Startseite Mathematical modelling of platelet rich plasma clotting. Pointwise unified model
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Mathematical modelling of platelet rich plasma clotting. Pointwise unified model

  • Anna A. Andreeva , Mohan Anand , Alexey I. Lobanov EMAIL logo , Andrey V. Nikolaev , Mikhail A. Panteleev und Modepalli Susree
Veröffentlicht/Copyright: 31. Oktober 2018

Abstract

The mechanistic modelling of blood clotting and fibrin-polymer mesh formation is of significant value for medical and biophysics applications. This paper presents a combination of two pointwise kinetic models represented by system of ODEs. One of them represents the reaction dynamics of clotting factors including the role of the platelet membranes. The second one describes the fibrin-polymer formation as a multistage polymerization process with a sol-gel transition at the final stage. Complex-value second order Rosenbrock method (CROS) is employed for the computational experiments. A sensitivity analysis method built into the computational scheme helps clarify non-evident dependencies in the exhaustive system of ODEs. The unified model was primarily verified using conditions of factor VII deficiency. The model, however requires a significant effort to be tested against experimental data available.

MSC 2010: 65L04; 65L12; 92C05; 92C40; 92C45; 92C50
  1. Funding: We thank the Department of Science and Technology for financial support (grant No. INT/RUS/RFBR/P-180). This work was supported within frameworks of the state task for ICP RAS 0082-2014-0001. State registration No. AAAA-A17-117040610310-6. This work was also supported by RFBR project No. 15-51-45109.

References

[1] S. S. Ahmad, R. Rawala-Sheikh, and P. Walsh, Comparative interactions of factor IX and factor IXa with human platelets. J. Biological Chemistry264 (1989), No. 6, 3244-3251.10.1016/S0021-9258(18)94058-5Suche in Google Scholar

[2] S. S. Ahmad, J. M. Scandura, and P. N. Walsh, Structural and functional characterization of platelet receptor-mediated factor viii binding. J. Biological Chemistry275 (2000), No. 17, 13071-13081.10.1074/jbc.275.17.13071Suche in Google Scholar

[3] M. Anand, K. Rajagopal, and K. R. Rajagopal, A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency. J. Theor. Biology253 (2008), No. 4, 725-738.10.1016/j.jtbi.2008.04.015Suche in Google Scholar

[4] F. I. Ataullakhanov, E. S. Lobanova, O. L. Morozova, E. E. Shnol, E. A. Ermakova, A. A. Butylin, and A. N. Zaikin, Intricate regimes of propagation of an excitation and self-organization in the blood clotting model. Physics-Uspekhi50 (2007), No. 1, 79-94.10.1070/PU2007v050n01ABEH006156Suche in Google Scholar

[5] F. I. Ataullakhanov, V. I. Zarnitsyna, A. Yu. Kondratovich, E. S. Lobanova, and V. I. Sarbash, A new class of stopping self- sustained waves: a factor determining the spatial dynamics of blood coagulation. Physics-Uspekhi45 (2002), No. 6, 619-636.10.1070/PU2002v045n06ABEH001090Suche in Google Scholar

[6] J. D. Cooper and A. K. Ritchey, Response to treatment and adverse events associated with use of recombinant activated factor VII in children: a retrospective cohort study. Ther. Adv. Drug Saf. (2017), 51-59.10.1177/2042098616673991Suche in Google Scholar

[7] M. F. Hockin, K. C. Jones, S. J. Everse, and K. G. Mann, A model for the stoichiometric regulation of blood coagulation. J. Biological Chemistry277 (2002), No. 21, 18322-18333.10.1074/jbc.M201173200Suche in Google Scholar

[8] S. Krishnaswamy, K. C. Jones, K. G. Mann, and G. Kenneth, Prothrombinase complex assembly. Kinetic mechanism of enzyme assembly on phospholipid vesicles. J. Biological Chemistry263 (1988), No. 8, 3823-3834.10.1016/S0021-9258(18)68999-9Suche in Google Scholar

[9] A. L. Kuharsky and A. L. Fogelson, Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition. Biophys. J.80 (2001), No. 3, 1050-1074.10.1016/S0006-3495(01)76085-7Suche in Google Scholar

