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. 2016 Feb 26:16:163.
doi: 10.1186/s12885-016-2164-x.

Differences in predictions of ODE models of tumor growth: a cautionary example

Hope Murphy  1 , Hana Jaafari  2 , Hana M Dobrovolny  3
Affiliations

Differences in predictions of ODE models of tumor growth: a cautionary example

Hope Murphy et al. BMC Cancer. .

Abstract

Background: While mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer.

Methods: We examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model.

Results: We find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used.

Conclusion: Our results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

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Figures

Fig. 1
Fig. 1
Model fits to data. Best fits of the ODE tumor growth models to the first half of the data from Worschech et al. [43]. Parameter estimates are given in the table below the graph
Fig. 2
Fig. 2
ODE models’ predicted time course of tumor growth. Each model was fit to the first seven time points and parameter estimates were used to extrapolate the remaining seven time points. The SSR for each prediction is given in the table below the graph
Fig. 3
Fig. 3
Model fits to data. Best fits of the ODE tumor growth models to the data from Worschech et al. [43]. Parameter estimates are given in the table below the graph
Fig. 4
Fig. 4
Estimates of clinically important measurements. Model predictions of the maximum tumor volume (left), doubling time (center), and minimum concentration of chemotherapy needed for eradication (right) based on parameter estimates from the half (top row) or the full (center row) Worschech data set. The bottom row shows the percent change in each of the predictions when the full data set is used rather than the truncated data set
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