An MCNP-based model of a linear accelerator x-ray beam

Photon GRID Radiation Therapy: A Physics and Dosimetry White Paper from the Radiosurgery Society (RSS) GRID/LATTICE, Microbeam and FLASH Radiotherapy Working Group

The limits of radiation tolerance, which often deter the use of large doses, have been a major challenge to the treatment of bulky primary and metastatic cancers. A novel technique using spatial modulation of megavoltage therapy beams, commonly referred to as spatially fractionated radiation therapy (SFRT) (e.g., GRID radiation therapy), which purposefully maintains a high degree of dose heterogeneity across the treated tumor volume, has shown promise in clinical studies as a method to improve treatment response of advanced, bulky tumors. Compared to conventional uniform-dose radiotherapy, the complexities of megavoltage GRID therapy include its highly heterogeneous dose distribution, very high prescription doses, and the overall lack of experience among physicists and clinicians. Since only a few centers have used GRID radiation therapy in the clinic, wide and effective use of this technique has been hindered. To date, the mechanisms underlying the observed high tumor response and low toxicity are still not well understood. To advance SFRT technology and planning, the Physics Working Group of the Radiosurgery Society (RSS) GRID/Lattice, Microbeam and Flash Radiotherapy Working Groups, was established after an RSS-NCI Workshop. One of the goals of the Physics Working Group was to develop consensus recommendations to standardize dose prescription, treatment planning approach, response modeling and dose reporting in GRID therapy. The objective of this report is to present the results of the Physics Working Group's consensus that includes recommendations on GRID therapy as an SFRT technology, field dosimetric properties, techniques for generating GRID fields, the GRID therapy planning methods, documentation metrics and clinical practice recommendations. Such understanding is essential for clinical patient care, effective comparisons of outcome results, and for the design of rigorous clinical trials in the area of SFRT. The results of well-conducted GRID radiation therapy studies have the potential to advance the clinical management of bulky and advanced tumors by providing improved treatment response, and to further develop our current radiobiology models and parameters of radiation therapy design.

Applications of MCNP simulation in treatment planning: a comparative study

Monte Carlo codes have been used for approximately 80 years to solve various problems in medical physics. In this paper, the importance of the MCNPX code in treatment planning is highlighted. As illustrative examples of the role of MCNPX in this field, some dosimetric parameters, isodose distribution curves, and figures of merit (FOMs) were considered for photon beams of various energies. To the best of the authors' knowledge, such a systematic study has not been done before. Tissue-air ratio values were obtained as a function of depth in tissue as well as field size. The results of the simulations were in agreement within 3.5% with experimental results reported in the literature. Backscatter factor values were calculated as a function of beam energy, and found to be in agreement with published experimental values within 5.9%. The isodose curves for different conditions and beam arrangements were also simulated. Besides, FOMs were calculated for different radiation energies. All the results were in agreement with related data in the literature. It is concluded that the MCNPX code and the models developed in the present study can be used in different conditions where these parameters are involved, improving individualized treatment planning for individual patients.

New capabilities of the Monte Carlo dose engine ARCHER-RT: Clinical validation of the Varian TrueBeam machine for VMAT external beam radiotherapy

PURPOSE

The Monte Carlo radiation transport method is considered the most accurate approach for absorbed dose calculations in external beam radiation therapy. In this study, an efficient and accurate source model of the Varian TrueBeam 6X STx Linac is developed and integrated with a fast Monte Carlo photon-electron transport absorbed dose engine, ARCHER-RT, which is capable of being executed on CPUs, NVIDIA GPUs, and AMD GPUs. This capability of fast yet accurate radiation dose calculation is essential for clinical utility of this new technology. This paper describes the software and algorithmic developments made to the ARCHER-RT absorbed dose engine.

