Monte Carlo simulation of electron beams from an accelerator head using PENELOPE

Inference of the optimal pretarget electron beam parameters in a Monte Carlo virtual linac model through simulated annealing

The purpose of this study was to develop an efficient method to determine the optimal intensity distribution of the pretarget electron beam in a Monte Carlo (MC) accelerator model able to most accurately reproduce a set of measured photon field profiles for a given accelerator geometry and nominal photon beam energy. The method has the ability to reduce the number of simulations required to commission a MC accelerator model and has achieved better agreement with measurement than other methods described in literature. The method begins from a cylindrically symmetric pretarget electron beam (radius of 0.5 cm) of uniform intensity. This beam is subdivided into annular regions of fluence for which each region is individually transported through the accelerator head and into a water phantom. A simulated annealing search is then performed to determine the optimal combination of weights of the annular fluences that provide a best match between the measured dose distributions and the weighted sum of annular dose distributions for particular pretarget electron energy. When restricted to Gaussian intensity distributions, the optimization determined an optimal FWHM=1.34 mm for 18.0 MeV electrons, with a RMSE=0.49% on 40 x 40 cm2 lateral profiles. When allowed to deviate from Gaussian intensities a further reduction in RMSE was achieved. For our Clinac 21 EX accelerator MC model (based on the 1996 Varian Oncology Systems, Monte Carlo Project package), the optimal unrestricted intensity distribution was found to be a Gaussian-like solution (18.0 MeV, FWHM= 1.10 mm, 40 x 40 cm2 profile, and RMSE=0.15%) with the presence of an extra focal halo contribution on the order of 10% of the maximum Gaussian intensity. Using the optimally derived intensity, 10 x 10 and 4 x 4 cm2 profiles were found to be in agreement with measurement with a maximum RMSE=0.49%. The optimized Gaussian and unrestricted values of the electron beam FWHM were both within the range of those inferred by focal spot image measurements performed by Jaffray et al. ["X-ray sources of medical linear accelerators: Focal and extra-focal radiation," Med. Phys. 20, 1417-1427 (1993)]. The inference of an extra focal pretarget electron component may be an indicator of a deficiency in the MC model and needs further investigation.

Simulação computacional de um feixe de fótons de 6 MV em diferentes meios heterogêneos utilizando o código PENELOPE

OBJETIVO: Utilizar o código PENELOPE e desenvolver geometrias onde estão presentes heterogeneidades para simular o comportamento do feixe de fótons nessas condições. MATERIAIS E MÉTODOS: Foram feitas simulações do comportamento da radiação ionizante para o caso homogêneo, apenas água, e para os casos heterogêneos, com diferentes materiais. Consideraram-se geometrias cúbicas para os fantomas e geometrias em forma de paralelepípedos para as heterogeneidades com a seguinte composição: tecido simulador de osso e pulmão, seguindo recomendações da International Commission on Radiological Protection, e titânio, alumínio e prata. Definiram-se, como parâmetros de entrada: a energia e o tipo de partícula da fonte, 6 MV de fótons; a distância fonte-superfície de 100 cm; e o campo de radiação de 10x 10 cm². RESULTADOS: Obtiveram-se curvas de percentual de dose em profundidade para todos os casos. Observou-se que em materiais com densidade eletrônica alta, como a prata, a dose absorvida é maior em relação à dose absorvida no fantoma homogêneo, enquanto no tecido simulador de pulmão a dose é menor. CONCLUSÃO: Os resultados obtidos demonstram a importância de se considerar heterogeneidades nos algoritmos dos sistemas de planejamento usados no cálculo da distribuição de dose nos pacientes, evitando-se sub ou superdosagem dos tecidos próximos às heterogeneidades.

eIMRT: a web platform for the verification and optimization of radiation treatment plans

The eIMRT platform is a remote distributed computing tool that provides users with Internet access to three different services: Monte Carlo optimization of treatment plans, CRT & IMRT treatment optimization, and a database of relevant radiation treatments/clinical cases. These services are accessible through a user-friendly and platform independent web page. Its flexible and scalable design focuses on providing the final users with services rather than a collection of software pieces. All input and output data (CT, contours, treatment plans and dose distributions) are handled using the DICOM format. The design, implementation, and support of the verification and optimization algorithms are hidden to the user. This allows a unified, robust handling of the software and hardware that enables these computation-intensive services. The eIMRT platform is currently hosted by the Galician Supercomputing Center (CESGA) and may be accessible upon request (there is a demo version at http://eimrt.cesga.es:8080/eIMRT2/demo; request access in http://eimrt.cesga.es/signup.html). This paper describes all aspects of the eIMRT algorithms in depth, its user interface, and its services. Due to the flexible design of the platform, it has numerous applications including the intercenter comparison of treatment planning, the quality assurance of radiation treatments, the design and implementation of new approaches to certain types of treatments, and the sharing of information on radiation treatment techniques. In addition, the web platform and software tools developed for treatment verification and optimization have a modular design that allows the user to extend them with new algorithms. This software is not a commercial product. It is the result of the collaborative effort of different public research institutions and is planned to be distributed as an open source project. In this way, it will be available to any user; new releases will be generated with the new implemented codes or upgrades.

