The delta envelope: a technique for dose distribution comparison

The gamma index is a tool that compares a dose distribution with a reference distribution by combining dose-difference and distance-to-agreement criteria. It has been widely used for ten years despite its high computational cost. This cost is due to both a search process for each reference point and the necessity to remove overestimations caused by the discrete nature of dose grids. The method proposed in this paper is much faster since it avoids both these problems. It consists in computing the delta envelope formed by the gamma ellipsoids around the points of the reference distribution. This delta envelope provides dose-difference tolerances that are then used to create new indices, called the delta indices, that provide useful information to interpret the deviations. Applied to both 1D and 2D test cases and compared to the gamma index, the S indices proved to be very accurate and intuitive. Their computational efficiency was evaluated on a 3D case: the delta envelope can be computed in 8 s on a 250 x 250 x 50 grid. Moreover it can be precomputed if the reference dose is known in advance. Then the delta indices are obtained in less than 2 s.