title: Practical aspects and uncertainty analysis of biological effective dose (BED) regarding its three-dimensional calculation in multiphase radiotherapy treatment plans.
abstract: OBJECTIVE
  There is a growing interest in the radiation oncology community to use the biological effective dose (BED) rather than the physical dose (PD) in treatment plan evaluation and optimization due to its stronger correlation with radiobiological effects. Radiotherapy patients may receive treatments involving a single only phase or multiple phases (e.g., primary and boost). Since most treatment planning systems cannot calculate the analytical BED distribution in multiphase treatments, an approximate multiphase BED expression, which is based on the total physical dose distribution, has been used. The purpose of this paper is to reveal the mathematical properties of the approximate BED formulation, relative to the true BED.
  
  
  METHODS
  The mathematical properties of the approximate multiphase BED equation are analyzed and evaluated. In order to better understand the accuracy of the approximate multiphase BED equation, the true multiphase BED equation was derived and the mathematical differences between the true and approximate multiphase BED equations were determined. The magnitude of its inaccuracies under common clinical circumstances was also studied. All calculations were performed on a voxel-by-voxel basis using the three-dimensional dose matrices.
  
  
  RESULTS
  Results showed that the approximate multiphase BED equation is accurate only when the dose-per-fractions (DPFs) in both the first and second phases are equal, which occur when the dose distribution does not significantly change between the phases. In the case of heterogeneous dose distributions, which significantly vary between the phases, there are fewer occurrences of equal DPFs and hence the inaccuracy of the approximate multiphase BED is greater. These characteristics are usually seen in the dose distributions being delivered to organs at risk rather than to targets.
  
  
  CONCLUSIONS
  The finding of this study indicates that the true multiphase BED equation should be implemented in the treatment planning systems due to the inconsistent accuracy of the approximate multiphase BED equation in most of the clinical situations.
authors.affiliation: Department of Radiology, University of Texas Health Science Center at San Antonio, San Antonio, Texas 78229 and Cancer Therapy and Research Center, San Antonio, Texas 78229.
authors.forename: Kevin I
authors.initials: KI
authors.lastname: Kauweloa
authors.affiliation: Department of Radiology, University of Texas Health Science Center at San Antonio, San Antonio, Texas 78229 and Cancer Therapy and Research Center, San Antonio, Texas 78229.
authors.forename: Alonso N
authors.initials: AN
authors.lastname: Gutierrez
authors.affiliation: Department of Radiology, University of Texas Health Science Center at San Antonio, San Antonio, Texas 78229 and Cancer Therapy and Research Center, San Antonio, Texas 78229.
authors.forename: Angelo
authors.initials: A
authors.lastname: Bergamo
authors.affiliation: Department of Radiology, University of Texas Health Science Center at San Antonio, San Antonio, Texas 78229 and Cancer Therapy and Research Center, San Antonio, Texas 78229.
authors.forename: Sotirios
authors.initials: S
authors.lastname: Stathakis
authors.affiliation: Department of Radiology, University of Texas Health Science Center at San Antonio, San Antonio, Texas 78229 and Cancer Therapy and Research Center, San Antonio, Texas 78229.
authors.forename: Nikos
authors.initials: N
authors.lastname: Papanikolaou
authors.affiliation: Department of Radiology, University of Texas Health Science Center at San Antonio, San Antonio, Texas 78229 and Cancer Therapy and Research Center, San Antonio, Texas 78229.
authors.forename: Panayiotis
authors.initials: P
authors.lastname: Mavroidis
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D012062:Relative Biological Effectiveness; D035501:Uncertainty