METHODS

AMD's Heterogeneous-Compute Interface for Portability (HIP) was implemented in ARCHER-RT to allow for device independent execution on NVIDIA and AMD GPUs. Architecture-specific atomic-add algorithms have been identified and both more accurate single-precision and double-precision computational absorbed dose calculation methods have been added to ARCHER-RT and validated through a test case to evaluate the accuracy and performance of the algorithms. The validity of the source model and the radiation transport physics were benchmarked against Monte Carlo simulations performed with EGSnrc. Secondary dose-check physics plans, and a clinical prostate treatment plan were calculated to demonstrate the applicability of the platform for clinical use. Absorbed dose difference maps and gamma analyses were conducted to establish the accuracy and consistency between the two Monte Carlo models. Timing studies were conducted on a CPU, an NVIDIA GPU, and an AMD GPU to evaluate the computational speed of ARCHER-RT.

RESULTS

Percent depth doses were computed for different field sizes ranging from 1.5 cm²  × 1.5 cm² to 22 cm²  × 40cm² and the two codes agreed for all points outside high gradient regions within 3%. Axial profiles computed for a 10 cm²  × 10 cm² field for multiple depths agreed for all points outside high gradient regions within 2%. The test case investigating the impact of native single-precision compared to double-precision showed differences in voxels as large as 71.47% and the implementation of KAS single-precision reduced the difference to less than 0.01%. The 3%/3mm gamma pass rates for an MPPG5a multileaf collimator (MLC) test case and a clinical VMAT prostate plan were 94.2% and 98.4% respectively. Timing studies demonstrated the calculation of a VMAT plan was completed in 50.3, 187.9, and 216.8 s on an NVIDIA GPU, AMD GPU, and Intel CPU, respectively.

CONCLUSION

ARCHER-RT is capable of patient-specific VMAT external beam photon absorbed dose calculations and its potential has been demonstrated by benchmarking against a well validated EGSnrc model of a Varian TrueBeam. Additionally, the implementation of AMD's HIP has shown the flexibility of the ARCHER-RT platform for device independent calculations. This work demonstrates the significant addition of functionality added to ARCHER-RT framework which has marked utility for both research and clinical applications and demonstrates further that Monte Carlo-based absorbed dose engines like ARCHER-RT have the potential for widespread clinical implementation.

Implementation of a simple clinical linear accelerator beam model in MCNP6 and comparison with measured beam characteristics

Monte Carlo N-Particle 6 (MCNP6) is the latest version of Los Alamos National Laboratory's powerful Monte Carlo software designed to compute general photon, neutron, and electron transport using stochastic algorithms. Here we provide a case study of modeling the photon beam of a Varian 600C Clinical Linear Accelerator (linac), which is used to deliver radiation therapy, along with a comparison to experimentally measured beam characteristics. The source definition parameters in MCNP6, including the energy spectrum and angular spectrum of the photons, secondary and tertiary collimators, and a water phantom that tallied dose delivered at different points along the phantom are included. The experimental data for comparison was in the form of a percent depth dose curve as well as crossline and inline beam profiles. Experimental depth dose curve and beam profiles were acquired using a standard 0.125 cc ion chamber within a water phantom. In the computational model, the simulated depth dose curve was computed by tallying the total energy deposited in a stack of vertical slices down the depth of the phantom for percent depth dose curves. The simulated beam profiles were computed in a similar fashion, by tallying the energy deposited in a horizontal row, both in the x- and y-directions of cubic cells located at various depths. For the percent depth dose curve, a mean absolute percentage difference of 1.02%, 1.07%, and 1.94% were calculated for field sizes of 5 × 5 cm², 10 × 10 cm² and 20 × 20 cm², respectively, between the model and experimental measurements were calculated. We present our model as an example to guide other MCNP6 users in the medical physics community to create similar beam models for biomedical dose estimation and research calculations for predicting dose to newly developed phantoms.

