Accuracy of deformable image registration-based intra-fraction motion management in Magnetic Resonance-guided radiotherapy.

Background and Purpose: Intra-fraction motion management is key in Stereotactic Ablative Radiotherapy (SABR) gated delivery. This study assessed the accuracy of automatic tumor segmentation in the delivery of MR-guided radiotherapy (MRgRT) by comparing it to manual delineations performed by experienced observers. Materials and Methods: Twenty patients previously treated with MR-guided SABR for thoracic and abdominal tumors were included. Five observers with at least two years of experience in MRgRT manually delineated the gross tumor volume (GTV) for 20 patients on 240 frames of a cine MRI on a sagittal plane. Deformable Image Registration (DIR) based GTV contours were propagated using four different algorithms from a reference frame to subsequent frames.Geometrical analysis based on the Dice Similarity Coefficient (DSC), centroid distance and Hausdorff Distance (HDD) were performed to assess the inter-observer variability and the accuracy of automatic segmentation. A Confidence Value (CV) metric for the reliability of the tumor auto-contouring was also calculated. Results: Inter-observer delineation variability resulted in mean DSC of 0.89, HDD of 5.8 mm and centroid distance of 1.7 mm. Tumor auto-contouring by the four DIR algorithms resulted in an excellent agreement with the manual delineations by the experienced observers. Mean DSC for each algorithm across all patients was greater than 0.90, whereas the HDD and centroid distances were below 4.0 mm and 1.5 mm, respectively. The CV showed a strong correlation with the DSC. Conclusions: DIR-based auto-contouring in MRgRT exhibited a high level of agreement with the manual contouring performed by experts, allowing accurate gated delivery.

Dosimetry in magnetic fields with dedicated MR-compatible ionization chambers.

MR-integrated radiotherapy requires suitable dosimetry detectors to be used in magnetic fields. This study investigates the feasibility of using dedicated MR-compatible ionization chambers at MR-integrated radiotherapy devices. MR-compatible ionization chambers (Exradin A19MR, A1SLMR, A26MR, A28MR) were precisely modeled and their relative response in a 6MV treatment beam in the presence of a magnetic field was simulated using EGSnrc. Monte Carlo simulations were carried out with the magnetic field in three orientations: the magnetic field aligned perpendicular to the chamber and beam axis (transverse orientation), the magnetic field parallel to the chamber as well as parallel to the beam axis. Monte Carlo simulation results were validated with measurements using an electromagnet with magnetic field strength upto 1.1 T with the chambers in transverse orientation. The measurements and simulation results were in good agreement, except for the A26MR ionization chamber in transverse orientation. The maximum increase in response of the ionization chambers observed was 8.6% for the transverse orientation. No appreciable change in chamber response due to the magnetic field was observed for the magnetic field parallel to the ionization chamber and parallel to the photon beam. Polarity and recombination correction factor were experimentally investigated in the transverse orientation. The polarity effect and recombination effect were not altered by a magnetic field. This study further investigates the response of the ionization chambers as a function of the chambers' rotation around their longitudinal axis. A variation in response was observed when the chamber was not rotationally symmetric, which was independent of the magnetic field.

Quantum versus classical Monte Carlo simulation of low-energy electron transport in condensed amorphous media.

