The von Willebrand factor (vWF) is a blood protein that is related to hemostasis. Changes to the protein structure can cause disease and difficulty for blood to clot, a disease known as the von Willebrand syndrome [1-3]. Hydrodynamic conditions can lead to flow-induced stress on the protein that can change its structure, when the flow is not physiological. Such non-physiological flow conditions occur when blood flows through vascular implants or other devices, like blood pumps. In this work, we use direct numerical simulations (DNS) of turbulent blood flow and transitional blood flow to calculate the distribution of stresses on particles that serve as models of individual vWF proteins. A case of fully developed flow and a case of Poiseuille-Couette flow are investigated. The protein motion in the flow field is calculated by Lagrangian Scalar Tracking (LST) of thousands of protein molecules that behave as passive particles in the flow field [4, 5]. These molecules have diffusivity that corresponds to the Stokes_Einstein diffusivity for vWF molecules. 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 LST allows the calculation of the shear stresses acting on the vWF along its trajectory. The distribution of the stresses as a function of time and as a function of the point of release is calculated in both flow cases. The fully developed turbulent flow can occur when blood moves through a blood pump, at Reynolds numbers comparable to those suggested in the FDA Critical Path Initiative [6], where the computational fluid dynamics community was asked to model blood flow and hemolysis. The Poiseuille-Couette flow occurs when blood moves through a Ventricular Assist Device (VAD) heart implant [7]. It is found that both the flow field and the location of vWF release are important for the shear stress distribution. We will discuss the methodology for calculating the stresses in the Lagrangian framework and the effects that the history of the stresses can have on vWF configuration within the flow field. Since the stress on the protein is a function of time, the history of stresses experienced by a vWF molecule is important, instead of only the average stress or the wall shear stress that is used conventionally.
Literature Cited:
[1] Schneider, S.W, Nuschele, S., Wixforth, A., Gorzelanny, C., Alexander-Katz, A., et al. Shear-induced unfolding triggers adhesion of von Willebrand factor fibers. Proc. Natl. Acad. Sci. USA 104, 7899–7903 (2007)
[2] Lippok, S., Radtke, M., Obser, T., Kleemeier, L., et al. Shear-Induced Unfolding and Enzymatic Cleavage of Full-Length VWF Multimers, Biophysical J. 110, 564-554 (2016)
[3] Bekard, I.B., Asimakis, P., Bertolini, J., & Dunstan, D.E. Review of the effects of shear flow in protein structure and function. Biopolymers 95(11) 733-745 (2011)
[4] Nguyen, Q. and D.V. Papavassiliou. A statistical model to predict streamwise turbulent dispersion from the wall at small times. Physics of Fluids, 28(12), Art. 125103 (2016)
[5] Nguyen, Q., Feher, S., and D.V. Papavassiliou, Lagrangian Modeling of Turbulent Dispersion from Instantaneous Point Sources at the Center of a Turbulent Flow Channel, Fluids, 2(3), Art. 46 (2017)
[6] Malinauskas R.A., Saha A., Sheldon M.I. Working with the Food and Drug Administration’s Center for Devices to advance regulatory science and medical device innovation. Artif Organs; 39:293-9, 2015.
[7] Coghill, P.A., Suren, K., Zheila J.A-N, Long, J.W. & Snyder T.A. Benchtop von Willebrand Factor Testing Comparison of Commercially Available Ventricular Assist Devices and Evaluation of Variables for a Standardized Test Method. ASAIO Journal,65(5):481-488, 2019.
