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Platelet deposition in non-parallel flow. (English) Zbl 1149.35332
Summary: This paper deals with flow- and surface-related aspects of primary hemostasis. It investigates the influence of both shear stress and changes in surface reactivity on platelet adhesion. For this purpose, a mathematical model based on the Navier-Stokes equations and on particle conservation is developed. Several vessel geometries of physiological relevance are considered, such as stagnation point flow, sudden expansion and t-junction. Model parameters have been optimized to fit corresponding experimental data. When platelet adhesion was assumed independent of shear, numerically predicted spatial platelet distribution did not match these data at all. However, when adhesion was assumed shear-dependent, better agreement was achieved. Further improvement was obtained when changes in surface reactivity due to platelet adhesion were taken into account. This was done by coupling platelet flux conditions to ordinary differential equations for the evolution of surface-bound platelets. Existence of weak solutions is shown for generalized parabolic systems having such boundary conditions. This, together with proofs for uniqueness and positivity of solutions, guarantees mathematical well posedness of the presented model. Limitations due to the complexity of the hemostatic system are discussed, as well as possible applications in practice. The findings of this paper contribute to understand the roles of flow and surface in primary hemostasis, which is of paramount interest in bioengineering and clinical practice.

35D05 Existence of generalized solutions of PDE (MSC2000)
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations
76Z05 Physiological flows
92-08 Computational methods for problems pertaining to biology
92C10 Biomechanics
35Q30 Navier-Stokes equations
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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