A diamond target for megavoltage cone-beam CT.

PURPOSE: To determine the properties of a megavoltage cone-beam CT system using the unflattened beam from a sintered diamond target at 4 and 6 MV. METHODS: A sintered diamond target was used in place of a graphite target as part of an imaging beam line (an unflattened beam from a graphite target) installed on a linear accelerator. The diamond target, with a greater density than the graphite target, permitted imaging at the lower beam energy (4 MV) required with the graphite target and the higher beam energy (6 MV) conventionally used with the tungsten/stainless steel target and stainless steel flattening filter. Images of phantoms and patients were acquired using the different beam lines and compared. The beam spectra and dose distributions were determined using Monte Carlo simulation. RESULTS: The diamond target allowed use of the same beam energy as for treatment, simplifying commissioning and quality assurance. Images acquired with the diamond target at 4 MV were similar to those obtained with the graphite target at 4 MV. The slight reduction in low energy photons due to the higher-Z sintering material in the diamond target had minimal effect on image quality. Images acquired at 6 MV with the diamond target showed a small decrease in contrast-to-noise ratio, resulting from a decrease in the fraction of photons in the beam in the energy range to which the detector is most sensitive. CONCLUSIONS: The diamond target provides images of a similar quality to the graphite target. Diamond allows use of the higher beam energy conventionally used for treatment, provides a higher dose rate for the same beam current, and potentially simplifies installation and maintenance of the beam line.

Simulation of large x-ray fields using independently measured source and geometry details.

PURPOSE: Obtain an accurate simulation of the dose from the 6 and 18 MV x-ray beams from a Siemens Oncor linear accelerator by comparing simulation to measurement. Constrain the simulation by independently determining parameters of the treatment head and incident beam, in particular, the energy and spot size. METHODS: Measurements were done with the treatment head in three different configurations: (1) The clinical configuration, (2) the flattening filter removed, and (3) the target and flattening filter removed. Parameters of the incident beam and treatment head were measured directly. Incident beam energy and spectral width were determined from the percent-depth ionization of the raw beam (as described previously), spot size was determined using a spot camera, and the densities of the flattening filters were determined by weighing them. Simulations were done with EGSnrc/BEAMnrc code. An asymmetric simulation was used, including offsets of the spot, primary collimator, and flattening filter from the collimator rotation axis. RESULTS: Agreement between measurement and simulation was obtained to the least restrictive of 1% or 1 mm at 6 MV, both with and without the flattening filter in place, except for the buildup region. At 18 MV, the agreement was 1.5%/1.5 mm with the flattening filter in place and 1%/1 mm with it removed, except for in the buildup region. In the buildup region, the discrepancy was 2%/2 mm at 18 MV and 1.5%/1.5 mm at 6 MV with the flattening filter either removed or in place. The methodology for measuring the source and geometry parameters for the treatment head simulation is described. Except to determine the density of the flattening filter, no physical modification of the treatment head is necessary to obtain those parameters. In particular, the flattening filter does not need to be removed as was done in this work. CONCLUSIONS: Good agreement between measured and simulated dose distributions was obtained, even in the buildup region. The simulation was tightly constrained by independent measurements of parameters of the incident beam and treatment head. The method of obtaining the input parameters is described, and can be carried out on a clinical linear accelerator.

Determination of electron energy, spectral width, and beam divergence at the exit window for clinical megavoltage x-ray beams.

Monte Carlo simulations of x-ray beams typically take parameters of the electron beam in the accelerating waveguide to be free parameters. In this paper, a methodology is proposed and implemented to determine the energy, spectral width, and beam divergence of the electron source. All treatment head components were removed from the beam path, leaving only the exit window. With the x-ray target and flattener out of the beam, uncertainties in physical characteristics and relative position of the target and flattening filter, and in spot size, did not contribute to uncertainty in the energy. Beam current was lowered to reduce recombination effects. The measured dose distributions were compared with Monte Carlo simulation of the electron beam through the treatment head to extract the electron source characteristics. For the nominal 6 and 18 MV x-ray beams, the energies were 6.51 +/- 0.15 and 13.9 +/- 0.2 MeV, respectively, with the uncertainties resulting from uncertainties in the detector position in the measurement and in the stopping power in the simulations. Gaussian spectral distributions were used, with full widths at half maximum ranging from 20 +/- 4% at 6 MV to 13 +/- 4% at 18 MV required to match the fall-off portion of the percent-depth ionization curve. Profiles at the depth of maximum dose from simulations that used the manufacturer-specified exit window geometry and no beam divergence were 2-3 cm narrower than measured profiles. Two simulation configurations yielding the measured profile width were the manufacturer-specified exit window thickness with electron source divergences of 3.3 degrees at 6 MV and 1.8 degrees at 18 MV and an exit window 40% thicker than the manufacturer's specification with no beam divergence. With the x-ray target in place (and no flattener), comparison of measured to simulated profiles sets upper limits on the electron source divergences of 0.2 degrees at 6 MV and 0.1 degrees at 18 MV. A method of determining source characteristics without mechanical modification of the treatment head, and therefore feasible in clinics, is presented. The energies and spectral widths determined using this method agree with those determined with only the exit window in the beam path.

