Optimal control of drug scheduling of nonlinear chemotherapy model with state constraints and parameter sensitivity analysis

Cancer chemotherapy scheduling presents a significant optimization challenge: it aims to minimize the tumor burden while adhering to toxicity and pharmacokinetic constraints. This study employs a bang-bang optimal control framework applied to a nonlinear cancer chemotherapy model with state constraints. The model incorporates pharmacodynamic parameters and cumulative toxicity limits and is numerically solved <i>via</i> a high-resolution discretization approach in the AMPL modeling environment with IPOPT. The proposed method yields a final tumor size of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>9.9466</mml:mn><mml:mo>×</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mn>10</mml:mn></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mtext>,</mml:mtext></mml:math> demonstrating a 32.8% improvement over previous optimization techniques. We also investigated the role of time-dependent tumor reduction constraints and performed a sensitivity analysis on key biological parameters, such as the tumor growth rate, drug responsiveness, and biochemical clearance. The proposed framework, through its integration of parameter sensitivity analysis and constrained optimal control, provides a basis for adaptive and patient-specific chemotherapy scheduling that can dynamically adjust to individual tumor and pharmacokinetic profiles. These findings highlight the potential of optimal control methods to inform personalized chemotherapy regimens and suggest directions for clinical translation. However, further validation using real patient data is necessary to confirm the robustness and applicability of the proposed approach.