Predicting the course of Gompertzian growth

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.

[1]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[2]  F. W. Weymouth,et al.  Latitude and Relative Growth in the Razor Clam, Siliqua Patula , 1931 .

[3]  V. P. Collins,et al.  Observations on growth rates of human tumors. , 1956, The American journal of roentgenology, radium therapy, and nuclear medicine.

[4]  Laird Ak.  DYNAMICS OF TUMOR GROWTH. , 1964 .

[5]  A. K. Laird.  Dynamics of Tumour Growth , 1964, British Journal of Cancer.

[6]  Tyler Sa,et al.  Dynamics of normal growth. , 1965 .

[7]  R. Baserga,et al.  THE RELATIONSHIP OF THE CELL CYCLE TO TUMOR GROWTH AND CONTROL OF CELL DIVISION: A REVIEW. , 1965, Cancer research.

[8]  A. K. Laird,et al.  Dynamics of relative growth. , 1965, Growth.

[9]  L. Israel,et al.  Growth fraction, resistance, schedule--doubling time relationship sequential versus simultaneous combinations, as evaluated by a mathematical model of response to chemotherapy. , 1971, European journal of cancer.

[10]  S. Salmon,et al.  Kinetics of tumor growth and regression in IgG multiple myeloma. , 1972, The Journal of clinical investigation.

[11]  Henry S. Shryock,et al.  The Methods and Materials of Demography. , 1973 .

[12]  W. Looney,et al.  Solid tumor models for the assessment of different treatment modalities: I. Radiation-induced changes in growth rate characteristics of a solid tumor model. , 1975, Proceedings of the National Academy of Sciences of the United States of America.