Variable Dose-Constraints Method for Enhancing Intensity-Modulated Radiation Therapy Treatment Planning

Norihisa Obata, Omar M. Abou Al-Ola, Ryosei Nakada, Takeshi Kojima and Tetsuya Yoshinaga ()
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Norihisa Obata: Graduate School of Health Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan
Omar M. Abou Al-Ola: Faculty of Science, Tanta University, El-Giesh St., Tanta 31527, Egypt
Ryosei Nakada: Radiation & Proton Therapy Office, Shizuoka Cancer Center, 1007 Shimonagakubo, Nagaizumi 411-8777, Japan
Takeshi Kojima: Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan
Tetsuya Yoshinaga: Institute of Biomedical Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan

Mathematics, 2024, vol. 12, issue 23, 1-26

Abstract: The conventional approach to intensity-modulated radiation therapy treatment planning involves two distinct strategies: optimizing an evaluation function while accounting for dose constraints, and solving feasibility problems using feasibility-seeking projection methods that incorporate inequality constraints. This paper introduces a novel iterative scheme within the framework of continuous dynamical systems, wherein constraint conditions dynamically evolve to enhance the optimization process. The validity of dynamically varying dose constraints is theoretically established through the foundation of continuous-time dynamical systems theory. In particular, we formalize a system of differential equations, with both beam coefficients and dose constraints modeled as state variables. The asymptotic stability of the system’s equilibrium is rigorously proven, ensuring convergence to a solution. In practical terms, we leverage a discretized iteration formula derived from the continuous-time system to achieve rapid computational speed. The mathematical structure of the proposed approach, which directly incorporates dose-volume constraints into the objective function, facilitates significant computational efficiency and solution refinement. The proposed method has an inherent dynamics that approaches more desirable solutions within the set of solutions when the solution to the optimization problem is not an isolated point. This property guarantees the identification of optimal solutions that respect the prescribed dose-volume constraints while enhancing accuracy when such constraints are feasible. By treating dose constraints as variables and concurrently solving the optimization problem with beam coefficients, we can achieve more accurate results when compared with using fixed values for prescribed dose conditions.

Keywords: dynamical system; piecewise-smooth system; optimization; intensity-modulated radiation therapy; stability of equilibrium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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