Optimal dynamic control approach in a multi-objective therapeutic scenario: Application to drug delivery in the treatment of prostate cancer

Abstract

Abstract Numerous problems encountered in computational biology can be formulated as optimization problems. In this context, optimization of drug release characteristics or dosing schedules for anticancer agents has become a prominent area not only for the development of new drugs, but also for established drugs. However, in complex systems, optimization of drug exposure is not a trivial task and cannot be efficiently addressed through trial-error simulation exercises. Finding a solution to those problems is a challenging task which requires more advanced strategies like optimal control theory. In this work, we perform an optimal control analysis on a previously developed computational model for the testosterone effects of triptorelin in prostate cancer patients with the goal of finding optimal drug-release characteristics. We demonstrate how numerical control optimization of non-linear models can be used to find better therapeutic approaches in order to improve the final outcome of the patients.

Author summary Mathematical models of the disease processes are widely used in computational biology to quantitatively describe the time course of disease progression and are often linked to pharmacokinetic–pharmacodynamic models in order to evaluate the effect of drug treatment on disease. Once the models are built from observed information and/or literature data, they can predict the dynamics of the system under different conditions through computer simulations. However, simulation exercises are not always effective to obtain the desired objectives due to the complexity of these systems. In this work, we optimized the release characteristics of a synthetic gonadotropin-releasing hormone analog used to induce chemical castration by inhibiting the testosterone levels in prostate cancer patients. The therapeutic goals to achieve were to minimize the initial flare up of testosterone levels and the time to reach testosterone values below castration limit, while maximizing the castration period of the patients. Our methodology, based on control theory, introduces a manipulable variable into the system’s equations to drive the model towards the established goals. We demonstrated how drug-release properties can be improved with the implementation of optimal control strategies to enhance the outcome of cancer patients. These methods are extrapolable to other problems encountered in the field.