A general methodology for three‐dimensional analysis of variation in target volume delineation

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Abstract
A generic method for three-dimensional (3-D) evaluation of target volume delineation in multiple imaging modalities is presented. The evaluation includes geometrical and statistical methods to estimate observer differences and variability in defining the Gross Tumor Volume (GTV) in relation to the diagnostic CT and MRI modalities. The geometrical method is based on mapping the 3-D shape of the target volume to a scalar representation, thus enabling a one-dimensional statistical analysis. The statistical method distinguishes observer and modality related uncertainties, which are expressed in terms of three error components: random observer deviations, systematic observer differences, and systematic modality differences. Monte Carlo simulations demonstrate that the standard errors of each of the three model parameters are inversely proportional to the square root of the product of the patient group size and the number of observers and proportional to the intraobserver variation. For 18 patients and 3 observers the standard errors of the estimated systematic modality and observer differences are 19% and 14% of the intraobserver standard deviation, respectively. A scalar representation of the shape of the prostate, delineated by 3 observers for 18 patients, was obtained by sampling the distance between the average center of gravity of the prostate in CT and the prostate surface for a large number of directions (2500), using polar coordinates. Observer variability and differences were obtained by applying the statistical method to the samples independently. The intraobserver variation for CT was largest in regions near the seminal vesicles (s.d: 3 mm) and the apex (s.d: 3 mm). The systematic observer variation in CT was largest in a region near the plexus Santorini, at the caudal-anterior side of the prostate (s.d.: 2 mm). The sensitivity for the choice of origin was tested by using the average center of gravity from axial MRI instead of CT. The results were almost identical. The polar map measures distances in the scanning directions. A correction procedure to get the variability in directions perpendicular to the surface of the prostate yielded variations that were a factor of 0.85 smaller for all directions. It is concluded that by separating the shape evaluation in a geometrical and a statistical part, the complexity of the analysis of 3-D shape differences can be significantly reduced. The method was successfully applied to a group of prostate patients, where we demonstrated that delineation variability is nonhomogeneous, with the largest variations occurring near the seminal vesicles and the apex.

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