Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code

Comprehensive Monte Carlo calculation of the point spread function for a commercial a-Si EPID

Images produced by commercial amorphous silicon electronic portal imaging devices (a-Si EPIDs) are subject to multiple blurring processes. Implementation of these devices for fluence measurement requires that the blur be removed from the images. A standard deconvolution operation can be performed to accomplish this assuming the blur kernel is spatially invariant and accurately known. This study determines a comprehensive blur kernel for the Varian aS500 EPID. Monte Carlo techniques are used to derive a dose kernel and an optical kernel, which are then combined to yield an overall blur kernel for both 6 and 15 MV photon beams. Experimental measurement of the line spread function (LSF) is used to verify kernel shape. Kernel performance is gauged by comparing EPID image profiles with in-air dose profiles measured using a diamond detector (approximating fluence) both before and after the EPID images have been deconvolved. Quantitative comparisons are performed using the chi metric, an extension of the well-known y metric, using acceptance criteria of 0.0784 cm (1 pixel width) distance-to-agreement (deltad) and 2% of the relative central axis fluence (deltaD). Without incorporating any free parameters, acceptance was increased from 49.0% of pixels in a cross-plane profile for a 6 MV 10 x 10 cm2 open field to 92.0%. For a 10 x 10 cm2 physically wedged field, acceptance increased from 40.3% to 73.9%. The effect of the optical kernel was found to be negligible for these chi acceptance parameters, however for (deltaD= 1%, deltad = 0.0784 cm) we observed an improvement from 66.1% (without) to 78.6% (with) of chi scores <1 (from 20.6% before deconvolution). It is demonstrated that an empirical kernel having a triple exponential form or a semiempirical kernel based on a simplified model of the detector stack can match the performance of the comprehensive kernel.

Head-and-neck IMRT treatments assessed with a Monte Carlo dose calculation engine

IMRT is frequently used in the head-and-neck region, which contains materials of widely differing densities (soft tissue, bone, air-cavities). Conventional methods of dose computation for these complex, inhomogeneous IMRT cases involve significant approximations. In the present work, a methodology for the development, commissioning and implementation of a Monte Carlo (MC) dose calculation engine for intensity modulated radiotherapy (MC-IMRT) is proposed which can be used by radiotherapy centres interested in developing MC-IMRT capabilities for research or clinical evaluations. The method proposes three levels for developing, commissioning and maintaining a MC-IMRT dose calculation engine: (a) development of a MC model of the linear accelerator, (b) validation of MC model for IMRT and (c) periodic quality assurance (QA) of the MC-IMRT system. The first step, level (a), in developing an MC-IMRT system is to build a model of the linac that correctly predicts standard open field measurements for percentage depth-dose and off-axis ratios. Validation of MC-IMRT, level (b), can be performed in a rando phantom and in a homogeneous water equivalent phantom. Ultimately, periodic quality assurance of the MC-IMRT system is needed to verify the MC-IMRT dose calculation system, level (c). Once the MC-IMRT dose calculation system is commissioned it can be applied to more complex clinical IMRT treatments. The MC-IMRT system implemented at the Royal Marsden Hospital was used for IMRT calculations for a patient undergoing treatment for primary disease with nodal involvement in the head-and-neck region (primary treated to 65 Gy and nodes to 54 Gy), while sparing the spinal cord, brain stem and parotid glands. Preliminary MC results predict a decrease of approximately 1-2 Gy in the median dose of both the primary tumour and nodal volumes (compared with both pencil beam and collapsed cone). This is possibly due to the large air-cavity (the larynx of the patient) situated in the centre of the primary PTV and the approximations present in the dose calculation.

