Generic and Specific Aspects in Growing avascular Tumors: First steps towards a quantitative single-cell-based approach

The understanding of the principles underlying tumor growth is essential in order to optimize treatment strategies. To identify the dominant mechanisms during tumor growth mathematical and computer-based models can be very useful since they allow to test competing hypotheses in caricatures of well-defined biological experiments free from unknown or uncontrolled influences. Clearly it is neither possible nor desirable to model an experimental situation in minute detail since (i) in general many details of the biological system under study are not known and (ii) incorporating too many and most often irrelevant details usually completely hides the view on essential ingredients and mechanisms. Therefore a major question is to which degree details must be incorporated into a model and which quantities in model and experiment should be compared in order to obtain an appropriate description of a biological system. One class of candidates are quantities that depend on the very specific biological situation, e.g. the growth law and morphology of a particular type of tumor in a particular situation. Another class of candidates are robust system properties as generic growth regimes which do neither depend on every detail of the model nor on every detail of the biological system. We here present a (i) cellular automaton approach, (ii) a lattice-free, fluid-like single-cell based approach (in which the model parameters are directly linked to kinetic and biomechanical quantities), and (iii) a number of heuristic approaches, all capable to describe the growth law of avascular tumors quantitatively. We suggest to evaluate the competing models based on a classification by their generic growth properties on which in a further step predictions, the hallmark of a model, can be based on. We show that this line of argument favors the direct, mechanistic model approaches (i.e., the cellular automaton and the fluid-like-model) over heuristic approaches concerning the system properties. We argue that the fluid-like model is an appropriate choice in the case of a quantitative description and motivate our line of argument by applications of this model type on further biological multicellular systems.