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Recent analysis of relapse data from 1173 untreated early stage breast cancer patients with 16-20 year follow-up shows that frequency of relapse has a double peaked distribution. There is a sharp peak at 18 months, a nadir at 50 months and a broad peak at 60 months. Patients with larger tumors more frequently relapse in the first peak while those with smaller tumors relapse equally in both peaks. No existing theory of tumor growth predicts this effect. To help understand this phenomenon, a model of metastatic growth has been proposed consisting of three distinct phases: a single cell, an avascular growth, and a vascularized lesion. Computer simulation of this model shows that the second relapse peak can be explained by a steady stochastic progression from one phase to the next phase. However, to account for the first relapse peak, a sudden perturbation of the development at the time of surgery is necessary. Model simulations predict that patients who relapse in the second peak would have micrometastases in states of relatively low chemosensitivity when adjuvant therapy is normally administered. The simulation predicts that 15% of T1, 39% of T2, and 51% of T3 staged patients benefit from adjuvant chemotherapy, partially offsetting the advantage of early detection. This suggests that early detection and adjuvant chemotherapy may not be symbiotic strategies. New therapies are needed to benefit patients who would relapse in the second peak.

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The breast cancer treatment failure rate remains unacceptably high. The current breast cancer treatment paradigm, based primarily on Gompertzian kinetics and animal models, advocates short-course, intensive chemotherapy subsequent to tumor debulking, citing drug resistance and host toxicity as the primary reasons for treatment failure. To better understand treatment failure, we have studied breast cancer from the perspective of computer modeling. Our results demonstrate breast cancers grow in an irregular fashion; this differs from the Gompertzian mode of animal models and thus challenges the validity of the current paradigm. Clinical and laboratory data support the concept of irregular growth rather than the common claim that human tumors grow in a Gompertzian fashion. Treatment failure mechanisms for breast cancer appear to differ from those for animal models, and thus treatments optimize on animal models may not be optimal for breast cancer. A failure mechanism consistent with our results involves temporarily dormant tumor cells in anatomical or pharmacological sanctuary, which eventually result in aggressive metastatic disease.

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Since adjuvant chemotherapy and hormonal therapy generally extend disease free survival in breast cancer rather than provide a cure, we have examined the current breast cancer paradigm. Heterogeneity is a fundamental characteristic of breast cancer tissue and a well recognized aspect of the disease. There are variations in natural history, histopathology, biochemistry and endocrinology, and molecular biology of cancer tissues and cells within the tissues. A variety of data indicate that growth kinetics are also variable, not only from tumor to tumor, but also during the natural history of an individual's tumor. To better understand kinetic heterogeneity, a stochastic numeric computer model of the natural history of breast cancer has been developed. To be consistent with inter- and intratumor kinetic heterogeneity and with late relapse, the model predicts that tumors grow in an irregular fashion with alternating periods of growth and periods of dormancy rather than the generally accepted modified exponential, or Gompertzian fasion. The prediction of irregular growth has been compared to data relevant to growth characteristics of human breast cancer. Much data support the concept of irregular kinetics and temporary dormancy rather than steady, Gompertzian growth of human breast cancer. Thus, in addition to drug resistance, kinetic heterogeneity may help explain the limited impact that traditional chemotherpeutic treatment has had on mortality from breast cancer. Although the mechanisms underlying irregular growth need to be better understood, non-Gompertzian growth kinetics indicates that there may be alternative approaches for breast cancer treatment.

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It is generally accepted that human cancers grow in an exponential or Gompertzian manner. This assumption is based on analysis of the growth of transplantable animal tumors and on averages of tumor growth in human populations. A computer model of breast cancer in individual patients has raised some doubts about this assumption. The computer model predicts an irregular pattern of tumor growth that incorporates plateaus or dormant periods separated by Gompertzian growth spurts. Since growth patterns involving plateaus are not predicted by conventionally accepted exponential or Gompertzian kinetics, sufficient documentation of their existence may be regarded as some evidence that the computer model is correct. The literature has been surveyed to identify growth patterns specifically predicted by the model. The literature contains clinical evidence from individual patients of this growth pattern in primary breast, large intestine and rectum, and pulmonary cancers and metastatic pulmonary cancer. Much data, including the only breast data, are not consistent with exponential or Gompertzian kinetics but are explainable by irregular growth kinetics. Exponential growth is valid for some tumors and for short times, but there are many papers citing significant deviations from that growth. Exponential growth may accurately describe averages of human tumor growth and growth of multipassaged experimental tumors, but it is not valid for all individual tumors.

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A computer program which accepts clinically relevant information can be used to predict breast cancer growth, response to chemotherapy, and disease-free survival. The computer output is patient individualized because the program is highly iterative and simulates up to 2500 patients with exactly the same clinical presentation. Computer predictions have been compared to a broad spectrum of breast cancer data, and a high degree of correlation has been established. There are numerous significant clinical implications which can be derived from the computer model. Among these are the following. (a) Breast cancer tumors do not grow continuously but may have up to five growth plateaus each lasting from a small fraction of a year up to approximately 8 yr. (b) Adjuvant chemotherapy, such as 6-mo treatment with cyclophosphamide-methotrexate-5-fluorouracil, does not eradicate tumors but just reduces the number of viable cells by a factor of 10 to 100 and sets the eventual growth back by several years. This may partially explain why the age-adjusted death rate from breast cancer has not changed in the past 50 yr. (c) The computer model challenges the underlying principles in support of short-term intensive adjuvant chemotherapy, namely Gompertzian kinetics and genetically acquired tumor resistance to drugs. (d) The computer model questions the evidence opposing long-term maintenance chemotherapy protocols and suggests that maintenance protocols should be reexamined.

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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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