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

2026-03-31

AI Summary

Existing open-source tools struggle to efficiently simulate one-dimensional network-based biological transport processes encountered in microfluidic organ-on-a-chip devices, vascular networks, and cell migration assays. To address this limitation, this work proposes BioNetFlux—a Python-based open-source framework that, for the first time, applies the hybridizable discontinuous Galerkin (HDG) method to solve coupled reaction-diffusion-chemotaxis partial differential equations on one-dimensional multi-branch networks. The framework supports flexible graph-structured geometric modeling and offers high numerical accuracy, scalability, and a design oriented toward biological applications, thereby providing an efficient computational platform for simulating complex biological transport phenomena.

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.

Problem

• reaction-diffusion
• chemotaxis
• network geometries
• partial differential equations
• biological transport

Innovation

• Hybridized Discontinuous Galerkin
• reaction-diffusion-chemotaxis
• one-dimensional networks
• organ-on-chip
• PDE on graphs