Monte Carlo simulation of RapidArc radiotherapy delivery

RapidArc radiotherapy technology from Varian Medical Systems is one of the most complex delivery systems currently available, and achieves an entire intensity-modulated radiation therapy (IMRT) treatment in a single gantry rotation about the patient. Three dynamic parameters can be continuously varied to create IMRT dose distributions-the speed of rotation, beam shaping aperture and delivery dose rate. Modeling of RapidArc technology was incorporated within the existing Vancouver Island Monte Carlo (VIMC) system (Zavgorodni et al 2007 Radiother. Oncol. 84 S49, 2008 Proc. 16th Int. Conf. on Medical Physics). This process was named VIMC-Arc and has become an efficient framework for the verification of RapidArc treatment plans. VIMC-Arc is a fully automated system that constructs the Monte Carlo (MC) beam and patient models from a standard RapidArc DICOM dataset, simulates radiation transport, collects the resulting dose and converts the dose into DICOM format for import back into the treatment planning system (TPS). VIMC-Arc accommodates multiple arc IMRT deliveries and models gantry rotation as a series of segments with dynamic MLC motion within each segment. Several verification RapidArc plans were generated by the Eclipse TPS on a water-equivalent cylindrical phantom and re-calculated using VIMC-Arc. This includes one 'typical' RapidArc plan, one plan for dual arc treatment and one plan with 'avoidance' sectors. One RapidArc plan was also calculated on a DICOM patient CT dataset. Statistical uncertainty of MC simulations was kept within 1%. VIMC-Arc produced dose distributions that matched very closely to those calculated by the anisotropic analytical algorithm (AAA) that is used in Eclipse. All plans also demonstrated better than 1% agreement of the dose at the isocenter. This demonstrates the capabilities of our new MC system to model all dosimetric features required for RapidArc dose calculations.

CTmod-a toolkit for Monte Carlo simulation of projections including scatter in computed tomography

The CTmod toolkit is a set of C++ class libraries based on the CERN's application development framework ROOT. It uses the Monte Carlo method to simulate energy imparted to a CT-scanner detector array. Photons with a given angle-energy distribution are emitted from the X-ray tube approximated by a point source, transported through a phantom, and their contribution to the energy imparted per unit surface area of each detector element is scored. Alternatively, the scored quantity may be the fluence, energy fluence, plane fluence, plane energy fluence, or kerma to air in the center of each detector element. Phantoms are constructed from homogenous solids or voxel arrays via overlapping. Implemented photon interactions (photoelectric effect, coherent scattering, and incoherent scattering) are restricted to the energy range from 10 to 200keV. Variance reduction techniques include the collision density estimator and survival biasing combined with the Russian roulette. The toolkit has been used to estimate the amount of scatter in cone beam computed tomography and planar radiography.

Azimuthal particle redistribution for the reduction of latent phase-space variance in Monte Carlo simulations

It is well known that the use of a phase space in Monte Carlo simulation introduces a baseline level of variance that cannot be suppressed through the use of standard particle recycling techniques. This variance (termed latent phase-space variance by Sempau et al) can be a significant limiting factor in achieving accurate, low-uncertainty dose scoring results, especially near the surface of a phantom. A BEAMnrc component module (MCTWIST) has been developed to reduce the presence of latent variance in phase-space-based Monte Carlo simulations by implementing azimuthal particle redistribution (APR). For each recycled use of a phase-space particle a random rotation about the beam's central axis is applied, effectively utilizing cylindrical symmetry of the particle fluence and therefore providing a more accurate representation of the source. The MCTWIST module is unique in that no physical component is actually added to the accelerator geometry. Beam modifications are made by directly transforming particle characteristics outside of BEAMnrc/EGSnrc particle transport. Using MCTWIST, we have demonstrated a reduction in latent phase-space variance by more than a factor of 20, for a 10 x 10 cm(2) field, when compared to standard phase-space particle recycling techniques. The reduction in latent variance has enabled the achievement of dramatically smoother in-water dose profiles. This paper outlines the use of MCTWIST in Monte Carlo simulation and quantifies for the first time the latent variance reduction resulting from exploiting cylindrical phase-space symmetry.

SBRT of lung tumours: Monte Carlo simulation with PENELOPE of dose distributions including respiratory motion and comparison with different treatment planning systems

The purpose of this work was to simulate with the Monte Carlo (MC) code PENELOPE the dose distribution in lung tumours including breathing motion in stereotactic body radiation therapy (SBRT). Two phantoms were modelled to simulate a pentagonal cross section with chestwall (unit density), lung (density 0.3 g cm(-3)) and two spherical tumours (unit density) of diameters respectively of 2 cm and 5 cm. The phase-space files (PSF) of four different SBRT field sizes of 6 MV from a Varian accelerator were calculated and used as beam sources to obtain both dose profiles and dose-volume histograms (DVHs) in different volumes of interest. Dose distributions were simulated for five beams impinging on the phantom. The simulations were conducted both for the static case and including the influence of respiratory motion. To reproduce the effect of breathing motion different simulations were performed keeping the beam fixed and displacing the phantom geometry in chosen positions in the cranial and caudal and left-right directions. The final result was obtained by combining the different position with two motion patterns. The MC results were compared with those obtained with three commercial treatment planning systems (TPSs), two based on the pencil beam (PB) algorithm, the TMS-HELAX (Nucletron, Sweden) and Eclipse (Varian Medical System, Palo Alto, CA), and one based on the collapsed cone algorithm (CC), Pinnacle(3) (Philips). Some calculations were also carried out with the analytical anisotropic algorithm (AAA) in the Eclipse system. All calculations with the TPSs were performed without simulated breathing motion, according to clinical practice. In order to compare all the TPSs and MC an absolute dose calibration in Gy/MU was performed. The analysis shows that the dose (Gy/MU) in the central part of the gross tumour volume (GTV) is calculated for both tumour sizes with an accuracy of 2-3% with PB and CC algorithms, compared to MC. At the periphery of the GTV the TPSs overestimate the dose up to 10%, while in the lung tissue close to the GTV PB algorithms overestimate the dose and the CC underestimates it. When clinically relevant breathing motions are included in the MC simulations, the static calculations with the TPSs still give a relatively accurate estimate of the dose in the GTV. On the other hand, the dose at the periphery of the GTV is overestimated, compared to the static case.

