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The blood protein Von Willebrand Factor (VWF) is critical in facilitatingarterial thrombosis. At pathologically high shear rates the protein unfolds andbinds to the arterial wall, enabling the rapid deposition of platelets from theblood. We present a novel continuum model for VWF dynamics in flow based on amodified viscoelastic fluid model that incorporates a single constitutiverelation to describe the propensity of VWF to unfold as a function of thescalar shear rate. Using experimental data of VWF unfolding in pure shear flow,we fix the parameters for VWF's unfolding propensity and the maximum VWFlength, so that the protein is half unfolded at a shear rate of approximately5,000 s$^{-1}$. We then use the theoretical model to predict VWF's behaviour intwo complex flows where experimental data is challenging to obtain: pureelongational flow and stenotic arterial flow.  In pure elongational flow, our model predicts that VWF is 50% unfolded atapproximately 2,000 s$^{-1}$, matching the established hypothesis that VWFunfolds at lower shear rates in elongational flow than in shear flow. Wedemonstrate the sensitivity of this elongational flow prediction to the valueof maximum VWF length used in the model, which varies significantly acrossexperimental studies, predicting that VWF can unfold between 600 - 3,200s$^{-1}$ depending on the selected value. Finally, we examine VWF dynamics in arange of idealised arterial stenoses, predicting the relative extension of VWFin elongational flow structures in the centre of the artery compared tohigh-shear regions near the arterial walls.

A continuum model for the elongation and orientation of Von Willebrand Factor with applications in arterial flow