Alex F. Bielajew

Presta: The parameter reduced electron-step transport algorithm for electron monte carlo transport

A new electron transport algorithm for use with electron Monte Carlo transport codes is presented. Its components are: a path-length correction (PLC) algorithm which is based on the multiple scattering theory of Moliere and which takes into account the differences between the straight path length and the total curved path length for each electron step; a lateral correlation algorithm (LCA) which takes into account lateral transport; and a boundary crossing algorithm (BCA) which ensures that electrons are transported accurately in the vicinity of interfaces. The algorithm has been implemented in the EGS4 code system and a variety of tests validating the algorithms are presented. In its standard configuration, use of this algorithm will allow the inexperienced user to obtain reliable results from the EGS Monte Carlo code without having to do a detailed study of the electron transport parameters. In many situations, substantial savings in computing time may be realized in comparison to the present EGS algorithm. The developments described in this report may be adapted to other electron transport codes where many of the same conclusions may be drawn.

Description and dosimetric verification of the PEREGRINE Monte Carlo dose calculation system for photon beams incident on a water phantom.

PEREGRINE is a three-dimensional Monte Carlo dose calculation system written specifically for radiotherapy. This paper describes the implementation and overall dosimetric accuracy of PEREGRINE physics algorithms, beam model, and beam commissioning procedure. Particle-interaction data, tracking geometries, scoring, variance reduction, and statistical analysis are described. The BEAM code system is used to model the treatment-independent accelerator head, resulting in the identification of primary and scattered photon sources and an electron contaminant source. The magnitude of the electron source is increased to improve agreement with measurements in the buildup region in the largest fields. Published measurements provide an estimate of backscatter on monitor chamber response. Commissioning consists of selecting the electron beam energy, determining the scale factor that defines dose per monitor unit, and describing treatment-dependent beam modifiers. We compare calculations with measurements in a water phantom for open fields, wedges, blocks, and a multileaf collimator for 6 and 18 MV Varian Clinac 2100C photon beams. All calculations are reported as dose per monitor unit. Aside from backscatter estimates, no additional, field-specific normalization is included in comparisons with measurements. Maximum discrepancies were less than either 2% of the maximum dose or 1.2 mm in isodose position for all field sizes and beam modifiers.

On the condensed history technique for electron transport

Abstract In this report we discuss the theory of the “condensed history technique”, an approximate solution to the Boltzmann transport equation that sums the effect of up to thousands of discrete, small momentum transfer elastic and inelastic collisions into single larger-effect quasi-events. This technique saves much calculational effort at the expense of introducing errors that are now understood quantitatively in terms of the development presented herein. We apply our analysis to modern realizations of the condensed history method, namely those of EGS/PRESTA, ETRAN/TLC, FLUKA, PENELOPE, and LLCA. We have also constructed an algorithm that exhibits smaller large step size instabilities than all of these methods and give several examples.

Differences in electron depth‐dose curves calculated with EGS and ETRAN and improved energy‐range relationships

For 1-50 MeV electrons incident on a water phantom there are systematic differences in the depth-dose curves calculated by the Monte Carlo codes EGS and ETRAN (and its descendants SANDYL, CYLTRAN, ACCEPT, and the ITS system). Compared to ETRAN, the EGS code calculates a higher surface dose and a slightly slower dose falloff past the dose maximum. The discrepancy in the surface dose is shown to exist because the modified Landau energy-loss straggling distribution used in ETRAN underestimates the mean energy loss by about 10% since it underestimates the number of large energy-loss events. Comparison to experimental data shows a preference for the EGS depth-dose curves at 10 and 20 MeV. Since various dosimetry protocols assign electron beam energies based on measured depth-dose curves in water, formulas based on these more accurate EGS4 calculations are presented: relating the mean energy of an incident electron beam to R50, the depth at which the dose in a water phantom falls to 50% of its maximum value; and relating the most probable energy of the incident beam to the projected range of the depth-dose curve. A study is presented of the effects of the incident electron spectrum on the calculated depth-dose curve.

On the representation of electron multiple elastic-scattering distributions for Monte Carlo calculations

Abstract A new representation of elastic electron–nucleus (Coulomb) multiple-scattering distributions is developed. Using the screened Rutherford cross section with the Moliere screening parameter as an example, a simple analytic angular transformation of the Goudsmit–Saunderson multiple-scattering distribution accounts for most of the structure of the angular distribution leaving a residual 3-parameter (path-length, transformed angle and screening parameter) function that is reasonably slowly varying and suitable for rapid, accurate interpolation in a computer-intensive algorithm. The residual function is calculated numerically for a wide range of Moliere screening parameters and path-lengths suitable for use in a general-purpose condensed-history Monte Carlo code. Additionally, techniques are developed that allow the distributions to be scaled to account for energy loss. This new representation allows “on-the-fly” sampling of Goudsmit–Saunderson angular distributions in a screened Rutherford approximation suitable for Class II condensed-history Monte Carlo codes.

