Blood coagulation: a puzzle for biologists, a maze for mathematicians - Modeling of Physiological Flows - page 40

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Blood coagulation: a puzzle for biologists,
a maze for mathematicians
Antonio Fasano, Rafael F. Santos, and Adelia Sequeira
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 bleed-
ing 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 incom-
plete. Indeed, our conclusion is that mathematicians are still in front of the huge task
Antonio Fasano
University of Firenze, Department of Mathematics “U. Dini”, Viale Morgagni 67/a, 50134 Firenze,
Italy
and
IASI-CNR, Viale Manzoni 30, 00185 Roma, Italy
e-mail: [e-mail]
Rafael F. Santos
University of Algarve, Department of Mathematics, Campus de Gambelas, 2005-139 Faro, Portugal
and
CEMAT/IST, Av. Rovisco Pais, 1049-001, Lisboa, Portugal
e-mail: [e-mail]
Adelia Sequeira ( )
Instituto Superior Tecnico, Technical University of Lisbon, Department of
Mathematics
and
CEMAT/IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
e-mail: [e-mail]