A beam source model for scanned proton beams

A beam source model, i.e. a model for the initial phase space of the beam, for scanned proton beams has been developed. The beam source model is based on parameterized particle sources with characteristics found by fitting towards measured data per individual beam line. A specific aim for this beam source model is to make it applicable to the majority of the various proton beam systems currently available or under development, with the overall purpose to drive dose calculations in proton beam treatment planning. The proton beam phase space is characterized by an energy spectrum, radial and angular distributions and deflections for the non-modulated elementary pencil beam. The beam propagation through the scanning magnets is modelled by applying experimentally determined focal points for each scanning dimension. The radial and angular distribution parameters are deduced from measured two-dimensional fluence distributions of the elementary beam in air. The energy spectrum is extracted from a depth dose distribution for a fixed broad beam scan pattern measured in water. The impact of a multi-slab range shifter for energy modulation is calculated with an own Monte Carlo code taking multiple scattering, energy loss and straggling, non-elastic and elastic nuclear interactions in the slab assembly into account. Measurements for characterization and verification have been performed with the scanning proton beam system at The Svedberg Laboratory in Uppsala. Both in-air fluence patterns and dose points located in a water phantom were used. For verification, dose-in-water was calculated with the Monte Carlo code GEANT 3.21 instead of using a clinical dose engine with approximations of its own. For a set of four individual pencil beams, both with the full energy and range shifted, 96.5% (99.8%) of the tested dose points satisfied the 1%/1 mm (2%/2 mm) gamma criterion.

Automatic determination of primary electron beam parameters in Monte Carlo simulation

In order to obtain realistic and reliable Monte Carlo simulations of medical linac photon beams, an accurate determination of the parameters that define the primary electron beam that hits the target is a fundamental step. In this work we propose a new methodology to commission photon beams in Monte Carlo simulations that ensures the reproducibility of a wide range of clinically useful fields. For such purpose accelerated Monte Carlo simulations of 2 x 2, 10 x 10, and 20 x 20 cm2 fields at SSD = 100 cm are carried out for several combinations of the primary electron beam mean energy and radial FWHM. Then, by performing a simultaneous comparison with the correspondent measurements for these same fields, the best combination is selected. This methodology has been employed to determine the characteristics of the primary electron beams that best reproduce a Siemens PRIMUS and a Varian 2100 CD machine in the Monte Carlo simulations. Excellent agreements were obtained between simulations and measurements for a wide range of field sizes. Because precalculated profiles are stored in databases, the whole commissioning process can be fully automated, avoiding manual fine-tunings. These databases can also be used to characterize any accelerators of the same model from different sites.

Monte Carlo simulation of MOSFET detectors for high-energy photon beams using the PENELOPE code

The aim of this work was the Monte Carlo (MC) simulation of the response of commercially available dosimeters based on metal oxide semiconductor field effect transistors (MOSFETs) for radiotherapeutic photon beams using the PENELOPE code. The studied Thomson&Nielsen TN-502-RD MOSFETs have a very small sensitive area of 0.04 mm(2) and a thickness of 0.5 microm which is placed on a flat kapton base and covered by a rounded layer of black epoxy resin. The influence of different metallic and Plastic water build-up caps, together with the orientation of the detector have been investigated for the specific application of MOSFET detectors for entrance in vivo dosimetry. Additionally, the energy dependence of MOSFET detectors for different high-energy photon beams (with energy >1.25 MeV) has been calculated. Calculations were carried out for simulated 6 MV and 18 MV x-ray beams generated by a Varian Clinac 1800 linear accelerator, a Co-60 photon beam from a Theratron 780 unit, and monoenergetic photon beams ranging from 2 MeV to 10 MeV. The results of the validation of the simulated photon beams show that the average difference between MC results and reference data is negligible, within 0.3%. MC simulated results of the effect of the build-up caps on the MOSFET response are in good agreement with experimental measurements, within the uncertainties. In particular, for the 18 MV photon beam the response of the detectors under a tungsten cap is 48% higher than for a 2 cm Plastic water cap and approximately 26% higher when a brass cap is used. This effect is demonstrated to be caused by positron production in the build-up caps of higher atomic number. This work also shows that the MOSFET detectors produce a higher signal when their rounded side is facing the beam (up to 6%) and that there is a significant variation (up to 50%) in the response of the MOSFET for photon energies in the studied energy range. All the results have shown that the PENELOPE code system can successfully reproduce the response of a detector with such a small active area.

Comparison of PENELOPE Monte Carlo dose calculations with Fricke dosimeter and ionization chamber measurements in heterogeneous phantoms (18 MeV electron and 12 MV photon beams)

Different measurements of depth-dose curves and dose profiles were performed in heterogeneous phantoms and compared to dose distributions calculated by a Monte Carlo code. These heterogeneous phantoms consisted of lung and/or bone heterogeneities. Irradiations and simulations were carried out for an 18 MeV electron beam and a 12 MV photon beam. Depth-dose curves were measured with Fricke dosimeters and with plane and cylindrical ionization chambers. Dose profiles were measured with a small cylindrical ionization chamber at different depths. The LINAC was modelled using the PENELOPE code and phase space files were used as input data for the calculations of the dose distributions in every simulation. The detectors (Fricke dosimeters and ionization chambers) were not modelled in the geometry. There is generally a good agreement between the measurements and PENELOPE. Some discrepancies exist, near interfaces, between the ionization chamber and PENELOPE due to the attenuation of the lower energy electrons by the wall of the ionization chamber.