Measurement of multiple scattering of 13 and 20 MeV electrons by thin foils.

To model the transport of electrons through material requires knowledge of how the electrons lose energy and scatter. Theoretical models are used to describe electron energy loss and scatter and these models are supported by a limited amount of measured data. The purpose of this work was to obtain additional data that can be used to test models of electron scattering. Measurements were carried out using 13 and 20 MeV pencil beams of electrons produced by the National Research Council of Canada research accelerator. The electron fluence was measured at several angular positions from 0 degree to 90 degrees for scattering foils of different thicknesses and with atomic numbers ranging from 4 to 79. The angle, theta 1/e at which the fluence has decreased to 1/e of its value on the central axis was used to characterize the distributions. Measured values of theta 1/e ranged from 1.5 degrees to 8 degrees with a typical uncertainty of about 1%. Distributions calculated using the EGSnrc Monte Carlo code were compared to the measured distributions. In general, the calculated distributions are narrower than the measured ones. Typically, the difference between the measured and calculated values of theta 1/e is about 1.5%, with the maximum difference being 4%. The measured and calculated distributions are related through a simple scaling of the angle, indicating that they have the same shape. No significant trends with atomic number were observed.

The effect of beam purity and scanner complexity on proton CT accuracy.

PURPOSE: To determine the dependence of the accuracy in reconstruction of relative stopping power (RSP) with proton computerized tomography (pCT) scans on the purity of the proton beam and the technological complexity of the pCT scanner using standard phantoms and a digital representation of a pediatric patient. METHODS: The Monte Carlo method was applied to simulate the pCT scanner, using both a pure proton beam (uniform 200 MeV mono-energetic, parallel beam) and the Northwestern Medicine Chicago Proton Center (NMCPC) clinical beam in uniform scanning mode. The accuracy of the simulation was validated with measurements performed at NMCPC including reconstructed RSP images obtained with a preclinical prototype pCT scanner. The pCT scanner energy detector was then simulated in three configurations of increasing complexity: an ideal totally absorbing detector, a single stage detector and a multi-stage detector. A set of 15 cm diameter water cylinders containing either water alone or inserts of different material, size, and position were simulated at 90 projection angles (4° steps) for the pure and clinical proton beams and the three pCT configurations. A pCT image of the head of a detailed digital pediatric phantom was also reconstructed from the simulated pCT scan with the prototype detector. RESULTS: The RSP error increased for all configurations for insert sizes under 7.5 mm in radius, with a sharp increase below 5 mm in radius, attributed to a limit in spatial resolution. The highest accuracy achievable using the current pCT calibration step phantom and reconstruction algorithm, calculated for the ideal case of a pure beam with totally absorbing energy detector, was 1.3% error in RSP for inserts of 5 mm radius or more, 0.7 mm in range for the 2.5 mm radius inserts, or better. When the highest complexity of the scanner geometry was introduced, some artifacts arose in the reconstructed images, particularly in the center of the phantom. Replacing the step phantom used for calibration with a wedge phantom led to RSP accuracy close to the ideal case, with no significant dependence of RSP error on insert location or material. The accuracy with the multi-stage detector and NMCPC beam for the cylindrical phantoms was 2.2% in RSP error for inserts of 5 mm radius or more, 0.7 mm in range for the 2.5 mm radius inserts, or better. The pCT scan of the pediatric phantom resulted in mean RSP values within 1.3% of the reference RSP, with a range error under 1 mm, except in exceptional situations of parallel incidence on a boundary between low and high density. CONCLUSIONS: The pCT imaging technique proved to be a precise and accurate imaging tool, rivaling the current x-rays based techniques, with the advantage of being directly sensitive to proton stopping power rather than photon interaction coefficients. Measured and simulated pCT images were obtained from a wobbled proton beam for the first time. Since the in-silico results are expected to accurately represent the prototype pCT, upcoming measurements using the wedge phantom for calibration are expected to show similar accuracy in the reconstructed RSP.

