Modelling tissue self-organization: from micro to macro models
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Accepted version
Author(s)
Degond, PAA
Peurichard, D
Type
Journal Article
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.
Date Issued
2017
Date Acceptance
2016-10-21
Citation
Lecture Notes in Computational Science and Engineering, 2017, 122, pp.93-108
ISSN
1439-7358
Publisher
Springer Verlag (Germany)
Start Page
93
End Page
108
Journal / Book Title
Lecture Notes in Computational Science and Engineering
Volume
122
Copyright Statement
© Springer International Publishing AG, part of Springer Nature 2017. The final publication is available at Springer via https://doi.org/10.1007/978-3-319-73371-5_5 .
Sponsor
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
Subjects
Science & Technology
Life Sciences & Biomedicine
Oncology
Mathematical & Computational Biology
LINKED FIBERS
PARTICLE
Publication Status
Published
Date Publish Online
2018-03-17