Reaction-diffusion waves of blood coagulation

Galochkina, Tatiana; Bouchnita, Anass; Kurbatova, Polina; Volpert, Vitaly

doi:10.1016/j.mbs.2017.03.008

Cited by 20 publications

(29 citation statements)

References 50 publications

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“…Speed of propagation. The wave speed c for system (2) converges to the speed c 0 for the single equation 3in the limit of large reaction rate constants [90,91].…”

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 89%

“…The speed c 0 for the single equation can be approximated by the narrow reaction zone method and by a piecewise linear approximation [91]. They give a good approximation for the speed of the complete system and of the experimental results ( Figure 3).…”

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 98%

“…Therefore, if we consider system (2) on the whole axis it has a travelling wave solution u(x, t) = w(x − ct) [90,91,92,93]. Here c is the wave speed, and the function w(x) satisfies the equation…”

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 99%

“…These factors promote the conversion of prothrombin into thrombin. Taking the initiation into account, instead of a simplified one-equation model (3) we obtain Reprinted with permission from [91].…”

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 99%

“…It is proved that the vector-function F (u) in (2) has the same number of zeros as the scalar equation, u + = 0, u 0 , and u − . The matrices F (u ± ) have all eigenvalues in the left-half plane, and the matrix F (u 0 ) has a positive eigenvalue[90],[91]. In this case the thrombin free equilibrium u + is stable.…”

mentioning

confidence: 99%

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Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Belyaev

Dunster

Gibbins

et al. 2018

Physics of Life Reviews

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Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modeling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational modeling of thrombosis with the specific focus on the analysis of unresolved challenges. They include: a) fundamental issues related to physics of platelet aggregates and fibrin gels; b) computational challenges and limitations for solution of the models that combine cell adhesion, hydrodynamics and chemistry; c) biological mysteries and unknown parameters of processes; d) biophysical complexities of the spatiotemporal networks' regulation. Both relatively classical approaches and innovative computational techniques for their solution are considered; the subjects discussed with relation to thrombosis modeling include coarse-graining, continuum versus particle-based modeling, multiscale models, hybrid models, parameter estimation and others. Fundamental understanding gained from theoretical models are highlighted and a description of future prospects in the field and the nearest possible aims are given.

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“…Speed of propagation. The wave speed c for system (2) converges to the speed c 0 for the single equation 3in the limit of large reaction rate constants [90,91].…”

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 89%

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 98%

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 99%

Section: Clot Growth As a Reaction-diffusion Wavementioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Belyaev

Dunster

Gibbins

et al. 2018

Physics of Life Reviews

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show abstract

Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

Terekhov

Butakov

Danilov

et al. 2023

Numer Methods Biomed Eng

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In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier–Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite‐volume methods for the Navier–Stokes equations, advection–diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier–Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf‐sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.

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Clustering of Thrombin Generation Test Data Using a Reduced Mathematical Model of Blood Coagulation

et al. 2019

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Reaction-diffusion waves of blood coagulation

Cited by 20 publications

References 50 publications

Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Dynamic adaptive moving mesh finite‐volume method for the blood flow and coagulation modeling

Clustering of Thrombin Generation Test Data Using a Reduced Mathematical Model of Blood Coagulation

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