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

BMC Cancer

Research Article

Hana M. Dobrovolny¹  Hana Jaafari¹  Hope Murphy² 

[1] Department of Physics & Astronomy, Texas Christian University, 2800 S. University Drive, 76129, Fort Worth, TX, USA;Department of Physics, Utica College, Utica, NY, USA;

关键词: Tumor growth;    Mathematical model;    Ordinary differential equation;    Cancer;    Chemotherapy;   

DOI  :  10.1186/s12885-016-2164-x

 received in 2015-08-21, accepted in 2016-02-14,  发布年份 2016

来源: Springer

【 摘 要 】

BackgroundWhile 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.MethodsWe 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.ResultsWe 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.ConclusionOur results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

【 授权许可】

CC BY   
© Murphy et al. 2016

【 图 表 】

12951_2015_155_Article_IEq25.gif

12951_2015_155_Article_IEq24.gif

Fig. 2

12951_2017_270_Article_IEq5.gif

Fig. 3

Fig. 1

12951_2015_111_Article_IEq1.gif

Fig. 6

Fig. 4

Fig. 1

12951_2017_315_Article_IEq1.gif

Fig. 1

12951_2015_155_Article_IEq23.gif

12951_2015_155_Article_IEq22.gif

12951_2015_155_Article_IEq21.gif

12951_2015_155_Article_IEq20.gif

12951_2015_155_Article_IEq19.gif

12951_2015_155_Article_IEq18.gif