Computational modeling of blood clotting for predictions of post-surgical hemorrhagic and thromboembolic complications in Mechanical Circulatory Support Devices

Introduction
Hemorrhagic and thromboembolic events are post-surgical complications in LVAD patients. Thrombosis in LVADs can have fatal consequences either by device failure or emboli causing stroke but thrombi differ; the concentrations of proteins and cells vary depending on the flow characteristics. Red thrombi have been shown to respond more successfully to thrombolytics, whereas white thrombi have shown a better response to antiplatelet pharmacological agents. Thrombolytics and antiplatelet agents combined with platelet and protein damage, can also cause susceptibility to hemorrhage. While various numerical models of shear stress induced thrombosis exist they cannot distinguish between different clinical manifestations. This work aims to increase the utility of thrombosis modelling to assess the likelihood of hemorrhage versus thrombosis, and differentiate between platelet rich and protein rich thrombi.

Methods
Eight steady state, convection-diffusion-reaction equations were solved including: von Willebrand factor (vWf) (collapsed, unfolded, fragmented), platelets (nonactivated, activated, receptor shed), an example platelet agonist and hemoglobin. Source terms for mechanical activation and receptor shedding from platelets used power law functions of shear stress and time. Rate constants for vWf unfolding and collapsing were dependent on the local flow type: rotating, shearing or extensional. Platelets attached to the walls according to a modified thrombus susceptibility potential. Blood flow was solved in Ansys Fluent with reaction equations implemented as User Defined Functions. Individual models were first compared with literature results from stenosis-like geometries. The model was then applied to the HeartMateII and will be extended to HVAD.

Results
Results for shear induced vWf unfolding were in good agreement with the literature in both symmetric and asymmetric stenosed flows. Qualitative agreement in regions of high platelet deposition was found. The relative numbers of platelets deposited in the different regions of the HeartMate II was in agreement with the number of thrombi in literature studies, while the location of maximum stretched vWf concentration agreed with the location of laminated, protein rich thrombi.

Discussion
Initial results demonstrate qualitative agreement with the literature and future work will compare different operating conditions and different rotary VADs.