PURPOSE: Classical trajectory Monte Carlo (MC) simulations modelling radiation-induced damage on subcellular length scales ignore quantum effects that may be non-negligible as electron energy decreases below 1 keV. This work investigates quantum mechanical (QM) treatments of low-energy electron transport in condensed media, comparing with classical MC. METHODS: QM calculations involve a simplified model of electron transport in water with a plane wave incident on a cylinder ("droplet") consisting of a cluster of point scatterers (positioned randomly but constrained by a minimum separation, dmin). The system of coupled equations for the electron wavefield incident on each scatterer is solved numerically and results are averaged over many clusters with different point scatterer positions. Average QM cluster cross sections and scattering event densities are compared with analogues computed within the corresponding classical MC model, and relative errors on MC results are calculated. RESULTS: Differences between QM and MC results for both cluster cross section and scattering event density are sensitive to electron energy (wavelength), structure (dmin), and single-scatterer elastic/inelastic cross sections. Relative errors on cluster cross sections generally differ from errors on scattering event densities. The introduction of inelastic scatter generally increases relative errors (compared to calculations with the same single-scatterer elastic cross section) with some exceptions. Accounting for structure (dmin≠0) enhances differences between QM and MC results. CONCLUSIONS: The quantum wave nature of electrons is non-negligible for simulations of low-energy electron transport within small-scale biological targets. The development of more realistic models of electron transport in condensed media is motivated for future work.

On the conversion of dose to bone to dose to water in radiotherapy treatment planning systems.

BACKGROUND AND PURPOSE: Conversion factors between dose to medium (Dm,m) and dose to water (Dw,w) provided by treatment planning systems that model the patient as water with variable electron density are currently based on stopping power ratios. In the current paper it will be illustrated that this conversion method is not correct. MATERIALS AND METHODS: Monte Carlo calculations were performed in a phantom consisting of a 2 cm bone layer surrounded by water. Dw,w was obtained by modelling the bone layer as water with the electron density of bone. Conversion factors between Dw,w and Dm,m were obtained and compared to stopping power ratios and ratios of mass-energy absorption coefficients in regions of electronic equilibrium and interfaces. Calculations were performed for 6 MV and 20 MV photon beams. RESULTS: In the region of electronic equilibrium the stopping power ratio of water to bone (1.11) largely overestimates the conversion obtained using the Monte Carlo calculations (1.06). In that region the MC dose conversion corresponds to the ratio of mass energy absorption coefficients. Near the water to bone interface, the MC ratio cannot be determined from stopping powers or mass energy absorption coefficients. CONCLUSION: Stopping power ratios cannot be used for conversion from Dm,m to Dw,w provided by treatment planning systems that model the patient as water with variable electron density, either in regions of electronic equilibrium or near interfaces. In regions of electronic equilibrium mass energy absorption coefficient ratios should be used. Conversions at interfaces require detailed MC calculations.

A comparative study of automatic image segmentation algorithms for target tracking in MR-IGRT.

On-board magnetic resonance (MR) image guidance during radiation therapy offers the potential for more accurate treatment delivery. To utilize the real-time image information, a crucial prerequisite is the ability to successfully segment and track regions of interest (ROI). The purpose of this work is to evaluate the performance of different segmentation algorithms using motion images (4 frames per second) acquired using a MR image-guided radiotherapy (MR-IGRT) system. Manual con-tours of the kidney, bladder, duodenum, and a liver tumor by an experienced radiation oncologist were used as the ground truth for performance evaluation. Besides the manual segmentation, images were automatically segmented using thresholding, fuzzy k-means (FKM), k-harmonic means (KHM), and reaction-diffusion level set evolution (RD-LSE) algorithms, as well as the tissue tracking algorithm provided by the ViewRay treatment planning and delivery system (VR-TPDS). The performance of the five algorithms was evaluated quantitatively by comparing with the manual segmentation using the Dice coefficient and target registration error (TRE) measured as the distance between the centroid of the manual ROI and the centroid of the automatically segmented ROI. All methods were able to successfully segment the bladder and the kidney, but only FKM, KHM, and VR-TPDS were able to segment the liver tumor and the duodenum. The performance of the thresholding, FKM, KHM, and RD-LSE algorithms degraded as the local image contrast decreased, whereas the performance of the VP-TPDS method was nearly independent of local image contrast due to the reference registration algorithm. For segmenting high-contrast images (i.e., kidney), the thresholding method provided the best speed (< 1 ms) with a satisfying accuracy (Dice = 0.95). When the image contrast was low, the VR-TPDS method had the best automatic contour. Results suggest an image quality determination procedure before segmentation and a combination of different methods for optimal segmentation with the on-board MR-IGRT system.