A pulse-rate dependence of dose per monitor unit and its significant effect on wedged-shaped fields delivered with variable dose rate and a moving jaw.

Wedge-shaped dose distributions are delivered on some modern linear accelerators with a virtual wedge, combining variable dose rate and a moving jaw. Drift in the wedge factor and wedge angle of a 20 X 20 cm field for the 60 degree virtual wedge was found commonplace in several models of linear accelerator from one manufacturer. It was found that errors in dose delivery both on and off axis could exceed 5% if quality assurance checks are limited to 10 X 10 cm or smaller fields or wedge angles of 45 degrees or less. A procedure to easily identify and remedy the problem is presented. In each case the change was due to variation in dose per monitor unit (D/MU) with the electron beam pulse rate. The variation was traced to a pair of circuit boards in the dosimetry system, one for each output measurement channel. Wedge factors and dose profiles measured before and after board replacement on 4 accelerators, and for a set of defective boards placed on one of the accelerators, were compared. The effect was largest for the wedge with the steepest profile (60 degree wedge angle) and the largest field measured: 20 X 20 cm. In this case, a 1% variation in D/MU with a factor of 5 reduction in pulse rate corresponded to an average 0.8% change in wedge factor and 0.8% change in the off axis ratio at 8.5 cm off axis on the high dose side of the wedge field, 0.3% on the low dose side. After board replacement, wedge factors and profiles measured on the 4 machines generally agreed to 2% for the full range of wedge angles and field sizes. Quality assurance of virtual wedges is discussed in light of the new findings.

Final Aperture Superposition Technique applied to fast calculation of electron output factors and depth dose curves.

The Final Aperture Superposition Technique (FAST) is described and applied to accurate, near instantaneous calculation of the relative output factor (ROF) and central axis percentage depth dose curve (PDD) for clinical electron beams used in radiotherapy. FAST is based on precalculation of dose at select points for the two extreme situations of a fully open final aperture and a final aperture with no opening (fully shielded). This technique is different than conventional superposition of dose deposition kernels: The precalculated dose is differential in position of the electron or photon at the downstream surface of the insert. The calculation for a particular aperture (x-ray jaws or MLC, insert in electron applicator) is done with superposition of the precalculated dose data, using the open field data over the open part of the aperture and the fully shielded data over the remainder. The calculation takes explicit account of all interactions in the shielded region of the aperture except the collimator effect: Particles that pass from the open part into the shielded part, or visa versa. For the clinical demonstration, FAST was compared to full Monte Carlo simulation of 10 x 10, 2.5 x 2.5, and 2 x 8 cm2 inserts. Dose was calculated to 0.5% precision in 0.4 x 0.4 x 0.2 cm3 voxels, spaced at 0.2 cm depth intervals along the central axis, using detailed Monte Carlo simulation of the treatment head of a commercial linear accelerator for six different electron beams with energies of 6-21 MeV. Each simulation took several hours on a personal computer with a 1.7 Mhz processor. The calculation for the individual inserts, done with superposition, was completed in under a second on the same PC. Since simulations for the pre calculation are only performed once, higher precision and resolution can be obtained without increasing the calculation time for individual inserts. Fully shielded contributions were largest for small fields and high beam energy, at the surface, reaching a maximum of 5.6% at 21 MeV. Contributions from the collimator effect were largest for the large field size, high beam energy, and shallow depths, reaching a maximum of 4.7% at 21 MeV. Both shielding contributions and the collimator effect need to be taken into account to achieve an accuracy of 2%. FAST takes explicit account of the shielding contributions. With the collimator effect set to that of the largest field in the FAST calculation, the difference in dose on the central axis (product of ROF and PDD) between FAST and full simulation was generally under 2%. The maximum difference of 2.5% exceeded the statistical precision of the calculation by four standard deviations. This occurred at 18 MeV for the 2.5 x 2.5 cm2 field. The differences are due to the method used to account for the collimator effect.

Sensitivity of large-field electron beams to variations in a Monte Carlo accelerator model.

