Resumen:
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The present dissertation is devoted to mathematical modelling and simulation of a specific problem in early vascular morphogenesis, a process that constitutes the initial step in the generation of the vascular system in vertebrates. More precisely, a combined mathematical, computational and experimental approach is used to get new insights into key molecular and cellular mechanisms underlying the self-assembly of new blood vessels. The thesis is divided in three main sections: Preliminaries (Chapter 1), Research Work (Chapters 2 and 3) and Perspectives and Conclusions (Chapters 4 and 5). An overview of the field together with an introduction to the main problem is presented in Chapter 1, where the main literature on the subject is reviewed from a critical point of view. In Chapter 2, a new mechanism and a new hybrid mathematical model for early vascular patterning in the embryo are proposed and examined. The study of the proposed model raises a number of new biological hypotheses, many of which are beyond the current experimental reach. In some particular cases, however, they have been validated in a controlled situation using simplified in vitro assays, as shown in Chapter 3. While doing so, relevant quantitative information related with the kinetic and diffusive properties of a key molecule in vascular development (VEGF) was also obtained. Chapter 4 is devoted to future perspectives in the field under consideration. In particular, two ongoing projects that are extensions of the work here considered are outlined. Finally, the main conclusions of this study are gathered in Chapter 5.
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