Modeling insight into spontaneous regression of tumors

The phenomenon of spontaneous regression of benign and malignant tumors is well documented in the literature and is commonly attributed to the inducti on of apoptosis or activation of the immune system. We attempt at evaluatin g the role of random effects in this phenomenon. To this end, we consider a stochastic model of tumor growth which is descriptive of the fact that tum ors are inherently prone to spontaneous regression due to the random nature of their development. The model describes a population of actively prolife rating cells which may give rise to differentiated cells. The process of ce ll differentiation is irreversible and terminates in cell death. We formula te the model in terms of temporally inhomogeneous Markov branching processe s with two types of cells so that the expected total number of neoplastic c ells is consistent with the observed mean growth kinetics. Within the frame work of this model, the extinction probability for proliferating cells tend s to one as time tends to infinity. Given the event of nonextinction, the d istribution of tumor size is asymptotically exponential. The limiting condi tional distribution of tumor size is in good agreement with epidemiologic d ata on advanced lung cancer. (C) 1999 Elsevier Science Inc. All rights rese rved.