Influence of photon energy cuts on PET Monte Carlo simulation results.

PURPOSE: The purpose of this work is to study the influence of photon energy cuts on the results of positron emission tomography (PET) Monte Carlo (MC) simulations. METHODS: MC simulations of PET scans of a box phantom and the NEMA image quality phantom are performed for 32 photon energy cut values in the interval 0.3-350 keV using a well-validated numerical model of a PET scanner. The simulations are performed with two MC codes, egs_pet and GEANT4 Application for Tomographic Emission (GATE). The effect of photon energy cuts on the recorded number of singles, primary, scattered, random, and total coincidences as well as on the simulation time and noise-equivalent count rate is evaluated by comparing the results for higher cuts to those for 1 keV cut. To evaluate the effect of cuts on the quality of reconstructed images, MC generated sinograms of PET scans of the NEMA image quality phantom are reconstructed with iterative statistical reconstruction. The effects of photon cuts on the contrast recovery coefficients and on the comparison of images by means of commonly used similarity measures are studied. RESULTS: For the scanner investigated in this study, which uses bismuth germanate crystals, the transport of Bi X(K) rays must be simulated in order to obtain unbiased estimates for the number of singles, true, scattered, and random coincidences as well as for an unbiased estimate of the noise-equivalent count rate. Photon energy cuts higher than 170 keV lead to absorption of Compton scattered photons and strongly increase the number of recorded coincidences of all types and the noise-equivalent count rate. The effect of photon cuts on the reconstructed images and the similarity measures used for their comparison is statistically significant for very high cuts (e.g., 350 keV). The simulation time decreases slowly with the increase of the photon cut. CONCLUSIONS: The simulation of the transport of characteristic x rays plays an important role, if an accurate modeling of a PET scanner system is to be achieved. The simulation time decreases slowly with the increase of the cut which, combined with the accuracy loss at high cuts, means that the usage of high photon energy cuts is not recommended for the acceleration of MC simulations.

On the Monte Carlo simulation of electron transport in the sub-1 keV energy range.

PURPOSE: The validity of "classic" Monte Carlo (MC) simulations of electron and positron transport at sub-1 keV energies is investigated in the context of quantum theory. METHODS: Quantum theory dictates that uncertainties on the position and energy-momentum four-vectors of radiation quanta obey Heisenberg's uncertainty relation; however, these uncertainties are neglected in "classical" MC simulations of radiation transport in which position and momentum are known precisely. Using the quantum uncertainty relation and electron mean free path, the magnitudes of uncertainties on electron position and momentum are calculated for different kinetic energies; a validity bound on the classical simulation of electron transport is derived. RESULTS: In order to satisfy the Heisenberg uncertainty principle, uncertainties of 5% must be assigned to position and momentum for 1 keV electrons in water; at 100 eV, these uncertainties are 17 to 20% and are even larger at lower energies. In gaseous media such as air, these uncertainties are much smaller (less than 1% for electrons with energy 20 eV or greater). CONCLUSIONS: The classical Monte Carlo transport treatment is questionable for sub-1 keV electrons in condensed water as uncertainties on position and momentum must be large (relative to electron momentum and mean free path) to satisfy the quantum uncertainty principle. Simulations which do not account for these uncertainties are not faithful representations of the physical processes, calling into question the results of MC track structure codes simulating sub-1 keV electron transport. Further, the large difference in the scale at which quantum effects are important in gaseous and condensed media suggests that track structure measurements in gases are not necessarily representative of track structure in condensed materials on a micrometer or a nanometer scale.

Investigation of voxel warping and energy mapping approaches for fast 4D Monte Carlo dose calculations in deformed geometries using VMC++.

