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Construction of a Growth Curve for Mammary Tumors of the Rat¹

Division of Biology and Medicine, Lawrence Radiation Laboratory, University of California, Berkeley, California 94720

Age at mammary tumor onset must be known accurately when the goal of an experiment is the study of latency or age dependence. Yet it is often difficult to establish the time of onset of many primary animal tumors with any degree of certainty. Empiric growth curves have been constructed as an aid in the study of the age dependence of spontaneous and raidationinduced fibroadenoma and mammary carcinoma of the rat. These growth curves permit all such tumors to be referred back to a common stage of development regardless of their size when first detected.

Growth data were obtained from 117 fibroadenomas and 24 carcinomas that developed in either irradiated rats or aging controls. The size at which mammary tumors are just detectable was determined to be a diameter of 1 cm (corresponding to a weight of 0.5 gm), and this was selected as the "reference size." Tumor age was defined as the number of days a tumor had been growing since it was "reference size."

The growth patterns of individual fibroadenomas were variable, reflecting a wide range in their proportions of epithelial and connective tissue and the presence or absence of secretory activity. The growth rates of secretory and nonsecretory fibroadenomas were found to be indistinguishable.

Growth of fibroadenoma from 0.5 to 5.0 gm was nearly exponential. Growth rate gradually decreased, and eventually a limiting size was approached. The growth of this tumor was described well by the Gompertz function. W = W₀e^A/(1--t) The initial weight was fixed at W_o = 0.5 gm, and the parameters A and were machine-calculated from the original growth data by a least-squares fitting method. The computed values were A = 0.077 day^-1 and = 0.0135 day^-1, corresponding to an initial doubling time of 9.0 days, and the approach to limiting size of 149 gm at 370 days (t 5), respectively. Tumor age estimated from this curve was reliable to within ±20 days (one S.D.).

A Gompertz curve was also fitted to the growth data of mammary carcinoma. The carcinomas grew somewhat more rapidly at first, A = 0.097 day^-1, and tended to approach a limiting size sooner, = 0.019 day^-1, than fibroadenoma.

The growth rate of this primary fibroadenoma of the rat was compared with the growth rates of several other rodent tumors by use of the method of Laird (15). Normalization of the size and time scales of the Gompertz curve of fibroadenoma yielded an adjusted curve that was superimposable on Laird's theoretic curve of tumor growth.

Extrapolation of the Gompertz equations derived for fibroadenoma and mammary carcinoma back to the time each might have existed as a single cell gave reasonable values—109 and 83 days, respectively—for the time needed to grow from a single cell to a detectable size, 0.5 gm.

¹ Work performed under auspices of the U. S. Atomic Energy Commission.

² Present address: Kansas City General Hospital, Kansas City, Missouri.

Received 1/11/66. Accepted 4/ 4/67.