A cylindrical model of the rectum: comparing dose–volume, dose–surface and dose–wall histograms in the radiotherapy of prostate cancer

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Abstract
The calculation of the percentage cumulative histogram of the rectal wall (DWH) in prostate cancer radiotherapy may be subject to large uncertainties due to the difficulty of assessing the wall thickness on CT images. For this reason often only the external contour is used to define the rectum and then the percentage cumulative dose-volume histogram (DVH) of the rectum including any filling is calculated as a 'surrogate' for the DWH. More recently, other approaches using only the external contour have been proposed to estimate the DWH such as the percentage normalized dose-surface histograms (NDSH). A similar concept can be used when considering the solid rectum (the percentage normalized DVH, NDVH). The purpose of this investigation was to assess the relationships between rectal DVH, NDVH, DSH, NDSH and DWH in the common case of three- and four-field techniques in prostate cancer irradiation. Analytical relationships between the above parameters have been derived for a cylindrical rectum model in the case of three- and four-field techniques. The model is applied to the case of an empty rectum, a full rectum and to the more realistic mixed full/empty rectum situation for a four-field technique delivering 76 Gy (ICRU dose) with 18 MV x-rays. Different positions of the lateral beam with respect to the rectum axis were simulated. In the case of no lumen variation along the z-axis, the DWH is found to be very close to the DVH and to the DSH for empty and full rectum, respectively. The largest differences (up to 15%) between DVH and DSH were seen in the high-dose region (>70 Gy). In the more realistic case of lumen variation along the z-axis, the DWH always lies between NDVH and NDSH and, excluding the full-rectum situation, the DWH differs from the DVH by less than 7% in the 50-75 Gy range. In the case of significant portions of rectum being completely shielded, the DVH may differ from the NDVH/NDSH/DWH by up to 10-15%. In most clinical situations NDVH is within a few per cent of DWH, whilst NDSH may differ from DWH by up to 15-20%, especially in the high-dose region (V70). In conclusion, for most situations, the DVH is highly correlated with NDVH and DWH. A high degree of consistency between NDVH and DWH was found in most clinical cases whilst largest deviations between NDSH and DWH were evident in the high-dose region (70-75 Gy). In the less common case of a very full rectum a poorer correlation between DVH/NDVH and DWH was found whilst NDSH mimicked the DWH very well. In summary, except for the case of a 'very full' rectum, NDVH may be used as a robust surrogate for DWH. The DVH seems to be sufficiently robust if the rectum is prevalently empty.

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