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Blood coagulation: A puzzle for biologists, a maze for mathematicians

  • Antonio Fasano
  • Rafael F. Santos
  • Adélia Sequeira
Part of the MS&A — Modeling, Simulation and Applications book series (MS&A, volume 5)

Abstract

We present a concise summary of mathematical models for the formation and dissolution of blood clots (in other words for the process of hemostasis). For lack of space we restrict our attention to very few models, selected from a very large literature, trying to emphasize the variety of methods and viewpoints. A peculiar aspect concerning hemostasis is the fact that a new interpretation of its extremely complex biological mechanism has been found rather recently, so that most of the mathematical models should be revisited. Also in view of this fact we believed that it was absolutely necessary to write an extensive introduction to the various aspects of hemostasis, including some history, and not disregarding a description of bleeding disorders (another large field of investigation for mathematical modelling), from which much has been learned about the role and importance of each of the numerous elements intervening in hemostasis. We realize that our work is necessarily incomplete. Indeed, our conclusion is that mathematicians are still in front of the huge task of keeping up with the developments of the medical theory and of the therapeutical practice of this multifaceted subject.

Keywords

Blood Coagulation Tissue Factor Disseminate Intravascular Coagulation Disseminate Intravascular Coagulation 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.

Notes

Acknowledgements

Work partially supported by the Italian MIUR Project “Math. Models for Multicomponent Systems in Environmental and Medical Sciences”, by the research center CEMAT/IST through FCT’s funding program and by the project PTDC/MAT/68166/2006. The authors are grateful to Dr. Jeremi Mizerski for his useful suggestions. Acknowledgments are also due to Jevgenija Pavlova, doctoral student at IST, for her assistance in the preparation of all the figures included in this paper.

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Copyright information

© Springer-Verlag Italia 2012

Authors and Affiliations

  • Antonio Fasano
    • 1
    • 2
  • Rafael F. Santos
    • 3
    • 4
  • Adélia Sequeira
    • 4
    • 5
  1. 1.Department of Mathematics “U. Dini”University of FirenzeFirenzeItaly
  2. 2.IASI-CNRRomaItaly
  3. 3.University of AlgarveDepartment of MathematicsFaroPortugal
  4. 4.CEMAT/ISTLisboaPortugal
  5. 5.Department of MathematicsInstituto Superior Técnico, Technical University of LisbonLisboaPortugal

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