Backscatter towards the monitor ion chamber in high-energy photon and electron beams: charge integration versus Monte Carlo simulation

The effect of electron backscatter and charge build up in media on beam current transformer signal for ultra-high dose rate (FLASH) electron beam monitoring

Objective.Beam current transformers (BCT) are promising detectors for real-time beam monitoring in ultra-high dose rate (UHDR) electron radiotherapy. However, previous studies have reported a significant sensitivity of the BCT signal to changes in source-to-surface distance (SSD), field size, and phantom material which have until now been attributed to the fluctuating levels of electrons backscattered within the BCT. The purpose of this study is to evaluate this hypothesis, with the goal of understanding and mitigating the variations in BCT signal due to changes in irradiation conditions.Approach.Monte Carlo simulations and experimental measurements were conducted with a UHDR-capable intra-operative electron linear accelerator to analyze the impact of backscattered electrons on BCT signal. The potential influence of charge accumulation in media as a mechanism affecting BCT signal perturbation was further investigated by examining the effects of phantom conductivity and electrical grounding. Finally, the effectiveness of Faraday shielding to mitigate BCT signal variations is evaluated.Main Results.Monte Carlo simulations indicated that the fraction of electrons backscattered in water and on the collimator plastic at 6 and 9 MeV is lower than 1%, suggesting that backscattered electrons alone cannot account for the observed BCT signal variations. However, our experimental measurements confirmed previous findings of BCT response variation up to 15% for different field diameters. A significant impact of phantom type on BCT response was also observed, with variations in BCT signal as high as 14.1% when comparing measurements in water and solid water. The introduction of a Faraday shield to our applicators effectively mitigated the dependencies of BCT signal on SSD, field size, and phantom material.Significance.Our results indicate that variations in BCT signal as a function of SSD, field size, and phantom material are likely driven by an electric field originating in dielectric materials exposed to the UHDR electron beam. Strategies such as Faraday shielding were shown to effectively prevent these electric fields from affecting BCT signal, enabling reliable BCT-based electron UHDR beam monitoring.

Nontarget and Out-of-Field Doses from Electron Beam Radiotherapy

In clinical radiotherapy, the most important aspects are the dose distribution in the target volume and healthy organs, including out-of-field doses in the body. Compared to photon beam radiation, dose distribution in electron beam radiotherapy has received much less attention, mainly due to the limited range of electrons in tissues. However, given the growing use of electron intraoperative radiotherapy and FLASH, further study is needed. Therefore, in this study, we determined out-of-field doses from an electron beam in a phantom model using two dosimetric detectors (diode E and cylindrical Farmer-type ionizing chamber) for electron energies of 6 MeV, 9 MeV and 12 MeV. We found a clear decrease in out-of-field doses as the distance from the field edge and depth increased. The out-of-field doses measured with the diode E were lower than those measured with the Farmer-type ionization chamber at each depth and for each electron energy level. The out-of-field doses increased when higher energy megavoltage electron beams were used (except for 9 MeV). The out-of-field doses at shallow depths (1 or 2 cm) declined rapidly up to a distance of 3 cm from the field edge. This study provides valuable data on the deposition of radiation energy from electron beams outside the irradiation field.

Measured and Monte Carlo simulated electron backscatter to the monitor chamber for the Varian TrueBeam Linac

To accurately simulate therapeutic electron beams using Monte Carlo methods, backscatter from jaws into the monitor chamber must be accounted for via the backscatter factor, S _b. Measured and simulated values of S _b for the TrueBeam are investigated. Two approaches for measuring S _b are presented. Both require service mode operation with the dose and pulse forming networking servos turned off in order to assess changes in dose rate with field size. The first approach samples an instantaneous dose rate, while the second approach times the delivery of a fixed number of monitor units to assess dose rate. Dose rates were measured for 6, 12 and 20 MeV electrons for jaw- or MLC-shaped apertures between [Formula: see text] and [Formula: see text] cm². The measurement techniques resulted in values of S _b that agreed within 0.21% for square and asymmetric fields collimated by the jaws. Measured values of S _b were used to calculate the forward dose component in a virtual monitor chamber using BEAMnrc. Based on this forward component, simulated values of S _b were calculated and compared to measurement and Varian's VirtuaLinac simulations. BEAMnrc results for jaw-shaped fields agreed with measurements and with VirtuaLinac simulations within 0.2%. For MLC-shaped fields, the respective measurement techniques differed by as much as 0.41% and BEAMnrc results differed with measurement by as much as 0.4%, however, all measured and simulated values agreed within experimental uncertainty. Measurement sensitivity was not sufficient to capture the small backscatter effect due to the MLC, and Monte Carlo predicted backscatter from the MLC to be no more than 0.3%. Backscatter from the jaws changed the electron dose rate by up to 2.6%. This reinforces the importance of including a backscatter factor in simulations of electron fields shaped with secondary collimating jaws, but presents the option of ignoring it when jaws are retracted and collimation is done with the MLC.

