  The present work was inspired by the recent developments in laboratory
experiments made on chip, where 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
was 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 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.
