Hyperbolastic growth models: theory and application

Mohammad Tabatabai¹ , David Keith Williams² and Zoran Bursac²

¹Department of Mathematical Sciences, Cameron University, 2800 W Gore Blvd., Lawton, OK 73505, USA

²Department of Biostatistics, University of Arkansas for Medical Sciences, Slot 820, Little Rock, AR 72205, USA

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Theoretical Biology and Medical Modelling 2005, 2:14doi:10.1186/1742-4682-2-14


Published:	30 March 2005

Abstract

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.