Jaw position uncertainty and adjacent fields in breast cancer radiotherapy

Locoregional treatment of breast cancer involves adjacent, half blocked fields matched at isocenter. The objective of this work is to study the dosimetric effects of the uncertainties in jaw positioning for such a case, and how a treatment planning protocol including adjacent field overlap of 1 mm affects the dose distribution. A representative treatment plan, involving 6 and 15 photon beams, for a patient treated at our hospital is chosen. Monte Carlo method (EGSnrc/BEAMnrc) is used to simulate the treatment. Uncertainties in jaw positioning of ± 1 mm are addressed, which implies extremes in reality of 2 mm field gap/overlap when planning adjacent fields without overlap and 1 mm gap or 3 mm overlap for a planning protocol with 1 mm overlap. Dosimetric parameters for PTV, lung and body are analyzed. Treatment planning protocol with 1 mm overlap of the adjacent fields does not considerably counteract possible underdosage of the target in the case studied. PTV-V95% is for example reduced from 95% for perfectly aligned fields to 90% and 91% for 2 mm and 1 mm gap, respectively. However, the risk of overdosage in PTV and in healthy soft tissue is increased when following the protocol with 1 mm overlap. A 3 mm overlap compared to 2 mm overlap results in an increase in maximum dose to PTV, PTV-D2%, from 113% to 121%. V120% for 'Body-PTV' is also increased from 5 cm(3) to 14 cm(3). A treatment planning protocol with 1 mm overlap does not considerably improve the coverage of PTV in the case of erroneous jaw positions causing gap between fields, but increases the overdosage in PTV and doses to healthy tissue, in the case of overlapping fields, for the case investigated.

Monte Carlo modeling of HD120 multileaf collimator on Varian TrueBeam linear accelerator for verification of 6X and 6X FFF VMAT SABR treatment plans

A Monte Carlo (MC) validation of the vendor-supplied Varian TrueBeam 6 MV flattened (6X) phase-space file and the first implementation of the Siebers-Keall MC MLC model as applied to the HD120 MLC (for 6X flat and 6X flattening filter-free (6X FFF) beams) are described. The MC model is validated in the context of VMAT patient-specific quality assurance. The Monte Carlo commissioning process involves: 1) validating the calculated open-field percentage depth doses (PDDs), profiles, and output factors (OF), 2) adapting the Siebers-Keall MLC model to match the new HD120-MLC geometry and material composition, 3) determining the absolute dose conversion factor for the MC calculation, and 4) validating this entire linac/MLC in the context of dose calculation verification for clinical VMAT plans. MC PDDs for the 6X beams agree with the measured data to within 2.0% for field sizes ranging from 2 × 2 to 40 × 40 cm2. Measured and MC profiles show agreement in the 50% field width and the 80%-20% penumbra region to within 1.3 mm for all square field sizes. MC OFs for the 2 to 40 cm2 square fields agree with measurement to within 1.6%. Verification of VMAT SABR lung, liver, and vertebra plans demonstrate that measured and MC ion chamber doses agree within 0.6% for the 6X beam and within 2.0% for the 6X FFF beam. A 3D gamma factor analysis demonstrates that for the 6X beam, > 99% of voxels meet the pass criteria (3%/3 mm). For the 6X FFF beam, > 94% of voxels meet this criteria. The TrueBeam accelerator delivering 6X and 6X FFF beams with the HD120 MLC can be modeled in Monte Carlo to provide an independent 3D dose calculation for clinical VMAT plans. This quality assurance tool has been used clinically to verify over 140 6X and 16 6X FFF TrueBeam treatment plans.

Clinical implementation of enhanced dynamic wedges into the Pinnacle treatment planning system: Monte Carlo validation and patient-specific QA

