February  2009, 25(1): 175-194. doi: 10.3934/dcds.2009.25.175

A mathematical model of blood coagulation induced by activation sources

1. 

National Research Centre for Haematology, 125167 Moscow, Russian Federation, Russian Federation

2. 

Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense, 28040 Madrid, Spain

Received  August 2007 Revised  February 2008 Published  June 2009

In this work a mathematical model for blood coagulation induced by an activator source is presented. Blood coagulation is viewed as a process resulting in fibrin polymerization, which is considered as the first step towards thrombi formation. We derive and study a system for the first moments of the polymer concentrations and the activating variables. Analysis of this last model allows us to identify parameter regions which could lead to thrombi formation, both in homeostatic and pathological situations.
Citation: Georgy Th. Guria, Miguel A. Herrero, Ksenia E. Zlobina. A mathematical model of blood coagulation induced by activation sources. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 175-194. doi: 10.3934/dcds.2009.25.175
[1]

Grzegorz Karch, Kanako Suzuki, Jacek Zienkiewicz. Finite-time blowup of solutions to some activator-inhibitor systems. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4997-5010. doi: 10.3934/dcds.2016016

[2]

Marie Henry. Singular limit of an activator-inhibitor type model. Networks and Heterogeneous Media, 2012, 7 (4) : 781-803. doi: 10.3934/nhm.2012.7.781

[3]

Huiqiang Jiang. Global existence of solutions of an activator-inhibitor system. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 737-751. doi: 10.3934/dcds.2006.14.737

[4]

Shanshan Chen, Junping Shi, Guohong Zhang. Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 1843-1866. doi: 10.3934/dcdsb.2020042

[5]

Shaohua Chen. Some properties for the solutions of a general activator-inhibitor model. Communications on Pure and Applied Analysis, 2006, 5 (4) : 919-928. doi: 10.3934/cpaa.2006.5.919

[6]

Xiaoli Wang, Guohong Zhang. Bifurcation analysis of a general activator-inhibitor model with nonlocal dispersal. Discrete and Continuous Dynamical Systems - B, 2021, 26 (8) : 4459-4477. doi: 10.3934/dcdsb.2020295

[7]

Victor Ogesa Juma, Leif Dehmelt, Stéphanie Portet, Anotida Madzvamuse. A mathematical analysis of an activator-inhibitor Rho GTPase model. Journal of Computational Dynamics, 2022, 9 (2) : 133-158. doi: 10.3934/jcd.2021024

[8]

Miguel A. Herrero, Marianito R. Rodrigo. Remarks on accessible steady states for some coagulation-fragmentation systems. Discrete and Continuous Dynamical Systems, 2007, 17 (3) : 541-552. doi: 10.3934/dcds.2007.17.541

[9]

Maxime Breden. Applications of improved duality lemmas to the discrete coagulation-fragmentation equations with diffusion. Kinetic and Related Models, 2018, 11 (2) : 279-301. doi: 10.3934/krm.2018014

[10]

Jacek Banasiak. Blow-up of solutions to some coagulation and fragmentation equations with growth. Conference Publications, 2011, 2011 (Special) : 126-134. doi: 10.3934/proc.2011.2011.126

[11]

Jacek Banasiak. Global solutions of continuous coagulation–fragmentation equations with unbounded coefficients. Discrete and Continuous Dynamical Systems - S, 2020, 13 (12) : 3319-3334. doi: 10.3934/dcdss.2020161

[12]

Iñigo U. Erneta. Well-posedness for boundary value problems for coagulation-fragmentation equations. Kinetic and Related Models, 2020, 13 (4) : 815-835. doi: 10.3934/krm.2020028

[13]

Ankik Kumar Giri. On the uniqueness for coagulation and multiple fragmentation equation. Kinetic and Related Models, 2013, 6 (3) : 589-599. doi: 10.3934/krm.2013.6.589

[14]

Jacek Banasiak. Transport processes with coagulation and strong fragmentation. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 445-472. doi: 10.3934/dcdsb.2012.17.445

[15]

Adélia Sequeira, Rafael F. Santos, Tomáš Bodnár. Blood coagulation dynamics: mathematical modeling and stability results. Mathematical Biosciences & Engineering, 2011, 8 (2) : 425-443. doi: 10.3934/mbe.2011.8.425

[16]

Jacek Banasiak, Wilson Lamb. Coagulation, fragmentation and growth processes in a size structured population. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 563-585. doi: 10.3934/dcdsb.2009.11.563

[17]

Pierre Degond, Maximilian Engel. Numerical approximation of a coagulation-fragmentation model for animal group size statistics. Networks and Heterogeneous Media, 2017, 12 (2) : 217-243. doi: 10.3934/nhm.2017009

[18]

Jacek Banasiak, Luke O. Joel, Sergey Shindin. The discrete unbounded coagulation-fragmentation equation with growth, decay and sedimentation. Kinetic and Related Models, 2019, 12 (5) : 1069-1092. doi: 10.3934/krm.2019040

[19]

Wilson Lamb, Adam McBride, Louise Smith. Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5177-5187. doi: 10.3934/dcds.2013.33.5177

[20]

Prasanta Kumar Barik, Ankik Kumar Giri. A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation. Kinetic and Related Models, 2018, 11 (5) : 1125-1138. doi: 10.3934/krm.2018043

2021 Impact Factor: 1.588

Metrics

  • PDF downloads (153)
  • HTML views (0)
  • Cited by (7)

[Back to Top]