Breast cancer is a disease moderately responsive to chemotherapy. While its curability is inversely related to the tumor burden, a relevant number of patients still progress to metastatic disease even after adjuvant chemotherapy. Also, high-dose chemotherapy appears promising, but can not yet be considered ultimately curative of breast cancer. Different variables, biological, kinetic and treatment-related, account for the clinical behaviour of this disease. In order to improve its curability, they will all need to be taken into account in planning future treatment strategies. One of the most effective ways to understand and predict the clinical behaviour of breast cancer is the development of appropriate mathematical models explaining its growth-patterns. Aim of this paper is to review the two fundamental models, the exponential and the Gompertzian. The exponential model is at the basis of the Skipper-Schabel and the Goldie-Coldman hypotheses, while the Norton-Simon hypothesis has been formulated from the gompertzian model. The latter appears to better fit the vast amount of clinical data which are presently available: from Bloom's analysis of untreated breast cancer patients, to the results of large clinical trials, to the data emerged from the recent meta-analysis. Characteristic of a gompertzian growth pattern is that exponential growth is matched by exponential retardation of growth. In 1943 Delbruck and Luria demonstrated that random mutations could account for the development of virus resistance in bacteria and were able to estimate the rate of mutation as a function of the growth rate of bacteria. Shortly after Law demonstrated that resistance to methotrexate in murine leukemia occurred similarly. The concept of combination chemotherapy actually derived from the idea that cancer cells could be resistant to chemotherapy even before exposure to it. Goldie and Coldman applied the Delbruck/Luria model to hypothesize the use of non cross-resistant alternating combination chemotherapy as a better way to eliminate the risk of resistance. They also suggested that many different drugs were to be used as soon as possible, when the tumor size is still small. Most of their predictions were based on the Skipper/Schabel model of the exponential growth of cancer and on its deriving log-kill model. A large amount of clinical data are now suggesting that the behaviour of breast cancer is best described by gompertzian growth: in particular, gompertzian growth is a tenable model of breast cancer growth for both the unperturbed and the perturbed (by treatment) states.(ABSTRACT TRUNCATED AT 400 WORDS)
