Modelling vascular morphogenesis: current views on blood vessels development

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In this work we present a comprehensive account of our current knowledge on vascular morphogenesis, both from a biological and a mathematical point of view. To this end, we first describe the basic steps in the known mechanisms of blood vessel morphogenesis, whose structure, function and unfolding properties are examined. We then provide a wide, although by no means exhaustive, account of mathematical models which are used to describe and discuss particular aspects of the overall biological process considered. We finally summarize the approaches presented, and suggest possible directions for future research. Details about some of the major signalling molecules involved are included in a first Appendix at the end of the paper. A second Appendix provides a brief overview of design principles for vascular nets, a subject that has deserved considerable attention over the years.
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