Design of personalized cancer treatments by use of optimal control problems: The case of chronic myeloid leukemia.

The advances in the mathematical explanation of the dynamics underlying treated cancer has opened the door to the mathematical design of optimal therapies. In parallel, the improvements and cost reductions in experimentation and data analysis techniques have made the formulation of personalized therapies possible. However, the design of cancer therapies making use of optimal control theory has not fully considered this possibility in detail. In this paper we contribute to the existing literature by analyzing the diverse alternatives that optimal therapy models offer to design personalized treatments. Taking as the starting point the Chronic Myeloid Leukemia (CML) optimal therapy model in [25], we design personalized optimal therapy models for patients with: CML; CML with intrinsic and/or induced resistance to the administered drug; CML and suffering high drug toxicity and/or allergy to the administered drug; and CML with presence of adverse factors. Along the paper we show that the clinical and medical applicability -the ultimate objective of this biomathematical research- of our proposed personalized models relies on the joint and proper use of the implemented calibration, simulation, and mathematical approaches and techniques. All the theoretical results generated by our personalized optimal therapy models are corroborated by clinical evidence.

The effects of time valuation in cancer optimal therapies: a study of chronic myeloid leukemia.

BACKGROUND: The mathematical design of optimal therapies to fight cancer is an important research field in today's Biomathematics and Biomedicine given its relevance to formulate patient-specific treatments. Until now, however, cancer optimal therapies have considered that malignancy exclusively depends on the drug concentration and the number of cancer cells, ignoring that the faster the cancer grows the worse the cancer is, and that early drug doses are more prejudicial. Here, we analyze how optimal therapies are affected when the time evolution of treated cancer is envisaged as an additional element determining malignancy, analyzing in detail the implications for imatinib-treated Chronic Myeloid Leukemia. METHODS: Taking as reference a mathematical model describing Chronic Myeloid Leukemia dynamics, we design an optimal therapy problem by modifying the usual malignancy objective function, unaware of any temporal dimension of cancer malignance. In particular, we introduce a time valuation factor capturing the increase of malignancy associated to the quick development of the disease and the persistent negative effects of initial drug doses. After assigning values to the parameters involved, we solve and simulate the model with and without the new time valuation factor, comparing the results for the drug doses and the evolution of the disease. RESULTS: Our computational simulations unequivocally show that the consideration of a time valuation factor capturing the higher malignancy associated with early growth of cancer and drug administration allows more efficient therapies to be designed. More specifically, when this time valuation factor is incorporated into the objective function, the optimal drug doses are lower, and do not involve medically relevant increases in the number of cancer cells or in the disease duration. CONCLUSIONS: In the light of our simulations and as biomedical evidence strongly suggests, the existence of a time valuation factor affecting malignancy in treated cancer cannot be ignored when designing cancer optimal therapies. Indeed, the consideration of a time valuation factor modulating malignancy results in significant gains of efficiency in the optimal therapy with relevant implications from the biomedical perspective, specially when designing patient-specific treatments.