A unified approach for inversion problems in intensity-modulated radiation therapy

Yair Censor, Thomas Bortfeld, Benjamin Martin, Alexei Trofimov

Research output: Contribution to journalArticlepeer-review


We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.

Original languageEnglish
Pages (from-to)2353-2365
Number of pages13
JournalPhysics in Medicine and Biology
Issue number10
StatePublished - 21 May 2006

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging


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