Mass-Preserving Approximation of a Chemotaxis Multi-Domain Transmission Model for Microfluidic Chips

The present work is inspired by the recent developments in laboratory experiments madeon chips, where the culturing of multiple cell species was possible. The model is based on coupledreaction-diffusion-transport equations with chemotaxis and takes into account the interactions amongcell populations and the possibility of drug administration for drug testing effects. Our effort isdevoted to the development of a simulation tool that is able to reproduce the chemotactic movementand the interactions between different cell species (immune and cancer cells) living in a microfluidicchip environment. The main issues faced in this work are the introduction of mass-preserving andpositivity-preserving conditions, involving the balancing of incoming and outgoing fluxes passingthrough interfaces between 2D and 1D domains of the chip and the development of mass-preservingand positivity preserving numerical conditions at the external boundaries and at the interfacesbetween 2D and 1D domains.