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Differential Equation Models of Neoadjuvant Chemotherapeutic Treatment Strategies for Stage III Breast Cancer

In this study, we investigate different neoadjuvant chemotherapy treatment strategies for patients with Stage III breast cancer. We use two deterministic models to illustrate the effect of chemotherapy on tumor growth and a patient's health. The models consist of a system of three differential equations representing (1) the tumor growth rate, (2) the change in the patient's health (a variable between 0 and 1), and (3) the rate at which the drug combination, cyclophosphamide and adriamycin, dissipates after administration. The intrinsic growth rate of the tumor is exponential in model A, and logistic in model B. In our numerical solutions, success is determined by whether the tumor can be reduced to an operable size (1 x 109 cells) before the patient's health falls to a fatal level (0.1). By varying the frequency and dosage of chemotherapy, we evaluate the effectiveness of various treatment schedules for patients beginning treatment with different sized tumors. We observe that patients diagnosed with smaller tumors show faster success if the chemotherapy dosages are kept constant. On the other hand, patients with larger tumors survive longer when the dosage at each chemotherapy session is proportional to the tumor size and the patient's health.

Article Number:
BU-1522-M

Year:
1999

Authors:
Edith Aguirre, University of Texas- El Paso
Tametra Smith, Howard University
Jennifer Stancil, University of North Carolina-Chapel Hill
Nicolas Davidenko, Harvard University

differential_equation_models_of_neoadjuvant_chemotherapeutic_treatment_strategies_for_stage_iii_breast_cancer_patients.pdf