Implementation of the ETAR method for 3D inhomogeneity correction using FFT

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Abstract
The equivalent tissue‐air‐ratio (ETAR) method employs three‐dimensional (3D) CT pixel information to approximate scatter dose contribution for inhomogeneity correction. In general, the calculation provides better agreement with measurements than the one‐dimensional (1D) methods typically used in commercial treatment planning systems. In its original implementation, the 3D formulation of the ETAR method is modified empirically as a 2D calculation in order to reduce computation time. The modification compromises the use of the method in several treatment geometries. An examination of the ETAR formulation shows that the calculation can be expressed as a convolution and thus can be performed in 3D using fast Fourier transform (FFT) techniques. The algorithm has been implemented as a 3D FFT convolution. Making use of the symmetric properties of the FFT, the new approach shows significant savings in computation time without excessive memory requirement. Despite its fundamental limitations when applied to regions of electronic disequilibrium, the ETAR method offers a practical solution to improving current dose calculation in 3D treatment planning, particularly when the more advanced scatter ray‐tracing dose calculation algorithms remain impractical for clinical use. Recent work to extend the method to approximate electron transport is also encouraging.

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