A growth model for primary cancer (II). New rules, progress curves and morphology transitions

In the present paper we extend the analysis of another model recently proposed to simulate the growth of carcinoma “in situ”, which includes cell proliferation, motility and death, as well as chemotactic interactions among cells. The tumour patterns generated by two distinct growth rules are characterised by its gyration radius, surface roughness, total number of cancer cells, and number of cells on tumour periphery. Our results indicate that very distinct morphological patterns follow Gompertz growth curves and their gyration radii increase linearly in time and scale, in the asymptotic limit, as a square root of the total number of tumour cells. In contrast, these distinct tumour patterns exhibit different scaling laws for their surfaces. Thus, some biological features of malignant behaviour seem to influence particularly the structure of the tumour border, while its gyration radius and progress curve are described by more robust functions. Finally, for both rules used, morphology transitions as well as a transient behaviour up to the onset of the phase of rapid growth in the Gompertz curves are observed.