A preliminary dosimetric characterization of chemical vapor deposition diamond detector prototypes in photon and electron radiotherapy beams

Three radiation detectors based on polycrystalline diamond films with different thickness and resistivity, obtained by microwave chemical vapor deposition, were tested to assess their suitability for relative dosimetry of photon and electron beams supplied by clinical linear accelerators. All samples showed a linear response as a function of the absorbed dose. The sensitivity per unit of detector sensitive volume spanned between 7 and 43 nC Gy(-1) mm(-3) with an applied electric field of 40 kV/cm. The dose rate dependence was evaluated following the Fowler theory and delta coefficient values between 0.95 and 1.00 were found for the three samples when polarized at 40 kV/cm. Percentage depth dose curves, output factors, and normalized dose profiles were determined for 6 and 10 MV photon beams and for 6 and 15 MeV electron beams. The results obtained with the diamond detectors were in good agreement with those obtained by reference detector measurements [all the data were within the experimental uncertainty of 1% (1sigma)].

Modelling of electron contamination in clinical photon beams for Monte Carlo dose calculation

The purpose of this work is to model electron contamination in clinical photon beams and to commission the source model using measured data for Monte Carlo treatment planning. In this work, a planar source is used to represent the contaminant electrons at a plane above the upper jaws. The source size depends on the dimensions of the field size at the isocentre. The energy spectra of the contaminant electrons are predetermined using Monte Carlo simulations for photon beams from different clinical accelerators. A 'random creep' method is employed to derive the weight of the electron contamination source by matching Monte Carlo calculated monoenergetic photon and electron percent depth-dose (PDD) curves with measured PDD curves. We have integrated this electron contamination source into a previously developed multiple source model and validated the model for photon beams from Siemens PRIMUS accelerators. The EGS4 based Monte Carlo user code BEAM and MCSIM were used for linac head sinulation and dose calculation. The Monte Carlo calculated dose distributions were compared with measured data. Our results showed good agreement (less than 2% or 2 mm) for 6, 10 and 18 MV photon beams.

Reference photon dosimetry data and reference phase space data for the 6MV photon beam from Varian Clinac 2100 series linear accelerators

The current study presents the reference photon dosimetry data (RPDD) and reference phase space data (RPSD) for the 6 MV photon beam from Varian 2100 series linear accelerators. The RPDD provide the basic photon dosimetry data, typically collected during the initial commissioning of a new linear accelerator, including output factors, depth dose data, and beam profile data in air and in water. The RPSD provide the full phase space information, such as position, direction, and energy for each particle generated inside the head of any particular linear accelerator in question. The dosimetric characteristics if the 6 MV photon beam from the majority of the aforementioned accelerators, which are unaltered from the manufacturer's original specifications, can be fully described with these two data sets within a clinically acceptable uncertainty (approximately +/-2 %). The current study also presents a detailed procedure to establish the RPDD and RPSD using measured data and Monte Carlo calculations. The RPDD were constructed by compiling our own measured data and the average data based on the analysis of more than 50 sets of measured data from the Radiological Physics Center (RPC) and 10 sets of clinical dosimetry data obtained from 10 different institutions participating in the RPC's quality assurance monitoring program. All the measured data from the RPC and the RPC-monitored institutions were found to be within a statistically tight range (i.e., 1sigma approximately 1% or less) for each dosimetric quantity. The manufacturer's standard data, except for in-air off-axis factors that are available only from the current study, were compared with the RPDD, showing that the manufacturer's standard data could also be used as the RPDD for the photon beam studied in this study. The RPSD were obtained from Monte Carlo calculations using the BEAMnrc/ DOSXYZnrc code system with 6.2 MeV (a spread of 3% full width at half maximum) and 1.0 mm full width at half maximum as the values of the energy and radial spread of a Gaussian electron pencil beam incident on the target, respectively. The RPSD were capable of generating Monte Carlo data that agreed with the RPDD within the acceptance criteria adopted in the current study (e.g., 1% or 1 mm for depth dose). A complete set of the RPDD and RPSD from the current study is available from the RPC website (http://rpc.mdanderson.org) or via mass storage media such as DVD or CD-ROM upon request.

