The use of Monte Carlo simulations in diagnostic medical imaging research is widespread due to its flexibility and ability to estimate quantities that are challenging to measure empirically. However, any new Monte Carlo simulation code needs to be validated before it can be used reliably. The type and degree of validation required depends on the goals of the research project, but, typically, such validation involves either comparison of simulation results to physical measurements or to previously published results obtained with established Monte Carlo codes. The former is complicated due to nuances of experimental conditions and uncertainty, while the latter is challenging due to typical graphical presentation and lack of simulation details in previous publications. In addition, entering the field of Monte Carlo simulations in general involves a steep learning curve. It is not a simple task to learn how to program and interpret a Monte Carlo simulation, even when using one of the publicly available code packages. This Task Group report provides a common reference for benchmarking Monte Carlo simulations across a range of Monte Carlo codes and simulation scenarios. In the report, all simulation conditions are provided for six different Monte Carlo simulation cases that involve common x-ray based imaging research areas. The results obtained for the six cases using four publicly available Monte Carlo software packages are included in tabular form. In addition to a full description of all simulation conditions and results, a discussion and comparison of results among the Monte Carlo packages and the lessons learned during the compilation of these results are included. This abridged version of the report includes only an introductory description of the six cases and a brief example of the results of one of the cases. This work provides an investigator the necessary information to benchmark his/her Monte Carlo simulation software against the reference cases included here before performing his/her own novel research. In addition, an investigator entering the field of Monte Carlo simulations can use these descriptions and results as a self-teaching tool to ensure that he/she is able to perform a specific simulation correctly. Finally, educators can assign these cases as learning projects as part of course objectives or training programs.

This paper presents the implementation of the bremsstrahlung cross-section enhancement (BCSE) variance-reduction technique into the EGSnrc/BEAMnrc system. BCSE makes the simulation of x-ray production from bremsstrahlung targets more efficient; it does so by artificially making the rare event of bremsstrahlung emission more abundant, which increases the number of statistically-independent photons that contribute to reducing the variance of the quantity of interest without increasing the CPU time appreciably. BCSE does not perturb the charged-particle transport in EGSnrc and it is made compatible with all other variance-reduction techniques already used in EGSnrc and BEAMnrc, including range rejection, uniform bremsstrahlung splitting, and directional bremsstrahlung splitting. When optimally combining BCSE with splitting to simulate typical situations of interest in medical physics research and in clinical practice, efficiencies can be up to five orders of magnitude larger than those obtained with analog simulations, and up to a full order of magnitude larger than those obtained with optimized splitting alone (which is the state-of-the-art of the EGSnrc/BEAMnrc system before this study was carried out). This study recommends that BCSE be combined with the existing splitting techniques for all EGSnrc/BEAMnrc simulations that involve bremsstrahlung targets, both in the kilovoltage and megavoltage range. Optimum crosssection enhancement factors for typical situations in diagnostic x-ray imaging and in radiotherapy are recommended, along with an easy algorithm for simulation optimization.

This study benchmarks the EGSnrc Monte Carlo code in the energy range of interest to kilovoltage medical physics applications (5-140 keV) against experimental measurements of charged particle backscatter coefficients. The benchmark consists of experimental data from 20 different published experiments (1954-2007) covering 35 different elements (4

In a typical x-ray tube, off-focal radiation is mainly generated by the backscattered electrons that reenter the anode outside the focal spot. In this study, BEAMnrc (an EGSnrc user-code) is modified to simulate off-focal radiation. The modified BEAMnrc code is used to study the characteristics of electrons that backscatter from the anode, and to quantify their effect on the output of typical x-ray systems. Results show that the first generation backscatter coefficient is approximately 50% for tungsten anodes at diagnostic energies, and approximately 38% for molybdenum anodes at mammography energies. Second and higher generations of backscatter have a relatively minor contribution. At the patient plane, our simulation results are in excellent agreement with experimental measurements in the literature for the spectral shape of both the primary and the off-focal components, and also for the integral off-focal-to-primary ratio. The spectrum of the off-focal component at the patient plane is softer than the primary, which causes a slight softening in the overall spectrum. For typical x-ray systems, the off-focal component increases patient exposure (for a given number of incident primary electrons) by up to 11% and reduces the half-value layer and the effective energy of the average spectrum by up to 7% and 3%, respectively. The larger effects are for grounded cathode tubes, smaller interelectrode distance, higher tube voltage, lighter filtration, and less collimation. Simulation time increases by approximately 30% when the off-focal radiation is included, but the overall simulation time remains of the order of a few minutes. This study concludes that the off-focal radiation can have a non-negligible effect on the output parameters of x-ray systems and that it should be included in x-ray tube simulations for more realistic modeling of these systems.

Specifying photon spectra of clinical linacs using a functional form is useful for many applications, including virtual source modelling and spectral unfolding from dosimetric measurements such as transmission data or depth-dose curves. In this study, 11 functional forms from the literature are compiled and quantitatively compared. A new function is proposed which offers improvements over existing ones. The proposed function is simple, physics-based and has four free parameters, one of which is the mean incident electron kinetic energy. A comprehensive benchmark set of validated, high-precision Monte Carlo spectra is generated and used to evaluate the strengths and limitations of different functions. The benchmark set has 65 spectra (3.5-30 MV) from Varian, Elekta, Siemens, Tomotherapy, Cyberknife and research linacs. The set includes spectra on- and off-axis from linacs with and without a flattening filter, and in treatment and imaging modes. The proposed function gives the lowest spectral deviations among all functions. It reproduces the energy fluence values in each bin for the benchmark set with a normalized root-mean-square deviation of 1.7%. The mean incident electron kinetic energy, maximum photon energy, most-probable energy and average energy are reproduced, on average, within 1.4%, 4.3%, 3.9% and 0.6% of their true values, respectively. The proposed function is well behaved when used for spectral unfolding from dosimetric data. The contribution of the 511 keV annihilation peak and the energy spread of the incident electron beam can be added as additional free parameters.

In the presence of realistic experimental noise, the proposed approach significantly improves the accuracy and robustness of the spectral unfolding problem for all therapy and MV imaging beams of clinical interest.

Accurate transmission measurements require accounting for a number of influence quantities which, if ignored, can collectively introduce errors larger than 10%. Accurate transmission calculations require the use of the most accurate data and physics options available in EGSnrc, particularly the more accurate bremsstrahlung angular sampling option and the newly added modeling of photonuclear attenuation. Comparison between measurements and calculations implies that EGSnrc is accurate within 0.2% for relative ion chamber response calculations. Photon cross section uncertainties are the ultimate limiting factor for the accuracy of the calculated transmission data (Monte Carlo or analytical).

The approach proposed in an earlier study for unfolding photon spectra and incident electron energies from transmission data is accurate and practical for clinical use.