ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

In order to have a better understanding of platelet activation, we employed convectiondiffusion-reaction
(CDR) equations for the distribution of coagulant factors. These
coagulant factors, in the vicinity of platelets and over a critical amount, can result in
activation of platelets. Here, in this model, we are concerned in thrombin concentration
([T] in unit/ml) and neglected other factors; as previously shown in [12], thrombin is the
most predominant factor in platelet activation. The CDR equation in 2D for thrombin
can be written as (10). In (10), the last term includes the reaction which results in
inactivation of thrombin. The reaction coefficient, Γ, is derived from the relation that
Sorenson et al. proposed in [2], where we assumed uniform concentration of heparin
and anti-thrombin (ATIII). Here, D, the diffusion coefficient for thrombin is assumed to
be constant with the value of 4.16×10 -17 cm 2 /s. We used alternating direction implicit
(ADI) scheme to solve the equation on a structured grid over the whole domain, which
overlay the cells and fluid. The fluid velocity is averaged from the DPD solution and
thrombin concentration on the grid points, which overlaid platelets, are set to zero.