Quantifying the accuracy of affine transformations for modeling organ motion variabilities in external beam radiotherapy of prostate cancer

The present study is one part of an investigation of the hypothesis that a previously formulated statistical model of organ motion can predict a more accurate distribution of dose to the target volume and normal tissues than would otherwise be calculated based only on the static anatomical information available in the planning CT scan. This study concerns utilizing affine transformations to model the day-to-day variability in the shape and size of the prostate, bladder, and rectum. Using data from a CT serial imaging study, the accuracy of this affine approximation was quantified for each organ by calculating the distance between corresponding points on the surface of the organ as delineated in the initial and subsequent CT scans, after the initial surface was transformed onto the subsequent scans using the affine transformation calculated for that organ motion. It was found that the distance between corresponding points on the two surfaces was less than 7.45 mm for 95% of the prostate points analyzed (average 2.7 mm), less than 10.6 mm for 95% of the bladder points analyzed (average 3.4 mm), and less than 14.5 mm for 95% of those rectum points for which this distance could be quantified (average 5.5 mm). However, on certain CT planes the rectum surfaces exhibited deviations that could not be properly quantified with the method utilized, and consequently the distance values for the rectum are not an accurate representation of the true accuracy of the affine transformation.