A THEORETICAL EXPLANATION OF CONCOMITANT RESISTANCE

Concomitant resistance is a tumor growth dynamic which results when th e growth of a second tumor implant is inhibited by the presence of the first. Recently, we modeled tumor growth in the presence of a regener ating liver after partial hepatectomy (Michelson and Leith, Bull. Math . Biol. 57, 345-366, 1995), with an interlocking pair of growth contro l triads to account for the accelerated growth observed in both tissue s. We also modeled tumor dormancy and recurrence as a dynamic equilibr ium achieved between proliferating and quiescent subpopulations. In th is paper those studies are extended to initially model the concomitant resistance case. Two interlocking model systems are proposed. In one an interactive competition between the tumor implants is described, wh ile in the other purely proportional growth inhibition is described. T he equilibria and dynamics of each system when the coefficients are he ld constant are presented for three subcases of model parameters. We s how that the dynamic called concomitant resistance can be real or appa rent, and that if the model coefficients are held constant, the only w ay to truly achieve concomitant resistance is by forcing one of the tu mors into total quiescence. If this is the true state of the inhibited implant, then a non-constant recruitment signal is required to insure regrowth when the inhibitor mass is excised. We compare these theoret ical results to a potential explanation of the phenomenon provided by Prehn (Cancer Res. 53, 3266-3269, 1993).