The goal of this work is to present a systematic Monte Carlo validation study on the clinical implementation of the enhanced dynamic wedges (EDWs) into the Pinnacle(3) (Philips Medical Systems, Fitchburg, WI) treatment planning system (TPS) and QA procedures for patient plan verification treated with EDWs. Modeling of EDW beams in the Pinnacle(3) TPS, which employs a collapsed-cone convolution superposition (CCCS) dose model, was based on a combination of measured open-beam data and the 'Golden Segmented Treatment Table' (GSTT) provided by Varian for each photon beam energy. To validate EDW models, dose profiles of 6 and 10 MV photon beams from a Clinac 2100 C/D were measured in virtual water at depths from near-surface to 30 cm for a wide range of field sizes and wedge angles using the Profiler 2 (Sun Nuclear Corporation, Melbourne, FL) diode array system. The EDW output factors (EDWOFs) for square fields from 4 to 20 cm wide were measured in virtual water using a small-volume Farmer-type ionization chamber placed at a depth of 10 cm on the central axis. Furthermore, the 6 and 10 MV photon beams emerging from the treatment head of Clinac 2100 C/D were fully modeled and the central-axis depth doses, the off-axis dose profiles and the output factors in water for open and dynamically wedged fields were calculated using the Monte Carlo (MC) package EGS4. Our results have shown that (1) both the central-axis depth doses and the off-axis dose profiles of various EDWs computed with the CCCS dose model and MC simulations showed good agreement with the measurements to within 2%/2 mm; (2) measured EDWOFs used for monitor-unit calculation in Pinnacle(3) TPS agreed well with the CCCS and MC predictions within 2%; (3) all the EDW fields satisfied our validation criteria of 1% relative dose difference and 2 mm distance-to-agreement (DTA) with 99-100% passing rate in routine patient treatment plan verification using MapCheck 2D diode array.

Design and dosimetry of a few leaf electron collimator for energy modulated electron therapy

Despite the capability of energy modulated electron therapy (EMET) to achieve highly conformal dose distributions in superficial targets it has not been widely implemented due to problems inherent in electron beam radiotherapy such as planning dosimetry accuracy, and verification as well as a lack of systems for automated delivery. In previous work we proposed a novel technique to deliver EMET using an automated "few leaf electron collimator" (FLEC) that consists of four motor-driven leaves fit in a standard clinical electron beam applicator. Integrated with a Monte Carlo based optimization algorithm that utilizes patient-specific dose kernels, a treatment delivery was incorporated within the linear accelerator operation. The FLEC was envisioned to work as an accessory tool added to the clinical accelerator. In this article the design and construction of the FLEC prototype that match our compact design goals are presented. It is controlled using an in-house developed EMET controller. The structure of the software and the hardware characteristics of the EMET controller are demonstrated. Using a parallel plate ionization chamber, output measurements were obtained to validate the Monte Carlo calculations for a range of fields with different energies and sizes. Further verifications were also performed for comparing 1-D and 2-D dose distributions using energy independent radiochromic films. Comparisons between Monte Carlo calculations and measurements of complex intensity map deliveries show an overall agreement to within +/- 3%. This work confirms our design objectives of the FLEC that allow for automated delivery of EMET. Furthermore, the Monte Carlo dose calculation engine required for EMET planning was validated. The result supports the potential of the prototype FLEC for the planning and delivery of EMET.

[Estimation of collimator scatter factor, S(c), of small field sizes using long-SCD method and two saturation models]

To estimate the collimator scatter factor, S(c) of small field sizes in which a mini-phantom cannot be fully included at the nominal treatment distance (NTD=100 cm), we measured the in-air output of 4 MV and 10 MV X-rays of a Varian's Clinac 2100 C/D using a mini-phantom at NTD and at a long source-to-chamber distance (SCD=200 cm) with field-size defined at the isocenter down to 4.6 x 4.6 cm(2) and 2.3 x 2.3 cm(2), respectively. We then compared the fitted curve to the NTD dataset by a cumulative exponential distribution model with that by a cumulative Gaussian distribution (error function) model containing a zero-field extrapolated term derived from the long SCD dataset. The results showed that the zero-field extensions of two fitted curves coincided for a 4 MV X-ray, but a large discrepancy was seen between them for a 10 MV X-ray. Therefore, the S(c) of small field sizes not measurable using a mini-phantom at the NTD can be well estimated by applying the cumulative exponential model to the NTD dataset in the case of a 4 MV X-ray beam filtrated with a cone-shaped flattener. However, to estimate the S(c) of such small field sizes in the case of a 10 MV X-ray beam filtrated with a bell-shaped flattener, we consider it preferable to also measure in-air output at a long SCD and to apply the cumulative Gaussian model as described here.