Large efficiency improvements in BEAMnrc using directional bremsstrahlung splitting

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

The separation of the head and phantom scatter components from a phase space description

The formalism based on phantom and collimator scatter factors for high energy photon beams is deduced using a phase space description. The phantom scatter factors (Sp) depend on the field size and shape at the level of the phantom and are generally considered independent of the collimation details used to form the desired field provided the effect of contaminant electrons can be neglected. As demonstrated in this work, this behaviour leads to the applicability of the Clarkson method in irregular fields. However, for a given field formed with a tertiary collimator it is not a priori clear that the variations of extrafocal radiation due to secondary collimator setting do not affect the phantom scatter correction factors. In fact, the extrafocal radiation has a lower mean energy than that of unscattered photons, and this radiation can reach points well outside the radiation field increasing the irradiated phantom volume. Besides, transmission through the blocks contributes to phantom scatter. Therefore, for a given block-defined field, the associated phantom scatter dose, per unit of fluence in air on the central axis, should in principle increase when enlarging the secondary collimator field. To confirm this, isocentric Sp data for 6 MV photons were measured at 10 cm depth in water, reducing with cerrobend blocks several fields formed with the secondary collimators. In particular, when a 30 x 30 cm2 collimator field is reduced with blocks to a 7 x 7 cm2 field, the dose per unit of fluence in air is 1.4% higher than that of the square collimator field equating the given block field. Our calculations indicate that in this case the block transmission accounts for only 0.2% of this increment, showing that the remaining effect is due to extrafocal radiation. As a concluding remark, this work contributes to a better understanding of the classical Clarkson method for irregular fields giving, additionally, a formal interpretation of the commonly used quantities.

An investigation of accelerator head scatter and output factor in air

Our purpose in this study was to investigate whether the Monte Carlo simulation can accurately predict output factors in air. Secondary goals were to study the head scatter components and investigate the collimator exchange effect. The Monte Carlo code, BEAMnrc, was used in the study. Photon beams of 6 and 18 MV were from a Varian Clinac 2100EX accelerator and the measurements were performed using an ionization chamber in a mini-phantom. The Monte Carlo calculated in air output factors was within 1% of measured values. The simulation provided information of the origin and the magnitude of the collimator exchange effect. It was shown that the collimator backscatter to the beam monitor chamber played a significant role in the beam output factors. However the magnitude of the scattered dose contributions from the collimator at the isocenter is negligible. The maximum scattered dose contribution from the collimators was about 0.15% and 0.4% of the total dose at the isocenter for a 6 and 18 MV beam, respectively. The scattered dose contributions from the flattening filter at the isocenter were about 0.9-3% and 0.2-6% of the total dose for field sizes of 4x4 cm2-40x40 cm2 for the 6 and 18 MV beam, respectively. The study suggests that measurements of head scatter factors be done at large depth well beyond the depth of electron contamination. The insight information may have some implications for developing generalized empirical models to calculate the head scatter.

Performance characteristics of a microMOSFET as anin vivodosimeter in radiation therapy

The commercially available microMOSFET dosimeter was characterized for its dosimetric properties in radiotherapy treatments. The MOSFET exhibited excellent correlation with the dose and was linear in the range of 5-500 cGy. No measurable effect in response was observed in the temperature range of 20-40 degrees C. No significant change in response was observed by changing the dose rate between 100 and 600 monitor units (MU) min(-1) or change in the dose per pulse. A 3% post-irradiation fading was observed within the first 5 h of exposure and thereafter it remained stable up to 60 h. A uniform energy response was observed in the therapy range between 4 MV and 18 MV. However, below 0.6 MeV (Cs-132), the MOSFET response increased with the decrease in energy. The MOSFET also had a uniform dose response in 6-20 MeV electron beams. The directional dependence of MOSFET was within +/-2% for all the energies studied. The inherent build-up of the MOSFET was evaluated dosimetrically and found to have varying water equivalent thickness, depending on the energy and the side of the beam entry. At depth, a single calibration factor obtained by averaging the MOSFET response over different field sizes, energies, orientation and depths reproduced the ion chamber measured dose to within 5%. The stereotactic and the penumbral measurements demonstrated that the MOSFET could be used in a high gradient field such as IMRT. The study showed that the microMOSFET dosimeter could be used as an in vivo dosimeter to verify the dose delivery to the patient to within +/-5%.

