Multi objective optimization of drug regimens in cancer chemotherapy using a PK-PD model

Mathematical modeling and methods from control theory are employed to optimize drug regimens in cancer chemotherapy. In this paper, we utilized a PK-PD model to describe the effects of drugs on the tumor cells. In chemotherapy, it is essential to prescribe the drug dosages in a way that the number of cancer cells decreases while the least side effects are imposed to the patient. So, the consideration of simultaneous drug effects on both cancer and healthy cells (in this paper white blood cells) in an optimal drug regimen is necessary. Therefore, we have considered two cost functions to minimize the area under curve of tumors as well as the side effects on the patient during chemotherapy. Using these cost functions the drug regimens are calculated with the multi objective optimization (MOO) method. Thereafter, the best drug regimen from the set of these optimal regimens can be appropriately selected by oncologists according to the specific conditions of the patient. Numerical simulations are given to illustrate the flexibility of the proposed method.