Efficient photon beam dose calculations using DOSXYZnrc with BEAMnrc

This study examines the efficiencies of doses calculated using DOSXYZnrc for 18 MV (10 X 10 cm2 field size) and 6 MV (10 X 10 cm2 and 20 X 20 cm2 field sizes) photon beams simulated using BEAMnrc. Both phase-space sources and full BEAMnrc simulation sources are used in the DOSXYZnrc calculations. BEAMnrc simulation sources consist of a BEAMnrc accelerator simulation compiled as a shared library and run by the user code (DOSXYZnrc in this case) to generate source particles. Their main advantage is in eliminating the need to store intermediate phase-space files. In addition, the efficiency improvements due to photon splitting and particle recycling in the DOSXYZnrc simulation are examined. It is found that photon splitting increases dose calculation efficiency by a factor of up to 6.5, depending on beam energy, field size, voxel size, and the type of secondary collimation used in the BEAMnrc simulation (multileaf collimator vs photon jaws). The optimum efficiency with photon splitting is approximately 55% higher than that with particle recycling, indicating that, while most of the gain is due to time saved by reusing source particle data, there is significant gain due to the uniform distribution of interaction sites and faster DOSXYZnrc simulation time when photon splitting is employed. Use of optimized directional bremsstrahlung splitting in the BEAMnrc simulation sources increases the efficiency of photon beam simulations sufficiently that the peak efficiencies (i.e., with optimum setting of the photon splitting number) of DOSXYZnrc simulations using these sources are only 3-13% lower than those with phase-space file sources. This points towards eliminating the need for storing intermediate phase-space files.

Fifty years of Monte Carlo simulations for medical physics

Monte Carlo techniques have become ubiquitous in medical physics over the last 50 years with a doubling of papers on the subject every 5 years between the first PMB paper in 1967 and 2000 when the numbers levelled off. While recognizing the many other roles that Monte Carlo techniques have played in medical physics, this review emphasizes techniques for electron-photon transport simulations. The broad range of codes available is mentioned but there is special emphasis on the EGS4/EGSnrc code system which the author has helped develop for 25 years. The importance of the 1987 Erice Summer School on Monte Carlo techniques is highlighted. As an illustrative example of the role Monte Carlo techniques have played, the history of the correction for wall attenuation and scatter in an ion chamber is presented as it demonstrates the interplay between a specific problem and the development of tools to solve the problem which in turn leads to applications in other areas.

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.

Evaluation of the analytical anisotropic algorithm in an extreme water-lung interface phantom using Monte Carlo dose calculations

Our study compares the performance of the analytical anisotropic algorithm (AAA), a new superposition–convolution algorithm recently implemented in the Eclipse (Varian Medical Systems, Palo Alto, CA) Integrated Treatment Planning System (TPS), to that of the pencil beam convolution (PBC) algorithm in an extreme (C‐shaped, horizontal and vertical boundaries) water–lung interface phantom. Monte Carlo (MC) calculated dose distributions for a variety of clinical beam configurations at nominal energies of 6‐MV and 18‐MV are used as benchmarks in the comparison. Dose profiles extracted at three depths (4, 10, and 16 cm), two‐dimensional (2D) maps of the dose differences, and dose difference statistics are used to quantify the accuracy of both photon‐dose calculation algorithms. Results show that the AAA is considerably more accurate than the PBC, with the standard deviation of the dose differences within a region encompassing the lung block reduced by a factor of 2 and more. Confidence limits with the AAA were 4% or less for all beam configurations investigated; with the PBC, confidence limits ranged from 3.5% to 11.2%. Finally, AAA calculations for the small 4×4 18‐MV beam, which is poorly modeled by PBC (dose differences as high as 16.1%), provided the same accuracy as the PBC model of the 6‐MV beams commonly acceptable in clinical situations.

PACS number: 87.53.Bn

Dose evaluation in lung-equivalent media in high-energy photon external radiotherapy

In high-energy photon external radiotherapy treatment planning systems (TPSs) are used to calculate the dose to the target volume and the dose distribution around it. Commonly used TPSs include algorithms based on measurements in water and often fail in the estimate of dose in the presence of heterogeneities. In this study TL detectors were used to study the reliability of the Cadplan (Varian) TPS in the presence of low-density heterogeneities such as the lung for 6 and 18 MV photon beams at different field sizes. TL measurements were compared with TPS calculations and Monte Carlo simulations performed with the PENELOPE MC code. In a phantom with lung heterogeneity, TL measurements and MC simulations agreed, with an average deviation inside the lung of 2%. In contrast, TPS results overestimated the dose inside the lung, with a maximum deviation of 39% for the 18 MV photon beam and a field size of 2 x 2 cm(2).

