Free Access
Issue
Math. Model. Nat. Phenom.
Volume 11, Number 6, 2016
Pharmacokinetics-Pharmacodynamics
Page(s) 28 - 44
DOI https://doi.org/10.1051/mmnp/201611603
Published online 04 January 2017
  1. M. Anand, K. Rajagopal, K. R. Rajagopal. A model for the formation and lysis of blood clots. Pathophysiology of haemostasis and thrombosis 34.2-3 (2005), 109–120. [CrossRef] [PubMed] [Google Scholar]
  2. J. Ansell, J. Hirsh, E. Hylek, A. Jacobson, M. Crowther, G. Palareti. Pharmacology and management of the vitamin K antagonists: American College of Chest Physicians evidence-based clinical practice guidelines. Chest Journal, 133 (2008), 160S–198S. [CrossRef] [PubMed] [Google Scholar]
  3. J. P. Antovic, M. Blombäck. Essential Guide to Blood Coagulation. Wiley Online Library (2013). [Google Scholar]
  4. N. Bessonov, E. Babushkina, S.F. Golovashchenko, A. Tosenberger. F. Ataullakhanov, M. Panteleev, A. Tokarev, V. Volpert. Numerical modelling of cell distribution in blood flow. Math. Model. Nat. Phenom., 9 (2014), no. 6, 69–84. [CrossRef] [MathSciNet] [Google Scholar]
  5. N. Bessonov, A. Sequeira, S. Simakov, Yu. Vassilevski, V. Volpert. Methods of blood flow modelling. Math. Model. Nat. Phenom., 11 (2016), no. 1, 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bouchnita, A. Tosenberger, V. Volpert. On the regimes of blood coagulation. Applied Mathematics Letters 51 (2016), 74–79. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. J. Fasco, L. M. Principe, W. A. Walsh, P. A. Friedman. Warfarin inhibition of vitamin K 2, 3-epoxide reductase in rat liver microsomes. Biochemistry, 22(24) (1983), 5655–5660. [CrossRef] [PubMed] [Google Scholar]
  8. N. Filipovic, M. Kojic, A. Tsuda. Modelling thrombosis using dissipative particle dynamics method. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 366(1879) (2008), 3265–3279. [CrossRef] [Google Scholar]
  9. A. L. Fogelson, N. Tania. Coagulation under flow: the influence of flow-mediated transport on the initiation and inhibition of coagulation. Pathophysiology of haemostasis and thrombosis, 34(2-3) (2005), 91–108. [CrossRef] [PubMed] [Google Scholar]
  10. Y. V. Krasotkina, E. I. Sinauridze, F. I. Ataullakhanov. Spatiotemporal dynamics of fibrin formation and spreading of active thrombin entering non-recalcified plasma by diffusion. Biochimica et Biophysica Acta (BBA)-General Subjects, 1474(3) (2000), 337–345. [Google Scholar]
  11. S. Kumar, J. R. M. Haigh, G. Tate, M. Boothby, D. N. Joanes, J. A. Davies, B. E. Roberts, M. P. Feely. Effect of warfarin on plasma concentrations of vitamin K dependent coagulation factors in patients with stable control and monitored compliance. British journal of haematology, 74(1) (1990), 82–85. [CrossRef] [PubMed] [Google Scholar]
  12. A. Hensen, E. A. Loeliger. Antithrombin III. Its metabolism and its function in blood coagulation. Thrombosis et diathesis haemorrhagica 83 (1962): 1–1. [Google Scholar]
  13. J. Hirsh, J. E. Dalen, D. R. Anderson, L. Poller, H. Bussey, J. Ansell, D. Deykin. Oral anticoagulants: mechanism of action, clinical effectiveness, and optimal therapeutic range. Chest Journal, 119 (2001), 8S–21S. [CrossRef] [Google Scholar]
  14. J. Hirsh, T.E. Warkentin, S. G. Shaughnessy, S.S. Anand, J. L. Halperin, R. Raschke, C. Granger, E. M. Ohman, J. E. Dalen. Heparin and low-molecular-weight heparin mechanisms of action, pharmacokinetics, dosing, monitoring, efficacy, and safety. Chest Journal, 119 (2001), 64S–94S. [CrossRef] [Google Scholar]
  15. M. F. Hockin, K. C. Jones, S. J. Everse, K. G. Mann. A model for the stoichiometric regulation of blood coagulation. Journal of Biological Chemistry, 277(21) (2002), 18322–18333. [CrossRef] [PubMed] [Google Scholar]
  16. N. HG. Holford. Clinical pharmacokinetics and pharmacodynamics of warfarin. Understanding the dose-effect relationship. Clinical pharmacokinetics 11.6 (1986), 483–504. [CrossRef] [PubMed] [Google Scholar]
  17. K. Leiderman, A. L. Fogelson. Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow. Mathematical Medicine and Biology, (2010), dqq005. [Google Scholar]
