Interlocking triads of growth control in tumors.

A pair of growth control triads are used to describe coincident tumor growth and liver regeneration after partial hepatectomy. The models are extensions of previous growth control models which describe tumor growth in an unperturbed host (Michelson and Leith, 1991, Bull. math. Biol. 53, 639-656; idem, 1992, Proceedings of the Third International Conference on Communications and Control, Vol. 2, pp. 481-490; idem, 1992 Bull. math. Biol. 55, 993-1011; idem, J. theor. Biol. 169, 327-338). The linkage between the two triads depends upon systemic signals carried by soluble factors, and mathematical descriptors based upon biological first principals are proposed. The sources of the growth factors, their targets and the processing of their signals are investigated. Analyses of equilibrium in the constant coefficients case and simulated growth curves for the dynamic system are presented, and the effects of growth factor-induced mitogenesis and angiogenesis are discussed in particular. A case is made for early and late responses in the coupled control system. The biology of the signal processing paradigm is placed within a new theoretical context and discussed with regard to tumor adaptation, liver differentiation and the development of a tumor hypoxic fraction.