Beamlet dose distribution compression and reconstruction using wavelets for intensity modulated treatment planning

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Abstract
Intensity modulated radiation therapy (IMRT) treatment planning is often formulated as the optimization of weights of fixed-geometry subfields (beamlets). Efficient optimization techniques can be based on direct storage of the influence matrix relating beamlet weights to dose values. However, direct storage of beamlet dose distributions for IMRT treatment planning can easily exceed several gigabytes, and is therefore often not feasible. We present a method for rapidly calculating full three-dimensional IMRT dose distributions, based on a vector of beamlet weights. The method is based on compressed beamlet dose distributions using fast digital wavelet transforms and so-called hard thresholding. We studied the method with a rectangular beamlet of 0.5 cm x 0.5 cm cross section from a monoenergetic 6 MeV photon point source simulated in homogeneous (water) and heterogeneous (CT-data) phantoms. Dose was calculated using the accurate VMC+ + Monte Carlo engine. The beamlet dose distributions were wavelet transformed and compressed by dropping wavelet coefficients below a given threshold value. Dose is then computed using the remaining wavelets. Selection of the wavelet basis function, decomposition level, and threshold values, for different slice orientations (transverse or parallel to the beam) and varying angles of beamlet incidence are studied. A typical in-slice compression ratio for a plane containing a beamlet was 32:1 using the sym2 wavelet and a threshold of 0.01, with a typical root-mean-square error, for voxels above 50% of the maximum dose, of about 0.04%. The overall compression performance, which includes many planes with little information content, is on the order of 100:1 or greater compared to full matrix storage. Although other methods are available to make the use of stored influence matrix values more feasible in IMRT treatment planning (such as using coarse grids or restricting values to defined volumes of interest) we conclude that wavelet compression facilitates the storage and use of full pencil dose deposition (influence matrix) data in IMRT treatment planning.