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.
Bibliographical noteKAUST 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.