About this Journal Submit a Manuscript Table of Contents
Journal of Theoretical Medicine
Volume 2 (2000), Issue 4, Pages 307-315
http://dx.doi.org/10.1080/10273660008833057

New Dimensions in Gompertzian Growth

1Biomathematics Resource Core, Mayo Clinic Comprehensive Cancer Center, Mayo Clinic and Mayo Foundation, Rochester, MN 55905, USA
2Department of Biochemistry and Molecular Biology, Mayo Clinic Comprehensive Cancer Center, Mayo Clinic and Mayo Foundation, Rochester, MN 55905, USA
3Stem Cell Laboratory, Mayo Clinic Comprehensive Cancer Center, Mayo Clinic and Mayo Foundation, Rochester, MN 55905, USA

Received 13 December 1998; Accepted 25 February 1999

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Gompertz function was formulated to represent an actuarial curve, yet it often fits growth of organisms, organs and tumors. Despite numerous attempts, no consensus has been forged about the biological foundation of the broad applicability of the model. Here we revisit the Gompertzian notion of the “power to grow” and equate it with growth fraction. Aside from conferring biological interpretability to the model, this approach allows leading to the possibility of exploring the behavior of Gompertzian growth with fractal kinetics. Significantly, we found that empirical models such as the logistic model, the von Bertalanffy model and the von Bertalanffy Richards model, together with the originative Gompertz model, are special cases of Gampertzian growth in fractal space. This finding permits an analysis of the growth kinetics of tumors which might affect model based design of Chemotherapy protocols.