Complexity and mathematical tools toward the modelling of multicellular growing systems

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Abstract

This paper deals with a multiscale modelling approach to complex biological systems constituted by several interacting entities. The methodology is based on mathematical kinetic theory for active particles and is focused on the modelling of complex multicellular systems under therapeutic actions at the cellular level and mutations with onset of new populations. Asymptotic hyperbolic methods are developed to derive models at the macroscopic scale of tissues from the underlying description at the level of cells for a open system with variable number of populations.

Keywords

Living matters
Evolution
Mutations
System biology
Nonlinear Interactions
Stochastic games
Active particles

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Partially supported by the European Union FP7 Health Research Grant number FP7-HEALTH-F4-2008-202047, Termination of developmental processes and their reactivation in adult life; and by Ministerio de Ciencia e Innovación (Spain), Project MTM2008-05271 and Junata de Andalucía Project P08-FQM-4267.