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 240 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.

In 147 cases of mammary carcinoma, 388 serial mammographies were performed before final treatment. The average retrospective observation time was 27 months with a range of two months to 11 years. The number of serial mammographies per case ranged between two and 11. The tumor volume doubling times (TV); obtained by measuring the growth of the tumor nucleus shadow in the mammographies, ranged from 44 to 1869 days with an average of 212 days. No correlation between volume doubling time and histologic differentiation could be found. One hundred of these cancer patients were found in a screening population of 22,000 women receiving serial mammographies in a time period ranging from two to 16 years. An additional 40 cancer patients surfaced in this group without roentgenologic but with foregoing clinical or thermographic abnormalities before final diagnosis. An additional 21 cancer patients surfaced without any foregoing abnormalities. The follow-up tumor ranged between three months and two years with a mean time of one year and nine months. Not considering tumor size, pathologic-thermographic signs appeared with greater frequency the faster the tumor grew. Theoretically, an average of more than 16 years should elapse before an initial tumor cell develops into a 10-mm primary mammary carcinoma (30 doubling times). Therefore the length of time necessary for a 2-mm tumor to grow to a size of 10-mm is, on the average, four years.

Adsorptive endocytosis of five different lysosomal enzymes from various human and non-human sources was susceptible to inhibition by mannose and l-fucose, methyl alpha-d-mannoside, alpha-anomeric p-nitrophenyl glycosides of mannose and l-fucose, mannose 6-phosphate and fructose 1-phosphate. A few exceptions from this general scheme were observed for particular enzymes, particularly for beta-glucuronidase from human urine. The inhibition of alpha-N-acetylglucosaminidase endocytosis by mannose, p-nitrophenyl alpha-d-mannoside and mannose 6-phosphate was shown to be competitive. The loss of endocytosis after alkaline phosphatase treatment of lysosomal enzymes supports the hypothesis that the phosphorylated sugars compete with a phosphorylated carbohydrate on the enzymes for binding to the cell-surface receptors [Kaplan, Achord & Sly (1977) Proc. Natl. Acad. Sci. U.S.A.74, 2026-2030]. Endocytosis of ;low-uptake' forms of alpha-N-acetylglucosaminidase and alpha-mannosidase was likewise susceptible to inhibition by sugar phosphates and by alkaline phosphatase treatment, suggesting that ;low-uptake' forms are either contaminated with ;high-uptake' forms or are internalized via the same route as ;high-uptake' forms. The existence of an alternative route for adsorptive endocytosis of lysosomal enzymes is indicated by the unaffected adsorptive endocytosis of rat liver beta-glucuronidase in the presence of phosphorylated sugars and after treatment with alkaline phosphatase.