Mathematical analysis of approximate biological effective dose (BED) calculation for multi-phase radiotherapy treatment plans

Abstract

Purpose: There is growing interest about biological effective dose (BED) and its application in treatment plan evaluation due to its stronger correlation with treatment outcome. An approximate biological effective dose (BED A ) equation was introduced in order to simplify BED calculations by treatment planning systems in multi-phase treatments. The purpose of this work is to reveal its mathematical properties relative to the true, multi-phase BED (BED T ) equation. Methods : The BED T equation was derived and used to reveal the mathematical properties of BED A . MATLAB (MathWorks, Natick, MA) was used to simulate and analyze common and extreme clinical multi-phase cases. In those cases, percent error and Bland-Altman analysis were used to study the significance of the inaccuracies of BED A for different combinations of total doses, numbers of fractions, doses per fractions and α/β values. All the calculations were performed on a voxel-basis in order to study how dose distributions would affect the accuracy of BED A . Results: When the voxel dose-per-fractions (DPF) delivered by both phases are equal, BED A and BED T are equal (0% error). In heterogeneous dose distributions, which significantly vary between the phases, there are fewer occurrences of equal DPFs and hence the imprecision of BED A is greater. It was shown that as the α/β ratio increased the accuracy of BED A would improve. Examining twenty-four cases, it was shown that the range of DPF ratios for 3% P error varied from 0.32 to 7.50Gy, whereas for P error of 1% the range varied from 0.50 to 2.96Gy. Conclusion : The DPF between the different phases should be equal in order to render BED A accurate. OARs typically receive heterogeneous dose distributions hence the probability of equal DPFs is low. Consequently, the BED A equation should only be used for targets or OARs that receive uniform or very similar dose distributions by the different treatment phases. --------------------------- Cite this article as : Kauweloa KI, Gutierrez AN, Bergamo A, Stathakis S, Papaniko-laou N, Mavroidis P. Mathematical analysis of approximate biological effective dose (BED) calculation for multi-phase radiotherapy treatment plans. Int J Cancer Ther Oncol 2014; 2(2):020226. DOI: 10.14319/ijcto.0202.26