Breast cancer mortality rates across the entire population in the USA have remained almost unchanged since 1970 . In terms of numbers, it is estimated that 43 300 women died of breast cancer in the USA in 1999 . Those who succumbed to this disease did so as a consequence of metastatic dissemination or the treatment of metastasis. A large percentage of these women were treated with cytotoxic chemotherapy, with drugs that are demonstrated to be effective against breast carcinoma cells both in vitro and in vivo. Nevertheless, despite being treated with the optimal doses at the optimal schedule, a significant percentage of women will relapse and die. For example, recurrence-free and survival rates at 10 years for women receiving polychemotherapy, for all ages, as estimated in the Oxford Overview, were 44 and 51.3%, respectively .
This leads us to ask several questions. First, why are these treatments unable to cure a large percentage of women? Is it the result of cells that are resistant, either kinetically or by means of clonal evolution, to the drugs? Is it a problem of inefficient delivery to the tumor cells or a problem that pertains to the tumor microenvironment? A second question, undoubtedly related to the first set of questions, is why does breast cancer continue to recur up to 20 years after treatment of the primary tumor [4,5,6,7,8,9,10].
One discipline that can be helpful in answering the questions posed above is mathematical modeling. It has been observed that trial and error manipulation of cancer treatment can be an inefficient method of understanding and developing treatment strategies [11,12**]. The use of mathematical models can aid researchers by explaining why some strategies fail; by suggesting refinements to current clinical approaches; and, finally, by suggesting alternative treatment strategies based on mathematical models that are derived from both known and hypothesized physiologic phenomena. Furthermore, many variations in the alternative strategies can be tested rapidly in silico (on the computer), to determine their effectiveness in a clinical setting. Although modeling strategies cannot replace experimental and clinical results, they can both eliminate some treatment strategies and suggest alternative strategies that may not be apparent just from trial and error manipulation.