From kinetic models of multicellular growing systems to macroscopic biological tissue models

This paper deals with the derivation of macroscopic equations of biological tissues for a class of nonlinear equations, with quadratic type nonlinearity, modeling complex multicellular systems. Cellular interactions generate both modification of biological functions and proliferative/destructive events. The asymptotic analysis refers to the derivation of hyperbolic models focused on the influence of existence of a global equilibrium solution. The asymptotic analysis shows how the macroscopic tissue behavior can be described from the underlying cellular description and that this specific biological state modifies the structure of the models obtained by different assumptions. The approach is proposed as an alternative to the phenomenological of continuum mechanics for growing tissues. (C) 2010 Elsevier Ltd. All rights reserved.