Abstract
The present work is inspired by the recent developments in laboratory experiments made on chips, where the culturing of multiple cell species was possible. The model is based on coupled reaction-diffusion-transport equations with chemotaxis and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects. Our effort is devoted to the development of a simulation tool that is able to reproduce the chemotactic movement and the interactions between different cell species (immune and cancer cells) living in a microfluidic chip environment. The main issues faced in this work are the introduction of mass-preserving and positivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passing through interfaces between 2D and 1D domains of the chip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2D and 1D domains.
Highlights
The aim of the present work is to study both the modelling and numerical approximation of a chemotaxis-reaction-diffusion mathematical system describing the qualitative behavior of different cell species living in a confined environment
In order to ensure the conservation of the total mass when the mass-exchange occurs, we introduce suitable transmission conditions at the interface between 2D and 1D domains
In order to perform a numerical verification of this property, we consider the numerical approximation at the interface between 1D-1D models in the numerical example
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. The aim of the present work is to study both the modelling and numerical approximation of a chemotaxis-reaction-diffusion mathematical system describing the qualitative behavior of different cell species living in a confined environment. This work is inspired by laboratory experiments made on microfluidic chip [1], where some populations cohexist and interact. There has been the development of a new approach to biological studies aimed at reconstructing organs and complex biological processes on a chip [2]. The fundamental idea is that the comprehension of the sophisticated physiology of organisms, based on the complex behavior and interaction of cell populations, tissues, and organs, needs interdisciplinary contributions from biology to mathematics
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