Studying the Growth Kinetics of Untreated Clinical Tumors by Using an Advanced Discrete Simulation Model

Prior to an eventual clinical adaptation and validation of any clinically oriented model, a thorough study of its dynamic behavior is a sine qua non. Such a study can also elucidate aspects of the interplay of the involved biological mechanisms. Toward this goal, the paper focuses on an in-depth investigation of the free growth behavior of a macroscopically homogeneous malignant tumor system, using a discrete model of tumor growth. We demonstrate that when a clinical tumor grows exponentially, the following preconditions must be fulfilled: (a) time- and space-independent tumor dynamics, in terms of the transition rates among the considered cell categories and the duration of the cell cycle phases, and (b) a tumor system in a state of population equilibrium. Moreover, constant tumor dynamics during the simulation are assumed. In order to create a growing tumor, a condition that the model parameters must fulfill has been derived based on an analytical treatment of the model’s assumptions. A detailed parametric analysis of the model has been performed, in order to determine the impact and the interdependences of its parameters with focus on the free growth rate and the composition of cell population. Constraining tumor cell kinetics, toward limiting the number of possible solutions (i.e., sets of parameters) to the problem of adaptation to the real macroscopic features of a tumor, is also discussed. After completing all parametric studies and after adapting and validating the model on clinical data, it is envisaged to end up with a reliable tool for supporting clinicians in selecting the most appropriate pattern, extracted from several candidate therapeutic schemes, by exploiting tumor- and patient-specific imaging, molecular and histological data.