In this chapter, we present recent works concerned with the derivation of a macroscopic model for complex interconnected fiber networks from an agent-based model, with applications to, but not limited to, adipose tissue self-organization. Starting from an agent-based model for interconnected fibers interacting through alignment interactions and having the ability to create and suppress cross-links, the formal limit of large number of individuals is first investigated. It leads to a kinetic system of two equations: one for the individual fiber distribution function and one for the distribution function of connected fiber pairs. The hydrodynamic limit, in a regime of instantaneous fiber linking/unlinking then leads to a macroscopic model describing the evolution of the fiber local density and mean orientation. These works are the first attempt to derive a macroscopic model for interconnected fibers from an agent-based formulation and represent a first step towards the formulation of a large scale synthetic tissue model which will serve for the investigation of large scale effects in tissue homeostasis.
CITATION STYLE
Degond, P., & Peurichard, D. (2017). Modelling tissue self-organization: From micro to macro models. In Lecture Notes in Computational Science and Engineering (Vol. 122, pp. 93–108). Springer Verlag. https://doi.org/10.1007/978-3-319-73371-5_5
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