title: Accelerating Monte Carlo simulations of radiation therapy dose distributions using wavelet threshold de-noising.
abstract: The Monte Carlo dose calculation method works by simulating individual energetic photons or electrons as they traverse a digital representation of the patient anatomy. However, Monte Carlo results fluctuate until a large number of particles are simulated. We propose wavelet threshold de-noising as a postprocessing step to accelerate convergence of Monte Carlo dose calculations. A sampled rough function (such as Monte Carlo noise) gives wavelet transform coefficients which are more nearly equal in amplitude than those of a sampled smooth function. Wavelet hard-threshold de-noising sets to zero those wavelet coefficients which fall below a threshold; the image is then reconstructed. We implemented the computationally efficient 9,7-biorthogonal filters in the C language. Transform results were averaged over transform origin selections to reduce artifacts. A method for selecting best threshold values is described. The algorithm requires about 336 floating point arithmetic operations per dose grid point. We applied wavelet threshold de-noising to two two-dimensional dose distributions: a dose distribution generated by 10 MeV electrons incident on a water phantom with a step-heterogeneity, and a slice from a lung heterogeneity phantom. Dose distributions were simulated using the Integrated Tiger Series Monte Carlo code. We studied threshold selection, resulting dose image smoothness, and resulting dose image accuracy as a function of the number of source particles. For both phantoms, with a suitable value of the threshold parameter, voxel-to-voxel noise was suppressed with little introduction of bias. The roughness of wavelet de-noised dose distributions (according to a Laplacian metric) was nearly independent of the number of source electrons, though the accuracy of the de-noised dose image improved with increasing numbers of source electrons. We conclude that wavelet shrinkage de-noising is a promising method for effectively accelerating Monte Carlo dose calculations by factors of 2 or more.
authors.affiliation: Department of Radiation Oncology, Mallinckrodt Institute of Radiology, Washington University School of Medicine, St. Louis, Missouri 63110, USA. deasy@radonc.wustl.edu
authors.forename: Joseph O
authors.initials: JO
authors.lastname: Deasy
authors.forename: M Victor
authors.initials: MV
authors.lastname: Wickerhauser
authors.forename: Mathieu
authors.initials: M
authors.lastname: Picard
mesh_terms: D000465:Algorithms; D004583:Electrons; D008175:Lung Neoplasms / Q000532:radiotherapy; D015233:Models, Statistical; D009010:Monte Carlo Method; D019047:Phantoms, Imaging; D011874:Radiometry / Q000379:methods*; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D012984:Software