Monte Carlo source model for photon beam radiotherapy: photon source characteristics

A major barrier to widespread clinical implementation of Monte Carlo dose calculation is the difficulty in characterizing the radiation source within a generalized source model. This work aims to develop a generalized three-component source model (target, primary collimator, flattening filter) for 6- and 18-MV photon beams that match full phase-space data (PSD). Subsource by subsource comparison of dose distributions, using either source PSD or the source model as input, allows accurate source characterization and has the potential to ease the commissioning procedure, since it is possible to obtain information about which subsource needs to be tuned. This source model is unique in that, compared to previous source models, it retains additional correlations among PS variables, which improves accuracy at nonstandard source-to-surface distances (SSDs). In our study, three-dimensional (3D) dose calculations were performed for SSDs ranging from 50 to 200 cm and for field sizes from 1 x 1 to 30 x 30 cm2 as well as a 10 x 10 cm2 field 5 cm off axis in each direction. The 3D dose distributions, using either full PSD or the source model as input, were compared in terms of dose-difference and distance-to-agreement. With this model, over 99% of the voxels agreed within +/-1% or 1 mm for the target, within 2% or 2 mm for the primary collimator, and within +/-2.5% or 2 mm for the flattening filter in all cases studied. For the dose distributions, 99% of the dose voxels agreed within 1% or 1 mm when the combined source model-including a charged particle source and the full PSD as input-was used. The accurate and general characterization of each photon source and knowledge of the subsource dose distributions should facilitate source model commissioning procedures by allowing scaling the histogram distributions representing the subsources to be tuned.

Effect of statistical uncertainties on Monte Carlo treatment planning

This paper reviews the effect of statistical uncertainties on radiotherapy treatment planning using Monte Carlo simulations. We discuss issues related to the statistical analysis of Monte Carlo dose calculations for realistic clinical beams using various variance reduction or time saving techniques. We discuss the effect of statistical uncertainties on dose prescription and monitor unit calculation for conventional treatment and intensity-modulated radiotherapy (IMRT) based on Monte Carlo simulations. We show the effect of statistical uncertainties on beamlet dose calculation and plan optimization for IMRT and other advanced treatment techniques such as modulated electron radiotherapy (MERT). We provide practical guidelines for the clinical implementation of Monte Carlo treatment planning and show realistic examples of Monte Carlo based IMRT and MERT plans.

Monte Carlo simulation of large electron fields

Accurate simulation of large electron fields may lead to improved accuracy in Monte Carlo treatment planning while simplifying the commissioning procedure. We have used measurements made with wide-open jaws and no electron applicator to adjust simulation parameters. Central axis depth dose curves and profiles of 6-21 MeV electron beams measured in this geometry were used to estimate source and geometry parameters, including those that affect beam symmetry: incident beam direction and offset of the secondary scattering foil and monitor chamber from the beam axis. Parameter estimation relied on a comprehensive analysis of the sensitivity of the measured quantities, in the large field, to source and geometry parameters. Results demonstrate that the EGS4 Monte Carlo system is capable of matching dose distributions in the largest electron field to the least restrictive of 1 cGy or 1 mm, with D(max) of 100 cGy, over the full energy range. This match results in an underestimation of the bremsstrahlung dose of 10-20% at 15-21 MeV, exceeding the combined experimental and calculational uncertainty in this quantity of 3%. The simulation of electron scattering at energies of 15-21 MeV in EGS4 may be in error. The recently released EGSnrc/BEAMnrc system may provide a better match to measurement.

ORANGE: a Monte Carlo dose engine for radiotherapy

This study presents data for the verification of ORANGE, a fast MCNP-based dose engine for radiotherapy treatment planning. In order to verify the new algorithm, it has been benchmarked against DOSXYZ and against measurements. For the benchmarking, first calculations have been done using the ICCR-XIII benchmark. Next, calculations have been done with DOSXYZ and ORANGE in five different phantoms (one homogeneous, two with bone equivalent inserts and two with lung equivalent inserts). The calculations have been done with two mono-energetic photon beams (2 MeV and 6 MeV) and two mono-energetic electron beams (10 MeV and 20 MeV). Comparison of the calculated data (from DOSXYZ and ORANGE) against measurements was possible for a realistic 10 MV photon beam and a realistic 15 MeV electron beam in a homogeneous phantom only. For the comparison of the calculated dose distributions and dose distributions against measurements, the concept of the confidence limit (CL) has been used. This concept reduces the difference between two data sets to a single number, which gives the deviation for 90% of the dose distributions. Using this concept, it was found that ORANGE was always within the statistical bandwidth with DOSXYZ and the measurements. The ICCR-XIII benchmark showed that ORANGE is seven times faster than DOSXYZ, a result comparable with other accelerated Monte Carlo dose systems when no variance reduction is used. As shown for XVMC, using variance reduction techniques has the potential for further acceleration. Using modern computer hardware, this brings the total calculation time for a dose distribution with 1.5% (statistical) accuracy within the clinical range (less then 10 min). This means that ORANGE can be a candidate for a dose engine in radiotherapy treatment planning.

Commissioning of a medical accelerator photon beam Monte Carlo simulation using wide-field profiles

A method for commissioning an EGSnrc Monte Carlo simulation of medical linac photon beams through wide-field lateral profiles at moderate depth in a water phantom is presented. Although depth-dose profiles are commonly used for nominal energy determination, our study shows that they are quite insensitive to energy changes below 0.3 MeV (0.6 MeV) for a 6 MV (15 MV) photon beam. Also, the depth-dose profile dependence on beam radius adds an additional uncertainty in their use for tuning nominal energy. Simulated 40 cm x 40 cm lateral profiles at 5 cm depth in a water phantom show greater sensitivity to both nominal energy and radius. Beam parameters could be determined by comparing only these curves with measured data.

