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The delta envelope: A technique for dose distribution comparison
Author(s) -
Blanpain Baptiste,
Mercier David
Publication year - 2009
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.3070546
Subject(s) - envelope (radar) , mathematics , grid , distribution (mathematics) , ellipsoid , point (geometry) , algorithm , computer science , mathematical optimization , mathematical analysis , geometry , physics , telecommunications , radar , astronomy
The γ 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 δ envelope formed by the γ ellipsoids around the points of the reference distribution. This δ envelope provides dose‐difference tolerances that are then used to create new indices, called the δ indices, that provide useful information to interpret the deviations. Applied to both 1D and 2D test cases and compared to the γ index, the δ indices proved to be very accurate and intuitive. Their computational efficiency was evaluated on a 3D case: the δ envelope can be computed in 8 s on a 250 × 250 × 50 grid. Moreover it can be precomputed if the reference dose is known in advance. Then the δ indices are obtained in less than 2 s .