A Nonconvex Optimization Approach to IMRT Planning with Dose–Volume Constraints

Kelsey Maass (), Minsun Kim () and Aleksandr Aravkin ()
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Kelsey Maass: Department of Applied Mathematics, University of Washington, Seattle, Washington 98195
Minsun Kim: Department of Radiation Oncology, University of Washington, Seattle, Washington 98195
Aleksandr Aravkin: Department of Applied Mathematics, University of Washington, Seattle, Washington 98195

INFORMS Journal on Computing, 2022, vol. 34, issue 3, 1366-1386

Abstract: Fluence map optimization for intensity-modulated radiation therapy planning can be formulated as a large-scale inverse problem with competing objectives and constraints associated with the tumors and organs at risk. Unfortunately, clinically relevant dose–volume constraints are nonconvex, so standard algorithms for convex problems cannot be directly applied. Although prior work focuses on convex approximations for these constraints, we propose a novel relaxation approach to handle nonconvex dose–volume constraints. We develop efficient, provably convergent algorithms based on partial minimization, and show how to adapt them to handle maximum-dose constraints and infeasible problems. We demonstrate our approach using the CORT data set and show that it is easily adaptable to radiation treatment planning with dose–volume constraints for multiple tumors and organs at risk. Summary of Contribution: This paper proposes a novel approach to deal with dose–volume constraints in radiation treatment planning optimization, which is inherently nonconvex, mixed-integer programming. The authors tackle this NP-hard problem using auxiliary variables and continuous optimization while preserving the problem’s nonconvexity. Algorithms to efficiently solve the nonconvex optimization problem presented in this paper yield computation speeds suitable for a busy clinical setting.

Keywords: healthcare; radiation therapy; nonconvex optimization; treatment planning (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:34:y:2022:i:3:p:1366-1386

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