Math. Model. Nat. Phenom.
Volume 11, Number 6, 2016Pharmacokinetics-Pharmacodynamics
|Page(s)||28 - 44|
|Published online||04 January 2017|
An Individualized Blood Coagulation Model to Predict INR Therapeutic Range During Warfarin Treatment
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
* Corresponding author. E-mail:
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.
Mathematics Subject Classification: 35Q53 / 34B20 / 35G31
Key words: blood coagulation / warfarin / PK-PD
© EDP Sciences, 2016
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