Monte Carlo modeling of the ModuLeaf miniature MLC for small field dosimetry and quality assurance of the clinical treatment planning system

The purpose of this investigation was the verification of both the measured data and quality of the implementation of the add-on ModuLeaf miniature multileaf collimator (ML mMLC) into the clinical treatment planning system for conformal stereotactic radiosurgery treatment. To this end the treatment head with ML mMLC was modeled in the BEAMnrc Monte Carlo (MC) code. The 6 MV photon beams used in the setup were first benchmarked with a set of measurements. A total ML mMLC transmission of 1.13% of the 10 x 10 cm2 open field dose was measured and reproduced with the BEAMnrc/DOSXYZnrc code. Correspondence between calculated and measured output factors (OFs) was within 2%. Correspondence between MC and measured profiles was within 2% dose and 2 mm distance, only for the smallest 0.5 x 0.5 cm2 field the results were within 3% dose. In the next step, the MC model was compared with Gafchromic film measurements and Pinnacle(3) 7.4 f (convolution superposition algorithm) calculated dose distributions, using a gamma evaluation comparison, for a multi-beam patient setup delivered to a Lucytrade mark phantom. The gamma evaluation of the MC versus Gafchromic film resulted in 3.4% of points not fulfilling gamma <or= 1 for a 2%/2 mm criterion, the Pinnacle(3) 7.4 f versus Gafchromic results 3.8% and Pinnacle versus MC less than 1%. For specific patients with lesions of 8 cc and 0.2 cc, Monte Carlo and Pinnacle simulations of the plans were performed and compared using DVH evaluation. DVHs corresponded within 2% dose and 2% volume.

Ecliptic method for the determination of backscatter into the beam monitor chambers in photon beams of medical accelerators

A new method to measure the effect of the backscatter into the beam monitor chambers in linear accelerators is introduced from first principles. The technique, applicable to high-energy photon beams, is similar to the well-known telescopic method although here the heavy blocks are replaced by a very small, centred block on the shadow tray, thus the name 'ecliptic method'. This effect, caused mainly by backscattering from the secondary collimators, is known to be an output factor constituent and must be accounted for when detailed calculations involving the machine's head are required. Since its magnitude is generally small, experimental errors might obscure the behaviour of the phenomenon. Consequently, the procedure introduced goes along with an uncertainty assessment. Our theory was confirmed via measurements in cobalt-60 beams, where the studied effect does not contribute to the output factor. Measurements were also performed on our Saturne 41 linear accelerator and the results were qualitatively similar to those described elsewhere. The collimation systems were studied separately by varying one jaw setting while keeping the other at its maximum value. In the light of these results, we deduced an algorithm that can correlate the former data with the effect of backscattering to the beam monitor chambers for any rectangular field within 0.5%, which is of the order of the experimental uncertainty (0.6%). As we show, the experimental procedure is safe, simple, not invasive for the linac and requires only basic dosimetry equipment.

[Approximation of collimator scatter factor Sc by a saturation model]

To more easily estimate accurate values of collimator scatter facor, S(c), we suggest a two-component saturation model that accounts for scatter from the primary collimator and flattening filter and from the collimator jaws. This model, which assumes an exponential distribution of scatter intensity, was tested by in-air measurements using a mini-phantom for 4 MV and 10 MV X-rays of a Clinac 2100 C/D linear accelerator. The results showed a good fit of this model to our measured data (R(2)>0.9993). When the measured value was divided into the primary collimator/flattening filter component and the collimator jaw component, as expected, the former component showed a rapid and full saturation curve with increased field size, while the latter showed an almost linearly increasing curve. Therefore, we think that this saturation model is useful for the estimation of S(c) and is applicable to monitor unit calculation for an asymmetric field.

Measurements of in-air output ratios for a linear accelerator with and without the flattening filter

The in-air output ratio (Sc) for photon beams from linear accelerators describes the change of in-air output as a function of the collimator settings. The physical origin of the Sc is mainly due to the change in scattered radiation that can reach the point of measurement as the geometry of the head changes. The flattening filter (FF) and primary collimator are the major sources of scattered radiation. The change in amount of backscattered radiation from the collimator into the beam-monitoring chamber also contributes to the variation of output. In this work, we measured the Sc and backscatter factors (Sb) into the beam-monitoring chamber for a linear accelerator with and without the FF. We measured the Sc with a Farmer-type chamber in a miniphantom at the depth of 10 g/cm2 for 6- and 18-MV x-ray beams from a Varian Clinac 2100EX linear accelerator. The Sb were measured with a universal pulse counter and a diode array with build-in counting hardware and software. The head scatter component (Sh) was then derived from the relationship Sc= Sh x Sb, where Sb was the linear fit of measured results. Significant differences were observed for Sc with and without the FF. Within the range of experimental uncertainty, the Sb was similar with and without the FF. The variations in Sh differed significantly over the range of field sizes of 3 X 3 to 40 X 40 cm2 with and without the FF; for the 6-MV beam, it was 8% vs 3%, and for the 18-MV beam, 7% vs 1%. By analyzing the contributions of backscatter factor and total in-air output ratios with and without the FF, we directly gained insight into the contributions of different components to the total variations in Sc of a linear accelerator. Sc, Sb, and Sh are basic and useful dosimetric quantities for delivery of intensity-modulated radiation therapy using a linear accelerator operating in a mode without the FF.