Comparison of dose calculation algorithms in phantoms with lung equivalent heterogeneities under conditions of lateral electronic disequilibrium

An extensive set of benchmark measurement of PDDs and beam profiles was performed in a heterogeneous layer phantom, including a lung equivalent heterogeneity, by means of several detectors and compared against the predicted dose values by different calculation algorithms in two treatment planning systems. PDDs were measured with TLDs, plane parallel and cylindrical ionization chambers and beam profiles with films. Additionally, Monte Carlo simulations by means of the PENELOPE code were performed. Four different field sizes (10 x 10, 5 x 5, 2 x 2, and 1 x 1 cm2) and two lung equivalent materials (CIRS, p(w)e=0.195 and St. Bartholomew Hospital, London, p(w)e=0.244-0.322) were studied. The performance of four correction-based algorithms and one based on convolution-superposition was analyzed. The correction-based algorithms were the Batho, the Modified Batho, and the Equivalent TAR implemented in the Cadplan (Varian) treatment planning system and the TMS Pencil Beam from the Helax-TMS (Nucletron) treatment planning system. The convolution-superposition algorithm was the Collapsed Cone implemented in the Helax-TMS. The only studied calculation methods that correlated successfully with the measured values with a 2% average inside all media were the Collapsed Cone and the Monte Carlo simulation. The biggest difference between the predicted and the delivered dose in the beam axis was found for the EqTAR algorithm inside the CIRS lung equivalent material in a 2 x 2 cm2 18 MV x-ray beam. In these conditions, average and maximum difference against the TLD measurements were 32% and 39%, respectively. In the water equivalent part of the phantom every algorithm correctly predicted the dose (within 2%) everywhere except very close to the interfaces where differences up to 24% were found for 2 x 2 cm2 18 MV photon beams. Consistent values were found between the reference detector (ionization chamber in water and TLD in lung) and Monte Carlo simulations, yielding minimal differences (0.4%+/-1.2%). The penumbra broadening effect in low density media was not predicted by any of the correction-based algorithms, and the only one that matched the experimental values and the Monte Carlo simulations within the estimated uncertainties was the Collapsed Cone Algorithm.

Electron beam quality correction factors for plane-parallel ionization chambers: Monte Carlo calculations using the PENELOPE system

Simulations of three plane-parallel ionization chambers have been used to determine directly the chamber- and quality-dependent factors fc,Q, instead of the product (Sw,air p)Q, and kQ,Q0 (or kQ,Q,int) for a broad range of electron beam qualities (4-20 MeV) using divergent monoenergetic beams and phase-space data from two accelerators. An original calculation method has been used which circumvents the weakness of the so far assumed independence between stopping-power ratios and perturbation factors. Very detailed descriptions of the geometry and materials of the chambers have been obtained from the manufacturers, and prepared as input to the PENELOPE 2003 Monte Carlo system using a computer code that includes correlated sampling and particle splitting. Values of the beam quality factors have been determined for the case of an electron reference beam. The calculated values have been compared with those in the IAEA TRS-398 dosimetry protocol and the differences analysed. The results for a NACP-02 chamber show remarkably good agreement with TRS-398 at high electron beam qualities but differ slightly at low energies. Arguments to explain the differences include questioning the undemonstrated assumption that the NACP is a 'perturbation-free' chamber even at very low electron beam energies. Results for Wellhöfer PPC-40 and PPC-05 chambers cannot be compared with data from others for these chambers because no calculations or reliable experimental data exist. It has been found that the results for the PPC-40 are very close to those of a Roos chamber, but the values for the PPC-05 are considerably different from those of a Markus chamber, and rather approach those of a Roos chamber. Results for monoenergetic electrons and accelerator phase-space data have been compared to assess the need for detailed and costly simulations, finding very small differences. This questions the emphasis given in recent years to the use of 'realistic' source data for accurate electron beam dosimetry.

Monte Carlo computation of dosimetric amorphous silicon electronic portal images

This study develops and tests a method to compute dosimetric images for an amorphous silicon (a-Si) flat-panel detector so that an accurate quantitative comparison between measured and computed portal images may be made. An EGS4-based Monte Carlo (MC) algorithm is developed to efficiently tally the energy deposition through the use of a virtual detector dose-scoring methodology. The complete geometry of the a-Si imager is utilized in the MC calculation up to the imager rear housing, which is replaced with a uniform thickness material slab. The detector-mounting hardware is modeled as a uniform backscattering material. The amount of backscatter material required to reproduce the measured backscatter is 0.98 g/cm2 of water. A flood-field irradiation, performed in the measurement imaging session, is used to cross-calibrate the computed images with the measured images. Calibrated MC-computed images reproduce measured field-size dependencies of the electronic portal imaging device (EPID) response to within <1%, without the need for optical glare or other empirical corrections. A 10% dose difference between measured and computed images was observed outside the field edge for a 10 x 10 cm2 field that was entirely blocked by the multileaf collimator (MLC). However, this error corresponded with less than 0.15% of the open-field dose. For 10 x 10 cm2 fields produced by 5 and 20 mm dynamically sweeping MLC gaps, more than 98% of the points were found to have a gamma less than one with a 2%, 2 mm criteria. For an intensity modulated radiation therapy (IMRT) patient test field, over 99% of the points were found to have a gamma less than one with a 2%, 2 mm criteria. This study demonstrates that MC can be an effective tool for predicting measured a-Si portal images and may be useful for IMRT EPID-based dosimetry.

