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 ar e extensions of previous growth control models which describe tumor gr owth in an unperturbed host (Michelson and Leith, 1998, Bull. math. Bi ol. 53, 639-656; idem, 1992, Proceedings of the Third International Co nference on Communications and Control, Vol. 2, pp. 481-490; idem, 199 2, Bull. math. Biol. 55, 993-1011; idem, J. theor, Biol. 169, 327-338) . The linkage between the two triads depends upon systemic signals car ried by soluble factors, and mathematical descriptors based upon biolo gical 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 simulate d 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 couple d control system. The biology of the signal processing paradigm is pla ced within a new theoretical context and discussed with regard to tumo r adaptation, liver differentiation and the development of a tumor hyp oxic fraction.