On an optimal control problem describing lactate production inhibition

ABSTRACT

Altered metabolism, characterized by high concentration levels of lactate enzyme, contributes to tumor development, malignancy, and metastasis and introduces metabolic liabilities that can be employed in cancer treatment. Here, this paper aims to reach a desired lactate concentration, under the action of an optimal treatment dose, represented by a control, at an optimal treatment time. We consider an objective functional to be minimized associated with a system modeling lactate dynamics in the presence of control. We show the existence of a minimizer of this functional, and we derive a first-order necessary optimality condition.

KEYWORDS:

• Altered metabolism
• glioma treatment
• lactate dehydrogenase
• first-order necessary optimality conditions

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 49J20
• 49K20
• 35K61
• 35K57
• 92C17

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and useful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).