Use of the Leksell Gamma Knife for localized small field lens irradiation in rodents

For most basic radiobiological research applications involving irradiation of small animals, it is difficult to achieve the same high precision dose distribution realized with human radiotherapy. The precision for irradiations performed with standard radiotherapy equipment is +/-2 mm in each dimension, and is adequate for most human treatment applications. For small animals such as rodents, whose organs and tissue structures may be an order of magnitude smaller than those of humans, the corresponding precision required is closer to +/-0.2 mm, if comparisons or extrapolations are to be made to human data. The Leksell Gamma Knife is a high precision radiosurgery irradiator, with precision in each dimension not exceeding 0.5 mm, and overall precision of 0.7 mm. It has recently been utilized to treat ocular melanoma and induce targeted lesions in the brains of small animals. This paper describes the dosimetry and a technique for performing irradiation of a single rat eye and lens with the Gamma Knife while allowing the contralateral eye and lens of the same rat to serve as the "control". The dosimetry was performed with a phantom in vitro utilizing a pinpoint ion chamber and thermoluminescent dosimeters, and verified by Monte Carlo simulations. We found that the contralateral eye received less than 5% of the administered dose for a 15 Gy exposure to the targeted eye. In addition, after 15 Gy irradiation 15 out of 16 animals developed cataracts in the irradiated target eyes, while 0 out of 16 contralateral eyes developed cataracts over a 6-month period of observation. Experiments at 5 and 10 Gy also confirmed the lack of cataractogenesis in the contralateral eye. Our results validate the use of the Gamma Knife for cataract studies in rodents, and confirmed the precision and utility of the instrument as a small animal irradiator for translational radiobiology experiments.

A simplified model of the source channel of the Leksell GammaKnife® tested with PENELOPE

Monte Carlo simulations using the code PENELOPE have been performed to test a simplified model of the source channel geometry of the Leksell GammaKnife. The characteristics of the radiation passing through the treatment helmets are analysed in detail. We have found that only primary particles emitted from the source with polar angles smaller than 3 degrees with respect to the beam axis are relevant for the dosimetry of the Gamma Knife. The photon trajectories reaching the output helmet collimators at (x, v, z = 236 mm) show strong correlations between rho = (x2 + y2)(1/2) and their polar angle theta, on one side, and between tan(-1)(y/x) and their azimuthal angle phi, on the other. This enables us to propose a simplified model which treats the full source channel as a mathematical collimator. This simplified model produces doses in good agreement with those found for the full geometry. In the region of maximal dose, the relative differences between both calculations are within 3%, for the 18 and 14 mm helmets, and 10%, for the 8 and 4 mm ones. Besides, the simplified model permits a strong reduction (larger than a factor 15) in the computational time.

Benchmark of PENELOPE code for low-energy photon transport: dose comparisons with MCNP4 and EGS4

The expanding clinical use of low-energy photon emitting 125I and 103Pd seeds in recent years has led to renewed interest in their dosimetric properties. Numerous papers pointed out that higher accuracy could be obtained in Monte Carlo simulations by utilizing newer libraries for the low-energy photon cross-sections, such as XCOM and EPDL97. The recently developed PENELOPE 2001 Monte Carlo code is user friendly and incorporates photon cross-section data from the EPDL97. The code has been verified for clinical dosimetry of high-energy electron and photon beams, but has not yet been tested at low energies. In the present work, we have benchmarked the PENELOPE code for 10-150 keV photons. We computed radial dose distributions from 0 to 10 cm in water at photon energies of 10-150 keV using both PENELOPE and MCNP4C with either DLC-146 or DLC-200 cross-section libraries, assuming a point source located at the centre of a 30 cm diameter and 20 cm length cylinder. Throughout the energy range of simulated photons (except for 10 keV), PENELOPE agreed within statistical uncertainties (at worst +/- 5%) with MCNP/DLC-146 in the entire region of 1-10 cm and with published EGS4 data up to 5 cm. The dose at 1 cm (or dose rate constant) of PENELOPE agreed with MCNP/DLC-146 and EGS4 data within approximately +/- 2% in the range of 20-150 keV, while MCNP/DLC-200 produced values up to 9% lower in the range of 20-100 keV than PENELOPE or the other codes. However, the differences among the four datasets became negligible above 100 keV.

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.

Dosimetry for radiocolloid therapy of cystic craniopharyngiomas

The dosimetry for radiocolloid therapy of cystic craniopharyngiomas is investigated. Analytical calculations based on the Loevinger and the Berger formulas for electrons and photons, respectively, are compared with Monte Carlo simulations. The role of the material of which the colloid introduced inside the craniopharyngioma is made of as well as that forming the cyst wall is analyzed. It is found that the analytical approaches provide a very good description of the simulated data in the conditions where they can be applied (i.e., in the case of a uniform and infinite homogeneous medium). However, the consideration of the different materials and interfaces produces a strong reduction of the dose delivered to the cyst wall in relation to that predicted by the Loevinger and the Berger formulas.

Calculations of electron fluence correction factors using the Monte Carlo code PENELOPE

In electron-beam dosimetry, plastic phantom materials may be used instead of water for the determination of absorbed dose to water. A correction factor phi(water)plastic is then needed for converting the electron fluence in the plastic phantom to the fluence at an equivalent depth in water. The recommended values for this factor given by AAPM TG-25 (1991 Med. Phys. 18 73-109) and the IAEA protocols TRS-381 (1997) and TRS-398 (2000) disagree, in particular at large depths. Calculations of the electron fluence have been done, using the Monte Carlo code PENELOPE, in semi-infinite phantoms of water and common plastic materials (PMMA, clear polystyrene, A-150, polyethylene, Plastic water and Solid water (WT1)). The simulations have been carried out for monoenergetic electron beams of 6, 10 and 20 MeV, as well as for a realistic clinical beam. The simulated fluence correction factors differ from the values in the AAPM and IAEA recommendations by up to 2%, and are in better agreement with factors obtained by Ding et al (1997 Med. Phys. 24 161-76) using EGS4. Our Monte Carlo calculations are also in good accordance with phi(water)plastic values measured by using an almost perturbation-free ion chamber. The important interdependence between depth- and fluence-scaling corrections for plastic phantoms is discussed. Discrepancies between the measured and the recommended values of phi(water)plastic may then be explained considering the different depth-scaling rules used.

