Quantifying cell migration distance as a contributing factor to the development of rectal toxicity after prostate radiotherapy.

Purpose: Spatial information is usually neglected in mathematical models of radiation-induced toxicity. In the presence of inhomogeneous dose distributions produced by intensity modulated radiation therapy (IMRT) and volumetric arc therapy, this may be a limitation. We present a model to quantify the spatial characteristics of the dose distribution on the rectum through the quantification of the distribution of distances between dose points on the surface of the rectum in three-dimensions. The method allows us to evaluate the hypothesis that distances between lower and higher dose regions on the rectum influence radiation damage repair due to the migration of normal cells into damaged areas, and consequently, the development of radiation-induced toxicity in patients treated with radiation for prostate cancer. Methods: We present a method to compute distances between dose points on the surface of the rectum in three dimensions (3D) and to generate distance maps representing the distances between specific dose regions on the rectum. We introduce the concept of the distance dose surface histogram (DDSH), which is computed from the distance maps. The DDSH is a 2D histogram of rectum area on a grid defined by pairwise combinations of dose and distance. Each bin in the DDSH quantifies the area of the rectum exposed to a given dose and at a given distance from other another dose region on the rectum. By summing across the columns and rows of the DDSH, we can generate the dose surface histogram (DSH) and distance surface histogram (DiSH) for a particular dose region. The DiSH is a marginal histogram showing the distribution of distances for the dose points in a specific dose region from another region. We computed the DDSH, DiSH, and DSH for 33 patients treated with IMRT for prostate cancer, nine of whom developed late Grade 2 or higher late rectal toxicity. Results: We show how even though the total area of the rectum exposed to a given dose may be the same for different patients, the distribution of distances for points receiving that dose can be different depending on the shape and contiguity of the region(s) containing those dose points. We also show that area of the rectum in the region receiving more than 75 Gy and at a distance of 16 to 22 mm from the 50 Gy isodose line was significantly correlated to the development of toxicity (p = 0.004, two sided t-test). This suggests that examining the distance distribution of points in specific dose regions could provide valuable additional information in predicting the risk of a patient developing radiation-induced rectal toxicity. Conclusions: We present a new method to quantify the spatial distribution of points in a given region relative to other regions on the rectum. The method provides a means to evaluate the hypothesis that distances between lower and higher dose regions on the rectum influence radiation damage repair due to the migration of normal cells into damaged areas, and may be a contributing factor to the development of radiation-induced toxicity in patients treated with radiation for prostate cancer.