The von Willebrand syndrome [1-3] is a disease that appears when the von Willebrand factor (vWF) – a blood protein that affects blood clotting – loses its functionality. Flow-induced stresses on vWF often affect its structure as blood flows in cardiovascular implants, like heart valves or ventricular assist devices (VADs). While a lot of attention has been given to the effects of shear stresses on the vWF, this work is focused on the calculation of extensional stresses on the vWF. A direct numerical simulation (DNS) approach is used to model turbulent blood flow in a fully-developed, stationary flow channel. Pressure driven flow and shear driven flow (i.e., a Poiseuille flow and a Poiseuille-Couette flow) are used as models for flow in blood pumps and VADs, respectively. The presence of vWF is modeled as particles that move in the simulated flow field, and the extensional stresses along the trajectories of the vWF particles are calculated using a Lagrangian approach. Several thousands of protein molecules that behave as passive particles are released in the flow field. [4, 5]. These model molecules have diffusivity obtained by the Stokes-Einstein formula. The vWF particles are released at different locations in the flow field, including the viscous wall subregion, the buffer region, the log layer and the outer region of the flow. The distribution of the extensional stresses is calculated in both flow cases. Even though the simulations are conducted with dimensionless equations, the Poiseuille flow can be related to turbulent flow through a blood pump, at Reynolds numbers comparable to those suggested in the FDA Critical Path Initiative [6], in order to compare the results to practical cases. The Poiseuille-Couette flow can be related to blood flow in typical VADs [7]. It is found that both the flow field and the location of vWF release are important for the extensional stress distribution. While the average stress is below the critical value for vWF damage, there are instances where a portion of the vWF model particles experience extensional stresses that are above the critical values. The history of stresses on the vWF is also quantified, and it is shown that when we account for history, the level of stress of the vWF is significantly larger. A designer of a medical device needs to be aware of these issues, and to account for the distribution of stresses, not only the average stress, when designing a device.
ACKNOWLEDGMENTS
The financial support of the National Science Foundation (Grant No CBET- 1803014) is gratefully acknowledged. In addition, we acknowledge the use of computing facilities at the University of Oklahoma Supercomputing Center for Education and Research (OSCER) and at XSEDE (under allocation CTS-090025).
Literature Cited
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