Classical Mathematical Models for Description and Forecast of Experimental Tumor Growth

Sebastien Benzekry 1, * Clare Lamont 2 Afshin Beheshti 2 Amanda Tracz 3 John M. Ebos 3 Lynn Haltky 2 Philip Hahnfeldt 2
* Corresponding author
1 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative and discriminant analyses were performed for the purpose of comparing alternative models for their abilities to describe and predict tumor growth. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The models included in the study comprised the exponential (with or without free initial volume), exponential-linear, power law, Gompertz, logistic, generalized logistic and von Bertalanffy models, as well as a model with dynamic carrying capacity. For the breast data, the observed linear dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power for this data set, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. In contrast to the breast data, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day lung data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement of predictions. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.
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Sebastien Benzekry, Clare Lamont, Afshin Beheshti, Amanda Tracz, John M. Ebos, et al.. Classical Mathematical Models for Description and Forecast of Experimental Tumor Growth. PLoS Computational Biology, Public Library of Science, 2014, 10 (8), pp.e1003800. ⟨10.1371/journal.pcbi.1003800⟩. ⟨hal-00922553v6⟩

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