Decelerating growth and human breast cancer

Abstract

Background: Improved understanding of human breast cancer growth rates may have many clinical applications. Previous reports have used small numbers of patients and assumed an exponential growth rate.

Methods: The exponential equation and the most commonly used decelerating growth equations, the Gompertz equation and seven generalized forms of the logistic equation, were fitted to mammographic measurements of primary breast cancer using the least squares method. An average of 3.4 observations was made in 113 patients, whereas two measurements were made in another 335 patients. Tumors were assumed to originate as a single cell with the lethal tumor volume assumed to be 2(40) cells.

Results: All decelerating equations tested provided a better fit than the exponential, whereas a form of the logistic equation provided the best fit to the data. Limitations in the number of tumor measurements, the assumption of maximal tumor size, and biases inherent in the method of data collection are reviewed. These observations suggest families of curves that characterize breast cancer growth during the early period of clinical observation.

Conclusions: Breast cancer growth in the early clinical period was modeled by a form of the logistic equation. The exponential equation fit the data least well.