Adjustments made to Monte Carlo models during the commissioning of the simulation should be physically realistic and correspond to actual machine characteristics. Large electron fields, with the jaws fully open and the applicator removed, are sensitive to important source and geometry parameters and may provide the most accurate beam models, including those collimated by an applicator. We report on the results of a comprehensive Monte Carlo sensitivity study documenting the response of these large fields to changes in the configuration of a Siemens Primus linear accelerator. The study was performed for 6, 9 12, 15, 18 and 21 MeV configurations, and included variations of thickness, position and lateral alignment of all treatment head components. Variations of electron beam characteristics were also included in the study. Results were classified by their impact on central-axis depth dose distributions, including the bremsstrahlung tail, and on beam profiles near D(max) and in the bremsstrahlung region. Low-energy results show an increased sensitivity to electron beam properties. High-energy bremsstrahlung profiles are shown to be useful in determining misalignments between the beam axis and mechanical isocentre. For all energies, the alignment of the secondary scattering foil and monitor chamber are shown to be critical for correctly modelling beam asymmetries. The results suggest a methodology for commissioning of electron beams using Monte Carlo treatment head simulation.

Calculation of x-ray spectra for radiosurgical beams.

As conformal radiosurgery using micromultileaf collimators gains feasibility, dose calculation algorithms based on Monte Carlo or convolution techniques may become necessary. These require radiosurgical x-ray spectra. The most accurate method currently available to estimate clinical radiosurgery spectra is the Monte Carlo method. In this study the EGS4 Monte Carlo system was used to simulate the thick target of a 6 MV linear accelerator used for radiosurgery in our center. The calculated spectrum was attenuated through any significant mass thickness of material downstream from the target. The attenuated thick-target spectral distributions calculated both with and without the flattening filter were compared to the attenuated, thin target spectrum based on the small angle Schiff analytical spectrum calculated for the same target and attenuator material, as well as with a published spectrum from a full Monte Carlo simulation of a treatment head with a flattener in place. The Schiff spectrum neglects contributions from lower-energy scattered electrons that significantly degrade the quality of the beam. The flattener is removed from our accelerator during radiosurgery to increase the dose rate to approximately 750 cGy/min for a 10 x 10 cm2 field at the depth of dose maximum. This leaves a substantial fluence of photons below 1 MeV that are not observed in published spectra calculated for accelerators with flattening filters. Removal of the flattening filter has a measurable effect on the central axis depth dose, reducing the percentage dose at 10 cm depth from 59.2% to 54.3% for a 10 mm diam field. Radiosurgical off-axis ratios and percentage depth dose distributions calculated from these spectra with the EGS4 Monte Carlo code were compared to measured data. Measured and calculated dose distributions both with and without flattener were in good agreement. The dose distributions were found to be insensitive to the differences in the various calculated spectral distributions. Thus, although the attenuated Schiff spectrum is significantly harder than the clinical beam, it is adequate for dose calculations of radiosurgical beams.

Computer aided design and verification of megavoltage tissue compensators for oblique beams.

A computer based radiotherapy dose compensator system is presented. A plane of uniform dose (pud) is chosen which passes through the central axis at a reference depth in the patient. The pud is oriented at an arbitrary angle. Tissues thicknesses are the ray line distances from the patient surface to the pud. Relative dose estimates on the pud are derived from tissue-air ratio, tissue-maximum ratio, or tissue-phantom ratio tables interpolated for field size and tissue thickness. An inverse square law correction is also applied. Compensator thicknesses are calculated from measured effective attenuation coefficients to attenuate the beam by a factor proportional to the estimated dose on the pud. Water phantom measurements for 60Co for both oblique incidence and wedge geometries demonstrate dose uniformity to better than +/- 4%. Dose measurement with radiographic films sandwiched between the two halves of a wax phantom verify adequate compensation for neck irradiation by 60Co opposed lateral beams and 6-MV x-ray inferiorly angled lateral beams. Compensator factors used for absolute dose determination are accurate to better than +/- 3%. The dose modeling routine, QCBEAM, is found to be sufficiently accurate for routine compensator verification for these geometries.

Electron spectra derived from depth dose distributions.

