FROM PASSIVE DIFFUSION TO ACTIVE CELLULAR MIGRATION IN MATHEMATICAL-MODELS OF TUMOR INVASION

Mathematical models of tumour invasion appear as interesting tools for connecting the information extracted from medical imaging techniques and the large amount of data collected at the cellular and molecular l evels. Most of the recent studies have used stochastic models of cell translocation for the comparison of computer simulations with histolog ical solid tumour sections in order to discriminate and characterise e xpansive growth and active cell movements during host tissue invasion. This paper describes how a deterministic approach based on reaction-d iffusion models and their generalisation in the mechano-chemical frame work developed in the study of biological morphogenesis can be an alte rnative for analysing tumour morphological patterns. We support these considerations by reviewing two studies. In the first example, success ful comparison of simulated brain tumour growth with a time sequence o f computerised tomography (CT) scans leads to a quantification of the clinical parameters describing the invasion process and the therapy. T he second example considers minimal hypotheses relating cell motility and cell traction forces. Using this model, we can simulate the bifurc ation from an homogeneous distribution of cells at the tumour surface toward a nonhomogeneous density pattern which could characterise a pre -invasive stage at the tumour-host tissue interface.