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

  • Lisette dePillis
  • Erica J. Graham
  • Kaitlyn Hood
  • Yanping Ma
  • Ami Radunskaya
  • Julie SimonsEmail author
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 158)


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.


International Normalize Ratio Reaction Zone Tissue Factor Factor Xiii Clot Formation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The work described in this chapter is a result of a collaboration made possible by the IMA’s workshop on WhAM! A Research Collaboration Workshop for Women in Applied Mathematics: Dynamical Systems with Applications to Biology and Medicine, and we would like to thank the IMA for its support. The authors would also like to thank Professor Aaron Fogelson (University of Utah) for generously providing Fortran codes and Professor Karin Leiderman (UC-Merced) for useful insights, in addition to Professor Stephen Duffull and Dr. Jim Faed of the University of Otago for helpful discussions. E.J. Graham gratefully acknowledges support from the National Science Foundation, DMS 0946431. K. Hood gratefully acknowledges partial support from the National Science Foundation, DGE 1144087. A. Radunskaya gratefully acknowledges partial support from the National Science Foundation, DMS 1016136. J. Simons gratefully acknowledges partial support from the National Science Foundation, DMS 104626.

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Copyright information

© Springer Science+Business Media, LLC 2015

Authors and Affiliations

  • Lisette dePillis
    • 1
  • Erica J. Graham
    • 2
  • Kaitlyn Hood
    • 3
  • Yanping Ma
    • 4
  • Ami Radunskaya
    • 5
  • Julie Simons
    • 6
    Email author
  1. 1.Department of MathematicsHarvey Mudd CollegeClaremontUSA
  2. 2.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  3. 3.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  4. 4.Department of MathematicsLoyola Marymount UniversityLos AngelesUSA
  5. 5.Department of MathematicsPomona CollegeClaremontUSA
  6. 6.Department of MathematicsTulane UniversityNew OrleansUSA

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