Dose uncertainties in photon pencil kernel calculations at off-axis positions

The purpose of this study was to investigate the specific problems associated with photon dose calculations in points located at a distance from the central beam axis. These problems are related to laterally inhomogeneous energy fluence distributions and spectral variations causing a lateral shift in the beam quality, commonly referred to as off-axis softening (OAS). We have examined how the dose calculation accuracy is affected when enabling and disabling explicit modeling of these two effects. The calculations were performed using a pencil kernel dose calculation algorithm that facilitates modeling of OAS through laterally varying kernel properties. Together with a multi-source model that provides the lateral energy fluence distribution this generates the total dose output, i.e., the dose per monitor unit, at an arbitrary point of interest. The dose calculation accuracy was evaluated through comparisons with 264 measured output factors acquired at 5, 10, and 20 cm depth in four different megavoltage photon beams. The measurements were performed up to 18 cm from the central beam axis, inside square fields of varying size and position. The results show that calculations including explicit modeling of OAS were considerably more accurate, up to 4%, than those ignoring the lateral beam quality shift. The deviations caused by simplified head scatter modeling were smaller, but near the field edges additional errors close to 1% occurred. When enabling full physics modeling in the dose calculations the deviations display a mean value of -0.1%, a standard deviation of 0.7%, and a maximum deviation of -2.2%. Finally, the results were analyzed in order to quantify and model the inherent uncertainties that are present when leaving the central beam axis. The off-axis uncertainty component showed to increase with both off-axis distance and depth, reaching 1% (1 standard deviation) at 20 cm depth.

Monte Carlo study of backscatter in a flattening filter free clinical accelerator

In conventional linear accelerators, the flattening filter provides a uniform lateral dose profile. In intensity modulated radiation therapy applications, however, the flatness of the photon field and hence the presence of a flattening filter, is not necessary. Removing the filter may provide some advantages, such as faster treatments and smaller out-of-field doses to the patients. In clinical accelerators the backscattered radiation dose from the collimators must be taken into account when the dose to the target volume in the patient is being determined. In the case of a conventional machine, this backscatter is known to great precision. In a flattening filter free accelerator, however, the amount of backscatter may be different. In this study we determined the backscatter contribution to the monitor chamber signal in a flattening filter free clinical accelerator (Varian Clinac 21EX) with Monte Carlo simulations. We found that with the exception of very small fields in the 18-MV photon mode, the contribution of backscattered radiation to the monitor signal did not differ from that of conventional machines with a flattening filter. Hence, a flattening filter free clinical accelerator would not necessitate a different backscatter correction.

Determination of the initial beam parameters in Monte Carlo linac simulation

For Monte Carlo linac simulations and patient dose calculations, it is important to accurately determine the phase space parameters of the initial electron beam incident on the target. These parameters, such as mean energy and radial intensity distribution, have traditionally been determined by matching the calculated dose distributions with the measured dose distributions through a trial and error process. This process is very time consuming and requires a lot of Monte Carlo simulation experience and computational resources. In this paper, we propose an easy, efficient, and accurate method for the determination of the initial beam parameters. We hypothesize that (1) for one type of linacs, the geometry and material of major components of the treatment head are the same; the only difference is the phase space parameters of the initial electron beam incident on the target, and (2) most linacs belong to a limited number of linac types. For each type of linacs, Monte Carlo treatment planning system (MC-TPS) vendors simulate the treatment head and calculate the three-dimensional (3D) dose distribution in water phantom for a grid of initial beam energies and radii. The simulation results (phase space files and dose distribution files) are then stored in a data library. When a MC-TPS user tries to model their linac which belongs to the same type, a standard set of measured dose data is submitted and compared with the calculated dose distributions to determine the optimal combination of initial beam energy and radius. We have applied this method to the 6 MV beam of a Varian 21EX linac. The linac was simulated using EGSNRC/BEAM code and the dose in water phantom was calculated using EGSNRC/DOSXYZ. We have also studied issues related to the proposed method. Several common cost functions were tested for comparing measured and calculated dose distributions, including chi2, mean absolute error, dose difference at the penumbra edge point, slope of the dose difference of the lateral profile, and the newly proposed Kappaalpha factor (defined as the fraction of the voxels with absolute dose difference less than alpha%). It was found that the use of the slope of the lateral profile difference or the difference of the penumbra edge points may lead to inaccurate determination of the initial beam parameters. We also found that in general the cost function value is very sensitive to the simulation statistical uncertainty, and there is a tradeoff between uncertainty and specificity. Due to the existence of statistical uncertainty in simulated dose distributions, it is practically impossible to determine the best energy/radius combination; we have to accept a group of energy/radius combinations. We have also investigated the minimum required data set for accurate determination of the initial beam parameters. We found that the percent depth dose curves along or only a lateral profile at certain depth for a large field size is not sufficient and the minimum data set should include several lateral profiles at various depths as well as the central axis percent depth dose curve for a large field size.