Photon beam relative dose validation of the DPM Monte Carlo code in lung-equivalent media

Validation experiments have been conducted using 6 and 15 MV photons in inhomogeneous (water/lung/water) media to benchmark the accuracy of the DPM Monte Carlo code for photon beam dose calculations. Small field sizes (down to 2 x 2 cm2) and low-density media were chosen for this investigation because the intent was to test the DPM code under conditions where lateral electronic disequilibrium effects are emphasized. The treatment head components of a Varian 21EX linear accelerator, including the jaws (defining field sizes of 2 x 2, 3 x 3 and 10 x 10 cm2), were simulated using the BEAMnrc code. The phase space files were integrated within the DPM code system, and central axis depth dose and profile calculations were compared against diode measurements in a homogeneous water phantom in order to validate the phase space. Results of the homogeneous phantom study indicated that the relative differences between DPM calculations and measurements were within +/- 1% (based on the rms deviation) for the depth dose curves; relative profile dose differences were on average within +/- 1%/1 mm. Depth dose and profile measurements were carried out using an ion-chamber and film, within an inhomogeneous phantom consisting of a 6 cm slab of lung-equivalent material embedded within solid water. For the inhomogeneous phantom experiment, DPM depth dose calculations were within +/- 1% (based on the rms deviation) of measurements; relative profile differences at depths within and beyond the lung were, on average, within +/- 2% in the inner and outer beam regions, and within 1-2 mm distance-to-agreement within the penumbral region. Relative point differences on the order of 2-3% were within the estimated experimental uncertainties. This work demonstrates that the DPM Monte Carlo code is capable of accurate photon beam dose calculations in situations where lateral electron disequilibrium effects are pronounced.

History by history statistical estimators in the BEAM code system

A history by history method for estimating uncertainties has been implemented in the BEAMnrc and DOSXYznrc codes replacing the method of statistical batches. This method groups scored quantities (e.g., dose) by primary history. When phase-space sources are used, this method groups incident particles according to the primary histories that generated them. This necessitated adding markers (negative energy) to phase-space files to indicate the first particle generated by a new primary history. The new method greatly reduces the uncertainty in the uncertainty estimate. The new method eliminates one dimension (which kept the results for each batch) from all scoring arrays, resulting in memory requirement being decreased by a factor of 2. Correlations between particles in phase-space sources are taken into account. The only correlations with any significant impact on uncertainty are those introduced by particle recycling. Failure to account for these correlations can result in a significant underestimate of the uncertainty. The previous method of accounting for correlations due to recycling by placing all recycled particles in the same batch did work. Neither the new method nor the batch method take into account correlations between incident particles when a phase-space source is restarted so one must avoid restarts.

Monte Carlo simulation of the Leksell Gamma Knife: I. Source modelling and calculations in homogeneous media

The Monte Carlo code PENELOPE has been used to simulate photon flux from the Leksell Gamma Knife, a precision method for treating intracranial lesions. Radiation from a single 6OCo assembly traversing the collimator system was simulated, and phase space distributions at the output surface of the helmet for photons and electrons were calculated. The characteristics describing the emitted final beam were used to build a two-stage Monte Carlo simulation of irradiation of a target. A dose field inside a standard spherical polystyrene phantom, usually used for Gamma Knife dosimetry, has been computed and compared with experimental results, with calculations performed by other authors with the use of the EGS4 Monte Carlo code, and data provided by the treatment planning system Gamma Plan. Good agreement was found between these data and results of simulations in homogeneous media. Owing to this established accuracy, PENELOPE is suitable for simulating problems relevant to stereotactic radiosurgery.

Experimental validation of the DPM Monte Carlo code using minimally scattered electron beams in heterogeneous media

A comprehensive set of measurements and calculations has been conducted to investigate the accuracy of the Dose Planning Method (DPM) Monte Carlo code for electron beam dose calculations in heterogeneous media. Measurements were made using 10 MeV and 50 MeV minimally scattered, uncollimated electron beams from a racetrack microtron. Source distributions for the Monte Carlo calculations were reconstructed from in-air ion chamber scans and then benchmarked against measurements in a homogeneous water phantom. The in-air spatial distributions were found to have FWHM of 4.7 cm and 1.3 cm, at 100 cm from the source, for the 10 MeV and 50 MeV beams respectively. Energy spectra for the electron beams were determined by simulating the components of the microtron treatment head using the code MCNP4B. Profile measurements were made using an ion chamber in a water phantom with slabs of lung or bone-equivalent materials submerged at various depths. DPM calculations are, on average, within 2% agreement with measurement for all geometries except for the 50 MeV incident on a 6 cm lung-equivalent slab. Measurements using approximately monoenergetic, 50 MeV, 'pencil-beam'-type electrons in heterogeneous media provide conditions for maximum electronic disequilibrium and hence present a stringent test of the code's electron transport physics; the agreement noted between calculation and measurement illustrates that the DPM code is capable of accurate dose calculation even under such conditions.