Individual-based approaches to birth and death in avascular tumors

The understanding of the principles and the dominant mechanisms underlying tumor growth is an essential precondition in order to optimize treatment strategies. Mathematical and computer-based models can contribute to this since they allow testing of competing hypotheses in well-defined caricatures of biological experiments free from unknown or uncontrolled influences. In this paper, we focus on avascular tumor spheroids in vitro. This-system has been extensively studied experimentally. We present a single-cell based approach that allows the linking of model parameters to experimental accessible biomechanical and kinetic parameters and provides a potential, at least partly quantitative, description of growing avascular tumors in stages which are not primarily determined by nutrient or oxygen supply. To illustrate this, we compare the growth curve obtained by computer simulations with this model to experimental results of Freyer and Sutherland [1]. Based on the results of our model, we identify different growth regimes. In our approach, cells behave like elastic, attracting particles,in a viscous environment with the additional capability of growth and division. Hence, the approach in principle accounts for viscoelastic and growth properties of tumor spheroids, and furthermore, allows us to take into account genetic modifications on the length scale of a single cell. In this context, we discuss how regimes of generic system behavior may be identified. Generic regimes, in particular, seem useful in classifying growing multicellular systems by certain characteristic features. To Motivate the use of individual-based models, we present computer simulations with our model on a chemotherapy-inspired death process in d = 2 space dimensions. The results show the formation of morphological patterns which are characteristic for the growth regime of the unperturbated cell assembly before the death process starts. (C) 2003 Elsevier Science Ltd. All rights reserved.