Dosimetric IMRT verification with a flat-panel EPID

A convolution-based calibration procedure has been developed to use an amorphous silicon flat-panel electronic portal imaging device (EPID) for accurate dosimetric verification of intensity-modulated radiotherapy (IMRT) treatments. Raw EPID images were deconvolved to accurate, high-resolution 2-D distributions of primary fluence using a scatter kernel composed of two elements: a Monte Carlo generated kernel describing dose deposition in the EPID phosphor, and an empirically derived kernel describing optical photon spreading. Relative fluence profiles measured with the EPID are in very good agreement with those measured with a diamond detector, and exhibit excellent spatial resolution required for IMRT verification. For dosimetric verification, the EPID-measured primary fluences are convolved with a Monte Carlo kernel describing dose deposition in a solid water phantom, and cross-calibrated with ion chamber measurements. Dose distributions measured using the EPID agree to within 2.1% with those measured with film for open fields of 2 x 2 cm2 and 10 x 10 cm2. Predictions of the EPID phantom scattering factors (SPE) based on our scatter kernels are within 1% of the SPE measured for open field sizes of up to 16 x 16 cm2. Pretreatment verifications of step-and-shoot IMRT treatments using the EPID are in good agreement with those performed with film, with a mean percent difference of 0.2 +/- 1.0% for three IMRT treatments (24 fields).

Contamination dose from photoneutron processes in bodily tissues during therapeutic radiation delivery

Dose to the total body from induced radiation resulting from primary exposure to radiotherapeutic beams is not detailed in routine treatment planning though this information is potentially important for better estimates of health risks including secondary cancers. This information can also allow better management of patient treatment logistics, suggesting better timing, sequencing, and conduct of treatment. Monte Carlo simulations capable of taking into account all interactions contributing to the dose to the total body, including neutron scattering and induced radioactivity, provide the most versatile and accurate tool for investigating these effects. MCNPX code version 2.2.6 with full IAEA library of photoneutron cross sections is particularly suited to trace not only photoneutrons but also protons and heavy ion particles that result from photoneutron interactions. Specifically, the MCNPX code is applied here to the problem of dose calculations in traditional (non-IMRT) photon beam therapy. Points of calculation are located in the head, where the primary irradiation has been directed, but also in the superior portion of the torso of the ORNL Mathematical Human Phantom. We calculated dose contributions from neutrons, protons, deutrons, tritons and He-3 that are produced at the time of photoneutron interactions in the body and that would not have been accounted for by conventional radiation oncology dosimetry.

Modelling 6 MV photon beams of a stereotactic radiosurgery system for Monte Carlo treatment planning

The goal of this work is to build a multiple source model to represent the 6 MV photon beams from a Cyberknife stereotactic radiosurgery system for Monte Carlo treatment planning dose calculations. To achieve this goal, the 6 MV photon beams have been characterized and modelled using the EGS4/BEAM Monte Carlo system. A dual source model has been used to reconstruct the particle phase space at a plane immediately above the secondary collimator. The proposed model consists of two circular planar sources for the primary photons and the scattered photons, respectively. The dose contribution of the contaminant electrons was found to be in the order of 10(-3) of the total maximum dose and therefore has been omitted in the source model. Various comparisons have been made to verify the dual source model against the full phase space simulated using the EGS4/BEAM system. The agreement in percent depth dose (PDD) curves and dose profiles between the phase space and the source model was generally within 2%/1 mm for various collimators (5 to 60 mm in diameter) at 80 to 100 cm source-to-surface distances (SSD). Excellent agreement (within 1%/1 mm) was also found between the dose distributions in heterogeneous lung and bone geometry calculated using the original phase space and those calculated using the source model. These results demonstrated the accuracy of the dual source model for Monte Carlo treatment planning dose calculations for the Cyberknife system.

