Sparsity constrained split feasibility for dose-volume constraints in inverse planning of intensity-modulated photon or proton therapy

Scott Penfold, Rafa L. Zalas, Margherita Casiraghi, Mark Brooke, Yair Censor, Reinhard Schulte

Research output: Contribution to journalArticlepeer-review


A split feasibility formulation for the inverse problem of intensity-modulated radiation therapy treatment planning with dose-volume constraints included in the planning algorithm is presented. It involves a new type of sparsity constraint that enables the inclusion of a percentage-violation constraint in the model problem and its handling by continuous (as opposed to integer) methods. We propose an iterative algorithmic framework for solving such a problem by applying the feasibility-seeking CQ-algorithm of Byrne combined with the automatic relaxation method that uses cyclic projections. Detailed implementation instructions are furnished. Functionality of the algorithm was demonstrated through the creation of an intensity-modulated proton therapy plan for a simple 2D C-shaped geometry and also for a realistic base-of-skull chordoma treatment site. Monte Carlo simulations of proton pencil beams of varying energy were conducted to obtain dose distributions for the 2D test case. A research release of the Pinnacle 3 proton treatment planning system was used to extract pencil beam doses for a clinical base-of-skull chordoma case. In both cases the beamlet doses were calculated to satisfy dose-volume constraints according to our new algorithm. Examination of the dose-volume histograms following inverse planning with our algorithm demonstrated that it performed as intended. The application of our proposed algorithm to dose-volume constraint inverse planning was successfully demonstrated. Comparison with optimized dose distributions from the research release of the Pinnacle 3 treatment planning system showed the algorithm could achieve equivalent or superior results.

Original languageEnglish
Pages (from-to)3599-3618
Number of pages20
JournalPhysics in Medicine and Biology
Issue number9
StatePublished - 5 Apr 2017

Bibliographical note

Publisher Copyright:
© 2017 Institute of Physics and Engineering in Medicine.


  • CQ-algorithm
  • automatic relaxation method
  • dose-volume constraints
  • intensity-modulated proton therapy
  • inverse planning
  • sparsity constraints
  • split feasibility

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging


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