Conversion coefficients for determination of dispersed photon dose during radiotherapy: NRUrad input code for MCNP

Radiotherapy is a common cancer treatment module, where a certain amount of dose will be delivered to the targeted organ. This is achieved usually by photons generated by linear accelerator units. However, radiation scattering within the patient’s body and the surrounding environment will lead to dose dispersion to healthy tissues which are not targets of the primary radiation. Determination of the dispersed dose would be important for assessing the risk and biological consequences in different organs or tissues. In the present work, the concept of conversion coefficient (F) of the dispersed dose was developed, in which F = (D_d/D_t), where D_d was the dispersed dose in a non-targeted tissue and D_t is the absorbed dose in the targeted tissue. To quantify D_d and D_t, a comprehensive model was developed using the Monte Carlo N-Particle (MCNP) package to simulate the linear accelerator head, the human phantom, the treatment couch and the radiotherapy treatment room. The present work also demonstrated the feasibility and power of parallel computing through the use of the Message Passing Interface (MPI) version of MCNP5.

Geometrical splitting technique to improve the computational efficiency in Monte Carlo calculations for proton therapy

PURPOSE

To present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation.

METHODS

The treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth-dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique.

RESULTS

A normalized computational efficiency gain of a factor of 10-20.3 was reached for phase space calculations for the different treatment head options simulated. Depth-dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth-dose with an average difference of (0.2 ± 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 ± 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria.

CONCLUSIONS

The authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.

Calculation of organ doses from breast cancer radiotherapy: a Monte Carlo study

The current study aimed to: a) utilize Monte Carlo simulation methods for the assessment of radiation doses imparted to all organs at risk to develop secondary radiation induced cancer, for patients undergoing radiotherapy for breast cancer; and b) evaluate the effect of breast size on dose to organs outside the irradiation field. A simulated linear accelerator model was generated. The in-field accuracy of the simulated photon beam properties was verified against percentage depth dose (PDD) and dose profile measurements on an actual water phantom. Off-axis dose calculations were verified with thermoluminescent dosimetry (TLD) measurements on a humanoid physical phantom. An anthropomorphic mathematical phantom was used to simulate breast cancer radiotherapy with medial and lateral fields. The effect of breast size on the calculated organ dose was investigated. Local differences between measured and calculated PDDs and dose profiles did not exceed 2% for the points at depths beyond the depth of maximum dose and the plateau region of the profile, respectively. For the penumbral regions of the dose profiles, the distance to agreement (DTA) did not exceed 2 mm. The mean difference between calculated out-of-field doses and TLD measurements was 11.4% ± 5.9%. The calculated doses to peripheral organs ranged from 2.32 cGy up to 161.41 cGy depending on breast size and thus the field dimensions applied, as well as the proximity of the organs to the primary beam. An increase to the therapeutic field area by 50% to account for the large breast led to a mean organ dose elevation by up to 85.2% for lateral exposure. The contralateral breast dose ranged between 1.4% and 1.6% of the prescribed dose to the tumor. Breast size affects dose deposition substantially.

Monte Carlo simulation for Neptun 10 PC medical linear accelerator and calculations of output factor for electron beam

AIM

Exact knowledge of dosimetric parameters is an essential pre-requisite of an effective treatment in radiotherapy. In order to fulfill this consideration, different techniques have been used, one of which is Monte Carlo simulation.

MATERIALS AND METHODS

This study used the MCNP-4C to simulate electron beams from Neptun 10 PC medical linear accelerator. Output factors for 6, 8 and 10 MeV electrons applied to eleven different conventional fields were both measured and calculated.

RESULTS

The measurements were carried out by a Wellhofler-Scanditronix dose scanning system. Our findings revealed that output factors acquired by MCNP-4C simulation and the corresponding values obtained by direct measurements are in a very good agreement.

CONCLUSION

In general, very good consistency of simulated and measured results is a good proof that the goal of this work has been accomplished.

Design and optimization of large area thin-film CdTe detector for radiation therapy imaging applications

PURPOSE

The authors investigate performance of thin-film cadmium telluride (CdTe) in detecting high-energy (6 MV) x rays. The utilization of this material has become technologically feasible only in recent years due to significant development in large area photovoltaic applications.

METHODS

The CdTe film is combined with a metal plate, facilitating conversion of incoming photons into secondary electrons. The system modeling is based on the Monte Carlo simulations performed to determine the optimized CdTe layer thickness in combination with various converter materials.

