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

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 o...

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Published inCancer research (Chicago, Ill.) Vol. 44; no. 9; pp. 4124 - 4130
Main Authors SPEER, J. F, PETROSKY, V. E, RETSKY, M. W, WARDWELL, R. H
Format Journal Article
LanguageEnglish
Published Philadelphia, PA American Association for Cancer Research 01.09.1984
Subjects
Biological and medical sciences
Breast Neoplasms - physiopathology
Breast Neoplasms - surgery
Cell Division
Computers
Gynecology. Andrology. Obstetrics
Humans
Kinetics
Mammary gland diseases
Medical sciences
Models, Biological
Stochastic Processes
Tumors
Human
Development
Tumor
Models
Mammary gland
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Summary: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.
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ISSN:0008-5472
1538-7445