Mass-preserving approximation of a chemotaxis multi-domain transmission model for microfluidic chips

t. The present work was inspired by the recent developments in laboratory experiments made on chip, where culturing of multiple cell species waspossible. The model is based on coupled reaction-diffusion-transport equationswith chemotaxis, and takes into account the interactions among cell populations and the possibility of drug administration for drug testing effects.Our effort was devoted to the development of a simulation tool that is able toreproduce the chemotactic movement and the interactions between differentcell species (immune and cancer cells) living in microfluidic chip environment.The main issues faced in this work are the introduction of mass-preservingand positivity-preserving conditions involving the balancing of incoming andoutgoing fluxes passing through interfaces between 2D and 1D domains of thechip and the development of mass-preserving and positivity preserving numerical conditions at the external boundaries and at the interfaces between 2Dand 1D domains