A new deformable geometry class for the VMC++ Monte Carlo code was implemented based on the voxel warping method. Alternative geometries which use tetrahedral sub-elements were implemented and efficiency improvements investigated. A new energy mapping method, based on calculating the volume overlap between deformed reference dose grid and the target dose grid, was also developed. Dose calculations using both the voxel warping and energy mapping methods were compared in simple phantoms as well as a patient geometry. The new deformed geometry implementation in VMC++ increased calculation times by approximately a factor of 6 compared to standard VMC++ calculations in rectilinear geometries. However, the tetrahedron-based geometries were found to improve computational efficiency, relative to the dodecahedron-based geometry, by a factor of 2. When an exact transformation between the reference and target geometries was provided, the voxel and energy warping methods produced identical results. However, when the transformation is not exact, there were discrepancies in the energy deposited on the target geometry which lead to significant differences in the dose calculated by the two methods. Preliminary investigations indicate that these energy differences may correlate with registration errors; however, further work is needed to determine the usefulness of this metric for quantifying registration accuracy.

A Monte Carlo method to evaluate the impact of positioning errors on detector response and quality correction factors in nonstandard beams.

During experimental procedures, an adequate evaluation of all sources of uncertainty is necessary to obtain an overall uncertainty budget. In specific radiation dosimetry applications where a single detector is used, common methods to evaluate uncertainties caused by setup positioning errors are not applicable when the dose gradient is not known a priori. This study describes a method to compute these uncertainties using the Monte Carlo method. A mathematical formalism is developed to calculate unbiased estimates of the uncertainties. The method is implemented in egs_chamber, an EGSnrc-based code that allows for the efficient calculation of detector doses and dose ratios. The correct implementation of the method into the egs_chamber code is validated with an extensive series of tests. The accuracy of the developed mathematical formalism is verified by comparing egs_chamber simulation results to the theoretical expectation in an ideal situation where the uncertainty can be computed analytically. Three examples of uncertainties are considered for realistic models of an Exradin A12 ionization chamber and a PTW 60012 diode, and results are computed for parameters representing nearly realistic positioning error probability distributions. Results of practical examples show that uncertainties caused by positioning errors can be significant during IMRT reference dosimetry as well as small field output factor measurements. The method described in this paper is of interest in the study of single-detector response uncertainties during nonstandard beam measurements, both in the scope of daily routine as well as when developing new dosimetry protocols. It is pointed out that such uncertainties should be considered in new protocols devoted to single-detector measurements in regions with unpredictable dose gradients. The method is available within the egs_chamber code in the latest official release of the EGSnrc system.

Fast and memory-efficient Monte Carlo-based image reconstruction for whole-body PET.

PURPOSE: Several studies have shown the benefit of an accurate system modeling using Monte Carlo techniques. For state-of-the-art whole-body positron emission tomography (PET) scanners, Monte Carlo-based image reconstruction is associated with a significant computational cost to calculate the system matrix as well as a large memory capacity to store it. In this article, the authors present a simulation-reconstruction framework to solve these problems on the Philips Gemini GS PET scanner. METHODS: A fast, realistic system matrix simulation module was developed using egs_pet, which is an efficient PET simulation code based on EGSnrc. The generated system matrix was then used in a rotator-based ordered subset expectation maximization (OS-EM) algorithm, which exploits the rotational symmetry of a cylindrical PET scanner. The system matrix was further compressed by using sparse storage techniques. RESULTS: The system matrix simulation took five days on 50 cores of Xeon 2.66 GHz, resulting in a system matrix of 2.01 GB. The entire system matrix could be stored in the main memory of a standard personal computer. The image quality in terms of contrast-noise trade-offs was considerably improved compared to a standard OS-EM algorithm. The image quality was also compared to the clinical software on the scanner using routine parameter settings. The contrast recovery coefficient of small hot spheres and cold spheres was significantly improved. CONCLUSIONS: The results indicated that the proposed framework could be used for this PET scanner with improved image quality. This method could also be applied to other state-of-the-art whole-body PET scanners and preclinical PET scanners with a similar shape.

