BioNetFlux: A Python Framework for Reaction--Diffusion--Chemotaxis Simulations on One-Dimensional Network Geometries

Abstract

We present BioNetFlux, an open-source Python framework for the numerical simulation of coupled systems of partial differential equations (PDEs) on one-dimensional multi-arc networks by the Hybridized Discontinuous Galerkin method. Its design targets biological transport phenomena on graph-like geometries that arise naturally in microfluidic organ-on-chip (OoC) devices, vascular networks, and in-vitro cell-migration assays.

Figures (7)

• Figure 1: Maze geometry (maze_3_data, scaled by $\ell=50$) with domain indices. Blue numbers label segments; red dots mark junctions (J), T-junctions (T), and boundary points (B).
• Figure 2: Immune-cell density $u$ (equation 0) at three time snapshots. The initial injection at domain 28 diffuses and migrates toward the chemoattractant sources via chemotaxis.
• Figure 3: Chemoattractant $\omega$ (equation 1). Produced by immune cells, $\omega$ diffuses rapidly ($\epsilon=900$) and decays slowly ($c=10^{-4}$).
• Figure 4: Tumour-cell density $v$ (equation 2). With near-zero diffusivity $\sigma=10^{-9}$, for this experiment, the tumour mass remains localised on domain 17 throughout the simulation.
• Figure 5: Chemoattractant $\varphi$ (equation 3). Produced by immune cells at rate $b=0.2$, $\varphi$ guides the chemotactic response of $u$.