A model for cell migration in tumour growth

Tumour growth results, in particular, from cell-cell interaction and tumour and healthy cell proliferation. The complexity of the cellular microenvironment may then be framed within the theory of mixtures by looking at cell populations as the constituents of a mixture. In this paper the balance equations are reviewed to account for directionality onto a collective migration of the tumour cell population, via an attractive force of the chemotactic type, in addition to the customary pressure term. The density of tumour cells turns out to be governed by a hyperbolic differential equation. By neglecting, as usual, the inertia term it follows that the density satisfies a backward, or forward, diffusion equation according as the attraction, or pressure effect, prevails. Uniqueness of the solution to the backward equation is investigated and a family of solutions is described. An estimate is given for the growth rate of a tumour profile.