Isodoses—a set theory-based patient-specific QA measure to compare planned and delivered isodose distributions in photon radiotherapy

The gamma index and dose–volume histogram (DVH)-based patient-specific quality assurance (QA) measures commonly applied in radiotherapy planning are unable to simultaneously deliver detailed locations and magnitudes of discrepancy between isodoses of planned and delivered dose distributions. By exploiting statistical classification performance measures such as sensitivity or specificity, compliance between a planned and delivered isodose may be evaluated locally, both for organs-at-risk (OAR) and the planning target volume (PTV), at any specified isodose level. Thus, a patient-specific QA tool may be developed to supplement those presently available in clinical radiotherapy.

A method was developed to locally establish and report dose delivery errors in three-dimensional (3D) isodoses of planned (reference) and delivered (evaluated) dose distributions simultaneously as a function the dose level and of spatial location. At any given isodose level, the total volume of delivered dose containing the reference and the evaluated isodoses is locally decomposed into four subregions: true positive—subregions within both reference and evaluated isodoses, true negative—outside of both of these isodoses, false positive—inside the evaluated isodose but not the reference isodose, and false negatives—inside the reference isodose but not the evaluated isodose. Such subregions may be established over the whole volume of delivered dose. This decomposition allows the construction of a confusion matrix and calculation of various indices to quantify the discrepancies between the selected planned and delivered isodose distributions, over the complete range of values of dose delivered. The 3D projection and visualization of the spatial distribution of these discrepancies facilitates the application of the developed method in clinical practice.

Several clinical photon radiotherapy plans were analyzed using the developed method. In some plans at certain isodose levels, dose delivery errors were found at anatomically significant locations. These errors were not otherwise highlighted—neither by gamma analysis nor by DVH-based QA measures. A specially developed 3D projection tool to visualize the spatial distribution of such errors against anatomical features of the patient aids in the proposed analysis of therapy plans.

The proposed method is able to spatially locate delivery errors at selected isodose levels and may supplement the presently applied gamma analysis and DVH-based QA measures in patient-specific radiotherapy planning.