Dormancy, regression, and recurrence: towards a unifying theory of tumor growth control

In several recent publications, mathematical models of autocrine-paracrine and autocrine-paracrine-endocrine controls of growth in both homogeneous and heterogeneous tumor populations were developed (Michelson & Leith, 1991, Bull. math. Biol. 53, 639-656; 1992a, Proc. Third Int. Conf. Comm. Control, pp. 481-490; 1992b, Bull, math. Biol. 55, 993-1011). For the homogeneous case, a generic tumor was modeled as a single, growing population using the Verhulst equation of logistic growth. The heterogeneous tumor was modeled as a pair of populations, one proliferating and one quiescent. Mitogenic signals were represented as modifications to the Malthusian growth parameters, and adaptational signals were represented as modifications to the logistic carrying capacities. Interactions between populations were represented by competitive feedback and transition rates. In this paper a theory of growth control is proposed to determine whether tumor dormancy, regression, and recurrence can be explained by a more unifying theory of signal processing. The models developed earlier form the basis for this analysis. Dormancy is described as an equilibrium state from which tumors may re-emerge if that equilibrium is disrupted. The types of disruption in signal processing needed to induce recurrence are discussed with respect to surgery and wound healing. Based on this theory, it appears that sort of feedback between the host's ability to support the proliferating 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.