Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical modeling of hydrodynaimcal activation of intravascular blood coagulation and formation of fibre-like structures in intensive blood flow
Oleksii Rukhlenko, Ksenia Zlobina, Georgy Guria

Last modified: 2014-03-31


Blood coagulation system disorders are the most common cause of death in Europe. It is well known that activation of blood coagulation system happens in a threshold manner and leads to avalanche-like fibrin generation and subsequent thrombus formation. While a lot of attention has been dedicated to the analysis of blood coagulation processes at low Reynolds numbers (Re < 10), clot formation at high Reynolds numbers (Re > 10) still remains poorly understood.

The pathways of blood coagulation system activation in intensive blood flow qualitatively differ from those in slow flows. Namely, in intensive flows vessel wall permeability for a number of procoagulant substances essentially depends on wall shear stress. Present work is devoted to theoretical study of processes of hydrodynamic activation of the coagulation system in intensive blood flow.

Typical scenarios of development of thrombus formation processes were established. It was shown that in intensive blood flow in presence of recirculation zone the formation of fibrin clot always passes the stage of fibre-like polymer structure formation. The direction of fibre-like structure growth is determined by the blood flow topology. Namely, the fibre-like structure grows along the border separating the straight and closed flow streamlines (separatrix). The subsequent development of coagulation processes may lead either to formation of massive solid thrombus or to formation of a filament-like loose polymer structure floating in the flow. Presented results give evidence for the fact that detection of fibre-like structures by means of ultrasound techniques may serve as an early predictor of subsequent thrombosis events.

Parametric diagrams of stability of liquid state of blood were obtained. It appeared that in intensive blood flow the activation of blood coagulation system may result not only from local blood flow reduction, as occurs at low Reynolds numbers, but also from the super-threshold increase of flow intensity. The dependence of blood coagulation threshold upon the geometrical parameters of atherosclerotic plaque was explored. The results indicate that under intensive blood flow conditions (Re ∼ 100) the most thrombogenous plaques are the medium-sized ones (resulting in less than 50% of lumen area reduction).


mathematical modeling; blood coagulation; vessel stenosis; pattern formation