I will start by presenting a new computational framework designed specifically for modeling of populations of living cells. The main applications are found in the study of embryo development, in wound healing processes, and in tumor models. The computational challenge is to bridge the vast scale separation inherent with these types of applications, and to provide for computational efficiency enough that
the model can be effectively parameterized.
In particular I propose to couple the population-level description with single cell models described within the general umbrella of stochastic reaction-diffusion processes. A multiscale analysis in this framework gives insight into convergence of numerical methods and hint at how effective (i.e. parallel) implementations should be designed. Examples in pattern formation, tumor modeling, and in the function of firing neurons will be discussed during the talk.
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