Special Issue: On Kinetic and Related ModelsNo Access

Biological transportation networks: Modeling and simulation

Giacomo Albi

M15 – Fakultät Mathematik, Technische Universität München, Boltzmann straße 3, Garching bei Mnchen D-85748, Germany

E-mail Address: giacomo.albi@ma.tum.de

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Marco Artina

M15 – Fakultät Mathematik, Technische Universität München, Boltzmann straße 3, Garching bei Mnchen D-85748, Germany

E-mail Address: marco.artina@ma.tum.de

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Massimo Foransier

M15 – Fakultät Mathematik, Technische Universität München, Boltzmann straße 3, Garching bei Mnchen D-85748, Germany

E-mail Address: massimo.fornasier@ma.tum.de

Chair of Applied Numerical Analysis.

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, and

Peter A. Markowich

Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal 23955-6900, Kingdom of Saudi Arabia

E-mail Address: peter.markowich@kaust.edu.sa

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https://doi.org/10.1142/S0219530515400059Cited by:21 (Source: Crossref)

Abstract

We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett.111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and basic analytical features like the gradient flow structure of the fluid transportation network model and the impact of the model parameters on the geometry and topology of network formation are analyzed. We also present a numerical finite-element based discretization scheme and discuss sample cases of network formation simulations.

Keywords:

AMSC: 35K55, 35B36, 92C42

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