of Utah,155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, USA

** Corresponding author. Email: guy{at}math.utah.edu

*** Email: fogelson{at}math.utah.edu

**** Email: keener{at}math.utah.edu


  Abstract

Blood clots are made up of platelets and fibrin gel, and the relative amount of fibrin is strongly influenced by the shear rate. In order to explore this phenomenon, this paper presents a model of fibrin gel formation over the surface of an injured blood vessel in a shear flow. A condition for gelation including source and sink terms of polymer is derived. A simplified model of coagulation, involving activation and inhibition of the enzyme thrombin and thrombin-mediated production of fibrin monomer, is combined with the model of gelation to explore how the shear rate and other parameters control the formation of fibrin gel. The results show that the thrombin inhibition rate, the gel permeability and the shear rate are key parameters in regulating the height of the fibrin gel.

Keywords: blood clotting; blood coagulation; gelation; Smoluchowski equation

Received on 16 September 2005. Revised on 2 May 2006.


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