DORMANCY, REGRESSION, AND RECURRENCE - TOWARDS A UNIFYING THEORY OF TUMOR-GROWTH CONTROL

In several recent publications, mathematical models of autocrine-parac rine and autocrine-paracrine-endocrine controls of growth in both homo geneous and heterogeneous tumor populations were developed (Michelson and Leith, 1991, Bull. math. Biol. 53, 639-656; 1992a, Proc. Third Int . Conf. Comm. Control, pp.481-490; 1992b, Bull. math. Biol. 55, 993-10 11). For the homogeneous case, a generic tumor was modeled as a single , growing population using the Verhulst equation of logistic growth. T he heterogeneous tumor was modeled as a pair of populations, one proli ferating and one quiescent. Mitogenic signals were represented as modi fications to the Malthusian growth parameters, and adaptational signal s were represented as modifications to the logistic carrying capacitie s. Interactions between populations were represented by competitive fe edback and transition rates. In this paper a theory of growth control is proposed to determine whether tumor dormancy, regression, and recur rence can be explained by a more unifying theory of signal processing. The models developed earlier form the basis for this analysis. Dorman cy is described as an equilibrium state from which tumors may re-emerg e if that equilibrium is disrupted. The types of disruption in signal processing needed to induce recurrence are discussed with respect to s urgery and wound healing. Based on this theory, it appears that some s ort of feedback between the host's ability to support the proliferatin g cells (adaptational signal processing) and the transition rates into and out of the proliferating and quiescent compartments must exist. A paradigm based on the development of hypoxia in a spherical tumor is proposed as that link.