Biological transportation networks: Modeling and simulation

Giacomo Albi; Marco Artina; Massimo Foransier; Peter A. Markowich

doi:10.1142/S0219530515400059

Biological transportation networks: Modeling and simulation

Giacomo Albi, Marco Artina, Massimo Foransier, Peter A. Markowich

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English (US)
Pages (from-to)	185-206
Number of pages	22
Journal	Analysis and Applications
Volume	14
Issue number	01
DOIs	https://doi.org/10.1142/S0219530515400059
State	Published - Sep 15 2015

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: G. Albi and M. Foransier acknowledge the support of the ERC-starting Grant Project High-dimensional Sparse Optimal Control. This research was also supported by TUM through the Von Neumann Professorship of PAM.

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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.",

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AU - Albi, Giacomo

AU - Artina, Marco

AU - Foransier, Massimo

AU - Markowich, Peter A.

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PY - 2015/9/15

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N2 - 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.

AB - 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.

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Biological transportation networks: Modeling and simulation

Abstract

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