Absolute dose calculations for Monte Carlo simulations of radiotherapy beams

Monte Carlo (MC) simulations have traditionally been used for single field relative comparisons with experimental data or commercial treatment planning systems (TPS). However, clinical treatment plans commonly involve more than one field. Since the contribution of each field must be accurately quantified, multiple field MC simulations are only possible by employing absolute dosimetry. Therefore, we have developed a rigorous calibration method that allows the incorporation of monitor units (MU) in MC simulations. This absolute dosimetry formalism can be easily implemented by any BEAMnrc/DOSXYZnrc user, and applies to any configuration of open and blocked fields, including intensity-modulated radiation therapy (IMRT) plans. Our approach involves the relationship between the dose scored in the monitor ionization chamber of a radiotherapy linear accelerator (linac), the number of initial particles incident on the target, and the field size. We found that for a 10 x 10 cm2 field of a 6 MV photon beam, 1 MU corresponds, in our model, to 8.129 x 10(13) +/- 1.0% electrons incident on the target and a total dose of 20.87 cGy +/- 1.0% in the monitor chambers of the virtual linac. We present an extensive experimental verification of our MC results for open and intensity-modulated fields, including a dynamic 7-field IMRT plan simulated on the CT data sets of a cylindrical phantom and of a Rando anthropomorphic phantom, which were validated by measurements using ionization chambers and thermoluminescent dosimeters (TLD). Our simulation results are in excellent agreement with experiment, with percentage differences of less than 2%, in general, demonstrating the accuracy of our Monte Carlo absolute dose calculations.

Dosimetric evaluation of the clinical implementation of the first commercial IMRT Monte Carlo treatment planning system at 6 MV

In this work we dosimetrically evaluated the clinical implementation of a commercial Monte Carlo treatment planning software (PEREGRINE, North American Scientific, Cranberry Township, PA) intended for quality assurance (QA) of intensity modulated radiation therapy treatment plans. Dose profiles calculated in homogeneous and heterogeneous phantoms using this system were compared to both measurements and simulations using the EGSnrc Monte Carlo code for the 6 MV beam of a Varian CL21EX linear accelerator. For simple jaw-defined fields, calculations agree within 2% of the dose at d(max) with measurements in homogeneous phantoms with the exception of the buildup region where the calculations overestimate the dose by up to 8%. In heterogeneous lung and bone phantoms the agreement is within 3%, on average, up to 5% for a 1 x 1 cm2 field. We tested two consecutive implementations of the MLC model. After matching the calculated and measured MLC leakage, simulations of static and dynamic MLC-defined fields using the most recent MLC model agreed to within 2% with measurements.

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.

Scattered radiation from applicators in clinical electron beams

In radiotherapy with high-energy (4-25 MeV) electron beams, scattered radiation from the electron applicator influences the dose distribution in the patient. In most currently available treatment planning systems for radiotherapy this component is not explicitly included and handled only by a slight change of the intensity of the primary beam. The scattered radiation from an applicator changes with the field size and distance from the applicator. The amount of scattered radiation is dependent on the applicator design and on the formation of the electron beam in the treatment head. Electron applicators currently applied in most treatment machines are essentially a set of diaphragms, but still do produce scattered radiation. This paper investigates the present level of scattered dose from electron applicators, and as such provides an extensive set of measured data. The data provided could for instance serve as example input data or benchmark data for advanced treatment planning algorithms which employ a parametrized initial phase space to characterize the clinical electron beam. Central axis depth dose curves of the electron beams have been measured with and without applicators in place, for various applicator sizes and energies, for a Siemens Primus, a Varian 2300 C/D and an Elekta SLi accelerator. Scattered radiation generated by the applicator has been found by subtraction of the central axis depth dose curves, obtained with and without applicator. Scattered radiation from Siemens, Varian and Elekta electron applicators is still significant and cannot be neglected in advanced treatment planning. Scattered radiation at the surface of a water phantom can be as high as 12%. Scattered radiation decreases almost linearly with depth. Scattered radiation from Varian applicators shows clear dependence on beam energy. The Elekta applicators produce less scattered radiation than those of Varian and Siemens, but feature a higher effective angular variance. The scattered radiation decreases somewhat with increasing field size and is spread uniformly over the aperture. Experimental results comply with the results of simulations of the treatment head and electron applicator, using the BEAM Monte Carlo code, and Siemens, but feature a higher effective angular variance. The scattered radiation decreases somewhat with increasing field size and is spread uniformly over the aperture. Experimental results comply with the results of simulations of the treatment head and electron applicator, using the BEAM Monte Carlo code.