Variance reduction techniques for fast Monte Carlo CBCT scatter correction calculations.

Several variance reduction techniques improving the efficiency of the Monte Carlo estimation of the scatter contribution to a cone beam computed tomography (CBCT) scan were implemented in egs_ctct, an EGSnrc-based application for CBCT-related calculations. The largest impact on the efficiency comes from the splitting + Russian Roulette techniques which are described in detail. The fixed splitting technique is outperformed by both the position-dependent importance splitting (PDIS) and the region-dependent importance splitting (RDIS). The superiority of PDIS over RDIS observed for a water phantom with bone inserts is not observed when applying these techniques to a more realistic human chest phantom. A maximum efficiency improvement of several orders of magnitude over an analog calculation is obtained. A scatter calculation combining the reported efficiency gain with a smoothing algorithm is already in the proximity of being of practical use if a medium size computer cluster is available.

Direct measurement of absorbed dose to water in HDR 192Ir brachytherapy: water calorimetry, ionization chamber, Gafchromic film, and TG-43.

PURPOSE: Gafchromic film and ionometric calibration procedures for HDR 192Ir brachytherapy sources in terms of dose rate to water are presented and the experimental results are compared to the TG-43 protocol as well as with the absolute dose measurement results from a water calorimetry-based primary standard. METHODS: EBT-1 Gafchromic films, an A1SL Exradin miniature Shonka thimble type chamber, and an SI HDR 1000 Plus well-type chamber (Standard Imaging, Inc., Middleton, WI) with an ADCL traceable Sk calibration coefficient (following the AAPM TG-43 protocol) were used. The Farmer chamber and Gafchromic film measurements were performed directly in water. All results were compared to direct and absolute absorbed dose to water measurements from a 4 degrees C stagnant water calorimeter. RESULTS: Based on water calorimetry, the authors measured the dose rate to water to be 361 +/- 7 microGy/(h U) at a 55 mm source-to-detector separation. The dose rate normalized to air-kerma strength for all the techniques agree with the water calorimetry results to within 0.83%. The overall 1-sigma uncertainty on water calorimetry, ionization chamber, Gafchromic film, and TG-43 dose rate measurement amounts to 1.90%, 1.44%, 1.78%, and 2.50%, respectively. CONCLUSIONS: This work allows us to build a more realistic uncertainty estimate for absorbed dose to water determination using the TG-43 protocol. Furthermore, it provides the framework necessary for a shift from indirect HDR 192Ir brachytherapy dosimetry to a more accurate, direct, and absolute measurement of absorbed dose to water.

Effective point of measurement of thimble ion chambers in megavoltage photon beams.

PURPOSE: Determine the effective point of measurement (EPOM) of 12 thimble ion chambers, including miniature chambers and three models widely used for clinical reference dosimetry. The EPOM is the point at which the measured dose would arise in the measurement medium in the absence of the probe: For cylindrical chambers, it is shifted upstream relative to the central axis of the chamber. Although current dosimetry protocols prescribe a blanket upstream EPOM shift of 0.6r, with r as the chamber cavity radius, it has been shown in recent years that the EPOM does, in fact, depend on every detail of the chamber design and on the beam characteristics. In the wake of this finding, the authors undertake a comprehensive study of the EPOM for a series of chambers in water. METHODS: This work relies on EGSnrc Monte Carlo calculations for the central axis depth dose in a water phantom and in ion chambers. They use a full Elekta Precise linac treatment head simulation to generate realistic photon beams with nominal energies of 6 and 25 MV and fields sizes of 10 x 10 and 40 x 40 cm2. The correct EPOM shift for the 12 ion chambers, modeled in realistic detail, is taken as the one minimizing the deviation of the ratio between the dose to water and the dose to the gas of the chamber cavity, according to a method proposed and validated in previous work. RESULTS: The analysis reveals that the actual EPOM shift is significantly smaller than the recommended value in current dosimetry protocols, by up to 25% for reference-class chambers and 80% for miniature chambers. The location of the EPOM also depends on the characteristics of the incident beam and varies in a well-defined way with the cavity length, the central electrode radius, and the thimble wall thickness. CONCLUSIONS: The authors confirm that an upstream EPOM shift of 0.6r is too large for thimble ion chambers in high energy photon beams. Proper values for the EPOM shift could be tabulated per beam and per chamber, but they envisage that a single shift for all practical beams may prove sufficient. Moreover, the systematic dependence on chamber characteristics provides evidence that a universal parametrization in terms of a few design parameters is conceivable and has implication for the calculation of chamber correction factors.

