American Institute of Mathematical Sciences

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

A mathematical model of blood coagulation induced by activation sources

Georgy Th. Guria 1, , Miguel A. Herrero 2, and  Ksenia E. Zlobina 1,

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.
Keywords: fibrin polymerization, activator-inhibitor systems, Aggregation-fragmentation equations, blood coagulation..
Mathematics Subject Classification: Primary: 34A34, 92B99; Secondary: 92B0.
Citation: Georgy Th. Guria, Miguel A. Herrero, Ksenia E. Zlobina. A mathematical model of blood coagulation induced by activation sources. Discrete & Continuous Dynamical Systems - A, 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 & Continuous Dynamical Systems - A, 2016, 36 (9) : 4997-5010. doi: 10.3934/dcds.2016016
[2]

Marie Henry. Singular limit of an activator-inhibitor type model. Networks & 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 & Continuous Dynamical Systems - A, 2006, 14 (4) : 737-751. doi: 10.3934/dcds.2006.14.737
[4]

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

Miguel A. Herrero, Marianito R. Rodrigo. Remarks on accessible steady states for some coagulation-fragmentation systems. Discrete & Continuous Dynamical Systems - A, 2007, 17 (3) : 541-552. doi: 10.3934/dcds.2007.17.541
[6]

Maxime Breden. Applications of improved duality lemmas to the discrete coagulation-fragmentation equations with diffusion. Kinetic & Related Models, 2018, 11 (2) : 279-301. doi: 10.3934/krm.2018014
[7]

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
[8]

Ankik Kumar Giri. On the uniqueness for coagulation and multiple fragmentation equation. Kinetic & Related Models, 2013, 6 (3) : 589-599. doi: 10.3934/krm.2013.6.589
[9]

Jacek Banasiak. Transport processes with coagulation and strong fragmentation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 445-472. doi: 10.3934/dcdsb.2012.17.445
[10]

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

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
[12]

Pierre Degond, Maximilian Engel. Numerical approximation of a coagulation-fragmentation model for animal group size statistics. Networks & Heterogeneous Media, 2017, 12 (2) : 217-243. doi: 10.3934/nhm.2017009
[13]

Wilson Lamb, Adam McBride, Louise Smith. Coagulation and fragmentation processes with evolving size and shape profiles: A semigroup approach. Discrete & Continuous Dynamical Systems - A, 2013, 33 (11&12) : 5177-5187. doi: 10.3934/dcds.2013.33.5177
[14]

Jacek Banasiak, Luke O. Joel, Sergey Shindin. The discrete unbounded coagulation-fragmentation equation with growth, decay and sedimentation. Kinetic & Related Models, 2019, 12 (5) : 1069-1092. doi: 10.3934/krm.2019040
[15]

Prasanta Kumar Barik, Ankik Kumar Giri. A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation. Kinetic & Related Models, 2018, 11 (5) : 1125-1138. doi: 10.3934/krm.2018043
[16]

Prasanta Kumar Barik. Existence of mass-conserving weak solutions to the singular coagulation equation with multiple fragmentation. Evolution Equations & Control Theory, 2019, 0 (0) : 0-0. doi: 10.3934/eect.2020012
[17]

Marie Doumic, Miguel Escobedo. Time asymptotics for a critical case in fragmentation and growth-fragmentation equations. Kinetic & Related Models, 2016, 9 (2) : 251-297. doi: 10.3934/krm.2016.9.251
[18]

Yuming Paul Zhang. On a class of diffusion-aggregation equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (2) : 907-932. doi: 10.3934/dcds.2020066
[19]

Weronika Biedrzycka, Marta Tyran-Kamińska. Self-similar solutions of fragmentation equations revisited. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 13-27. doi: 10.3934/dcdsb.2018002
[20]

Shin-Ichiro Ei, Hirofumi Izuhara, Masayasu Mimura. Infinite dimensional relaxation oscillation in aggregation-growth systems. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1859-1887. doi: 10.3934/dcdsb.2012.17.1859

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (15)
  • HTML views (0)
  • Cited by (4)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences