Electron dose calculation using multiple-scattering theory: thin planar inhomogeneities

Comparison of a finite-element multigroup discrete-ordinates code with Monte Carlo for radiotherapy calculations

Radiotherapy calculations often involve complex geometries such as interfaces between materials of vastly differing atomic number, such as lung, bone and/or air interfaces. Monte Carlo methods have been used to calculate accurately the perturbation effects of the interfaces. However, these methods can be computationally expensive for routine clinical calculations. An alternative approach is to solve the Boltzmann equation deterministically. We present one such deterministic code, Attila. Further, we computed a brachytherapy example and an external beam benchmark to compare the results with data previously calculated by MCNPX and EGS4. Our data suggest that the presented deterministic code is as accurate as EGS4 and MCNPX for the transport geometries examined in this study.

Influence of multiple scattering and energy loss straggling on the absorbed dose distributions of therapeutic light ion beams: I. Analytical pencil beam model

The lateral and longitudinal distributions of absorbed dose of broad and narrow light ion beams in water are investigated. An analytical algorithm based on the generalized Fermi-Eyges theory is developed and used to calculate the effects of multiple scattering and range straggling on the dose distribution of light ion beams in water. A first-order Gaussian multiple scattering and energy loss straggling approach is generally sufficiently accurate for describing the lateral and longitudinal spread of the Bragg peak and the associated energy deposition distribution of therapeutic light ion beams at ranges of clinical interest. Nuclear reactions are not taken into account in this study. The analytical algorithm given in the present study allows an accurate description of the radial spread and the range straggling of light ions traversing matter. A verification of this approach by comparing with experimental data, Monte Carlo methods and other analytical techniques will be presented in a forthcoming paper.

Electron dose calculation using multiple-scattering theory: a hybrid electron pencil-beam model

We have embedded the bipartition model into Fermi-Eyges multiple-scattering theory to produce a more accurate hybrid electron pencil-beam model, by using the fact that away from the edges of a large field, the electron distribution function exactly equals that for an infinitely wide electron beam. The bipartition model calculates various electron transport quantities in a homogeneous or horizontally layered medium with very high accuracy, for an infinitely broad beam. In our hybrid model, we use the bipartition model to calculate the longitudinal part of the pencil-beam distribution function, and the Fermi-Eyges theory to calculate its transverse part. Doing this allows calculation not only of dose distribution, but also of such quantities as electron fluence distribution, energy spectrum, angular distribution, and electron-charge distribution. Using the hybrid electron pencil-beam model, we have calculated the dose distribution for collimated electron beams and compared them with experimental data, for rectangular fields.

Dose calculations in proton beams: range straggling corrections and energy scaling

Three-dimensional dose planning systems employing accurate proton transport algorithms are essential for calculating absorbed dose distributions in proton therapy. In this paper, a pencil beam algorithm for the transport of protons in materials of interest for radiation therapy is developed. The Fermi-Eyges multiple-scattering theory is used to derive transport equations for calculating proton fluence and absorbed dose distributions. The multiple-scattering theory of Molière is used to predict mean square scattering angles and to develop an expression for calculating the root mean square (RMS) radial spread of a proton pencil beam, as a function of depth, in an arbitrary scattering material. A correction factor is suggested to account for the decrease in the radial spread at the end of the range due to range straggling. The effects of neglecting large-angle scattering events and the possibility of incorporating such events into the pencil beam algorithm are discussed. An energy scaling technique for determining the water-equivalent surface energy at a given depth in a heterogeneous scattering medium is developed. The water-equivalent energy, giving the same Molière scattering parameter B in water, is determined and the 1/e angle in water is scaled to the appropriate width in the scattering material. By using stored analytically or Monte Carlo calculated pencil beam distributions in water, the large-angle single-scattering events may be incorporated by approximating the scattering in an arbitrary material by the scattering in water for protons of the appropriate water-equivalent surface energy.