The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in flow based on a modified viscoelastic fluid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear flow, we fix the parameters for VWF’s unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately \(5000\,\text {s}^{-1}\). We then use the theoretical model to predict VWF’s behaviour in two complex flows where experimental data are challenging to obtain: pure elongational flow and stenotic arterial flow. In pure elongational flow, our model predicts that VWF is 50% unfolded at approximately \(2000\,\text {s}^{-1}\), matching the established hypothesis that VWF unfolds at lower shear rates in elongational flow than in shear flow. We demonstrate the sensitivity of this elongational flow prediction to the value of maximum VWF length used in the model, which varies significantly across experimental studies, predicting that VWF can unfold between \(2000\text { and }3200\,\text {s}^{-1}\) depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational flow structures in the centre of the artery compared to high shear regions near the arterial walls.

血液蛋白血管性血友病因子 (VWF) 对于促进动脉血栓形成至关重要。在病理学高剪切速率下，蛋白质展开并与动脉壁结合，使血液中的血小板快速沉积。我们提出了一种基于改进的粘弹性流体模型的新型 VWF 动力学连续体模型，该模型结合了单一本构关系来描述 VWF 作为标量剪切率函数展开的倾向。利用纯剪切流中VWF解折叠的实验数据，我们固定了VWF解折叠倾向和最大VWF长度的参数，使得蛋白质在大约\(5000\,\text {s}^{的剪切速率下半解折叠-1}\)。然后，我们使用理论模型来预测 VWF 在两种复杂血流中的行为，其中实验数据很难获得：纯伸长血流和狭窄动脉血流。在纯拉伸流中，我们的模型预测 VWF 在大约\(2000\,\text {s}^{-1}\)时展开 50% ，这与 VWF 在拉伸流中的剪切速率低于在拉伸流中展开的假设相匹配。剪切流。我们证明了这种拉伸流动预测对模型中使用的最大 VWF 长度值的敏感性，该值在实验研究中变化很大，预测 VWF 可以在\(2000\text { 和 }3200\,\text {s}之间展开^{-1}\)取决于所选值。最后，我们检查了一系列理想化动脉狭窄中的 VWF 动态，预测与动脉壁附近的高剪切区域相比，动脉中心的伸长血流结构中 VWF 的相对延伸。