A free boundary problem modeling thrombus growth Model development and numerical simulation using the phase field method
Abstract
The high shear rate thrombus formation, high shear rate thrombosis, was only recently recognized as an another way of thrombosis. The other one, the traditional one relies on the three constituent elements of Virchow triad - flow stasis, endothelial disruption, and hypercoagulable blood chemistry.
We review briefly currently available biochemical knowledge about the former process. The increased coagulability is related to the unfolding of von Willebrand Factor(vWF) from globular into linear, stranded, conformation. vWF creates nets, in which blood platelets get captured, forming the thrombus.
Afterwards some modelling approaches are mentioned, which take into account this phenomenon. We build our reformulation on one of these models, Weller's model , in the phase field setting.
We are able to simulate using the new method the results obtained by Weller, namely simulation of clotting in the perfusion chamber. We have performed simulations in the cylinder geometry as well.
We did a convergence study on two levels of refinement for each computational geometry. Our approach appears to us advantageous compared with the numerical treatment in the original work of Weller, where a sharp interface method,the level set method, is used.