Analysis of the dose-surface histogram and dose-wall histogram for the rectum and bladder

Dose distribution throughout a hollow organ is represented by either a dose-surface histogram (DSH) or a dose-wall histogram (DWH). A spherical shell model for the bladder and a cylindrical shell model for the rectum were introduced for quantifying the difference between the DWH and DSH. The difference was given by subtraction of the percent volume of the wall from the percent area of the surface for any specific dose level. Taking the dose-grid size and contour-delineation uncertainties into account, the DSH and DWH calculation errors were estimated by simplified formulas. The DSHs and DWHs for the rectum and bladder in patients undergoing four-field-prostate treatment and gynecological intracavitary brachytherapy were computed with a refined numerical algorithm. Results of the analytic models and the numerical calculations demonstrated that the difference between the DWH and DSH was small (about 5%) for a fully filled bladder or rectum but large (about 10%) for an empty rectum or a contracted bladder. The error of DSH was about 3%, which is smaller than that of DWH.