Ionization chamber gradient effects in nonstandard beam configurations.

PURPOSE: For the purpose of nonstandard beam reference dosimetry, the current concept of reporting absorbed dose at a point in water located at a representative position in the chamber volume is investigated in detail. As new nonstandard beam reference dosimetry protocols are under development, an evaluation of the role played by the definition of point of measurement could lead to conceptual improvements prior to establishing measurement procedures. METHODS: The present study uses the current definition of reporting absorbed dose to calculate ionization chamber perturbation factors for two cylindrical chamber models (Exradin A12 and A14) using the Monte Carlo method. The EGSnrc based user-code EGS_chamber is used to calculate chamber dose responses of 14 IMRT beams chosen to cause considerable dose gradients over the chamber volume as previously used by Bouchard and Seuntjens ["Ionization chamber-based reference dosimetry of intensity modulated radiation beams," Med. Phys. 31(9), 2454-5465 (2004)]. RESULTS: The study shows conclusively the relative importance of each physical effect involved in the nonstandard beam correction factors of 14 IMRT beams. Of all correction factors involved in the dosimetry of the beams studied, the gradient perturbation correction factor has the highest magnitude, on average, 11% higher compared to reference conditions for the Exradin A12 chamber and about 5% higher for the Extradin A14 chamber. Other perturbation correction factors (i.e., Pwall, Pstem, and Pcel) are, on average, less than 0.8% different from reference conditions for the chambers and beams studied. The current approach of reporting measured absorbed dose at a point in water coinciding with the location of the centroid of the chamber is the main factor responsible for large correction factors in nonstandard beam deliveries (e.g., intensity modulated radiation therapy) reported in literature. CONCLUSIONS: To reduce or eliminate the magnitude of perturbation correction factors in nonstandard beam reference dosimetry, two possible ways to report absorbed dose are suggested: (1) Reporting average dose to the sensitive volume of the chamber filled with water, combined with removing the reference field implicit gradient effect when measuring output factors, and (2) reporting average dose to the chamber itself during output factor verifications. The first option could be adopted if clinical beam correction factors are negligible. The second option could simplify quality assurance procedures when correction factors are not negligible and have to be calculated using Monte Carlo simulations.

The accuracy of EGSnrc, Geant4 and PENELOPE Monte Carlo systems for the simulation of electron scatter in external beam radiotherapy.

Three widely used Monte Carlo systems were benchmarked against recently published measurements of the angular distribution of 13 MeV and 20 MeV electrons scattered from foils of different atomic numbers and thicknesses. Source and geometry were simulated in detail to calculate electron fluence profiles 118.2 cm from the exit window. Results were compared to the measured fluence profiles and the characteristic angle where the fluence drops to 1/e of its maximum value. EGSnrc and PENELOPE results, on average, agreed with measurement within 1 standard deviation experimental uncertainty, with EGSnrc estimating slightly lower scatter than measurement and PENELOPE slightly higher scatter. Geant4.9.2 overestimated the characteristic angle for the lower atomic number foils by as much as 10%. Retuning of the scatter distributions in Geant4 led to a much better agreement with measurement, close to that achieved with the other codes. The 3% differences from measurement seen with all codes for at least some of the foils would result in clinically significant errors in the fluence profiles (2%/4 mm), given accurate knowledge of the electron source and treatment head geometry used in radiotherapy. Further improvement in simulation accuracy is needed to achieve 1%/1 mm agreement with measurement for the full range of beam energies, foil atomic number and thickness used in radiotherapy. EGSnrc would achieve this accuracy with an increase in thickness of the mylar sheets in the monitor chamber, PENELOPE with a decrease in thickness.