Radiation characteristics of helical tomotherapy

Helical tomotherapy is a dedicated intensity modulated radiation therapy (IMRT) system with on-board imaging capability (MVCT) and therefore differs from conventional treatment units. Different design goals resulted in some distinctive radiation field characteristics. The most significant differences in the design are the lack of flattening filter, increased shielding of the collimators, treatment and imaging operation modes and narrow fan beam delivery. Radiation characteristics of the helical tomotherapy system, sensitivity studies of various incident electron beam parameters and radiation safety analyses are presented here. It was determined that the photon beam energy spectrum of helical tomotherapy is similar to that of more conventional radiation treatment units. The two operational modes of the system result in different nominal energies of the incident electron beam with approximately 6 MeV and 3.5 MeV in the treatment and imaging modes, respectively. The off-axis mean energy dependence is much lower than in conventional radiotherapy units with less than 5% variation across the field, which is the consequence of the absent flattening filter. For the same reason the transverse profile exhibits the characteristic conical shape resulting in a 2-fold increase of the beam intensity in the center. The radiation leakage outside the field was found to be negligible at less than 0.05% because of the increased shielding of the collimators. At this level the in-field scattering is a dominant source of the radiation outside the field and thus a narrow field treatment does not result in the increased leakage. The sensitivity studies showed increased sensitivity on the incident electron position because of the narrow fan beam delivery and high sensitivity on the incident electron energy, as common to other treatment systems. All in all, it was determined that helical tomotherapy is a system with some unique radiation characteristics, which have been to a large extent optimized for intensity modulated delivery.

Enhanced spectral discrimination through the exploitation of interface effects in photon dose data

The convolution/superposition algorithm for computing dose from photon beams in radiation therapy planning requires knowledge of the energy spectrum. The algorithm can compute the dose for a polyenergetic beam as the weighted sum of the individual dose contributions from monoenergetic beams. In this study we exploit interface effects apparent in the dose distributions to discriminate among spectra of high energy photon beams. We have studied the sensitivity of the depth dose distribution to the energy components using a hypothetical beam for various field sizes and depths in water and water-lung-water media. Six theoretical spectra were simulated. We compared depth dose data from these spectra using three quantitative measures which are inherently free of normalization ambiguities: for homogeneous water, the ratio D20/D10 and a logarithmic derivative in the buildup region LD(build-up) and for inhomogeneous lung/water, the lung correction factor (CF). It was found that the ability of both the CF and the LD(build-up) tests to discriminate between the various theoretical spectra were superior to that of the D20/D10 test. This discriminating power of the CF test decreases with increasing field size due to restored electronic equilibrium. The CF test, though, has some advantages over the LD(build-up) test since it is less prone to electron contamination issues and numerical errors. A practical example with a 15 MV photon beam illustrates the process. Consequently, we suggest that as part of a beam-commissioning methodology, designated electronic disequilibrium test cases be implemented in unambiguously determining the correct energy spectrum to be used.

Using Monte Carlo simulations to commission photon beam output factors—a feasibility study

This study investigates the feasibility of using Monte Carlo methods to assist the commissioning of photon beam output factors from a medical accelerator. The Monte Carlo code, BEAMnrc, was used to model 6 MV and 18 MV photon beams from a Varian linear accelerator. When excellent agreements were obtained between the Monte Carlo simulated and measured dose distributions in a water phantom, the entire geometry including the accelerator head and the water phantom was simulated to calculate the relative output factors. Simulated output factors were compared with measured data, which consist of a typical commission dataset for the output factors. The measurements were done using an ionization chamber in a water phantom at a depth of 10 cm with a source-detector distance of 100 cm. Square fields and rectangular fields with widths and lengths ranging from 4 cm to 40 cm were studied. The result shows a very good agreement (< 1.5%) between the Monte Carlo calculated and the measured relative output factors for a typical commissioning dataset. The Monte Carlo calculated backscatter factors to the beam monitor chamber agree well with measured data in the literature. Monte Carlo simulations have also been shown to be able to accurately predict the collimator exchange effect and its component for rectangular fields. The information obtained is also useful to develop an algorithm for accurate beam modelling. This investigation indicates that Monte Carlo methods can be used to assist commissioning of output factors for photon beams.

Monte Carlo modelling of external radiotherapy photon beams

An essential requirement for successful radiation therapy is that the discrepancies between dose distributions calculated at the treatment planning stage and those delivered to the patient are minimized. An important component in the treatment planning process is the accurate calculation of dose distributions. The most accurate way to do this is by Monte Carlo calculation of particle transport, first in the geometry of the external or internal source followed by tracking the transport and energy deposition in the tissues of interest. Additionally, Monte Carlo simulations allow one to investigate the influence of source components on beams of a particular type and their contaminant particles. Since the mid 1990s, there has been an enormous increase in Monte Carlo studies dealing specifically with the subject of the present review, i.e., external photon beam Monte Carlo calculations, aided by the advent of new codes and fast computers. The foundations for this work were laid from the late 1970s until the early 1990s. In this paper we will review the progress made in this field over the last 25 years. The review will be focused mainly on Monte Carlo modelling of linear accelerator treatment heads but sections will also be devoted to kilovoltage x-ray units and 60Co teletherapy sources.

Development and clinical application of a fast superposition algorithm in radiation therapy

BACKGROUND AND PURPOSE

Dose calculation algorithms play a central role for the optimization and verification of treatment plans in radiation therapy. Complex treatment techniques like intensity modulated radiotherapy (IMRT) require accurate and fast dose algorithms especially for clinical cases which involve severe tissue inhomogeneities. For these cases the standard dose engine in current treatment planning systems--the convolution of photon pencil beams--usually fails to predict the dose with the required accuracy. The role of more accurate but time consuming dose calculations like superposition algorithms or Monte Carlo simulations in clinical practice is under investigation at several therapy centers.

PATIENTS AND METHODS

The paper presents the design, implementation and the first application of a superposition algorithm in a clinical setting at the German Cancer Research Center (DKFZ). It first describes in detail how the superposition algorithm is adapted to the dose delivery system at DKFZ in terms of standard dosimetric data. Then details of the implementation of the algorithm are given with a focus on various methods for the reduction of dose computation times. Next, the algorithm is evaluated in various experiments with dosimetric phantoms. These studies are employed for the development of time efficient sampling strategies of the elemental dose kernels. Finally, the algorithm is applied to dose calculations of clinical cases with tumors adjacent to lung tissue.

RESULTS

Severe differences in dose coverage of the tumors and dose burden of the surrounding tissues in comparison to standard pencil beam calculations are observed. A standard 4-7 beam plan in a convenient dose grid (approximately 3 mm in each direction) is calculated in about 30 min on a Pentium 4 (1.9 GHz) applying the superposition algorithm described here.

EGSNRCMonte Carlo study of the effect of photon energy and field margin in phantoms simulating small lung lesions

The dose distribution in small lung tumors (coin lesions) is affected by the combined effects of reduced attenuation of photons and extended range of electrons in lung. The increased range of electrons in low-density tissues can lead to loss of field flatness and increased penumbra width, especially at high energies. The EGSNRC Monte Carlo code, together with DOSXYZNRC, a three-dimensional voxel dose calculation module has been used to study the characteristics of the penumbra in the region of the target-lung interfaces for various radiation beam energies, lung densities, target-field edge distances, target size, and depth. The Monte Carlo model was validated by film measurements made in acrylic (simulating a tumor) imbedded in cork (simulating the lung). Beam profiles that are deemed to be acceptable are defined as those in which no point within the planning target volume (target volume plus 1 cm margin) received less than 95% of the dose prescribed to the center of the target. For parallel opposed beams and 2 cm cube target size, 6 MV photons produce superior dose distribution with respect to penumbra at the lateral, anterior, and posterior surfaces and midplane of the simulated target, with a target-field edge distance of 2.5 cm. A lesser target-field edge distance of 2.0 cm is required for 4 MV photons to produce acceptable dose distribution. To achieve equivalent dose distribution with 10 and 18 MV photons, a target-field edge distance of 3.0 and 3.5 cm, respectaively, is required. For a simulated target size of 4 cm cube, a target-field edge distance of 2, 2.5, and 3 cm is required for 6, 10, and 18 MV photons, respectively, to yield acceptable PTV coverage. The effect, which is predominant in determining the target dose, depends on the beam energy, target-field edge distance, lung density, and the depth and size of the target.

