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Despite internal complexity, tumor growth kinetics follow relatively simplemacroscopic laws that have been quantified by mathematical models. To resolvethis further, quantitative and discriminant analyses were performed for thepurpose of comparing alternative models for their abilities to describe andpredict tumor growth. For this we used two in vivo experimental systems, anectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopicallyxenografted human breast carcinoma. The goals were threefold: to 1) determine astatistical model for description of the volume measurement error, 2) establishthe descriptive power of each model, using several goodness-of-fit metrics anda study of parametric identifiability, and 3) assess the models ability toforecast future tumor growth.  Nine models were compared that included the exponential, power law, Gompertzand (generalized) logistic formalisms. The Gompertz and power law provided themost parsimonious and parametrically identifiable description of the lung data,whereas the breast data were best captured by the Gompertz andexponential-linear models. The latter also exhibited the highest predictivepower for the breast tumor growth curves, with excellent prediction scores(greater than 80$\%$) extending out as far as 12 days. In contrast, for thelung data, none of the models were able to achieve substantial prediction rates(greater than 70$\%$) further than the next day data point. In this context,adjunction of a priori information on the parameter distribution led toconsiderable improvement of predictions.  These results not only have important implications for biological theories oftumor growth and the use of mathematical modeling in preclinical anti-cancerdrug investigations, but also may assist in defining how mathematical modelscould serve as potential prognostic tools in the clinical setting.

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth