A stochastic numerical model of breast cancer growth that simulates clinical data.

Abstract

A new stochastic numerical model of breast cancer growth is developed. First, the model suggests that Gompertzian kinetics does apply but that from time to time, in random fashion, there occurs a spontaneous change in the growth rate or rate of decay of growth, such that the overall growth pattern occurs in a stepwise fashion. According to the model, the average time for the tumor burden to increase from one cell to detection is probably in the range of 8 years. Secondly, the model suggests that there is a linear relationship between the number of axillary lymph nodes positive for metastasis at diagnosis and the number of other metastatic sites. This can be described mathematically by the equation S = 0.24 + 0.35N where S is the number of other metastatic sites and N is the number of positive lymph nodes. The model has been verified by simulating three data sets: (a) the survival times of untreated breast cancer patients as described by Bloom et al. [Br. Med. J., 2: 213-221, 1962]; (b) the growth rates of breast cancers immediately prior to diagnosis as described by Heuser and Spratt [Cancer (Phila.), 43: 1888-1894, 1979]; and (c) the disease-free survival time postmastectomy as described by Fisher et al. [Surg. Gynecol. Obstet., 140: 528-534, 1975]. This model could have implications concerning the overall treatment rationale for breast cancer.