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von Willebrand Factor is a mechano-sensitive protein circulating in blood that mediates platelet adhesion to subendothelial collagen and platelet aggregation at high shear rates. Its hemostatic function and thrombogenic effect, as well as susceptibility to enzymatic cleavage, are regulated by a conformational change from a collapsed globular state to a stretched state. Therefore, it is essential to account for the conformation of the vWF multimers when modeling vWF-mediated thrombosis or vWF degradation. We introduce a continuum model of vWF unfolding that is developed within the framework of our multi-constituent model of platelet-mediated thrombosis. The model considers two interconvertible vWF species corresponding to the collapsed and stretched conformational states. vWF unfolding takes place via two regimes: tumbling in simple shear and strong unfolding in flows with dominant extensional component. These two regimes were demonstrated in a Couette flow between parallel plates and an extensional flow in a cross-slot geometry. The vWF unfolding model was then verified in several microfluidic systems designed for inducing high-shear vWF-mediated thrombosis and screening for von Willebrand Disease. The model predicted high concentration of stretched vWF in key regions where occlusive thrombosis was observed experimentally. Strong unfolding caused by the extensional flow was limited to the center axis or middle plane of the channels, whereas vWF unfolding near the channel walls relied upon the shear tumbling mechanism. The continuum model of vWF unfolding presented in this work can be employed in numerical simulations of vWF-mediated thrombosis or vWF degradation in complex geometries. However, extending the model to 3-D arbitrary flows and turbulent flows will pose considerable challenges.

Thrombosis under high-shear conditions is mediated by the mechanosensitive blood glycoprotein von Willebrand Factor (vWF). vWF unfolds in response to strong flow gradients and facilitates rapid recruitment of platelets in flowing blood. While the thrombogenic effect of vWF is well recognized, its conformational response in complex flows has largely been omitted from numerical models of thrombosis. We recently presented a continuum model for the unfolding of vWF, where we represented vWF transport and its flow-induced conformational change using convection-diffusion-reaction equations. Here, we incorporate the vWF component into our multi-constituent model of thrombosis, where the local concentration of stretched vWF amplifies the deposition rate of free-flowing platelets and reduces the shear cleaning of deposited platelets. We validate the model using three benchmarks: in vitro model of atherothrombosis, a stagnation point flow, and the PFA-100, a clinical blood test commonly used for screening for von Willebrand Disease (vWD). The simulations reproduced the key aspects of vWF-mediated thrombosis observed in these experiments, such as the thrombus location, thrombus growth dynamics, and the effect of blocking platelet-vWF interactions. The PFA-100 simulations closely matched the reported occlusion times for normal blood and several hemostatic deficiencies, namely, thrombocytopenia, vWD Type 1, and vWD Type 3. Overall, the multi-constituent model of thrombosis presented in this work enables macro-scale 3-D simulations of thrombus formation in complex geometries over a wide range of shear rates and accounts for qualitative and quantitative hemostatic deficiencies in patient blood. The results also demonstrate the utility of the continuum model of vWF unfolding that could be adapted to other numerical models of thrombosis.

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

Thromboembolic complications remain a central issue in management of patients on mechanical circulatory support. Despite the best practices employed in design and manufacturing of modern ventricular assist devices, complexity and modular nature of these systems often introduces internal steps and crevices in the flow path which can serve as nidus for thrombus formation. Thrombotic potential is influenced by multiple factors including the characteristics of the flow and surface chemistry of the biomaterial. This study explored these elements in the setting of blood flow over a micro-crevice using a multi-constituent numerical model of thrombosis. The simulations reproduced the platelet deposition patterns observed experimentally and elucidated the role of flow, shear rate, and surface chemistry in shaping the deposition. The results offer insights for design and operation of blood-contacting devices.

This study was undertaken to develop a numerical/computational simulation of von Willebrand Factor (vWF) - mediated platelet shear activation and deposition in an idealized stenosis. Blood is treated as a multi-constituent mixture comprised of a linear fluid component and a porous solid component (thrombus). Chemical and biological species involved in coagulation are modeled using a system of coupled convection-reaction-diffusion (CRD) equations. This study considers the cumulative effect of shear stress (history) on platelet activation. The vWF activity is modeled as an enhancement function for the shear stress accumulation and is related to the experimentally-observed unfolding rate of vWF. A series of simulations were performed in an idealized stenosis in which the predicted platelets deposition agreed well with previous experimental observations spatially and temporally, including the reduction of platelet deposition with decreasing expansion angle. Further simulation indicated a direct relationship between vWF-mediated platelet deposition and degree of stenosis. Based on the success with these benchmark simulations, it is hoped that the model presented here may provide additional insight into vWF-mediated thrombosis and prove useful for the development of more hemo-compatible blood-wetted devices in the future.

Cardiovascular Diseases, the common name for various Heart Diseases, are responsible for nearly 17.3 million deaths annually and remain the leading global cause of death in the world. It is estimated that this number will grow to more than 23.6 million by 2030, with almost 80% of all cases taking place in low and middle income countries. Surgical treatment of these diseases involves the use of blood-wetted devices, whose relatively recent development has given rise to numerous possibilities for design improvements. However, blood can be damaged when flowing through these devices due to the lack of biocompatibility of surrounding walls, thermal and osmotic effects and most prominently, due to the excessive exposure of blood cells to shear stress for prolonged periods of time. This extended exposure may lead to a rupture of membrane of red blood cells, resulting in a release of hemoglobin into the blood plasma, in a process called hemolysis. Moreover, exposure of platelets to high shear stresses can increase the likelihood of thrombosis. Therefore, regions of high shear stress and residence time of blood cells must be considered thoroughly during the design of blood-contacting devices. Though laboratory tests are vital for design improvements, in-vitro experiments have proven to be costly, time-intensive and ethically controversial. On the other hand, simulating blood behavior using Computational Fluid Dynamics (CFD) is considered to be an inexpensive and promising tool to help predicting blood damage in complex flows. Nevertheless, current state-of-the-art CFD models of blood flow to predict hemolysis are still far from being fully reliable and accurate for design purposes. Previous work have demonstrated that prediction of hemolysis can be dramatically improved when using a multiphase (i.e., phases are plasma, red blood cells and platelets) model of the blood instead of assuming the blood as a homogeneous mixture. Nonetheless, the accurate determination of how the cells segregate becomes the critical issue in reaching a truthful prediction of blood damage. Therefore, the attempt of this study is to develop and validate a numerical model based on Granular Kinetic Theory (GKT) for solid phases (i.e., cells treated as particles) that provides an improved prediction of blood cells segregation within the flow in a microtube. Simulations were based on finite volume method using Eulerian-Eulerian modeling for treatment of three-phase (liquid-red blood cells and platelets) flow including the GKT to deal with viscous properties of the solid phases. GKT proved to be a good model to predict particle concentration and pressure drop by taking into account the contribution of collisional, kinetic and frictional effects in the stress tensor of the segregated solid phases. Preliminary results show that the improved segregated model leads to a better prediction of spatial distribution of blood cells. Simulations were performed using ANSYS FLUENT platform.