Multi-Constituent Simulation of Thrombus Deposition

Abstract

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5 mm × 1.6 mm × 0.1 mm) with small crevices (125 μm × 75 μm and 125 μm × 137 μm). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

High fidelity computational simulation of thrombus formation in Thoratec HeartMate II continuous flow ventricular assist device

“…The mathematical details of this model have been recently reported in prior publications910, and are briefly summarized below.…”

Numerical Simulation of Red Blood Cell-Induced Platelet Transport in Saccular Aneurysms

“…A limitation of this study is the applied lift force model, see Equation (10), which was based exclusively on shear lift, derived from classical multicomponent theory [31,41,42]. Although this model has been effective in predicting moderate RBC depletion near the wall, it is not capable of predicting near-wall RBCs free layer.…”

“…γ m represents the dependence of the platelets transport flux intensity on the local shear rate which is proportional to the cells collision frequency; this function disappears as φ = 0. For the sake of simplicity, we assume f s (φ) = φ, and ξ = 6.0 × 10 −14 m −2 is an empirical constant from experiments [10]. The term C∇(1 + q(φ)) is the diffusive flux of the platelets responsible for the movement away from regions of high RBC content, such as the center of the blood vessel, and (1 + q(φ))∇C represents the RBCs-enhanced diffusion of the platelets in the direction of the gradient of the platelet concentration.…”

“…For example, when there exists unhealthy endothelium in the aneurysm, the thrombus may form, which can significantly lower the risk of rupture [1,2]. Thrombus formation is closely related to various physical and biological factors, including the hemodynamic fields, the distribution of the red blood cells (RBCs), and the concentration of the platelets [5][6][7][8][9][10][11]. Therefore, studying blood flow and platelets transport in the aneurysms is very meaningful both physically and biomedically.…”

A Short Review of Advances in the Modelling of Blood Rheology and Clot Formation

“…Separately, Wu et al [45] developed and simulated growth of a thrombus in a Navier-Stokes fluid using a set of 10 convection-reaction-diffusion equations which allowed for irregular thrombus shape, alteration of flow field due to growth of the thrombus, and thrombus embolization due to shear. These extensions are important when simulating blood flow over blood-wetted devices, and the authors presented illuminating results for the growth of thrombus on an injured blood vessel in vivo, and in a micro-crevice in vitro.…”