RESULTS

The authors establish a range of optimal parameters producing the highest DQE due to energy absorption, as well as signal and noise spatial spreading. The authors also analyze the influence of the patient scatter on image formation for a set of detector configurations. The results of absorbed energy simulation are used in device operation modeling to predict the detector output signal. Finally, the authors verify modeling results experimentally for the lowest considered device thickness.

CONCLUSIONS

The proposed CdTe-based large area thin-film detector has a potential of becoming an efficient low-cost electronic portal imaging device for radiation therapy applications.

Suggesting a new design for multileaf collimator leaves based on Monte Carlo simulation of two commercial systems

Due to intensive use of multileaf collimators (MLCs) in clinics, finding an optimum design for the leaves becomes essential. There are several studies which deal with comparison of MLC systems, but there is no article with a focus on offering an optimum design using accurate methods like Monte Carlo. In this study, we describe some characteristics of MLC systems including the leaf tip transmission, beam hardening, leakage radiation and penumbra width for Varian and Elekta 80-leaf MLCs using MCNP4C code. The complex geometry of leaves in these two common MLC systems was simulated. It was assumed that all of the MLC systems were mounted on a Varian accelerator and with a similar thickness as Varian's and the same distance from the source. Considering the obtained results from Varian and Elekta leaf designs, an optimum design was suggested combining the advantages of three common MLC systems and the simulation results of this proposed one were compared with the Varian and the Elekta. The leakage from suggested design is 29.7% and 31.5% of the Varian and Elekta MLCs. In addition, other calculated parameters of the proposed MLC leaf design were better than those two commercial ones. Although it shows a wider penumbra in comparison with Varian and Elekta MLCs, taking into account the curved motion path of the leaves, providing a double focusing design will solve the problem. The suggested leaf design is a combination of advantages from three common vendors (Varian, Elekta and Siemens) which can show better results than each one. Using the results of this theoretical study may bring about superior practical outcomes.

The impact of automatic wedge filter on photoneutron and photon spectra of an 18-MV photon beam

The effect of an automatic wedge filter on photon and photoneutron spectra of a medical linac was evaluated using the Monte Carlo method. The head of an Elekta SL75/25 was simulated using the MCNPX Monte Carlo code. The photon and photoneutron spectra for open and wedged beams were calculated at the isocentre with a source to axis distance of 100 cm. For a wedged beam, the neutron fluence was from 3.84 to 7.2 times higher for field sizes from 10 x 10 to 30 x 30 cm(2). The neutron fluence is decreased with field size for open beams and is increased with field size for wedged beams The photon beam spectra became harder and the mean energy was 6 % higher for a wedged beam, which led to a 4 % increase in relative depth dose and a better skin sparing effect. The results here recommend that the higher photoneutron fluence of the wedged beam should be taken into account in patient dosimetry and shielding calculations.

A virtual source model of electron contamination of a therapeutic photon beam

The most efficient way of generating particles for Monte Carlo (MC) dose calculation is through a virtual source model (VSM) of the linear accelerator head. We have previously developed a VSM based on three sources: a primary photon source, a secondary photon source and an electron contamination source (Sikora et al 2007). In this work, we present an improvement of the electron contamination source. The VSM of contamination electrons (eVSM) is derived from a full MC simulation of the accelerator head with the BEAMnrc MC system. It comprises a Gaussian source located at the base of the flattening filter. The eVSM models two effects: an energy-dependent source diameter and an angular dependence of the particle fluence. The air scatter of the contamination electrons is approximated by energetic properties of the eVSM so that explicit in-air transport is not required during MC simulation of the dose distributions in the patient. The calculations of electron dose distributions were compared between the eVSM and the full MC simulation. Good agreement was achieved for various rectangular field sizes as well as for complex conformal segment shapes for the contamination electrons of 6 and 15 MV beams. The 3D dose evaluation of the surface dose in a CT-based patient geometry shows high accuracy (2%/2 mm) of the eVSM for both energies. The model has one tunable parameter, the mean energy of the spectrum at the patient surface. High accuracy and efficiency of particle generation make the eVSM a valuable virtual source of contamination electrons for MC treatment planning systems.

