  Experiments of cell migration and chemotaxis assays have been classically
performed in the so-called Boyden Chambers. A recent technology, xCELLigence
Real Time Cell Analysis, is now allowing to monitor the cell migration in real
time. This technology measures impedance changes caused by the gradual increase
of electrode surface occupation by cells during the course of time and provide
a Cell Index which is proportional to cellular morphology, spreading, ruffling
and adhesion quality as well as cell number. In this paper we propose a
macroscopic mathematical model, based on \emph{advection-reaction-diffusion}
partial differential equations, describing the cell migration assay using the
real-time technology. We carried out numerical simulations to compare simulated
model dynamics with data of observed biological experiments on three different
cell lines and in two experimental settings: absence of chemotactic signals
(basal migration) and presence of a chemoattractant. Overall we conclude that
our minimal mathematical model is able to describe the phenomenon in the real
time scale and numerical results show a good agreement with the experimental
evidences.