Photonuclear dose calculations for high-energy photon beams from Siemens and Varian linacs

The dose from photon-induced nuclear particles (neutrons, protons, and alpha particles) generated by high-energy photon beams from medical linacs is investigated. Monte Carlo calculations using the MCNPX code are performed for three different photon beams from two different machines: Siemens 18 MV, Varian 15 MV, and Varian 18 MV. The linac head components are simulated in detail. The dose distributions from photons, neutrons, protons, and alpha particles are calculated in a tissue-equivalent phantom. Neutrons are generated in both the linac head and the phantom. This study includes (a) field size effects, (b) off-axis dose profiles, (c) neutron contribution from the linac head, (d) dose contribution from capture gamma rays, (e) phantom heterogeneity effects, and (f) effects of primary electron energy shift. Results are presented in terms of absolute dose distributions and also in terms of DER (dose equivalent ratio). The DER is the maximum dose from the particle (neutron, proton, or alpha) divided by the maximum photon dose, multiplied by the particle quality factor and the modulation scaling factor. The total DER including neutrons, protons, and alphas is about 0.66 cSv/Gy for the Siemens 18 MV beam (10 cm x 10 cm). The neutron DER decreases with decreasing field size while the proton (or alpha) DER does not vary significantly except for the 1 cm x 1 cm field. Both Varian beams (15 and 18 MV) produce more neutrons, protons, and alphas particles than the Siemens 18 MV beam. This is mainly due to their higher primary electron energies: 15 and 18.3 MeV, respectively, vs 14 MeV for the Siemens 18 MV beam. For all beams, neutrons contribute more than 75% of the total DER, except for the 1 cm x 1 cm field (approximately 50%). The total DER is 1.52 and 2.86 cSv/Gy for the 15 and 18 MV Varian beams (10 cm x 10 cm), respectively. Media with relatively high-Z elements like bone may increase the dose from heavy charged particles by a factor 4. The total DER is sensitive to primary electron energy shift. A Siemens 18 MV beam with 15 MeV (instead of 14 MeV) primary electrons would increase by 40% the neutron DER and by 210% the proton + alpha DER. Comparisons with measurements (neutron yields from different materials and neutron dose equivalent) are also presented. Using the NCRP risk assessment method, we found that the dose equivalent from leakage neutrons (at 50-cm off-axis distance) represent 1.1, 1.1, and 2.0% likelihood of fatal secondary cancer for a 70 Gy treatment delivered by the Siemens 18 MV, Varian 15 MV, and Varian 18 MV beams, respectively.

Convolution/superposition using the Monte Carlo method

The convolution/superposition calculations for radiotherapy dose distributions are traditionally performed by convolving polyenergetic energy deposition kernels with TERMA (total energy released per unit mass) precomputed in each voxel of the irradiated phantom. We propose an alternative method in which the TERMA calculation is replaced by random sampling of photon energy, direction and interaction point. Then, a direction is randomly sampled from the angular distribution of the monoenergetic kernel corresponding to the photon energy. The kernel ray is propagated across the phantom, and energy is deposited in each voxel traversed. An important advantage of the explicit sampling of energy is that spectral changes with depth are automatically accounted for. No spectral or kernel hardening corrections are needed. Furthermore, the continuous sampling of photon direction allows us to model sharp changes in fluence, such as those due to collimator tongue-and-groove. The use of explicit photon direction also facilitates modelling of situations where a given voxel is traversed by photons from many directions. Extra-focal radiation, for instance, can therefore be modelled accurately. Our method also allows efficient calculation of a multi-segment/multi-beam IMRT plan by sampling of beam angles and field segments according to their relative weights. For instance, an IMRT plan consisting of seven 14 x 12 cm2 beams with a total of 300 field segments can be computed in 15 min on a single CPU, with 2% statistical fluctuations at the isocentre of the patient's CT phantom divided into 4 x 4 x 4 mm3 voxels. The calculation contains all aperture-specific effects, such as tongue and groove, leaf curvature and head scatter. This contrasts with deterministic methods in which each segment is given equal importance, and the time taken scales with the number of segments. Thus, the Monte Carlo superposition provides a simple, accurate and efficient method for complex radiotherapy dose calculations.

Which accelerator photon beams are "clinic-like" for reference dosimetry purposes?

