Hyperbolastic growth models: theory and application

Background: Mathematical models describing growth kinetics are very important for predicting many biological phenomena such as tumor volume, speed of disease progression, and determination of an optimal radiation and/or chemotherapy schedule. Growth models such as logistic, Gompertz, Richards, and Weibull have been extensively studied and applied to a wide range of medical and biological studies. We introduce a class of three and four parameter models called hyperbolastic models for accurately predicting and analyzing self-limited growth behavior that occurs e. g. in tumors. To illustrate the application and utility of these models and to gain a more complete understanding of them, we apply them to two sets of data considered in previously published literature. Results: The results indicate that volumetric tumor growth follows the principle of hyperbolastic growth model type III, and in both applications at least one of the newly proposed models provides a better fit to the data than the classical models used for comparison. Conclusion: We have developed a new family of growth models that predict the volumetric growth behavior of multicellular tumor spheroids with a high degree of accuracy. We strongly believe that the family of hyperbolastic models can be a valuable predictive tool in many areas of biomedical and epidemiological research such as cancer or stem cell growth and infectious disease outbreaks.