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Book Sections Year : 2019

Population Modeling of Tumor Growth Curves, the Reduced Gompertz Model and Prediction of the Age of a Tumor

Abstract

Quantitative analysis of tumor growth kinetics has been widely carried out using mathematical models. In the majority of cases, individual or average data were fitted. Here, we analyzed three classical models (exponential, logistic and Gom-pertz within the statistical framework of nonlinear mixed-effects modelling , which allowed us to account for inter-animal variability within a population group. We used in vivo data of subcutaneously implanted Lewis Lung carcinoma cells. While the exponential and logistic models failed to accurately fit the data, the Gompertz model provided a superior descriptive power. Moreover, we observed a strong correlation between the Gompertz parameters. Combining this observation with rigorous population parameter estimation motivated a simplification of the standard Gompertz model in a reduced Gompertz model, with only one individual parameter. Using Bayesian inference, we further applied the population methodology to predict the individual initiation times of the tumors from only three measurements. Thanks to its simplicity, the reduced Gompertz model exhibited superior predictive power. The method that we propose here remains to be extended to clinical data, but these results are promising for the personalized estimation of the tumor age given limited data at diagnosis.
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Dates and versions

hal-02383995 , version 1 (28-11-2019)

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Cristina Vaghi, Anne Rodallec, Raphaelle Fanciullino, Joseph Ciccolini, Jonathan Paul M. Mochel, et al.. Population Modeling of Tumor Growth Curves, the Reduced Gompertz Model and Prediction of the Age of a Tumor. Mathematical and Computational Oncology, pp.87-97, 2019, ⟨10.1007/978-3-030-35210-3_7⟩. ⟨hal-02383995⟩
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