Injury-Initiated Clot Formation Under Flow: A Mathematical Model with Warfarin Treatment

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Book Chapter

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The formation of a thrombus (commonly referred to as a blood clot) can potentially pose a severe health risk to an individual, particularly when a thrombus is large enough to impede blood flow. If an individual is considered to be at risk for forming a thrombus, he/she may be prophylactically treated with anticoagulant medication such as warfarin. When an individual is treated with warfarin, a blood test that measures clotting times must be performed. The test yields a number known as the International Normalized Ratio (INR). The INR test must be performed on an individual on a regular basis (e.g., monthly) to ensure that warfarin’s anticoagulation action is targeted appropriately. In this work, we explore the conditions under which an injury-induced thrombus may form in vivo even when the in vitro test shows the appropriate level of anticoagulation action by warfarin. We extend previous models to describe the in vitro clotting time test, as well as thrombus formation in vivo with warfarin treatments. We present numerical simulations that compare scenarios in which warfarin doses and flow rates are modified within biological ranges. Our results indicate that traditional INR measurements may not accurately reflect in vivo clotting times.

Recommended Citation

dePillis L., Graham E.J., Hood K., Ma Y., Radunskaya A., Simons J. (2015) Injury-Initiated Clot Formation Under Flow: A Mathematical Model with Warfarin Treatment. In: Jackson T., Radunskaya A. (eds) Applications of Dynamical Systems in Biology and Medicine. The IMA Volumes in Mathematics and its Applications, vol 158. Springer, New York, NY