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Mathematical Model of Fibrin Polymerization

Published online by Cambridge University Press:  15 June 2011

A.I. Lobanov ,
A.V. Nikolaev  and
T.K. Starozhilova
A.I. Lobanov*
Affiliation:
Chair of Applied Mathematics, Moscow Institute of Physics and Technology, Moscow, Russia
A.V. Nikolaev
Affiliation:
Goldansky Department, Institute of Chemical Physics RAS, Moscow, Russia
T.K. Starozhilova
Affiliation:
Chair of Applied Mathematics, Moscow Institute of Physics and Technology, Moscow, Russia
*
⋆Corresponding author. E-mail: [email protected]
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Abstract

Blood clotting system (BCS) modelling is an important issue with a plenty of applications in medicine and biophysics. The BCS main function is to form a localized clot at the site of injury preventing blood loss. Mutual influence of fibrin clot consisting mainly of fibrin polymer gel and blood flow is an important factor for BCS to function properly. The process of fibrin polymer mesh formation has not adequately been described by current mathematical models. That is why it is not possible to define the borders of growing clot and model its interaction with a blood flow. This paper main goal is to propose physically well-founded mathematical model of fibrin polymerization and gelation. The proposed model defines the total length of fibrin polymer fibers in the unit volume, determines a position of the border between gel and liquid and allows to evaluate the permeability of growing gel. Without significant structural changes the proposed model could be modified to include the blood shear rate influence on the fibrin polymerization and gelation.

Keywords

fibrinclottingpolymerizationgelation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 7: Mathematical modeling in biomedical applications , 2011 , pp. 55 - 69
Copyright
© EDP Sciences, 2011

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References

World health report 2004 statistical annex [Electronic resource]: Annex Table 2: Deaths by cause, sex and mortality stratum in regions, estimates for 2002. World Health Organization. http://www.who.int/whr/2004/annex/en/index.html.
M., Anand, K., Rajagopal, K.R., Rajagopal A model incorporating some of the mechanical and biochemical factors underlying clot formation and dissolution in flowing blood. J. Theor. Med. 5 (2003), 183–218. Google Scholar
F.I., Ataullakhanov, G.T., Guriia, A.Iu., Safroshkina Spatial aspects of the dynamics of blood coagulation. II. Phenomenological model. Biofizika, 39 (1994) 97–104 (in Russian). Google Scholar
F.I., Ataullakhanov, V.I., Zarnitsina, et al. Spatio-temporal dynamics of blood coagulation and pattern formation. A theoretical approach. Int. J. Bifurc. Chaos, 12 (2002), No. 9, 1985–2002. Google Scholar
F.I., Ataullakhanov, G.T., Guriia. Spatial aspects of the dynamics of blood coagulation. I. Hypothesis Biofizika, 39 (1994), 89–96 (in Russian). Google Scholar
F.I., Ataullakhanov, R.I., Volkova, et al. Spatial aspects of blood coagulation dynamics. III. Growth of clots in vitro. Biofizika, 40 (1995) 1320–1328 (in Russian). Google Scholar
B., Blomback, K., Carlsson, et al. Fibrin in human plasma: gel architectures governed by rate and nature of fibrinogen activation. Thromb Res., 75 (1994), No. 5, 521–538. Google Scholar
M.E., Carr Jr., C.L., Hardin. Fibrin has larger pores when formed in the presence of erythrocytes Amer. J. Physiol., 253 (1987), No. 2, 1069–1073. Google Scholar
M.E., Carr Jr, J., Hermans. Size and density of fibrin fibers from turbidity. Macromolecules, 11 (1978), No. 1, 46–50. Google Scholar
C.E. Dempfle, P.N. Knoebl. Blood coagulation and inflammation in critical illness the importance of the protein C pathway. UNI-MED, Bremen, 2008.
S.L., Diamond. Engineering design of optimal strategies for blood clot dissolution. Ann. Rev. Biomed. Engrg, 1 (1999) 427–461. Google Scholar
M. Doi, S.F. Edwards. Theory of polymer dynamics. Acad. Press, New York, 1986.
E.A., Ermakova, M.A., Panteleev, E.E., Shnol. Blood coagulation and propagation of autowaves in flow. Pathophysiol. Haemost. Thromb., 34 (2005), No. 2-3, 135–142. Google Scholar
P.-G. de Gennes. Scaling concepts in polymer physics. Cornell, London, 1979.
R.R., Hantgan, J., Hermans. Assembly of fibrin. A light scattering study. J. Biol. Chem., 254 (1979) No. 22, 11272-11281. Google Scholar
R., Kita, A., Takahashi, et al. Formation of fibrin gel in fibrinogen-thrombin system: static and dynamic light scattering study. Biomacromolecules, 3 (2002), No. 5, 1013–1020. Google Scholar
R., Marchi, M., Meyer, et al. Biophysical characterization of fibrinogen Caracas I with an Aalpha-chain truncation at Aalpha-466 Ser: identification of the mutation and biophysical characterization of properties of clots from plasma and purified fibrinogen Blood Coagul. Fibrinolys., 15 (2004), No. 4, 285–293. Google Scholar
Marx, G.. Simulating fibrin clotting time. Med. Biol. Engrg. Comput., 44 (2006), 79–85. CrossRefGoogle ScholarPubMed
Medved’, L, Ugarova, T, et al. Electron microscope investigation of the early stages of fibrin assembly. Twisted protofibrils and fibers J. Mol. Biol., 216 (1990), No. 3, 503–509. CrossRefGoogle ScholarPubMed
M.W., Mosesson, J.P., DiOrio, et al. Evidence for a second type of fibril branch point in fibrin polymer networks, the trimolecular junction Blood, 82 (1993), No. 5, 1517–1521. Google Scholar
M.W., Mosesson. Fibrinogen and fibrin structure and functions. J. Thromb. Haemost., 3 (2005), No. 8, 1894–1904. Google Scholar
M.A., Panteleev, M.V., Ovanesov, et al. Spatial propagation and localization of blood coagulation are regulated by intrinsic and protein C pathways, respectively. Biophys. J. 90 (2006), No. 5, 1489–1500. Google Scholar
G.G. Tsipkin. Flows with phase transitions in porous media. Fizmatlit, Moscow, 2009 (in Russian).
J.W., Weisel. Fibrinogen and fibrin. Adv. Protein Chem., 70 (2005), 247–299. Google Scholar
J.W., Weisel, C., Nagaswami, L., Makowski. Twisting of fibrin fibers limits their radial growth. Proc. Nat. Acad. Sci. USA, 84 (1987), No. 24, 8991–8995. Google Scholar
D.M. Zubairov. Molecular basis of clotting and thrombus formation. Fen Press, Kazan, 2000 (in Russian).