Hyperbolastic growth models

Theory and application

Mohammad Tabatabai, David Keith Williams, Zoran Bursac

Research output: Contribution to journalArticle

45 Citations (Scopus)

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.

Original languageEnglish (US)
JournalTheoretical Biology and Medical Modelling
Volume2
DOIs
StatePublished - Mar 30 2005

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Model Theory
Growth Model
Growth
Tumor
Tumors
Model
Stem Cells
Tumor Growth
Chemotherapy
Infectious Diseases
Weibull
Cellular Spheroids
Biological Phenomena
Progression
Neoplasms
Logistics
Neoplastic Stem Cells
Cancer
Schedule
Kinetics

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Health Informatics

Cite this

Hyperbolastic growth models : Theory and application. / Tabatabai, Mohammad; Williams, David Keith; Bursac, Zoran.

In: Theoretical Biology and Medical Modelling, Vol. 2, 30.03.2005.

Research output: Contribution to journalArticle

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