Conditions of microvessel occlusion for blood coagulation in flow

Vessel occlusion is a perturbation of blood flow inside a blood vessel because of the fibrin clot formation. As a result, blood circulation in the vessel can be slowed down or even stopped. This can provoke the risk of cardiovascular events. In order to explore this phenomenon, we used a previously...

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Bibliographic Details
Published in:International journal for numerical methods in biomedical engineering 2017-09, Vol.33 (9), p.n/a
Main Authors: Bouchnita, A., Galochkina, T., Kurbatova, P., Nony, P., Volpert, V.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Blood circulation
Blood Coagulation
blood coagulation, Navier‐Stokes equations, reaction‐diffusion system, vascular occlusion
Blood flow
Blood Flow Velocity
Cardiovascular diseases
Clotting
Coagulation
Computational fluid dynamics
Computer simulation
Critical flow
Fibrin
Fibrin - metabolism
Flow velocity
Laminar flow
Mathematical models
Mathematics
Microvessels - pathology
Navier-Stokes equations
Occlusion
Perturbation methods
Porous media
Stokes law (fluid mechanics)
Thrombin
Thrombin - metabolism
Thrombosis - pathology
Wave propagation
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Summary:Vessel occlusion is a perturbation of blood flow inside a blood vessel because of the fibrin clot formation. As a result, blood circulation in the vessel can be slowed down or even stopped. This can provoke the risk of cardiovascular events. In order to explore this phenomenon, we used a previously developed mathematical model of blood clotting to describe the concentrations of blood factors with a reaction‐diffusion system of equations. The Navier‐Stokes equations were used to model blood flow, and we treated the clot as a porous medium. We identify the conditions of partial or complete occlusion in a small vessel depending on various physical and physiological parameters. In particular, we were interested in the conditions on blood flow and diameter of the wounded area. The existence of a critical flow velocity separating the regimes of partial and complete occlusion was demonstrated through the mathematical investigation of a simplified model of thrombin wave propagation in Poiseuille flow. We observed different regimes of vessel occlusion depending on the model parameters both for the numerical simulations and in the theoretical study. Then, we compared the rate of clot growth in flow obtained in the simulations with experimental data. Both of them showed the existence of different regimes of clot growth depending on the velocity of blood flow. Microvessel occlusion is the perturbation of blood flow inside a vein because of the formation of a fibrin clot. Mathematical model of clot growth was developed using a system of reaction‐diffusion coupled with the Navier‐Stokes equations for blood flow. Conditions of microvessel occlusion were identified using numerical simulations and mathematical investigation of simplified one‐dimensional model. Experimental data and numerical simulations confirmed the existence of different regimes of clot growth velocity depending on the velocity of blood flow.
ISSN:2040-7939
2040-7947
DOI:10.1002/cnm.2850