MathNeuro seminar (Benjamin Aymard, Imperial College)

Dr. Benjamin Aymard (Department of Chemical Engineering, Imperial College London, UK)

Title: Emergence of vascularization networks

Abstract: Networks are patterns created dynamically in order to optimize the distribution or the exchange of quantities in an environment. They appear naturally in Nature, for instance in human biology (neural network, respiratory network, blood network), in vegetal biology (branches, leaf skeleton, roots), in entomology (ant trails, insect nests) or in geology (erosion patterns, rivers, salt ponds), and have possibly many applications (tissue engineering, traffic network design and others). Despite the fact that these structures are sometimes separated by many physical scales, and rely on very different physics, they are very similar from mathematical point of view. The mechanisms underlying the formation of such networks are not entirely known, and we think that self organization could play a major role.

In this talk, we will focus on the formation of blood network. In doing so, we will try to keep, as much as possible, a general point of view, in order to be able to apply this methodology to other frameworks. We will start by reviewing and describing several existing networks. Then we will introduce the mathematical model we have designed: an hybrid continuum/agent-based model. Finally, after briefly introducing the corresponding numerical method, we will present numerical simulations of our model.

June 16, 11AM, Byron “Beige” Y506

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