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.

Fast, accurate photon beam accelerator modeling using BEAMnrc: a systematic investigation of efficiency enhancing methods and cross-section data.

In this work, an investigation of efficiency enhancing methods and cross-section data in the BEAMnrc Monte Carlo (MC) code system is presented. Additionally, BEAMnrc was compared with VMC++, another special-purpose MC code system that has recently been enhanced for the simulation of the entire treatment head. BEAMnrc and VMC++ were used to simulate a 6 MV photon beam from a Siemens Primus linear accelerator (linac) and phase space (PHSP) files were generated at 100 cm source-to-surface distance for the 10 x 10 and 40 x 40 cm2 field sizes. The BEAMnrc parameters/techniques under investigation were grouped by (i) photon and bremsstrahlung cross sections, (ii) approximate efficiency improving techniques (AEITs), (iii) variance reduction techniques (VRTs), and (iv) a VRT (bremsstrahlung photon splitting) in combination with an AEIT (charged particle range rejection). The BEAMnrc PHSP file obtained without the efficiency enhancing techniques under study or, when not possible, with their default values (e.g., EXACT algorithm for the boundary crossing algorithm) and with the default cross-section data (PEGS4 and Bethe-Heitler) was used as the "base line" for accuracy verification of the PHSP files generated from the different groups described previously. Subsequently, a selection of the PHSP files was used as input for DOSXYZnrc-based water phantom dose calculations, which were verified against measurements. The performance of the different VRTs and AEITs available in BEAMnrc and of VMC++ was specified by the relative efficiency, i.e., by the efficiency of the MC simulation relative to that of the BEAMnrc base-line calculation. The highest relative efficiencies were approximately 935 (approximately 111 min on a single 2.6 GHz processor) and approximately 200 (approximately 45 min on a single processor) for the 10 x 10 field size with 50 million histories and 40 x 40 cm2 field size with 100 million histories, respectively, using the VRT directional bremsstrahlung splitting (DBS) with no electron splitting. When DBS was used with electron splitting and combined with augmented charged particle range rejection, a technique recently introduced in BEAMnrc, relative efficiencies were approximately 420 (approximately 253 min on a single processor) and approximately 175 (approximately 58 min on a single processor) for the 10 x 10 and 40 x 40 cm2 field sizes, respectively. Calculations of the Siemens Primus treatment head with VMC++ produced relative efficiencies of approximately 1400 (approximately 6 min on a single processor) and approximately 60 (approximately 4 min on a single processor) for the 10 x 10 and 40 x 40 cm2 field sizes, respectively. BEAMnrc PHSP calculations with DBS alone or DBS in combination with charged particle range rejection were more efficient than the other efficiency enhancing techniques used. Using VMC++, accurate simulations of the entire linac treatment head were performed within minutes on a single processor. Noteworthy differences (+/- 1%-3%) in the mean energy, planar fluence, and angular and spectral distributions were observed with the NIST bremsstrahlung cross sections compared with those of Bethe-Heitler (BEAMnrc default bremsstrahlung cross section). However, MC calculated dose distributions in water phantoms (using combinations of VRTs/AEITs and cross-section data) agreed within 2% of measurements. Furthermore, MC calculated dose distributions in a simulated water/air/water phantom, using NIST cross sections, were within 2% agreement with the BEAMnrc Bethe-Heitler default case.

