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 induction of apoptosis or activation of the immune system. We attempt at evaluating 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 tumors are inherently prone to spontaneous regression due to the random nature of their development. The model describes a population of actively proliferating cells which may give rise to differentiated cells. The process of cell differentiation is irreversible and terminates in cell death. We formulate the model in terms of temporally inhomogeneous Markov branching processes with two types of cells so that the expected total number of neoplastic cells is consistent with the observed mean growth kinetics. Within the framework of this model, the extinction probability for proliferating cells tends to one as time tends to infinity. Given the event of nonextinction, the distribution of tumor size is asymptotically exponential. The limiting conditional distribution of tumor size is in good agreement with epidemiologic data on advanced lung cancer.