10/05/2012, 14:30 — 15:30 — Room P3.10, Mathematics Building
Jevgenija Pavlova , CEMAT/IST
Mathematical formulation and numerical simulation of a 1D synthetic
blood coagulation model
Blood coagulation is a biological process of fundamental
importance and extreme complexity. It consists on the formation of
blood clots at the site of vascular injury, preventing the blood
loss. This process involves complex interactions among multiple
molecular and cellular components in the blood and vessel wall, and
it is also influenced by the flow of blood.
Mathematical modeling of the blood coagulation and fibrinolysis
processes is a way of conceptualizing and understanding this
complicated system, helping to optimize design of artificial
devices and also to identify the regions of the arterial tree
susceptible to the formation of thrombotic plaques and possible
rupture in stenosed arteries. A good model should be simple enough
in order to be applied in numerical simulations, and at the same
time should be able to capture the process complexity, so to allow
its better understanding.
The blood coagulation model we are working on consists of a
system of convection-reaction-diffusion equations, describing the
cascade of biochemical reactions, coupled with rheological models
for the blood flow (Newtonian, shear-thinning and viscoelastic
models). We introduce the effect of blood slip at the vessel wall
emphasizing an extra supply of activated platelets to the clotting
site. We expect that such contribution could be dominant, resulting
in the acceleration of thrombin production and eventually of the
whole clot progression. Such model will have the capacity to
predict effects of specific perturbations in the hemostatic system
that can't be done by laboratory tests, and will assist in clinical
diagnosis and therapies of blood coagulation diseases.
Numerical results for 1D case will be presented, based on the
solution of a system of reaction-diffusion equations, using the
Finite Element Method. Evolution of concentration of biochemical
species and clot formation and growth will be investigated in the
injury site of the vessel wall.
