title: 3-D superposition for radiotherapy treatment planning using fast Fourier transforms.
abstract: Currently used radiotherapy treatment planning algorithms based on effective path length or scatter function methods do not model electron ranging from photon interaction sites. The superposition (or convolution) technique does model this effect, which is especially important at higher (linear accelerator) energies since the electron range is significant. Another advantage of this method is that it is conceptually simple and models the physical processes directly, rather than using empirically derived methods. A major disadvantage of superposition lies in the large amount of computer time required to generate a plan, especially in three dimensions. To help solve this problem, superposition using an invariant dose spread array (kernel) can be achieved by performing a convolution in Fourier space using fast Fourier transforms (FFTs). A method for 3 dimensional calculation of dose using FFTs is presented. Dose spread arrays are calculated using the EGS Monte Carlo code, and convolved with the TERMA (total energy released per unit mass). In both cases a 10 MV nominal beam energy is modelled by a 10 component spectrum, which is compared to the result obtained using monochromatic energy only (3.0 MeV at the surface). The FFT technique is shown to be significantly faster than standard convolution for medium to large TERMA and dose spread array sizes. The method is shown to be highly accurate for small fields in homogeneous media. For larger fields the central axis depth dose is accurate but the profile shape in the penumbral region becomes slightly distorted. This is because photons incident near the beam edges are not parallel to the cartesian coordinate system used as the convolution framework. However, this effect is sufficiently small to indicate that the convolution method is suitable for use in routine treatment planning.
authors.forename: D C
authors.initials: DC
authors.lastname: Murray
authors.forename: P W
authors.initials: PW
authors.lastname: Hoban
authors.forename: P E
authors.initials: PE
authors.lastname: Metcalfe
authors.forename: W H
authors.initials: WH
authors.lastname: Round
mesh_terms: D005583:Fourier Analysis; D006801:Humans; D008433:Mathematics; D015233:Models, Statistical; D011829:Radiation Dosage; D011881:Radiotherapy, Computer-Assisted