A three-source model for the calculation of head scatter factors

Accurate determination of the head scatter factor Sc is an important issue, especially for intensity modulated radiation therapy, where the segmented fields are often very irregular and much less than the collimator jaw settings. In this work, we report an Sc calculation algorithm for symmetric, asymmetric, and irregular open fields shaped by the tertiary collimator (a multileaf collimator or blocks) at different source-to-chamber distance. The algorithm was based on a three-source model, in which the photon radiation to the point of calculation was treated as if it originated from three effective sources: one source for the primary photons from the target and two extra-focal photon sources for the scattered photons from the primary collimator and the flattening filter, respectively. The field mapping method proposed by Kim et al. [Phys. Med. Biol. 43, 1593-1604 (1998)] was extended to two extra-focal source planes and the scatter contributions were integrated over the projected areas (determined by the detector's eye view) in the three source planes considering the source intensity distributions. The algorithm was implemented using Microsoft Visual C/C++ in the MS Windows environment. The only input data required were head scatter factors for symmetric square fields, which are normally acquired during machine commissioning. A large number of different fields were used to evaluate the algorithm and the results were compared with measurements. We found that most of the calculated Sc's agreed with the measured values to within 0.4%. The algorithm can also be easily applied to deal with irregular fields shaped by a multileaf collimator that replaces the upper or lower collimator jaws.

Using Monte Carlo methods to commission electron beams: a feasibility study

The purpose of this study was to investigate the feasibility of using Monte Carlo methods to assist in the commissioning of electron beams for a medical linear accelerator. The EGS4/BEAM code system was used to model an installed linear accelerator at this institution. Following an initial tuning of the input parameters, dosimetry data normally measured during the machine commissioning was calculated using the Monte Carlo code. All commissioning data was calculated for 6- and 12-MeV electron beams, and a subset of the commissioning data was calculated for the 20-MeV electron beams. On central axis, calculated percentage depth dose, cross-beam profiles, cone-insert ratios, and air-gap factors were generally within 2% of Dmax or 1 mm of the measured commissioning data; however, calculated open-cone ratios were not within 2%, in most cases. Calculated off-axis dose profiles for small fields were generally within the 2% (1-mm) criteria; however, calculated dose profiles for larger (open cone) fields frequently failed the 2% (1-mm) criteria. The remaining discrepancies between Monte Carlo calculations and measurement could be due to flaws in the Monte Carlo code, inaccuracies in the simulation geometry, the approximation of the initial source configuration, or a combination of the above. Although agreement between Monte Carlo calculated and measured doses was impressive and similar to previously published comparisons, our results did not prove our hypothesis that Monte Carlo calculations can generate electron commissioning data that is accurate within 2% of Dmax or 0.1 cm over the entire range of clinical treatment parameters. Although we believe that this hypothesis can be proved, it remains a challenge for the medical physics community. We intend to pursue this further by developing systematic methods for isolating causes of these differences.

Dosimetric characteristics of dynamic wedged fields: a Monte Carlo study

We have developed a Monte Carlo (MC) technique using the EGS4/BEAM system to calculate dosimetric characteristics of dynamic wedges (DW) for photon beam radiotherapy. The simulation of DW was accomplished by weighting the history numbers of the electrons, which are incident on the target in accordance with the segmented treatment table. Calculations were performed for DW with wedge angles ranging from 15 degrees to 60 degrees as well as for open fields with different field sizes for both degrees 6 and 18 MV beams. The MC-calculated percentage depth dose (PDD) and beam profiles agreed with the measurements within +/- 2% (of the dose maximum along the beam axis) or +/- 2 mm in high dose gradient region. The DW slightly affects energy spectra of photons and contaminating electrons. These slight changes have no significant effects on PDD as compared to the open field. The MC-calculated dynamic wedge factors agree with the measurements within +/- 2%. The MC method enables us to provide more detailed beam characteristics for DW fields than a measurement method. This beam characteristic includes photon energy spectra, mean energy, spectra of contaminating electrons and effects of moving jaw on off-axis beam quality. These data are potentially important for treatment planning involving dynamic wedges.