[10] J. H. Lawson, S. Butenas, and N. Ribarik, Complex-dependent inhibition of factor VIIa by antithrombin III and heparin. J. Biological Chemistry268 (1993), No. 2, 767-770.10.1016/S0021-9258(18)53998-3Suche in Google Scholar

[11] A. I. Lobanov, A. V. Nikolaev, and T. K. Starozhilova, Mathematical model of fibrin polymerization. Math. Model. Nat. Phe- nom.7 (2011), No. 6, 55-69.10.1051/mmnp/20116705Suche in Google Scholar

[12] K. G. Mann, M. E. Nesheim, W. R. Church, P. Haley, and S. Krishnaswamy, Surface-dependent reactions of the vitamin K-dependent enzyme complexes. Blood76 (1990), No. 1, 1-16.10.1182/blood.V76.1.1.1Suche in Google Scholar

[13] G. Marx and A. Blankenfeld, Kinetic and mechanical parameters of pure and cryoprecipitate fibrin. Blood Coagul. Fibrinolysis4 (1993), No. 1, 73-78.10.1097/00001721-199302000-00012Suche in Google Scholar

[14] P. de Moerloose, J. F. Schved, and D. Nugent, Rare coagulation disorders: fibrinogen, factor VII and factor XIII. Haemophilia22 (2016), No. 5, 61-65.10.1111/hae.12965Suche in Google Scholar PubMed

[15] D. M. Monroe, M. Hoffman, and H. R. Roberts, Platelets and thrombin generation. Review. Arterioscler. Thromb. Vasc. Biol.22 (2002), No. 9, 1381-1389.10.1161/01.ATV.0000031340.68494.34Suche in Google Scholar PubMed

[16] P. P. Naidu and M. Anand, Importance of VIIIa inactivation in a mathematical model for the formation, growth, and lysis of clots. Math. Modelling Natur. Phenom.9 (2014), No. 6, 17-33.10.1051/mmnp/20149603Suche in Google Scholar

[17] S. I. Obydenny, A. N. Sveshnikova, F. I. Ataullakhanov, and M. A. Panteleev, Dynamics of calcium spiking, mitochondrial collapse and phosphatidylserine exposure in platelet subpopulation during activation. J. Thrombosis Haemostasis14 (2016), No. 9, 1867-1881.10.1111/jth.13395Suche in Google Scholar PubMed

[18] E. S. Oran and J. P. Boris, Numerical Simulation of Reactive Flow. Elsivier Science Publ., Amsterdam, 1987.Suche in Google Scholar

[19] M. A. Panteleev, M. V. Ovanesov, D. A. Kireev, A. M. Shibeko, E. I. Sinauridze, N. M. Ananyeva, A. A. Butylin, E. L. Saenko, and F. I. Ataullakhanov, Spatial propagation and localization of blood coagulation are regulated by intrinsic and protein C pathways, respectively. Biophys J.90 (2006), No. 5, 1489-1500.10.1529/biophysj.105.069062Suche in Google Scholar PubMed PubMed Central

[20] M. A. Panteleev, M. V. Ovanesov, A. M. Shibeko, A. A. Tokarev, E. I. Sinauridze, and F. I. Ataullakhanov, Computer simulation study of blood coagulation control. Mathematical models and methods in biology and medicine. Bedlewo, Poland (2005), 12.Suche in Google Scholar

[21] N. A. Podoplelova, A. N. Sveshnikova, et al., Hysteresis-like binding of coagulation factors X/Xa to procoagulant activated platelets and phospholipids results from multistep association and membrane-dependent multimerization. Biochim. Biophys. Acta1858 (2016), No. 6, 1216-1227.10.1016/j.bbamem.2016.02.008Suche in Google Scholar PubMed

[22] S. K. Ramdass, K. P. Loh, and L. M. Howard, Thrombosis in a bleeding disorder: case of thromboembolism in factor VII deficiency. Clin. Case Rep.5 (2017), No. 3, 277-279.10.1002/ccr3.836Suche in Google Scholar PubMed PubMed Central

[23] A. S. Rukhlenko, K. E. Zlobina, and G. Th. Guria, Hydrodynamical activation of blood coagulation in stenosed vessels. Theoretical analysis. Computer Research and Modelling4 (2012), No. 1, 155-183 (in Russian).10.20537/2076-7633-2012-4-1-155-183Suche in Google Scholar

