Optimal Control of Medical Drug in a Nonlocal Model of Solid Tumor Growth

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular interactions through integral terms and drug-induced cell dea...

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Veröffentlicht in:	Journal of mathematical analysis and applications
Hauptverfasser:	Bouhamidi, Abderrahman, Imad, El Harraki, Melouani, Yassine
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier 12.03.2025
Schlagworte:	Mathematics Optimal control Partial Differential Equations Nonlocal Tumor Growth Model
ISSN:	0022-247X, 1096-0813
Online-Zugang:	Volltext
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Zusammenfassung:	This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular interactions through integral terms and drug-induced cell death. The model accounts for spatial heterogeneity in both tumor cell density and drug concentration while capturing the complex dynamics of drug resistance development. We first establish the well-posedness of the coupled system by proving the existence and uniqueness of a solution under appropriate regularity conditions. The optimal control problem is then formulated to minimize tumor size while accounting for drug toxicity constraints. Using variational methods, we derive the necessary optimality conditions and characterize the optimal control through an adjoint system. Theoretical results can help to design effective chemotherapy schedules that balance treatment efficacy with adverse effects.
ISSN:	0022-247X 1096-0813
DOI:	10.48550/arXiv.2503.09208