A method of simulating dynamic multileaf collimators using Monte Carlo techniques for intensity-modulated radiation therapy

A method of modelling the dynamic motion of multileaf collimators (MLCs) for intensity-modulated radiation therapy (IMRT) was developed and implemented into the Monte Carlo simulation. The simulation of the dynamic MLCs (DMLCs) was based on randomizing leaf positions during a simulation so that the number of particle histories being simulated for each possible leaf position was proportional to the monitor units delivered to that position. This approach was incorporated into an EGS4 Monte Carlo program, and was evaluated in simulating the DMLCs for Varian accelerators (Varian Medical Systems, Palo Alto. CA, USA). The MU index of each segment, which was specified in the DMLC-control data, was used to compute the cumulative probability distribution function (CPDF) for the leaf positions. This CPDF was then used to sample the leaf positions during a real-time simulation, which allowed for either the step-shoot or sweeping-leaf motion in the beam delivery. Dose intensity maps for IMRT fields were computed using the above Monte Carlo method, with its accuracy verified by film measurements. The DMLC simulation improved the operational efficiency by eliminating the need to simulate multiple segments individually. More importantly, the dynamic motion of the leaves could be simulated more faithfully by using the above leaf-position sampling technique in the Monte Carlo simulation.

Monte Carlo calculation of output factors for circular, rectangular, and square fields of electron accelerators (6-20 MeV)

Monte Carlo (MC) techniques can be used to build a simulation model of an electron accelerator to calculate output factors for electron fields. This can be useful during commissioning of electron beams from a linac and in clinical practice where irregular fields are also encountered. The Monte Carlo code BEAM/EGS4 was used to model electron beams (6-20 MeV) from a Varian 2100C linear accelerator. After optimization of the Monte Carlo simulation model, agreement within 1% to 2% was obtained between calculated and measured (with a Si diode) lateral and depth dose distributions or within 1 mm in the penumbral regions. Output factors for square, rectangular, and circular fields were measured using two different plane-parallel ion chambers (Markus and NACP) and compared to MC simulations. The agreement was usually within 1% to 2%. This study was not primarily concerned with minimizing the simulation time required to obtain output factors but some considerations with respect to this are presented. It would be particularly useful if the MC model could also be used to calculate output factors for other, similar linacs. To see if this was possible, the primary electron energies in the MC model were retuned to model a recently commissioned similar linac. Good agreement between calculated and measured output factors was obtained for most field sizes for this second accelerator.

Quantifying effects of lead shielding in electron beams: a Monte Carlo study

Lead shielding in contact with the patient's skin is often encountered in radiotherapy with electron beams. The influence of the lead shielding on dose distributions in the patient cannot fully be assessed using modern treatment planning systems. In this work the problem of quantifying the effect of lead shielding on dose distributions is addressed. Monte Carlo dose calculations were performed in a half-blocked water phantom shielded by lead, using a realistic model for the fluence of an electron linear accelerator. Electron beam energies of 6-20 MeV and lead thicknesses of 1-7 mm are used for 10 x 10 cm2 and 5 x 5 cm2 fields. The perturbation of the particle fluence and dose distributions in water introduced by the lead shielding is quantified. The effect of oblique electron beams on the dose perturbation is shown. A fictitious clinical example, the shielding of an eye in electron beam treatment, is used to demonstrate the usefulness of Monte Carlo based treatment planning algorithms that can incorporate the effects of lead shielding.

Incorporating dynamic collimator motion in Monte Carlo simulations: an application in modelling a dynamic wedge

In radiation therapy, new treatment modalities employing dynamic collimation and intensity modulation increase the complexity of dose calculation because a new dimension, time, has to be incorporated into the traditional three-dimensional problem. In this work, we investigated two classes of sampling technique to incorporate dynamic collimator motion in Monte Carlo simulation. The methods were initially evaluated for modelling enhanced dynamic wedges (EDWs) from Varian accelerators (Varian Medical Systems, Palo Alto, USA). In the position-probability-sampling or PPS method, a cumulative probability distribution function (CPDF) was computed for the collimator position, which could then be sampled during simulations. In the static-component-simulation or SCS method, a dynamic field is approximated by multiple static fields in a step-shoot fashion. The weights of the particles or the number of particles simulated for each component field are computed from the probability distribution function (PDF) of the collimator position. The CPDF and PDF were computed from the segmented treatment tables (STTs) for the EDWs. An output correction factor had to be applied in this calculation to account for the backscattered radiation affecting monitor chamber readings. Comparison of the phase-space data from the PPS method (with the step-shoot motion) with those from the SCS method showed excellent agreement. The accuracy of the PPS method was further verified from the agreement between the measured and calculated dose distributions. Compared to the SCS method, the PPS method is more automated and efficient from an operational point of view. The principle of the PPS method can be extended to simulate other dynamic motions, and in particular, intensity-modulated beams using multileaf collimators.