Ion chamber response and Awall correction factors in a 60Co beam by Monte Carlo simulation

The responses and wall correction factors for ion chambers in broad parallel 60Co beams have been calculated using Monte Carlo techniques. The calculated responses are in good agreement with Bragg-Gray cavity theory. In particular, the response divided by the wall correction factor Awall is found to be independent of the detectors shape but dependent on the material used for the chamber wall in a manner predicted by Bragg-Gray cavity theory. A simple theory is given which predicts the increase in response of a Farmer ion chamber due to an electrode of an arbitrary material and radius. The change in chamber response as a function of build-up cap composition is in good agreement with analytic expressions. The effect of guard regions in pancake chambers is found to be negligible. Embedding a pancake chamber in a flat phantom during calibration is shown to increase the response by 1.0+or-0.2%. Calculated values of Awall are in good agreement with most experimental results and with those given in the AAPM protocol but with a considerably lower uncertainty of +or-0.2%. When using these values with the AAPM protocol, the beta cep factor should not be used since it is included in these calculated values.

Photon beam relative dose validation of the DPM Monte Carlo code in lung-equivalent media.

Validation experiments have been conducted using 6 and 15 MV photons in inhomogeneous (water/lung/water) media to benchmark the accuracy of the DPM Monte Carlo code for photon beam dose calculations. Small field sizes (down to 2 x 2 cm2) and low-density media were chosen for this investigation because the intent was to test the DPM code under conditions where lateral electronic disequilibrium effects are emphasized. The treatment head components of a Varian 21EX linear accelerator, including the jaws (defining field sizes of 2 x 2, 3 x 3 and 10 x 10 cm2), were simulated using the BEAMnrc code. The phase space files were integrated within the DPM code system, and central axis depth dose and profile calculations were compared against diode measurements in a homogeneous water phantom in order to validate the phase space. Results of the homogeneous phantom study indicated that the relative differences between DPM calculations and measurements were within +/- 1% (based on the rms deviation) for the depth dose curves; relative profile dose differences were on average within +/- 1%/1 mm. Depth dose and profile measurements were carried out using an ion-chamber and film, within an inhomogeneous phantom consisting of a 6 cm slab of lung-equivalent material embedded within solid water. For the inhomogeneous phantom experiment, DPM depth dose calculations were within +/- 1% (based on the rms deviation) of measurements; relative profile differences at depths within and beyond the lung were, on average, within +/- 2% in the inner and outer beam regions, and within 1-2 mm distance-to-agreement within the penumbral region. Relative point differences on the order of 2-3% were within the estimated experimental uncertainties. This work demonstrates that the DPM Monte Carlo code is capable of accurate photon beam dose calculations in situations where lateral electron disequilibrium effects are pronounced.

Variance-Reduction Techniques

In this chapter, we discuss various techniques which may be used to make calculations more efficient. In some cases, these techniques require that no further approximations be made to the transport physics. In other cases, the gains in computing speed come at the cost of computing results which may be less accurate since approximations are introduced. The techniques may be divided into 3 categories: those that concern electron transport only, those that concern photon transport only, and other more general methods. The set of techniques we discuss does not represent an exhaustive list. There is much reference material available, and we only cite a few of them 1–5 . An especially rich source of references is McGrath and Crawford’s report 3 which contains an annotated bibliography. Instead, we shall concentrate on techniques that have been of considerable use to the authors and their close colleagues. However, it is appropriate to discuss briefly what we are trying to accomplish by employing variance-reduction techniques.

Electron beam dose distributions near standard inhomogeneities

At a recent workshop on electron beam dose planning, a set of standard geometries was defined to facilitate the comparison of electron beam treatment planning algorithms and dosimetric measurements. The geometries consist of one-, two- or three-dimensional inhomogeneities embedded near the entrance surface of a water phantom. In the three-dimensional case, the inhomogeneities are small cylinders of air or aluminium located on the beam axis. The authors have used a small (1 mm square by 0.1 mm thick) p-type silicon detector to measure the dose distributions behind these inhomogeneities for broad beams of 10 and 20 MeV electrons. The effect of the inhomogeneities is to perturb the dose in their vicinity by as much as 50% over a range of a few millimetres. These results provide a stringent test of techniques for calculating dose distributions. Current clinical algorithms do not accurately predict the dose distributions, but detailed Monte Carlo simulations are shown to be in good agreement with the experimental results.

Wall attenuation and scatter corrections for ion chambers: measurements versus calculations

In precision ion chamber dosimetry in air, the wall attenuation and scatter are corrected for by Awall. Using the EGS4 system the authors show that Monte Carlo calculated Awall factors predict relative variations in detector response with wall thickness which agree with all available experimental data within a statistical uncertainty of less than 0.1%. However, the calculated correction factors for use in exposure and air kerma standards are different by up to 1% from those obtained by extrapolating these same measurements. Using calculated correction factors would imply increase of 0.7-1.0% in the exposure and air kerma standards based on spherical and large diameter, large length cylindrical chambers and decreases of 0.2-0.5% for standards based on large diameter pancake chambers. Calculations are also shown to agree within 0.05% with the measurements of Rocha and co-workers for clinical chambers. These experimental data are not in exact agreement with the gamma values used in the AAPM protocol to obtain Awall. However, the AAPM final values of Awall agree within 0.2% with the more accurate values calculated.