[24] J. M. Scandura, S. S. Ahmad, and P. N. Walsh, A binding site expressed on the surface of activated human platelets is shared by factor X and prothrombin. Biochemistry35 (1996), No. 27, 8890-8902.10.1021/bi9525029Suche in Google Scholar

[25] P. O. Sevenet, D. A. Kaczor, and F. Depasse, Factor VII Deficiency. Clin. Appl. Thromb. Hemost. (2016) DOI: 10.1177/107602961667025.Suche in Google Scholar

[26] A. M. Shibeko, M. A. Panteleev, and F. I. Ataullakhanov, Binding of fibrinogen to fibrin as a regulator of fibrin polymerization initiation. Modelling of Blood Diseases. Lyon, France, 2007.Suche in Google Scholar

[27] A. M. Shibeko, Numerical modelling of fibrin clot formation and influence of blood flow. PhD. Thesys. Moscow, 2009 (in Russian).Suche in Google Scholar

[28] P. D. Shirkov, Optimal dissipative schemes with complex coeflcients for stiff ODE systems. Math. Modelling4 (1992), No. 8, 47-57 (in Russian).Suche in Google Scholar

[29] T. Skowerski, K. Bańska-Kisiel, P. Grzywocz, M. Skowerski, and Z. Gąsior, Pulmonary embolism in a patient with mild fac- tor VII deficiency after administration of recombinant activated factor VII during a urological procedure. Pol. Arch. Intern. Med.127 (2017), No. 4, 285-286.10.20452/pamw.4016Suche in Google Scholar

[30] S. J. Stanworth, J. Birchall, C. J. Doree, and C. Hyde, Recombinant factor VIIa for the prevention and treatment of bleed- ing in patients without haemophilia. Cochrane Database Syst Rev. (2007)(2):CD005011. Review. Update in: Cochrane Database Syst Rev. (2011)(2):CD005011.Suche in Google Scholar

[31] M. Susree and M. Anand, A mathematical model for in vitro coagulation of blood: role of platelet count and inhibition. Sãdhanã 42 (2017), No. 3, 291-305.Suche in Google Scholar

[32] A. N. Sveshnikova, A. V. Balatskiy, A. S. Demianova, T. O. Shepelyuk, S. S. Shakhidzhanov, M. N. Balatskaya, A. V. Pichugin, F. I. Ataullakhanov, and M. A. Panteleev, Systems biology insights into the meaning of the platelet’s dual- receptor thrombin signaling. J. Thromb. Haemost.14 (2016), No. 10, 2045-2057.10.1111/jth.13442Suche in Google Scholar

[33] S. W. Tam and T. C. Detwiler, Binding of thrombin to human platelet plasma membranes. Biochim. Biophys. Acta543 (1978), No. 2, 194-201.10.1016/0304-4165(78)90064-8Suche in Google Scholar

[34] J. W. Weisel and C. Nagaswami, Computer modelling of fibrin polymerization kinetics correlated with electron microscope and turbidity observations: clot structure and assembly are kinetically controlled. Biophys. J.63 (1992), No. 1, 11-28.Suche in Google Scholar

[35] E. M. Wiebe, A. R. Stafford, J. C. Fredenburgh, and J. I. Weitz, Enzyme catalysis and regulation: Mechanism of catalysis of inhibition of factor IXa by antithrombin in the presence of heparin or pentasacharide. J. Biological Chemistry278 (2003), No. 37, 35767-35774.10.1074/jbc.M304803200Suche in Google Scholar PubMed

[36] V. I. Zarnitsina, F. I. Ataullakhanov, A. I. Lobanov, and O. L. Morozova, Dynamics of spatially nonuniform patterning in the model of blood coagulation. Chaos11 (2001), No. 1, 57-70.10.1063/1.1345728Suche in Google Scholar PubMed

Received: 2017-11-13
Revised: 2018-06-19
Accepted: 2018-08-21
Published Online: 2018-10-31
Published in Print: 2018-11-27

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 9.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/rnam-2018-0022/pdf
Button zum nach oben scrollen