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    Biological transportation networks: Modeling and simulation

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    Type
    Article
    Authors
    Albi, Giacomo
    Artina, Marco
    Foransier, Massimo
    Markowich, Peter A. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2015-09-15
    Online Publication Date
    2015-09-15
    Print Publication Date
    2016-01
    Permanent link to this record
    http://hdl.handle.net/10754/622521
    
    Metadata
    Show full item record
    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.
    Citation
    Albi G, Artina M, Foransier M, Markowich PA (2016) Biological transportation networks: Modeling and simulation. Analysis and Applications 14: 185–206. Available: http://dx.doi.org/10.1142/S0219530515400059.
    Sponsors
    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.
    Publisher
    World Scientific Pub Co Pte Lt
    Journal
    Analysis and Applications
    DOI
    10.1142/S0219530515400059
    ae974a485f413a2113503eed53cd6c53
    10.1142/S0219530515400059
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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