Publication: A mathematical model of blood coagulation induced by activation sources
Loading...
Full text at PDC
Publication Date
2009-09
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Institute of Mathematical Sciences
Citations
Exportar
Abstract
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.
Description
UCM subjects
Unesco subjects
Keywords
Citation
F. I. Ataullakhanov and G. T. Guria, Spatial aspects of the dynamics of blood coagulation: I. Hypothesis, Biophysics, 39 (1994), 91–97.
F. I. Ataullakhanov, G. T. Guria and A. Yu. Safroshkina, Spatial aspects of the dynamics of blood coagulation: II. Phenomenological model, Biophysics, 39 (1994), 99–108.
F. I. Ataullakhanov, G. Th. Guria, V. I. Sarbash and R. I. Volkova, Spatiotemporal dynamics of clotting and pattern formation in human blood, Biochim Biophys Acta., 27 (1998), 453–468.
J. M. Ball and J. Carr, The discrete coagulation-fragmentation equations; existence, uniqueness, and density conservation, J. Statist. Phys., 61 (1990), 203–234.
D. Basmadjian, M. V. Sefton and S. A. Baldwin, Coagulation on biomaterials in flowing blood: Some theoretical considerations: Review, Biomaterials, 18 (1997), 1511–1522.
E. Beltrami and J. Jesty, Mathematical analysis of activation thresholds in enzyme-catalyzed positive feedbacks: Application to the feedbacks of blood coagulation, Proc. Natl. Acad. Sci. USA., 92 (1995), 8744–8748.
S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys., 15 (1943), 1–89.
S. C. Davies, J. R. King and J. A. D. Wattis, The Smoluchowski coagulation equations with continuous injection, J. Phys. A: Math. Gen., 32 (1999), 7745–7763.
M. De Cicco, The prothrombotic state in cancer: pathogenic mechanisms, Crit. Rev. Oncol. Hematol., 50 (2004), 187–196.
M. Doi and S. F. Edwards, “The Theory of Polymer Dynamics,” Oxford, 1994.
P. van Dongen and M. H. Ernst, Pre- and post-gel size distributions in (ir)reversible polymerisation, J. Phys. A: Math. Gen., 16 (1983), L327–L332.
P. G. J. van Dongen and M. H. Ernst, Kinetics of reversible polymerization, J. Stat. Phys., 37 (1984), 301–324.
C. T. Esmon, Crosstalk between inflammation and thrombosis, Maturitas, 47 (2004), 305–314.
J. D. Ferry, “Viscoelastic Properties of Polymers,” John Wiley & Sons, Canada, 1980.
S. K. Friedlander, “Smoke, Dust, and Haze: Fundamentals of Aerosol Dynamics,” Oxford, 2000.
A. Gierer and H. Meinhardt. A theory of biological pattern formation, Kybernetik ,12 (1972), 30–39.
K. Gregory and D. Basmadjian, An analysis of the contact phase of blood coagulation: Effects of shear rate and surface are intertwined, Ann. Biomed. Eng., 22 (1994), 184–193.
G. T. Guria, “Macroscopic Structures Formation in Blood Dynamics,” Doctoral thesis, Moscow, 2002.
R. D. Guy, A. L. Fogelson and J. P. Keener, Fibrin gel formation in a shear flow, Math. Med. Biol., 24 (2007), 111–130.
N. K. Halder, B. K. Chatterjee and S. C. Roy, The change of viscosity with concentration of suspended particles and a new concept of gelation, J. Phys.: Condens. Matter, 9 (1997), 8873–8878.
M. A. Herrero and M. R. Rodrigo, Remarks on accessible steady states for some coagulationfragmentation systems, Discrete Contin. Dyn. Syst. A, 17 (2007), 541–552.
M. F. Hockin, K. C. Jones, S. J. Everse and K. G. Mann, A model for the stoichiometric regulation of blood coagulation, J Biol Chem., 277 (2002), 18322–18333.
M. J. Johnson, I. D. Walker, M. W. Sproule and J. Conkie, Abnormal coagulation and deep venous thrombosis in patients with advanced cancer, Clin. Lab. Haematol., 21 (1999), 51–54.
M. Kaibara, Rheology of blood coagulation, Biorheology, 33 (1996), 101–117.
F. Leyvraz and H. R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys.A: Math. Gen., 14 (1981), 3389–3405.
J. A. Liggett, “Fluid Mechanics,” Mc Graw-Hill (1994)
R. J. Luddington, Thrombelastography/thromboelastometry, Clin. Lab. Haem., 27 (2005), 81–90.
K. G. Mann, K. Brummel-Ziedins, T. Orfeo and S. Butenas, Models of blood coagulation, Blood Cells Mol. Dis., 36 (2006), 108–117.
J. E. Martin and D. Adolf, The Sol-Gel transition in chemical gels, Ann. Rev.Phys. Chem., 42 (1991), 311–339.
J. B. McLeod, On an infinite set of nonlinear differential equations, Q. J. Math., 13 (1962), 119–128.
H. Meinhardt, “Models of Biological Pattern Formation,” Academic Press, Manchester, UK (1982)
D. Repke, C. H. Gemmell, A. Guha, V. T. Turitto, G. J. Broze and Y. Nemerson, Hemophilia as a defect of the tissue factor pathway of blood coagulation: Effect of factors VIII and IX on factor X activation in a continuous-flow reactor, Proc. Natl. Acad. Sci. U S A., 87 (1990), 7623–7627.
F. R. Rickles and A. Falanga, Molecular basis for the relationship between thrombosis and cancer, Thromb. Res., 102 (2001), V215–V224.
P. Sandkuhler, J. Sefcik and M. Morbidelli, Kinetics of gel formation in dilute dispersions with strong attractive particle interactions, Adv. Coll. Interf. Sci., 108–109 (2004), 133–143.
M. von Smoluchowski, Versuch einer mathematischen theorie der Koagulationskinetik kolloider Lösungen, Z. Phys. Chem., 92 (1917), 124–168.
D. Stauffer, Gelation in concentrated critically branched polymer solutions. Percolation scaling theory of intramolecular bond cycles, J. Chem. Soc., Faraday Trans. 2, 72 (1976), 1354–1364.
D. Stauffer, A. Coniglio and M. Adam, Gelation and critical phenomena, Adv. Polym. Sci., 44 (1982), 103–158.
W. H. Stockmayer, Theory of molecular size distribution and gel formation in branched-chain polymers, Jour. Chem. Phys., 11 (1943), 45–55.
K. V. Tyurin and M. A. Khanin, Hemostasis as an optimal system, Math. Biosci., 204 (2006), 167–184.
P. Wiltzius, G. Dietler, W. Känzig, A. Häberli and P. W. Straub, Fibrin polymerization studied by static and dynamic light-scattering as a function of fibrinopeptide A release, Biopolymers, 21 (1982), 2205–2223.
P. Wiltzius, G. Dietler, W. Känzig, V. Hoffman, A. Häberli and P. W. Straub, Fibrin aggregation before sol-gel transition, Biophys. J., 38 (1982), 123–132.
R. F. A. Zwaal and H. C. Hemker (ed.) “Blood Coagulation,” Elsevier, 1986.