A Comparison and Catalog of Intrinsic Tumor Growth Models

Abstract

Determining the dynamics and parameter values that drive tumor growth is of great interest to mathematical modelers, experimentalists and practitioners alike. We provide a basis on which to estimate the growth dynamics of ten different tumors by fitting growth parameters to at least five sets of published experimental data per type of tumor. These timescale tumor growth data are also used to determine which of the most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor. In order to compute the best-fit parameters, we implemented a hybrid local-global least squares minimization algorithm based on a combination of Nelder-Mead simplex direct search and Monte Carlo Markov Chain methods.

Estimating Tumor Growth Rates In Vivo

“…Recently, Sarapata and de Pillis [29] have examined the effectiveness of a half-dozen different models in fitting the growth rates of in vitro tumor growth in ten different types of cancer. While the survey in [29] is impressive for its scope, the behavior of cells grown in a laboratory setting where they always have an ample supply of nutrients is not the same as that of tumors in a human body.…”

“…While the survey in [29] is impressive for its scope, the behavior of cells grown in a laboratory setting where they always have an ample supply of nutrients is not the same as that of tumors in a human body.…”

Identifying density-dependent interactions in collective cell behaviour

“…Two of the primary advantages of the IBM is its ability to precisely replicate the initial condition from experimental data; and, the ease of which new mechanisms can be added. Our approach can, therefore, be applied to quantify experimental evidence for more complex mechanisms including chemotaxis [14,41]; mechanotaxis [42]; generalised growth laws [43], to name a few. However, we do not pursue such extensions here since we find that our simpler modelling framework can provide a good match to all our experimental data without including more complex mechanisms.…”

Investigating the Reproducibility of In Vitro Cell Biology Assays Using Mathematical Models

“…In fact, several studies argue that the logistic growth equation does not always match experimental data [66,97,124,130]. For example, Laird examines in vivo tumour growth data and shows that the standard logistic model does not match experimental data [66].…”

“…For example, Laird examines in vivo tumour growth data and shows that the standard logistic model does not match experimental data [66]. Similarly, Sarapata and de Pillis find that the logistic growth model does not always match experimental tumour growth data [97].…”