The technique of extracting electron energy spectra from measured distributions of dose along the central axis of clinical electron beams is explored in detail. Clinical spectra measured with this simple spectroscopy tool are shown to be sufficient in accuracy and resolution for use in Monte Carlo treatment planning. A set of monoenergetic depth dose curves of appropriate energy spacing, precalculated with Monte Carlo for a simple beam model, are unfolded from the measured depth dose curve. The beam model is comprised of a point electron and photon source placed in vacuum with a source-to-surface distance of 100 cm. Systematic error introduced by this model affects the calculated depth dose curve by no more than 2%/2 mm. The component of the dose due to treatment head bremsstrahlung, subtracted prior to unfolding, is estimated from the thin-target Schiff spectrum within 0.3% of the maximum total dose (from electrons and photons) on the beam axis. Optimal unfolding parameters are chosen, based on physical principles. Unfolding is done with the public-domain code FERDO. Comparisons were made to previously published spectra measured with magnetic spectroscopy and to spectra we calculated with Monte Carlo treatment head simulation. The approach gives smooth spectra with an average resolution for the 27 beams studied of 16+/-3% of the mean peak energy. The mean peak energy of the magnetic spectrometer spectra was calculated within 2% for the AECL T20 scanning beam accelerators, 3% for the Philips SL25 scattering foil based machine. The number of low energy electrons in Monte Carlo spectra is estimated by unfolding with an accuracy of 2%, relative to the total number of electrons in the beam. Central axis depth dose curves calculated from unfolded spectra are within 0.5%/0.5 mm of measured and simulated depth dose curves, except near the practical range, where 1%/1 mm errors are evident.

Monte Carlo based phase-space evolution for electron dose calculation.

A system of computer codes based on phase-space evolution is developed and applied to low energy therapeutic electron beams. Monte Carlo (EGS4) is used to pre-calculate the electron transport and dose deposition in a 0.5 cm width cubic voxel. Dose calculations at larger scales are computed from the pre-calculated data using phase-space evolution. This approach has the theoretical accuracy of Monte Carlo with potentially significant speed gains resulting from the pre-calculation. This study demonstrates the accuracy of this technique while providing a preliminary assessment of the calculation time. For a 4.3 MeV electron beam in water with a 0.5 cm thick slab of either water (homogeneous), air, or aluminum at 1 cm depth, we observe differences relative to Monte Carlo of less than 3% along the central axis for a pencil-beam. For a 3.5 cm x 3.5 cm field we observe a maximum difference on the central axis of 4% in the build-up region and less than 0.1 cm in the fall-off region for all three phantoms. Calculation times are disappointing; however, there is high potential for their reduction to values comparable to or better than condensed history Monte Carlo while retaining clinically acceptable accuracy.

Angular distribution of bremsstrahlung from 15-MeV electrons incident on thick targets of Be, Al, and Pb.

Bremsstrahlung spectra from thick cylindrical targets of Be, Al, and Pb have been measured at angles of 0 degrees, 1 degree, 2 degrees, 4 degrees, 10 degrees, 30 degrees, 60 degrees, and 90 degrees relative to the beam axis for electrons of 15-MeV incident energy. The spectra are absolute (photons per incident electron) and have a 145-keV lower-energy cutoff. The target thickness were nominally 110% of the electron CSDA range. A thin transmission detector, calibrated against a toroidal current monitor, was placed upstream of the target to measure the beam current. The spectrometer was a 20-cm-diam by 25-cm-long cylindrical NaI detector. Measured spectra were corrected for pile-up, background, detector response, detector efficiency, attenuation in materials between the target and detector and collimator effects. Spectra were also calculated using the EGS4 Monte Carlo system for simulating the radiation transport. There was excellent agreement between the measured and calculated spectral shapes. The measured yield of photons per incident electron was 9% and 7% greater than the calculated yield for Be and Al, respectively, and 2% less for Pb, all with an uncertainty of +/- 5%. There was no significant angular variation in the ratio of the measured and calculated yields. The angular distributions of bremsstrahlung calculated using available analytical theories dropped off more quickly with angle than the measured distributions. The predictions of the theories would be improved by including target-scattered photons.

Megavoltage imaging with low Z targets: implementation and characterization of an investigational system.

