Abstract
THE increase in volume or size with time that characterises many biological and physical systems is often well approximated retrospectively by mathematical ‘growth curves’. In some cases, however, growth may be sufficiently complicated for it to be impossible to predict later portions of the growth curve if observations are limited to a few early points. We report here the development of a generalised approach to the analysis of “Gompertzian” growth which enables accurate predictions of future growth for two model tumour systems. This mathematical method may be useful clinically, and expresses a property of biological growth that may be applicable to other systems.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Gompertz, B., Phil. Trans. R. Soc., 115, 513–585 (1825).
Laird, A. K., Br. J. Cancer, 18, 490–502 (1964).
McCredie, J. A., Inch, W. R., Kruuv, J., and Watson, T. A., Growth, 29, 331–347 (1965).
Simpson-Herren, L., and Lloyd, H. H., Cancer Chemother. Rep., 54, 143–174 (1970).
Shryock, H. S., and Siegel, J. S., The Methods and Materials of Demography (US Government Printing Office, Washington, DC, 1973).
Laird, A. K., Tyler, S. A., and Barton, A. D., Growth, 29, 233–248 (1965).
Weymouth, F. W., McMillin, H. C., and Rich, W. H., J. exp. Biol., 8, 228–249 (1931).
Laird, A. K., Growth, 29, 249–263 (1965).
Laird, A. K., Natn. Cancer Inst. Monogr., 30, 15–28 (1969).
Sullivan, P. W., and Salmon, S. E., J. clin. Invest., 51, 1697–1708 (1972).
Collins, V. P., Loeffler, K., and Tivey, H., Am. J. Roentgenol., 76, 988–1000 (1956).
Skipper, H. E., Schabel, F. M., Jr, and Wilcox, W. S., Cancer Chemother. Rep., 35, 1–111 (1964).
Wilcox, W. S., Griswold, D. P., and Laster, W. R., Jr, Cancer Chemother. Rep., 47, 27–39 (1965).
Duchatellier, M., and Israel, L., Eur. J. Cancer, 7, 545–549 (1971).
Looney, W. B., Trefil, J. S., Schaffner, J. C., Kovacs, C. J., and Hopkins, H. A., Proc. natn. Acad. Sci. U.S.A., 72, 2662–2666 (1975).
Baserga, R., Cancer Res., 25, 581–595 (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
NORTON, L., SIMON, R., BRERETON, H. et al. Predicting the course of Gompertzian growth. Nature 264, 542–545 (1976). https://doi.org/10.1038/264542a0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/264542a0
This article is cited by
-
Tumor growth and population modeling in a toxicant-stressed random environment
Journal of Mathematical Biology (2024)
-
Temporal and spatial topography of cell proliferation in cancer
Nature Cell Biology (2022)
-
Designing and interpreting 4D tumour spheroid experiments
Communications Biology (2022)
-
Can the Kuznetsov Model Replicate and Predict Cancer Growth in Humans?
Bulletin of Mathematical Biology (2022)
-
Sequential vs concurrent adjuvant chemotherapy of anthracycline and taxane for operable breast cancer
World Journal of Surgical Oncology (2021)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.