Novel approach for the Monte Carlo calculation of free-air chamber correction factors.

A self-consistent approach for the Monte Carlo calculation of free-air chamber (FAC) correction factors needed to convert the chamber reading into the quantity air-kerma at the point of measurement is introduced, and its implementation in the new EGSnrc user code egs_fac is discussed. To validate the method, comparisons between computed and measured FAC correction factors for attenuation Ax, scatter (Ascat), and electron loss (Aeloss) are performed in the medium energy range where the experimental determination is believed to be accurate. The Monte Carlo calculations utilize a full simulation of the x-ray tube with BEAMnrc and a detailed model of the parallel-plate FAC. Excellent agreement between the computed Ascat and Aeloss and the measured values for these correction factors currently used in the National Research Council (NRC) of Canada primary FAC standard is observed. Our simulations also agree with previous Monte Carlo results for Ascat and Aeloss for the 135 and 250 kVp Consultative Committee for Ionizing Radiation reference beam qualities. The computed attenuation correction agrees with the measured Aatt within the stated uncertainties, although the authors' simulations demonstrate that the evacuated-tube technique employed at NRC to measure the attenuation correction slightly overestimates Aatt in the medium energy range. The newly introduced corrections for backscatter, beam geometry, and lack of charged particle equilibrium along the beam axis are found to be negligible. On the other hand, the correction for photons leaking through the FAC aperture, currently ignored in the NRC standard, is shown to be significant.

Comparison of two methods to compute the absorbed dose to water for photon beams.

Cross-validation was performed between an in-house dose-to-water (D(water)) calculation method used at Virginia Commonwealth University and the VMC++ D(water) calculation during particle transport. The effect of Monte Carlo statistical precision was observed. The results of the two calculations on homogeneous phantoms with densities varying from 0.3 g cm(-3) to 2.95 g cm(-3) were compared. Depth and field size dependence were tested. D(water) calculations were compared in a bone-lung-bone phantom to observe how the calculations differed in steep density gradients. The methods were compared for five prostate and five head-and-neck (H/N) patient cases as well. In all phantom tests, the differences between the two D(water) calculations were less than 1%. The largest differences in patient cases was a prostate case in which 1% of the voxels with doses greater than 50% of the maximum dose had a systematic difference corresponding to 1.16% of the maximum dose. All differences were clinically insignificant.

Performance of a hybrid MC dose algorithm for IMRT optimization dose evaluation.

This paper presents a hybrid intensity modulated radiation therapy (IMRT) optimization strategy which combines the speed of pencil beam (PB) and the accuracy of Monte Carlo (MC) dose calculations. After an initial deliverable-based optimization using a PB algorithm, doses are recomputed using the VMC++ MC code to determine dose correction factors, which are then utilized during further PB-based optimization. The hybrid method is benchmarked with respect to full MC deliverable-based optimization for ten prostate and ten head-and-neck IMRT plans. Final optimized plans are compared in terms of dose-volume indices used for the plan optimization. Dose prediction errors (DPEs) and optimization convergence errors (OCEs) at intermediate steps of the hybrid sequence are evaluated. The hybrid method is found to produce optimized plans that are clinically equivalent to full MC-based optimization, yet requires only 40% of the number of MC dose calculations. With the hybrid strategy presented here, MC-based optimization results are achieved in 35 min or less on a modest computing cluster. While the initial PB-deliverable-based optimization is found to have DPEs and OCEs of up to 3 Gy relative to the 65-73 Gy prescription doses, application of the first MC correction reduces the average DPEs to less than 0.3 Gy for the prostate plans and less than 0.06 Gy for the head and neck plans. The maximum observed DPE or OCE is 0.7 Gy after 1 MC dose correction, indicating that a single MC dose calculation correction might be sufficient for IMRT optimization.