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. ©

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, the ability 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.

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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.

A new model for calculating electron beam dose has been developed. The algorithm is based on a two- or three-dimensional geometry defined by computerized tomography (CT) images. The Monte Carlo technique was used to solve the electron transport equation. However, in contrast to conventional Monte Carlo models (EGS4) several approximations and simplifications in the description of elementary electron processes were introduced reducing in this manner the computational time by a factor of about 35 without significant loss in accuracy. The Monte Carlo computer program does not need any precalculated data. The random access memory required is about 16 Mbytes for a 128(2) X 50 matrix, depending on the resolution of the CT cube. The Voxel Monte Carlo model (VMC) was tested in comparison to calculations by EGS4 and the "Hogstrom algorithm" (MDAH) using several fictive phantoms. In all cases a good coincidence has been found between EGS4 and VMC, especially near tissue inhomogeneities, whereas the MDAH algorithm has produced dose underestimations of up to 40%.

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.

In this report the condensed history Monte Carlo simulation of electron transport and its application to the calculation of ion chamber response is discussed. It is shown that the strong step-size dependencies and lack of convergence to the correct answer previously observed are the combined effect of the following artifacts caused by the EGS4/PRESTA implementation of the condensed history technique: dose underprediction due to PRESTA'S pathlength correction and lateral correlation algorithm; dose overprediction due to the boundary crossing algorithm; dose overprediction due to the breakdown of the fictitious cross section method for sampling distances between discrete interaction and the inaccurate evaluation of energy-dependent quantities. These artifacts are now understood quantitatively and analytical expressions for their effect are given.

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.