A mechanistic continuum model for the blood protein VWF and its role in arterial blood clotting*

Arterial blood clot formation (thrombosis) is the leading cause of both stroke and heart attack. Accurate prediction of clotting dynamics under high shear is a key part of developing safe and effective treatments. Thrombosis under pathologically high shear stresses relies on the protein Von Willebrand Factor (VWF). At high shear, VWF unfolds, which exposes binding sites, and facilitates rapid platelet deposition from the blood to the vessel walls.

We present a novel, 3D, mechanistic continuum model for VWF dynamics in flow and couple it to a model for thrombus initiation in an idealised arterial obstruction (stenosis). We model VWF dynamics using a modified viscoelastic fluid model with a single empirical constitutive law to describe VWF unfolding as a function of shear rate. We exploit the low concentration of VWF in the blood and the slow timescale of thrombus initiation to derive a reduced model where the fluid is approximated as Newtonian and we examine the initial location of platelet deposition prior to rapid thrombus growth. We use this model to investigate the effect of varying stenosis geometry and Reynolds number on the unfolding of VWF and subsequent platelet binding.