Dosimetric validation of the MCNPX Monte Carlo simulation for radiobiologic studies of megavoltage grid radiotherapy

PURPOSE

To validate the MCNPX Monte Carlo simulation for radiobiologic studies of megavoltage grid radiotherapy.

METHODS AND MATERIALS

EDR2 films, a scanning water phantom with microionization chamber and MCNPX Monte Carlo code, were used to study the dosimetric characteristics of a commercially available megavoltage grid therapy collimator. The measured dose profiles, ratios between maximum and minimum doses at 1.5 cm depth, and percentage depth dose curve were compared with those obtained in the simulations. The simulated two-dimensional dose profile and the linear-quadratic formalism of cell survival were used to calculate survival statistics of tumor and normal cells for the treatment of melanoma with a list of doses of the fractionated grid therapy.

RESULTS

A good agreement between the simulated and measured dose data was found. The therapeutic ratio based on normal cell survival has been defined and calculated for treating both the acute and late responding melanoma tumors. The grid therapy in this study was found to be advantageous for treating the acutely responding tumors, but not for late responding tumors.

CONCLUSIONS

Monte Carlo technique was demonstrated to be able to provide the dosimetric characteristics for grid therapy. The therapeutic ratio was dependent not only on the single alpha/beta value, but also on the individual alpha and beta values. Acutely responding tumors and radiosensitive normal tissues are more suitable for using the grid therapy.

Monte Carlo simulation of the photon beam characteristics from medical linear accelerators

The MCNPX code has been employed on a personal computer to calculate the dosimetric characteristics of the photon beams from the 6 MV Siemens MX2 and the 10 MV Varian Clinac 2100C linear accelerators. A model of the treatment head includes the major geometric structure within the beam path. The model was used to calculate the energy spectra of the photon beam, percentage depth dose and the dose profiles. The accuracy of the calculated results is examined by comparing them with the measured dose distributions for the two machines. The computed and measured depth dose curves agree to within 2% for all the depths beyond the build-up region for both treatment machines. The calculations agree to within 2% of the measured profiles within the 100-50% dose level. It has been found that the MCNPX code is an effective tool for simulating the clinical photon beam.

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.

Photon-beam subsource sensitivity to the initial electron-beam parameters

One limitation to the widespread implementation of Monte Carlo (MC) patient dose-calculation algorithms for radiotherapy is the lack of a general and accurate source model of the accelerator radiation source. Our aim in this work is to investigate the sensitivity of the photon-beam subsource distributions in a MC source model (with target, primary collimator, and flattening filter photon subsources and an electron subsource) for 6- and 18-MV photon beams when the energy and radial distributions of initial electrons striking a linac target change. For this purpose, phase-space data (PSD) was calculated for various mean electron energies striking the target, various normally distributed electron energy spread, and various normally distributed electron radial intensity distributions. All PSD was analyzed in terms of energy, fluence, and energy fluence distributions, which were compared between the different parameter sets. The energy spread was found to have a negligible influence on the subsource distributions. The mean energy and radial intensity significantly changed the target subsource distribution shapes and intensities. For the primary collimator and flattening filter subsources, the distribution shapes of the fluence and energy fluence changed little for different mean electron energies striking the target, however, their relative intensity compared with the target subsource change, which can be accounted for by a scaling factor. This study indicates that adjustments to MC source models can likely be limited to adjusting the target subsource in conjunction with scaling the relative intensity and energy spectrum of the primary collimator, flattening filter, and electron subsources when the energy and radial distributions of the initial electron-beam change.

