Clinical analysis of the approximate, 3-dimensional, biological effective dose equation in multiphase treatment plans

A multiphase, approximate biological effective dose (BED_A) equation was introduced because most treatment planning systems (TPS) are incapable of calculating the true BED (BED_T). This work investigates the accuracy and precision of the multiphase BED_A relative to the BED_T in clinical cases. Ten patients with head and neck cancer and 10 patients with prostate cancer were studied using their treatment plans from Pinnacle³ 9.2 (Philips Medical, Fitchburg, WI). The organs at risk (OARs) that were studied are the normal brain, left and right optic nerves, optic chiasm, spinal cord, brainstem, bladder, and rectum. BED_A and BED_T distributions were calculated using MATLAB 2010b (MathWorks, Natick, MA) and analyzed on a voxel basis for percent error, percent error volume histograms (PEVHs), Pearson correlation coefficient, and Bland-Altman analysis. The maximum BED values that were calculated using the BED_A and BED_T methods were also analyzed. BED_A was found to always underestimate BED_T. The accuracy and precision of BED_A distributions varied between the organs: for optic chiasm and brainstem, 50% of the patients had an overall BED_A percent error of <1%; for left and right optic nerves, rectum, and bladder, 60% to 70% of the patients had an overall BED_A percent error of <1%; and for normal brain and spinal cord, 80% of the patients had an overall BED_A percent error of <1%. BED_A distributions had maximum errors ranging from 2% to 11%, with the 11% error occurring for bladder. BED_A produced much more accurate maximum BED values with adjacent organs such as normal brain, bladder, and rectum. This study has shown that BED_A can calculate BED distributions with acceptable accuracy under certain circumstances. However, its consistency and accuracy strongly depend on the dose distributions of the different treatment phases. One should be cautious when using BED_A.