Superiorization of projection algorithms for linearly constrained inverse radiotherapy treatment planning

Florian Barkmann, Yair Censor, Niklas Wahl

Research output: Contribution to journalArticlepeer-review


Objective: We apply the superiorization methodology to the constrained intensity-modulated radiation therapy (IMRT) treatment planning problem. Superiorization combines a feasibility-seeking projection algorithm with objective function reduction: The underlying projection algorithm is perturbed with gradient descent steps to steer the algorithm towards a solution with a lower objective function value compared to one obtained solely through feasibility-seeking. Approach: Within the open-source inverse planning toolkit matRad, we implement a prototypical algorithmic framework for superiorization using the well-established Agmon, Motzkin, and Schoenberg (AMS) feasibility-seeking projection algorithm and common nonlinear dose optimization objective functions. Based on this prototype, we apply superiorization to intensity-modulated radiation therapy treatment planning and compare it with (i) bare feasibility-seeking (i.e., without any objective function) and (ii) nonlinear constrained optimization using first-order derivatives. For these comparisons, we use the TG119 water phantom, the head-and-neck and the prostate patient of the CORT dataset. Main results: Bare feasibility-seeking with AMS confirms previous studies, showing it can find solutions that are nearly equivalent to those found by the established piece-wise least-squares optimization approach. The superiorization prototype solved the linearly constrained planning problem with similar dosimetric performance to that of a general-purpose nonlinear constrained optimizer while showing smooth convergence in both constraint proximity and objective function reduction. Significance: Superiorization is a useful alternative to constrained optimization in radiotherapy inverse treatment planning. Future extensions with other approaches to feasibility-seeking, e.g., with dose-volume constraints and more sophisticated perturbations, may unlock its full potential for high performant inverse treatment planning.

Original languageEnglish
Article number1238824
JournalFrontiers in Oncology
StatePublished - 2023

Bibliographical note

Publisher Copyright:
Copyright © 2023 Barkmann, Censor and Wahl.


  • constrained treatment plan optimization
  • feasibility-seeking algorithm
  • IMRT
  • inverse planning
  • radiation therapy treatment planning
  • superiorization method

ASJC Scopus subject areas

  • Oncology
  • Cancer Research


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