Comparison of rectal dose histograms under conditions of nonlinear isodoses

Cumulative dose-volume histograms of organs-at-risk are commonly used as predictors of the likelihood and severity of toxicity. In the case of hollow organs such as the rectum, the dose-volume histogram of the organ disregarding the lumen (dose-wall histogram, DWH) can be difficult to outline, and where the voxel size approaches the wall thickness, poor dose statistics can result. Various surrogates for DWH have been proposed, including the dose-volume histogram of organ plus the lumen (DVH), the dose-surface histogram (DSH), the normalized dose-volume histogram of organ plus lumen (NDVH) and the normalized dose-surface histogram (NDSH). In order to test the relative relationships between these histogram types in the case of prostate radiotherapy, a cylindrical model of the rectum has been combined with an idealized nonlinear isodose model in order to allow typical isodose shapes from both conventional three-field radiotherapy and prostate IMRT to be studied. Analytic expressions for histogram values are derived, and implemented through a spreadsheet. Isodose shapes and positions from five patients are combined to generate typical isodose distributions for which histograms may be generated and compared. It is found that the plan type has little effect on the relative values of the histogram points, and that no other histogram acts as a robust estimate of the DWH under all conditions. However, if the irradiated portion of the rectum is empty, NDVH is a good surrogate for DWH.