  18. G. DO. Lowe. Virchow’s triad revisited: abnormal flow. Pathophysiology of haemostasis and thrombosis 33.5-6 (2003), 455–457. [CrossRef] [PubMed] [Google Scholar]
  19. P. W. Majerus, G.J. Broze, J. P. Miletich, D.M. Tollefsen. Anticoagulant thrombolytic, and antiplatelet drugs. Hardman JG, Limbird LE, eds. Goodman and Gilman’s The pharmacological basis of therapeutics. 9th ed. New York: McGraw-Hill, (1996), 1347–51. [Google Scholar]
  20. P.P. Naidu, M. Anand. Importance of VIIIa inactivation in a mathematical model for the formation, growth, and lysis of clots. Math. Model. Nat. Phenom., 9 (2014), no. 6, 17–33. [CrossRef] [MathSciNet] [Google Scholar]
  21. M.A. Panteleev, A.N. Sveshnikova, A.V. Belyaev, D.Y. Nechipurenko, I. Gudich, S.I. Obydenny, N. Dovlatova, S.C. Fox, E.L. Holmuhamedov. Systems biology and systems pharmacology of thrombosis. Math. Model. Nat. Phenom., 9 (2014), no. 6, 4–16. [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  22. E. A. Pogorelova, A. I. Lobanov. Influence of enzymatic reactions on blood coagulation autowave. Biophysics, 59.1, (2014), 110–118. [CrossRef] [Google Scholar]
  23. R.S. Porter, W.T. Sawyer, D.T. Lowenthal. Warfarin. Evans WE, Schentag JJ, Jusko WJ, eds. Applied pharmacokinetics. 2d ed. Spokane, Wash.: Applied Therapeutics, (1986), 1057–104. [Google Scholar]
  24. Prothrombin time. http://www.nlm.nih.gov/medlineplus/ency/article/003652.htm. Accessed: 2016-05-23 [Google Scholar]
  25. A. Sequeira, T. Bodnar. Blood coagulation simulations using a viscoelastic model. Math. Model. Nat. Phenom., 9 (2014), no. 6, 34–45. [CrossRef] [MathSciNet] [Google Scholar]
  26. J. Stenflo, J. W. Suttie. Vitamin K-dependent formation of gamma-carboxyglutamic acid. Annual review of biochemistry 46.1 (1977), 157–172. [CrossRef] [PubMed] [Google Scholar]
  27. J. M. Svec, R. W. Coleman, D. R. Mungall, T. M. Ludden. Bayesian pharmacokinetic/pharmacodynamic forecasting of prothrombin response to warfarin therapy: preliminary evaluation. Therapeutic drug monitoring, 7(2) (1985), 174–180. [CrossRef] [PubMed] [Google Scholar]
  28. T. L. Jackson, A. Radunskaya. Applications of Dynamical Systems in Biology and Medicine (Vol. 158). T. L. Jackson (Ed.). Springer, 2015. [Google Scholar]
  29. A.A. Tokarev, Yu.V. Krasotkina, M.V. Ovanesov, M.A. Panteleev, M.A. Azhigirova, V.A. Volpert, F.I. Ataullakhanov, A.A. Butilin. Spatial dynamics of contact-activated fibrin clot formation in vitro and in silico in Haemophilia B: effects of severity and Ahemphil B treatment. Math. Model. Nat. Phenom., 1 (2006), no. 2, 124–137. [Google Scholar]
  30. A. Tokarev, I. Sirakov, G. Panasenko, V. Volpert, E. Shnol, A. Butylin, F. Ataullakhanov. Continuous mathematical model of platelet thrombus formation in blood flow. Russian Journal of Numerical Analysis and Mathematical Modelling 27 (2012), no. 2, 192–212. [CrossRef] [Google Scholar]
  31. A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert. Modelling of thrombus growth in flow with a DPD-PDE method. Journal of Theoretical Biology, 337 (2013) 30–41. [Google Scholar]
  32. A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert. Modelling of platelet-fibrin clot formation in flow with a DPD-PDE method. Journal of mathematical biology, 72(3) (2016), 649–681. [Google Scholar]
  33. A. Tosenberger, N. Bessonov, V. Volpert. Influence of fibrinogen deficiency on clot formation in flow by hybrid model. Math. Model. Nat. Phenom., 10 (2015), no. 1, 36–47. [CrossRef] [MathSciNet] [Google Scholar]
  34. Volpert, A. I., Volpert, V. A., & Volpert, V. A. Traveling wave solutions of parabolic systems (Vol. 140). American Mathematical Soc, 1994. [Google Scholar]
  35. T. Wajima, G. K. Isbister, S. B. Duffull. A comprehensive model for the humoral coagulation network in humans. Clinical Pharmacology & Therapeutics, 86(3) (2009), 290–298. [Google Scholar]
  36. Warfarin INR targets. http://www.globalrph.com/warfarin_inr_targets.htm. Accessed: 2016-02-22. [Google Scholar]
  37. A. R. Wufsus, N. E. Macera, K. B. Neeves. The hydraulic permeability of blood clots as a function of fibrin and platelet density. Biophysical journal 104.8 (2013), 1812–1823. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.