Iwan Kawrakow

Accurate condensed history Monte Carlo simulation of electron transport. I. EGSnrc, the new EGS4 version

In this report a new EGS4 version, called EGSnrc to reflect the substantial changes made to the original code is reported, which incorporates a new any-angle multiple elastic scattering theory, an improved electron-step algorithm, a correct implementation of the fictitious cross section method for sampling distances between discrete interactions, a more accurate evaluation of energy loss, as well as an exact boundary crossing algorithm. It is demonstrated that EGSnrc allows for an artifact free Monte Carlo simulation of ion chamber response and backscattering, situations that have been considered in the past as the two of the most stringent tests of condensed history Monte Carlo codes. A detailed discussion of the effect of the various components of the condensed history simulation of electron transport on the simulated ion chamber response is given in the accompanying paper.

Report of the AAPM Task Group No. 105: Issues associated with clinical implementation of Monte Carlo‐based photon and electron external beam treatment planning

The Monte Carlo (MC) method has been shown through many research studies to calculate accurate dose distributions for clinical radiotherapy, particularly in heterogeneous patient tissues where the effects of electron transport cannot be accurately handled with conventional, deterministic dose algorithms. Despite its proven accuracy and the potential for improved dose distributions to influence treatment outcomes, the long calculation times previously associated with MC simulation rendered this method impractical for routine clinical treatment planning. However, the development of faster codes optimized for radiotherapy calculations and improvements in computer processor technology have substantially reduced calculation times to, in some instances, within minutes on a single processor. These advances have motivated several major treatment planning system vendors to embark upon the path of MC techniques. Several commercial vendors have already released or are currently in the process of releasing MC algorithms for photon and/or electron beam treatment planning. Consequently, the accessibility and use of MC treatment planning algorithms may well become widespread in the radiotherapy community. With MC simulation, dose is computed stochastically using first principles; this method is therefore quite different from conventional dose algorithms. Issues such as statistical uncertainties, the use of variance reduction techniques, theability to account for geometric details in the accelerator treatment head simulation, and other features, are all unique components of a MC treatment planning algorithm. Successful implementation by the clinical physicist of such a system will require an understanding of the basic principles of MC techniques. The purpose of this report, while providing education and review on the use of MC simulation in radiotherapy planning, is to set out, for both users and developers, the salient issues associated with clinical implementation and experimental verification of MC dose algorithms. As the MC method is an emerging technology, this report is not meant to be prescriptive. Rather, it is intended as a preliminary report to review the tenets of the MC method and to provide the framework upon which to build a comprehensive program for commissioning and routine quality assurance of MC-based treatment planning systems.

Investigation of variance reduction techniques for Monte Carlo photon dose calculation using XVMC

Several variance reduction techniques, such as photon splitting, electron history repetition, Russian roulette and the use of quasi-random numbers are investigated and shown to significantly improve the efficiency of the recently developed XVMC Monte Carlo code for photon beams in radiation therapy. It is demonstrated that it is possible to further improve the efficiency by optimizing transpon parameters such as electron energy cut-off, maximum electron energy step size, photon energy cut-off and a cut-off for kerma approximation, without loss of calculation accuracy. These methods increase the efficiency by a factor of up to 10 compared with the initial XVMC ray-tracing technique or a factor of 50 to 80 compared with EGS4/PRESTA. Therefore, a common treatment plan (6 MV photons, 10 x 10 cm2 field size, 5 mm voxel resolution, 1% statistical uncertainty) can be calculated within 7 min using a single CPU 500 MHz personal computer. If the requirement on the statistical uncertainty is relaxed to 2%, the calculation time will be less than 2 min. In addition, a technique is presented which allows for the quantitative comparison of Monte Carlo calculated dose distributions and the separation of systematic and statistical errors. Employing this technique it is shown that XVMC calculations agree with EGSnrc on a sub-per cent level for simulations in the energy and material range of interest for radiation therapy.

Large efficiency improvements in BEAMnrc using directional bremsstrahlung splitting.

The introduction into the BEAMnrc code of a new variance reduction technique, called directional bremsstrahlung splitting (DBS), is described. DBS uses a combination of interaction splitting for bremsstrahlung, annihilation, Compton scattering, pair production and photoabsorption, and Russian Roulette to achieve a much better efficiency of photon beam treatment head simulations compared to the splitting techniques already available in BEAMnrc (selective bremsstrahlung splitting, SBS, and uniform bremsstrahlung splitting, UBS). In a simulated 6 MV photon beam (10 x 10 cm2 field) photon fluence efficiency in the beam using DBS is over 8 times higher than with optimized SBS and over 20 times higher than with UBS, with a similar improvement in electron fluence efficiency in the beam. Total dose efficiency in a central-axis depth-dose curve improves by a factor of 6.4 over SBS at all depths in the phantom. The performance of DBS depends on the details of the accelerator being simulated. At higher energies, the relative improvement in efficiency due to DBS decreases somewhat, but is still a factor of 3.5 improvement over SBS for total dose efficiency using DBS in a simulated 18 MV photon beam. Increasing the field size of the simulated 6 MV beam to 40 x 40 cm2 (broad beam) causes the relative efficiency improvement of DBS to decrease by a factor of approximately 1.7 but is still up to 7 times more efficient than with SBS.