The poor quality of stereotactic radiotherapy portal images is a limiting factor in precise image registration. To alleviate this problem, a low atomic number (Z) target was implemented on our Siemens MXE linear accelerator. This investigational system was used to assess the performance of various target materials by filming an aluminum contrast object. Beryllium, carbon and conventional target materials were studied. The bremsstrahlung spectra of these materials were simulated using Monte Carlo techniques. These spectra were used to calculate the dependence of narrow beam contrast on phantom thickness for verification of the data measured from film. A Monte Carlo simulation of the beryllium spectrum in a wide beam geometry was used to evaluate the effect of phantom-to-film distance on contrast. Although the same degree of contrast improvement with distance was not realized in practice, the improvement in image quality rivaled that achieved using a scatter reduction grid. A comparison of conventional localization images of the head and neck of an anthropomorphic phantom with images produced with a beryllium or carbon target and a mammography film and screen system supports earlier suggestions that the technique is clinically useful.

The flatness of Siemens linear accelerator x-ray fields.

The primary definer for Siemens MXE and MDX linear accelerators projects a circular opening with a radius of 25 cm at 100 cm from the target. Our measurements of photon beam profiles, however, indicate that the photon fluence drops to 95% of the central axis value at a radius of 18 cm. The flattening filter for these machines projects a flattened field size that is much smaller than the primary definer would allow. The clinical implications of this mismatch for large rectangular fields and for fields defined by asymmetric jaws are discussed and solutions are considered. A large field flattener was designed for our Siemens MXE 6 MV beam using Monte Carlo simulation of the treatment head and water phantom. The accuracy required of source and geometry details for dose distributions calculation is presented. The key parameters are the mean energy and focal spot size of the electron beam incident on the exit window, the material composition, and thickness profile of the exit window, target, flattener, and primary collimator, and the position of the primary collimator relative to the target. Profiles were more sensitive than central axis depth doses to simulation details. The beam energy and primary collimator position were selected to achieve good agreement between measured and calculated dose distributions. The flattener we designed with Monte Carlo was machined from brass and mounted on our MXE treatment unit. Measurements demonstrate that the large field flattener extends the useful radius of the field out to 22 cm, right into the penumbra cast by the primary collimator.

Forward-directed bremsstrahlung of 10- to 30-MeV electrons incident on thick targets of Al and Pb.

Bremsstrahlung spectra from thick targets of Al and Pb have been measured absolutely (photons per incident electron) along the beam axis for electrons of 10-, 15-, 20-, 25-, and 30-MeV incident energy. The spectra have a 220-keV low-energy cutoff. The targets were cylinders with nominal thicknesses of 110% of the electron CSDA range. A thin transmission detector, calibrated against a toroidal current monitor, was placed upstream of the target to measure the beam current. The spectrometer was a 20-cm diameter by 25-cm-long cylindrical NaI detector. Measured spectra were corrected for pile-up, background, detector response, detector efficiency, attenuation in materials between the target and detector and the collimator effect. Spectra were calculated using the EGS4 Monte Carlo system for simulating the radiation transport. The simulation model included the small amount of material upstream of the target. This material contributed about 40% of the spectrum, but its presence or absence had little effect on the calculated bremsstrahlung yield. The shapes of the measured and calculated spectra were in excellent agreement. The ratio of the total number of photons in each measured spectrum to those in the corresponding calculated spectrum varied from 0.97 +/- 0.06 to 1.12 +/- 0.06, depending largely on the atomic number of the target. Absolute spectral measurements in the literature agreed with our calculations of spectral shape but showed a range of +/- 30% in the number of photons per incident electron relative to the calculated values, which is contrary to our result.

Accurate characterization of Monte Carlo calculated electron beams for radiotherapy.

Monte Carlo studies of dose distributions in patients treated with radiotherapy electron beams would benefit from generalized models of clinical beams if such models introduce little error into the dose calculations. Methodology is presented for the design of beam models, including their evaluation in terms of how well they preserve the character of the clinical beam, and the effect of the beam models on the accuracy of dose distributions calculated with Monte Carlo. This methodology has been used to design beam models for electron beams from two linear accelerators, with either a scanned beam or a scattered beam. Monte Carlo simulations of the accelerator heads are done in which a record is kept of the particle phase-space, including the charge, energy, direction, and position of every particle that emerges from the treatment head, along with a tag regarding the details of the particle history. The character of the simulated beams are studied in detail and used to design various beam models from a simple point source to a sophisticated multiple-source model which treats particles from different parts of a linear accelerator as from different sub-sources. Dose distributions calculated using both the phase-space data and the multiple-source model agree within 2%, demonstrating that the model is adequate for the purpose of Monte Carlo treatment planning for the beams studied. Benefits of the beam models over phase-space data for dose calculation are shown to include shorter computation time in the treatment head simulation and a smaller disk space requirement, both of which impact on the clinical utility of Monte Carlo treatment planning.

