  One of the most crucial and lethal characteristics of solid tumors is
represented by the increased ability of cancer cells to migrate and invade
other organs during the so-called metastatic spread. This is allowed thanks to
the production of matrix metalloproteinases (MMPs), enzymes capable of
degrading a type of collagen abundant in the basal membrane separating the
epithelial tissue from the connective one. In this work, we employ a
synergistic experimental and mathematical modelling approach to explore the
invasion process of tumor cells. A athematical model composed of
reaction-diffusion equations describing the evolution of the tumor cells
density on a gelatin substrate, MMPs enzymes concentration and the degradation
of the gelatin is proposed. This is completed with a calibration strategy. We
perform a sensitivity analysis and explore a parameter estimation technique
both on synthetic and experimental data in order to find the optimal parameters
that describe the in vitro experiments. A comparison between numerical and
experimental solutions ends the work.
