Geodesic
An Individualized Blood Coagulation Model to Predict INR Therapeutic Range During Warfarin Treatment
A. Bouchnita1, 2, 3, 4 ; K. Bouzaachane3, 5, 6 ; T. Galochkina2, 4, 7, 8 ; P. Kurbatova1 ; P. Nony1, 9 ; V. Volpert2, 4, 10
1 Laboratoire de Biométrie et Biologie Evolutive, UMR 5558 CNRS University Lyon 1, 69376 Lyon, France
2 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
3 Laboratory of Study and Research in Applied Mathematics, Mohammadia School of Engineers Mohamed V university, Rabat, Morocco
4 INRIA Team Dracula, INRIA Antenne Lyon la Doua, Villeurbanne, France
5 Laboratoire de Mathématiques Appliquées et Informatique, Faculté des Sciences et Techniques Caddi Ayyad University, Marrakech, Morocco
6 Ecole Supérieure de Technologie, Cadi Ayyad University, Marrakech, Morocco
7 Department of Biophysics, Faculty of Biology, M.V. Lomonosov Moscow State University Leninskie gory 1, Moscow, Russia
8 Federal Research Clinical Center of Federal Medical & Biological Agency of Russia Orekhovy boulevard 28, Moscow, Russia
9 Hospices Civils de Lyon, Service de Pharmacologie Clinique, Lyon, France
10 Laboratoire Poncelet, UMI 2615 CNRS, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 6, pp. 28-44.

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Deep venous thrombosis (DVT) is characterized by formation of blood clot within a deep vein. The resulting thrombus can partially or completely block blood circulation. It can also detach and migrate with the flow resulting in pulmonary embolism. Anticoagulant drugs such as warfarin are usually prescribed to prevent recurrent thrombosis. The action of warfarin is monitored using a blood test for the International Normalized Ratio (INR) which is based on prothrombin time measurement. A high INR indicates a predisposition of the patient to bleeding, while a low INR shows that the warfarin dose is insufficient to prevent thromboembolic events. The therapeutic target of INR varies from case to case depending on clinical indications. It tends to be in the range 2.0 – 3.0 in most conditions. In this work we develop a model describing blood clotting during warfarin treatment. The action of warfarin is introduced by a Pharmacokinetics-Pharmacodynamics (PK-PD) sub-model. It describes the inhibition of synthesis of the vitamin K dependent factors by warfarin in the liver. We generate a population of patients with individual characteristics and assess their response to warfarin treatment by comparing the simulated INR and the corresponding developed clot height. Using this approach, we determine the underlying causes behind thrombosis and bleeding persistence even for an INR in the normal range. Thus, we suggest a novel methodology to predict the targeted INR depending on individual patient characteristics.
DOI : 10.1051/mmnp/201611603

A. Bouchnita 1, 2, 3, 4 ; K. Bouzaachane 3, 5, 6 ; T. Galochkina 2, 4, 7, 8 ; P. Kurbatova 1 ; P. Nony 1, 9 ; V. Volpert 2, 4, 10

1 Laboratoire de Biométrie et Biologie Evolutive, UMR 5558 CNRS University Lyon 1, 69376 Lyon, France
2 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
3 Laboratory of Study and Research in Applied Mathematics, Mohammadia School of Engineers Mohamed V university, Rabat, Morocco
4 INRIA Team Dracula, INRIA Antenne Lyon la Doua, Villeurbanne, France
5 Laboratoire de Mathématiques Appliquées et Informatique, Faculté des Sciences et Techniques Caddi Ayyad University, Marrakech, Morocco
6 Ecole Supérieure de Technologie, Cadi Ayyad University, Marrakech, Morocco
7 Department of Biophysics, Faculty of Biology, M.V. Lomonosov Moscow State University Leninskie gory 1, Moscow, Russia
8 Federal Research Clinical Center of Federal Medical & Biological Agency of Russia Orekhovy boulevard 28, Moscow, Russia
9 Hospices Civils de Lyon, Service de Pharmacologie Clinique, Lyon, France
10 Laboratoire Poncelet, UMI 2615 CNRS, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia 
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A. Bouchnita; K. Bouzaachane; T. Galochkina; P. Kurbatova; P. Nony; V. Volpert. An Individualized Blood Coagulation Model to Predict INR Therapeutic Range During Warfarin Treatment. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 6, pp. 28-44. doi : 10.1051/mmnp/201611603. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611603/

[1] M. Anand, K. Rajagopal, K. R. Rajagopal A model for the formation and lysis of blood clots Pathophysiology of haemostasis and thrombosis 2005 109 120

[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 2008 160S 198S

[3] J. P. Antovic, M. Blombäck. Essential Guide to Blood Coagulation. Wiley Online Library (2013).

[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. 2014 69 84

[5] N. Bessonov, A. Sequeira, S. Simakov, Yu. Vassilevski, V. Volpert Methods of blood flow modelling Math. Model. Nat. Phenom. 2016 1 25

[6] A. Bouchnita, A. Tosenberger, V. Volpert On the regimes of blood coagulation Applied Mathematics Letters 2016 74 79

[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 1983 5655 5660

[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 2008 3265 3279

[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 2005 91 108

[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 2000 337 345

[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 1990 82 85

[12] A. Hensen, E. A. Loeliger Antithrombin III. Its metabolism and its function in blood coagulation Thrombosis et diathesis haemorrhagica 1962 1 1

[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 2001 8S 21S

[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 2001 64S 94S

[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 2002 18322 18333

[16] N. Hg. Holford Clinical pharmacokinetics and pharmacodynamics of warfarin. Understanding the dose-effect relationship Clinical pharmacokinetics 1986 483 504

[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

[18] G. Do. Lowe Virchow’s triad revisited: abnormal flow Pathophysiology of haemostasis and thrombosis 2003 455 457

[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.

[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. 2014 17 33

[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. 2014 4 16

[22] E. A. Pogorelova, A. I. Lobanov Influence of enzymatic reactions on blood coagulation autowave Biophysics 2014 110 118

[23] R.S. Porter, W.T. Sawyer, D.T. Lowenthal Warfarin Applied pharmacokinetics 1986 1057 104

[24] Prothrombin time. http://www.nlm.nih.gov/medlineplus/ency/article/003652.htm. Accessed: 2016-05-23

[25] A. Sequeira, T. Bodnar Blood coagulation simulations using a viscoelastic model Math. Model. Nat. Phenom. 2014 34 45

[26] J. Stenflo, J. W. Suttie Vitamin K-dependent formation of gamma-carboxyglutamic acid Annual review of biochemistry 1977 157 172

[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 1985 174 180

[28] T. L. Jackson, A. Radunskaya. Applications of Dynamical Systems in Biology and Medicine (Vol. 158). T. L. Jackson (Ed.). Springer, 2015.

[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. 2006 124 137

[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 2012 192 212

[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 2013 30 41

[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 2016 649 681

[33] A. Tosenberger, N. Bessonov, V. Volpert Influence of fibrinogen deficiency on clot formation in flow by hybrid model Math. Model. Nat. Phenom. 2015 36 47

[34] Volpert, A. I., Volpert, V. A., Volpert, V. A. Traveling wave solutions of parabolic systems (Vol. 140). American Mathematical Soc, 1994.

[35] T. Wajima, G. K. Isbister, S. B. Duffull A comprehensive model for the humoral coagulation network in humans Clinical Pharmacology & Therapeutics 2009 290 298

[36] Warfarin INR targets. http://www.globalrph.com/warfarin_inr_targets.htm. Accessed: 2016-02-22.

[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 2013 1812 1823

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