A convolution-adapted ratio-TAR algorithm for 3D photon beam treatment planning

A convolution-adapted ratio of tissue-air ratios (CARTAR) method of dose calculation has been developed at the Mallinckrodt Institute of Radiology. This photon pencil-beam algorithm has been developed and implemented specifically for three-dimensional treatment planning. In a standard ratio of tissue-air ratios (RTAR) algorithm, doses to points in irregular field geometries are not adequately modeled. This is inconsistent with the advent of conformal therapy, the goal of which is to conform the dose distribution to the target volume while sparing neighboring sensitive normal critical structures. This motivated us to develop an algorithm that can model the beam penumbra near irregular field edges, while retaining much of the speed for the original RTAR algorithm. The dose calculation algorithm uses two-dimensional (2D) convolutions, computed by 2D fast Fourier transform, of pencil-beam kernels with a beam transmission array to calculate 2D off-axis profiles at a series of depths. These profiles are used to replace the product of the transmission function and measured square-field boundary factors used in the standard RTAR calculation. The 2D pencil-beam kernels were derived from measured data for each modality using commonly available dosimetry equipment. The CARTAR algorithm is capable of modeling the penumbra near block edges as well as the loss of primary and scattered beam in partially blocked regions. This paper describes the dose calculation algorithm, implementation, and verification.