A MATHEMATICAL MODEL OF TUMOR GROWTH WITH SPATIALLY DECREASING DIFFUSION COEFFICIENT OF MITOTIC INHIBITOR

Abstract

Intercellular diffusion of mitosis inhibiting factors, maintained by proper intercellular contact, is one of the means of transferring “positional information”—a message to peripheral cells of a growing normal tissue instructing them where (at what size of the tissue) to stop their further proliferation by mitotic cell division. This property is commonly known as “contact cell inhibition of mitosis” in biology. In a growing tumor tissue, this regulatory mechanism is absent and as a result, peripheral cells of a tumor tissue, being devoid of any “positional information”, go on dividing successively, increasing the size of the tumor (uncontrolled growth). In this paper, the above idea has been captured in a reaction-diffusion model of tumor tissue growth with a spatially decreasing diffusion coefficient, D(r), of the mitotic inhibitor. This model merely provides an alternative explanation of certain observations on normal and tumor tissue growth. The solutions of the simple model (with (i) D=constant for normal tissue growth and (ii) D=D(r) for tumor tissue growth), discussed in this paper, quite reasonably agree with the characteristic patterns of normal and tumor tissue growth.