Blood coagulation: A puzzle for biologists, a maze for mathematicians
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, try
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Blood coagulation: a puzzle for biologists, a maze for mathematicians Antonio Fasano, Rafael F. Santos, and Ad´elia 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 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
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: [email protected]fi.it 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: [email protected] Ad´elia Sequeira ( ) Instituto Superior T´ecnico, Technical University of Lisbon, Department of Mathematics and CEMAT/IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal e-mail: [email protected]
Ambrosi D., Quarteroni A., Rozza G. (Eds.): Modeling of Physiological Flows. DOI 10.1007/978-88-470-1935-5 3, © Springer-Verlag Italia 2012
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A. Fasano, R.F. Santos, and A. Sequeira
of keeping up with the developments of the medical theory and of the therapeutical practice of this multifaceted subject.
3.1 Introduction Blood coagulation is a well familiar process following a wound and leading to bleeding termination (hemostasis). Such a goal is achieved by sealing the lesion with a clot (or thrombus). It is in fact much more important than that, since it intervenes in repairing small internal injuries that occur spontaneously in blood vessels. It is a physiological process which keeps alive any being provided with blood, but it can also be very harmful if it derails from its carefully planned path. Arteries or veins occlusion1 (thrombosis) can be the consequence of excessive coagulation, while e.g. spontaneous bleeding is related to defective parts of the coagulation machinery. The aim of this paper is to present a concise review of the literature concerning mathematical modelling of blood coagulation. Before we come to the mathematical models, it will be necessary to synthesize the present view of this incredibly complex biological
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