Previous work has demonstrated that, for photon beam dosimetry, TPR10(20) is not an ideal beam quality specifier for all bremsstrahlung beams, especially for lightly filtered beams in some standards laboratories. This paper addresses the following questions: Is TPR10(20) an adequate beam quality specifier for all modern clinical therapy accelerators? When can nonclinical beams in standards laboratories be used to calibrate ion chambers or measure kQ factors as a function of TPR10(20)? Based on detailed Monte Carlo simulations of Varian, Siemens, Elekta, and GE (Saturn) accelerators one can conclude that TPR10(20) is an adequate beam quality specifier for all these machines in the sense that for a given value of TPR10(20), the value of stopping-power ratios is the same. It is shown that, for the heavily filtered beams used in standards laboratories, TPR10(20) is an adequate beam quality specifier. It is also demonstrated that, for a larger range of bremsstrahlung beams than previously, %dd(10)x is a good beam quality specifier for all clinical beams as well as the lightly and heavily filtered beams in some standards laboratories. A criterion, based on the measured values of TPR10(20) and %dd(10)x for the beam, is proposed for determining whether a nonclinical beam is well specified by TPR10(20). Agreement between calculations for specific accelerators and measured beam quality specifiers is shown to be good, but agreement with published data for a variety of clinical accelerators is not as good. Possible reasons for the discrepancy are discussed.

Determining the incident electron fluence for Monte Carlo-based photon treatment planning using a standard measured data set

An accurate dose calculation in phantom and patient geometries requires an accurate description of the radiation source. Errors in the radiation source description are propagated through the dose calculation. With the emergence of linear accelerators whose dosimetric characteristics are similar to within measurement uncertainty, the same radiation source description can be used as the input to dose calculation for treatment planning at many institutions with the same linear accelerator model. Our goal in the current research was to determine the initial electron fluence above the linear accelerator target for such an accelerator to allow a dose calculation in water to within 1% or 1 mm of the measured data supplied by the manufacturer. The method used for both the radiation source description and the patient transport was Monte Carlo. The linac geometry was input into the Monte Carlo code using the accelerator's manufacturer's specifications. Assumptions about the initial electron source above the target were made based on previous studies. The free parameters derived for the calculations were the mean energy and radial Gaussian width of the initial electron fluence and the target density. A combination of the free parameters yielded an initial electron fluence that, when transported through the linear accelerator and into the phantom, allowed a dose-calculation agreement to the experimental ion chamber data to within the specified criteria at both 6 and 18 MV nominal beam energies, except near the surface, particularly for the 18 MV beam. To save time during Monte Carlo treatment planning, the initial electron fluence was transported through part of the treatment head to a plane between the monitor chambers and the jaws and saved as phase-space files. These files are used for clinical Monte Carlo-based treatment planning and are freely available from the authors.

A virtual photon energy fluence model for Monte Carlo dose calculation

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is also useful for IMRT applications because a full Monte Carlo simulation of the treatment head would be too time-consuming for many small fields.

Using a tungsten rollbar to characterize the source spot of a megavoltage bremsstrahlung linac

In photon teletherapy, the size and functional form of the photon source spot affect both the sharpness of the penumbra of treatment fields and the sharpness of portal images. Photon source spot parameters are also used in photon teletherapy dose calculation codes. A simple method for characterizing the source spot would complement the existing, more involved methods that have been described in the medical physics literature. Such a method, using a rollbar made of tungsten or other high-Z metal, is used in industrial radiography. We describe the use of a tungsten rollbar for characterizing the source spot edge spread function (and thereby the source spot size and shape) of a megavoltage bremsstrahlung photon source. We use Monte Carlo simulations to quantify anticipated experimental artifacts of the method, assuming typical spot sizes for circ-function, Gaussian, and Bennett line shapes. We illustrate the use of the rollbar method by characterizing the source spot of a typical 9 MV linac used for industrial radiography. The source spot is analyzed using two approaches: (a) fitting the rollbar image with analytic functions and (b) using Abel inversion to obtain the cylindrically symmetric spot profile consistent with the measured rollbar image. Monte Carlo simulations, based on a 6 MV photon teletherapy accelerator, suggest that aspects of the method are applicable to medical bremsstrahlung sources.