2026-03-12T14:09:20Z https://tokushima-u.repo.nii.ac.jp/oai

oai:tokushima-u.repo.nii.ac.jp:02013203 2025-04-28T07:00:07Z 1713853213384:1713853295607

Variable Dose-Constraints Method for Enhancing Intensity-Modulated Radiation Therapy Treatment Planning Obata, Norihisa Abou Al-Ola, Omar M. Nakada, Ryosei 兒島, 雄志 コジマ, タケシ Kojima, Takeshi 兒島 コジマ Kojima 雄志 タケシ Takeshi 40220694 吉永, 哲哉 ヨシナガ, テツヤ Yoshinaga, Tetsuya 吉永 ヨシナガ Yoshinaga 哲哉 テツヤ Tetsuya open access This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). dynamical system piecewise-smooth system optimization intensity-modulated radiation therapy stability of equilibrium 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. MDPI 2024-12-03 eng journal article VoR 415404 https://tokushima-u.repo.nii.ac.jp/records/2013203 https://doi.org/10.3390/math12233826 10.3390/math12233826 22277390 Mathematics 12 23 3826 https://tokushima-u.repo.nii.ac.jp/record/2013203/files/mathematics_12_23_3826.pdf application/pdf 806 KB 2025-04-23