The first aim of the course is to give a critical overview on a sufficiently wide spectrum of mathematical approaches that can be used to tackle biological and biomedical problems (ranging from physiological phenomena, such as embryogenesis, to pathological situations as cancer growth). We will then focus on cellular automata, such as the cellular Potts model, and on particle—based models. These approaches will be described with a sufficient level of theoretical detail, providing also representative applications. Finally, we will propose selected hybrid mathematical and computational environments where models of different nature coexist and are interfaced and integrated.

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Introduction on the spatio-temporal scales and levels characteristic of biological/biomedical phenomena (1 h) Overview on classical mathematical approaches used to analyze biomedical/biological problems, with particular emphasis for individual-based models (cellular automata) and discrete approaches (1 h) Cellular Potts model: description and applications (2 h) Particle-based models: description, analytical aspects and applications (2 h) Multiscale hybrid models: description, analytical aspects and applications (4 h)

Mixed mode

Oral presentation

P.D.1-1 - November