Platelet deposition in non-parallel flow

Abstract

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.

An ALE approach to mechano‐chemical processes in fluid–structure interactions

“…A plaque with a large core and a thin cap becomes vulnerable and may rupture, if the biomechanical forces reach a critical value. After plaque rupture, platelets in the blood flow adhere to the ruptured region and lead to thrombus formation . This far spread disease of arteries is related to coronary artery disease, stroke, and other conditions.…”

Blood Flow in Channel Constrictions: A Lattice-Boltzmann Consistent Comparison between Newtonian and Non-Newtonian Models

“…(Succi, 2001) LB is an explicit method in which the dynamics of a fluid is modeled using a set of interacting particles located in a discretized space and with a set of associated probability distribution functions that allows us to recover the macroscopic variables such as density, momentum and energy. Besides the LB method, other blood flow studies have been performed using more classical approaches such as finite elements, (Weller, 2008;Weller, 2010) finite volumes (Sorensen, Burgreen, Wagner, and Antaki, 1999a;Sorensen, Burgreen, Wagner, and Antaki, 1999b) and finite differences. (Fogelson and Guy, 2004;Anand, Rajagopal and Rajagopal, 2005;Lobanov and Staroszhilova, 2005) Some attempts towards including explicitly the red blood cells have also been proposed using, for instance, smoothed particle dynamics, (Wootton, Popel, and Alevriadou, 2002) multiscale simulations, (Xu, Chen, M., Rosen, and Alber, 2008) mean field theory (Pivkin and Karniadakis, 2008) and the cellular automata approach.…”

Transport of platelets induced by red blood cells based on mixture theory

“…Thrombosis is usually initiated as platelet adhesion on biological or artificial surfaces. Thrombus initiation and growth in vessels or on medical devices is strongly influenced by the number density of the platelets near the walls and surfaces (Cito, Mazzeo, & Badimon, 2013;Skorczewski, Erickson, & Fogelson, 2013;F. F. Weller, 2008;Yang, Jäger, Neuss-Radu, & Richter, 2016).…”