Mathematical Modeling of Thrombin Generation and Wave Propagation: From Simple to Complex Models and Backwards

Tokarev, Alexey; Ratto, Nicolas; Volpert, Vitaly

doi:10.1007/978-3-030-23433-1_1

Cited by 2 publications

(8 citation statements)

References 66 publications

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“…Theoretical modelling of blood coagulation provides a better understanding of this process in various experimental and physiological conditions. Kinetics curves in thrombin generation tests are described by kinetic ODE models (Chelle et al 2018;Dunster and King 2017;Hoffman et al 2005;Mann et al 2003) (see also Belyaev et al 2018;Panfilov 2019;Tokarev et al 2019 for a more complete literature review). Clot growth in a quiescent plasma is investigated with reaction-diffusion equations (Guria and Guria 2015;Pogorelova and Lobanov 2014;Zarnitsina et al 2001), clot growth in blood flow is studied by various continuous models (Belyaev et al 2015;Bouchnita et al 2020;Sequeira et al 2011;Bodnar and Sequeira 2008;Sequeira and Bodnar 2014), particle Fig.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, these constants are patient-specific with possibly large variations (see Andreeva et al 2018;Chelle et al 2018) and the references therein). Models with simpler kinetics impose some assumptions which can be difficult to verify (Tokarev et al 2019). Specific features of clot growth can depend on physiological conditions and can be influenced by many different factors, such as inflammation or hypoxia (Bouchnita et al 2017b).…”

Section: Discussionmentioning

confidence: 99%

“… 2018 ; Tokarev et al. 2019 ). Coagulation system is a cascade of proteolytic enzymatic reactions with each level consisting of two processes: zymogen (coagulation factor) activation to the active enzyme (activated coagulation factor), followed by its rapid irreversible trapping by inhibitors always circulating in blood.…”

Section: Thrombin Generation Curves and Parameter Identificationmentioning

confidence: 99%

“…Thrombin generation curves in platelet-poor plasma can be described by various ODE models representing equations of chemical kinetics for the reactions of plasma proteins called blood factors (see literature reviews in Belyaev et al 2018;Chelle et al 2018;Tokarev et al 2019). Coagulation system is a cascade of proteolytic enzymatic reactions with each level consisting of two processes: zymogen (coagulation factor) activation to the active enzyme (activated coagulation factor), followed by its rapid irreversible trapping by inhibitors always circulating in blood.…”

Section: Coagulation Cascadementioning

confidence: 99%

“…Various kinetic models are used to model thrombin generation curves (see, e.g., Belyaev et al 2018;Chelle et al 2018;Hemker 1993;Hemker and Beguin 1995;Tokarev et al 2019 and the references therein). The interest of model (1)-( 3) is that it contains a relatively small number of parameters, it includes the main blood factors, and it has a clear biophysical structure including the initiation, prolongation and inhibition stages of the coagulation cascade.…”

Section: Patient-specific Parameter Identificationmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Thrombin Generation Curves and Parameter Identificationmentioning

confidence: 99%

Section: Coagulation Cascadementioning

confidence: 99%

Section: Patient-specific Parameter Identificationmentioning

confidence: 99%

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Patient-Specific Modelling of Blood Coagulation

et al. 2021

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Competition of SARS-CoV-2 Variants in Cell Culture and Tissue: Wins the Fastest Viral Autowave

2022

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Replication of viruses in living tissues and cell cultures is a “number game” involving complex biological processes (cell infection, virus replication inside infected cell, cell death, viral degradation) as well as transport processes limiting virus spatial propagation. In epithelial tissues and immovable cell cultures, viral particles are basically transported via Brownian diffusion. Highly non-linear kinetics of viral replication combined with diffusion limitation lead to spatial propagation of infection as a moving front switching from zero to high local viral concentration, the behavior typical of spatially distributed excitable media. We propose a mathematical model of viral infection propagation in cell cultures and tissues under the diffusion limitation. The model is based on the reaction–diffusion equations describing the concentration of uninfected cells, exposed cells (infected but still not shedding the virus), virus-shedding cells, and free virus. We obtain the expressions for the viral replication number, which determines the condition for spatial infection progression, and for the final concentration of uninfected cells. We determine analytically the speed of spatial infection propagation and validate it numerically. We calibrate the model to recent experimental data on SARS-CoV-2 Delta and Omicron variant replication in human nasal epithelial cells. In the case of competition of two virus variants in the same cell culture, the variant with larger individual spreading speed wins the competition and eliminates another one. These results give new insights concerning the emergence of new variants and their spread in the population.

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Mathematical Modeling of Thrombin Generation and Wave Propagation: From Simple to Complex Models and Backwards

Cited by 2 publications

References 66 publications

Patient-Specific Modelling of Blood Coagulation

Patient-Specific Modelling of Blood Coagulation

Competition of SARS-CoV-2 Variants in Cell Culture and Tissue: Wins the Fastest Viral Autowave

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