GROWTH-FACTORS AND GROWTH-CONTROL OF HETEROGENEOUS CELL-POPULATIONS

In an earlier work a model of the autocrine and paracrine pathways of tumor growth control was developed (Michelson and Leith. 1991. Autocri ne and paracrine growth factors in tumor growth. Bull. math. Biol. 53, 639-656). The target population, a generic tumor, was modeled as a si ngle, homogeneous population using the standard Verhulst equation of l ogistic growth. Mitogenic signals were represented by modifications to the Malthusian growth parameter and adaptational signals were represe nted by modifications to the carrying capacity. Three growth scenarios were described: (1) normal tissue wound healing, (2) unperturbed tumo r growth, and (3) tumor growth in a radiation damaged environment, a p henomenon termed the Tumor Bed Effect (TBE). In this paper, we extend those results to include a ''triad'' of growth factor controls (autocr ine, paracrine and endocrine) and heterogeneity of the target populati on. The heterogeneous factors in the model represent either intrinsic, epigenetic or environmental differences in both normally differentiat ing tissues and tumors. Three types of growth are modeled: (1) normal tissue differentiation or wound healing, assuming no communication bet ween differentiated and undifferentiated cell compartments; (2) normal wound healing with feedback inhibition, due to signalling from the di fferentiated compartment; and (3) the development of hypoxia in a sphe rical tumor. The signal processing within the triad is discussed for e ach model and biologically reasonable constraints are defined for limi ts on growth control.