A comparative study of rectal dose histograms in prostate brachytherapy: Some analytic and numerical results

A cumulative dose histogram is the graph of an integral function integrated over a domain V ⊂ ℝ³ and is dubbed the dose-volume histogram (DVH), the dose-surface histogram (DSH) or the dose-wall histogram (DWH), depending on the dimension and structure of the region V. This paper presents a comparative study of the three rectal dose histograms for sixty patients as well as for a cylindrical model of the rectum; in particular, the DSH and DVH for the cylindrical model with one point source are computed analytically in terms of elliptic integrals. The difference among the three relative dose histograms, averaged over the sixty patients, is less than 5%, whereas that between DVH and DWH for various wall-thickness can be as large as 3-12 cm³ in the range 60-100 Gy. The paper also contains an error analysis using two simple models of the rectum, for which the true DSH and DWH can be computed via numerical integration, to evaluate the effect of digitization. The digitized computation agrees quite well with the pre-digitization numerical integration, within 1% or 0.2 cm³, because of the low dose-gradient effect near the rectum in prostate brachytherapy.