Journal of Applied and Numerical Optimization

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DOI: 10.23952/jano.8.2026.1.08
Volume 8, Issue 1, 1 April 2026, Pages 127-156

 

Abstract. Cancer treatment has advanced significantly over recent decades, with improvements in technology enabling radiation therapies that more precisely target tumors while sparing healthy tissue. One such approach is Intensity-Modulated Radiation Therapy or Intensity-Modulated Proton Therapy, which commonly relies on inverse planning. In inverse planning, clinicians specify acceptable radiation limits for healthy tissues while ensuring a sufficiently high dose to the tumor, and a computer-generated plan is produced to meet these criteria. In this work, we consider a key inverse-planning metric, the Dose-Volume Histogram (DVH). By interpreting the DVH as a probability distribution, we propose a framework to assess worst-case possible deviations from a reference DVH when generalized equivalent uniform dose constraints are imposed. We present several optimization models for solving the associated bounded moment problem, alongside closed-form bounds derived for four specific sequences of moments. To mitigate overly pessimistic outcomes associated with these formulations, we then introduce a mixed-integer programming approach that incorporates patient-specific anatomical and dosimetric information through a dose-deposition matrix. By embedding geometric considerations directly into the optimization model, the resulting DVH approximations achieve greater clinical relevance. Along with the incorporation of patient geometry, we also investigate strategies for controlling high-dose regions for organs at risk, comparing mean-tail dose and Conditional Value-at-Risk as two complementary approaches. Preliminary numerical experiments demonstrate how our formulations perform and highlight the tradeoffs between tractability and conservatism. The findings contribute to a clearer understanding of the effectiveness of moment-based DVH approximations in the context of radiation therapy planning.

 

How to Cite this Article:
A. Monegat, A. Morrison, B. Sadeghi, S. Welper, Y. Zinchenko, The shape of you: Incorporating patient geometry and controlling extreme dosage in radiation treatment planning, J. Appl. Numer. Optim. 8 (2026), 127-156.