Abstract
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.
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Acknowledgements
This work has been supported by the “Engineering and Physical Sciences Research Council” under grant ref: EP/M006883/1 and by the National Science Foundation under NSF Grant RNMS11-07444 (KI-Net). Pierre Degond acknowledges support from the Royal Society and the Wolfson foundation through a Royal Society Wolfson Research Merit Award. Pierre Degond is on leave from CNRS, Institut de Mathématiques de Toulouse, France. Diane Peurichard acknowledges support by the Vienna Science and Technology Fund (WWTF) under project number LS13-029.
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Degond, P., Peurichard, D. (2017). Modelling Tissue Self-Organization: From Micro to Macro Models. In: Gerisch, A., Penta, R., Lang, J. (eds) Multiscale Models in Mechano and Tumor Biology . Lecture Notes in Computational Science and Engineering, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-73371-5_5
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