Traveling wave solutions in the mathematical model of blood coagulation

Galochkina, Tatiana; Ouzzane, Hadjer; Bouchnita, Anass; Volpert, Vitaly

doi:10.1080/00036811.2016.1249863

Cited by 7 publications

(12 citation statements)

References 20 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%

“…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%

“…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: 99%

See 1 more Smart Citation

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

Belyaev

Dunster

Gibbins

et al. 2018

Physics of Life Reviews

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“…Minimax representation ( 12 ) allows the estimation of the wave speed c approximating the experimental data (Galochkina et al. 2017a , b ). In this work, we carry out numerical simulations of system ( 4 )–( 6 ) in order to determine the wave speed for the values of parameters corresponding to healthy subjects and to hemophilic patients.…”

Section: Reaction–diffusion Waves Of Blood Coagulationmentioning

confidence: 99%

Patient-Specific Modelling of Blood Coagulation

et al. 2021

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Blood coagulation represents one of the most studied processes in biomedical modelling. However, clinical applications of this modelling remain limited because of the complexity of this process and because of large inter-patient variation of the concentrations of blood factors, kinetic constants and physiological conditions. Determination of some of these patients-specific parameters is experimentally possible, but it would be related to excessive time and material costs impossible in clinical practice. We propose in this work a methodological approach to patient-specific modelling of blood coagulation. It begins with conventional thrombin generation tests allowing the determination of parameters of a reduced kinetic model. Next, this model is used to study spatial distributions of blood factors and blood coagulation in flow, and to evaluate the results of medical treatment of blood coagulation disorders.

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“…In the biologically relevant case, the vector-function F(u) in (4.7) has three zeros, 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 [69,70]. In this case the thrombin free equilibrium u + is stable.…”

Section: Existence and Stability Of Wavesmentioning

confidence: 99%

(INVITED) Reaction–diffusion waves in cardiovascular diseases

Panfilov¹,

Dierckx²,

Volpert³

2019

Physica D: Nonlinear Phenomena

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h i g h l i g h t s• Cardiovascular diseases are reviewed from joint grounds of reaction-diffusion waves.• Atherosclerosis is modeled as chronic inflammation of blood vessel walls.• The state-of-the-art models of thrombus formation are considered.• Cardiac arrhythmia modeling via reaction-diffusion equations is discussed.• Response function perturbation theory for cardiac arrhythmias is presented.

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Traveling wave solutions in the mathematical model of blood coagulation

Cited by 7 publications

References 20 publications

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

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

Patient-Specific Modelling of Blood Coagulation

(INVITED) Reaction–diffusion waves in cardiovascular diseases

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