BEAM: a Monte Carlo code to simulate radiotherapy treatment units.

This paper describes BEAM, a general purpose Monte Carlo code to simulate the radiation beams from radiotherapy units including high-energy electron and photon beams, 60Co beams and orthovoltage units. The code handles a variety of elementary geometric entities which the user puts together as needed (jaws, applicators, stacked cones, mirrors, etc.), thus allowing simulation of a wide variety of accelerators. The code is not restricted to cylindrical symmetry. It incorporates a variety of powerful variance reduction techniques such as range rejection, bremsstrahlung splitting and forcing photon interactions. The code allows direct calculation of charge in the monitor ion chamber. It has the capability of keeping track of each particle's history and using this information to score separate dose components (e.g., to determine the dose from electrons scattering off the applicator). The paper presents a variety of calculated results to demonstrate the code's capabilities. The calculated dose distributions in a water phantom irradiated by electron beams from the NRC 35 MeV research accelerator, a Varian Clinac 2100C, a Philips SL75-20, an AECL Therac 20 and a Scanditronix MM50 are all shown to be in good agreement with measurements at the 2 to 3% level. Eighteen electron spectra from four different commercial accelerators are presented and various aspects of the electron beams from a Clinac 2100C are discussed. Timing requirements and selection of parameters for the Monte Carlo calculations are discussed.

A modular method to handle multiple time-dependent quantities in Monte Carlo simulations.

A general method for handling time-dependent quantities in Monte Carlo simulations was developed to make such simulations more accessible to the medical community for a wide range of applications in radiotherapy, including fluence and dose calculation. To describe time-dependent changes in the most general way, we developed a grammar of functions that we call 'Time Features'. When a simulation quantity, such as the position of a geometrical object, an angle, a magnetic field, a current, etc, takes its value from a Time Feature, that quantity varies over time. The operation of time-dependent simulation was separated into distinct parts: the Sequence samples time values either sequentially at equal increments or randomly from a uniform distribution (allowing quantities to vary continuously in time), and then each time-dependent quantity is calculated according to its Time Feature. Due to this modular structure, time-dependent simulations, even in the presence of multiple time-dependent quantities, can be efficiently performed in a single simulation with any given time resolution. This approach has been implemented in TOPAS (TOol for PArticle Simulation), designed to make Monte Carlo simulations with Geant4 more accessible to both clinical and research physicists. To demonstrate the method, three clinical situations were simulated: a variable water column used to verify constancy of the Bragg peak of the Crocker Lab eye treatment facility of the University of California, the double-scattering treatment mode of the passive beam scattering system at Massachusetts General Hospital (MGH), where a spinning range modulator wheel accompanied by beam current modulation produces a spread-out Bragg peak, and the scanning mode at MGH, where time-dependent pulse shape, energy distribution and magnetic fields control Bragg peak positions. Results confirm the clinical applicability of the method.

Sci-Fri PM: Planning-01: Measured electron and x-ray angular distribution data for benchmarking Monte Carlo codes.

Monte Carlo (MC) studies of the output of medical linear accelerators have demonstrated that in-air profiles are useful in the beam commissioning process. A recent investigation of x-ray profiles (Tonkopi et al, Med. Phys 32 (9), 2005) showed very good agreement between measurement and EGSnrc calculations but to achieve this level of agreement the beam linac spot size, energy and angular divergence had to be treated as variables. In this project we carried out measurements and MC calculations for an electron accelerator for which the initial beam parameters are well known. Two sets of investigations were carried out. In the first we measured electron scatter distributions for a range of scattering foils and electron energies of 13 and 20 MeV. The profiles were parameterised and compared to EGSnrc Monte Carlo calculations. It was found that generally the EGSnrc calculations gave agreement with the measurements within 1.5 %. In the second investigation, which is on-going, in-air profiles were obtained for photon beams produced using different targets (from beryllium to lead). Measured angular distributions were obtained using ion chambers with different build-up caps (low and high-Z) and the sensitivity of the data to small changes in geometry (e.g., moving the x-ray target) was investigated. The photon energy fluence was calculated using EGSnrc and preliminary indications are that the measured and calculated distributions agree to better than 5 %. Work supported in part by NIH grant R01 CA104777-01A2.