History by history statistical estimators in the BEAM code system

A history by history method for estimating uncertainties has been implemented in the BEAMnrc and DOSXYznrc codes replacing the method of statistical batches. This method groups scored quantities (e.g., dose) by primary history. When phase-space sources are used, this method groups incident particles according to the primary histories that generated them. This necessitated adding markers (negative energy) to phase-space files to indicate the first particle generated by a new primary history. The new method greatly reduces the uncertainty in the uncertainty estimate. The new method eliminates one dimension (which kept the results for each batch) from all scoring arrays, resulting in memory requirement being decreased by a factor of 2. Correlations between particles in phase-space sources are taken into account. The only correlations with any significant impact on uncertainty are those introduced by particle recycling. Failure to account for these correlations can result in a significant underestimate of the uncertainty. The previous method of accounting for correlations due to recycling by placing all recycled particles in the same batch did work. Neither the new method nor the batch method take into account correlations between incident particles when a phase-space source is restarted so one must avoid restarts.

Efficiency improvements for ion chamber calculations in high energy photon beams

This article presents the implementation of several variance reduction techniques that dramatically improve the simulation efficiency of ion chamber dose and perturbation factor calculations. The cavity user code for the EGSnrc Monte Carlo code system is extended by photon cross-section enhancement (XCSE), an intermediate phase-space storage (IPSS) technique, and a correlated sampling (CS) scheme. XCSE increases the density of photon interaction sites inside and in the vicinity of the chamber and results-in combination with a Russian Roulette game for electrons that cannot reach the cavity volume-in an increased efficiency of up to a factor of 350 for calculating dose in a Farmer type chamber placed at 10 cm depth in a water phantom. In combination with the IPSS and CS techniques, the efficiency for the calculation of the central electrode perturbation factor Pcel can be increased by up to three orders of magnitude for a single chamber location and by nearly four orders of magnitude when considering the Pcel variation with depth or with distance from the central axis in a large field photon beam. The intermediate storage of the phase-space properties of particles entering a volume that contains many possible chamber locations leads to efficiency improvements by a factor larger than 500 when computing a profile of chamber doses in the field of a linear accelerator photon beam. All techniques are combined in a new EGSnrc user code egs_chamber. Optimum settings for the variance reduction parameters are investigated and are reported for a Farmer type ion chamber. A few example calculations illustrating the capabilities of the egs_chamber code are presented.

Efficient photon beam dose calculations using DOSXYZnrc with BEAMnrc

This study examines the efficiencies of doses calculated using DOSXYZnrc for 18MV (10×10cm2 field size) and 6MV (10×10cm2 and 20×20cm2 field sizes) photon beams simulated using BEAMnrc. Both phase-space sources and full BEAMnrc simulation sources are used in the DOSXYZnrc calculations. BEAMnrc simulation sources consist of a BEAMnrc accelerator simulation compiled as a shared library and run by the user code (DOSXYZnrc in this case) to generate source particles. Their main advantage is in eliminating the need to store intermediate phase-space files. In addition, the efficiency improvements due to photon splitting and particle recycling in the DOSXYZnrc simulation are examined. It is found that photon splitting increases dose calculation efficiency by a factor of up to 6.5, depending on beam energy, field size, voxel size, and the type of secondary collimation used in the BEAMnrc simulation (multileaf collimator vs photon jaws). The optimum efficiency with photon splitting is ∼55% higher than that with particle recycling, indicating that, while most of the gain is due to time saved by reusing source particle data, there is significant gain due to the uniform distribution of interaction sites and faster DOSXYZnrc simulation time when photon splitting is employed. Use of optimized directional bremsstrahlung splitting in the BEAMnrc simulation sources increases the efficiency of photon beam simulations sufficiently that the peak efficiencies (i.e., with optimum setting of the photon splitting number) of DOSXYZnrc simulations using these sources are only 3-13% lower than those with phase-space file sources. This points towards eliminating the need for storing intermediate phase-space files.

On the characterization and uncertainty analysis of radiochromic film dosimetry.

Radiochromic film is a dosimeter of choice in applications requiring high spatial resolution, two dimensional measurements, or minimum perturbation of the beam fluence. Since the measurement uncertainty in Gafchromic film dosimetry is thought to be significant compared to that of ionization chambers, a rigorous method to evaluate measurement uncertainties is desired. This article provides a method that takes into account the correlation between fit parameters as well as single dose values in order to obtain accurate uncertainties in absolute and relative measurements. A complete portrait of all sources of uncertainty in Gafchromic film dosimetry is given. The parametrization of variance as a function of the number of averaged pixels is obtained in order to accurately predict the uncertainty as a function of the size of the region of interest. The choice of functional form for the sensitometric curve is based on four criteria and a convergence of global net optical density uncertainty to 0.0013 is demonstrated. A minimum number of 12 points is recommended to characterize the sensitometric curve to a sufficient precision on the uncertainty estimation. Uncertainty levels of 0.9% on absolute dose measurements and 0.45% on relative measurements are achieved using a 12-point calibration curve with 220 cGy and repeating measurements five times. Uncertainties of 0.8% and 0.4% are achievable when using 35 points during film characterization. Ignoring covariance terms is shown to lead to errors in the estimation of uncertainty.

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.

On the effective point of measurement in megavoltage photon beams

This paper presents a numerical investigation of the effective point of measurement of thimble ionization chambers in megavoltage photon beams using Monte Carlo simulations with the EGSNRC system. It is shown that the effective point of measurement for relative photon beam dosimetry depends on every detail of the chamber design, including the cavity length, the mass density of the wall material, and the size of the central electrode, in addition to the cavity radius. Moreover, the effective point of measurement also depends on the beam quality and the field size. The paper therefore argues that the upstream shift of 0.6 times the cavity radius, recommended in current dosimetry protocols, is inadequate for accurate relative photon beam dosimetry, particularly in the build-up region. On the other hand, once the effective point of measurement is selected appropriately, measured depth-ionization curves can be equated to measured depth-dose curves for all depths within +/- 0.5%.