An MCNP-based model of a medical linear accelerator x-ray photon beam

The major components in the x-ray photon beam path of the treatment head of the VARIAN Clinac 2300 EX medical linear accelerator were modeled and simulated using the Monte Carlo N-Particle radiation transport computer code (MCNP). Simulated components include x-ray target, primary conical collimator, x-ray beam flattening filter and secondary collimators. X-ray photon energy spectra and angular distributions were calculated using the model. The x-ray beam emerging from the secondary collimators were scored by considering the total x-ray spectra from the target as the source of x-rays at the target position. The depth dose distribution and dose profiles at different depths and field sizes have been calculated at a nominal operating potential of 6 MV and found to be within acceptable limits. It is concluded that accurate specification of the component dimensions, composition and nominal accelerating potential gives a good assessment of the x-ray energy spectra.

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.

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.

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

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

Monte Carlo dosimetry of a tandem positioned beta-emitting intravascular brachytherapy source train

Prevention of restenosis following interventional coronary procedures with catheter based beta-emitting sources is currently under clinical trial investigations. Systems utilizing fixed length source trains limit the clinician's ability to increase the radiation source length as required. A technique known as "pull back" is used when the segment of artery requiring radiation is longer than the available fixed length source train. In this instance, tandem positioning of the fixed length source is used to treat the longer length of artery. The aim of this study was to examine the dosimetry of the junction region associated with pull back treatments using a commercially available 90Sr/Y catheter based intravascular brachytherapy source train. Dose profiles were calculated, using the Monte Carlo code MCNP4B, at radial distances of 1.5, 2.0, and 2.5 mm for pull back techniques using 2.5 mm overlapping, abutting, and 2.5 mm spaced source trains. Results at the protocol prescription radius of 2 mm showed a junction dose elevated 61% above prescription for 2.5 mm overlapping source trains. For 2.5 mm spaced trains, this figure falls to 64% below prescription dose. In contrast, abutted source trains exhibited only a 1% depression below prescription dose in the junction region. The reference point dose rate per unit activity of this source was found to be consistent with previous studies.

Irregular field calculation on the central beam axis of photon beams using sector-integration

A method is proposed for calculation of irregular field factors on the central beam axis and homogeneous medium for x-ray beams. The irregular field factor is introduced as the ratio of the output of a field with and without blocks on the central beam axis. The algorithm is based on the sector-integration method and the circular field quantities are calculated from in-phantom measurements. These circular field quantities are the output per beam monitor unit for circular fields defined by a hypothetical secondary collimator and reduced to a circular field by blocking. A derivation of the sector-integration equation is given from first principles. As it is shown, the circular field quantities are evaluated from data measured for rectangular, block shaped fields. Such quantities contain all beam components, including photons scattered from the blocks, the block tray, and photons scattered in the phantom. Consequently, the so called primary and secondary beam components are readily incorporated in this approach. Once the circular field quantities have been determined from rectangular field data, the irregular field factors for other geometry can be calculated. Irregular field factors for square, rectangular and circular block-shaped fields were calculated for 6 MV photon beams and compared with measured values. The results agree within 0.7%, even for heavy blocked field cases, i.e., a 40 x 40 cm2 collimator field blocked to a 5 x 5 cm2 field. The method was tested for a particular source to surface distance, depth, phantom composition, and source to block distance. Calculation of irregular field factors in another set up conditions requires the measurement of the appropriate input data.

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

The Monte Carlo code PENELOPE has been used to simulate electron beams from a Siemens Mevatron KDS linac with nominal energies of 6, 12 and 18 MeV. Owing to its accuracy, which stems from that of the underlying physical interaction models, PENELOPE is suitable for simulating problems of interest to the medical physics community. It includes a geometry package that allows the definition of complex quadric geometries, such as those of irradiation instruments, in a straightforward manner. Dose distributions in water simulated with PENELOPE agree well with experimental measurements using a silicon detector and a monitoring ionization chamber. Insertion of a lead slab in the incident beam at the surface of the water phantom produces sharp variations in the dose distributions, which are correctly reproduced by the simulation code. Results from PENELOPE are also compared with those of equivalent simulations with the EGS4-based user codes BEAM and DOSXYZ. Angular and energy distributions of electrons and photons in the phase-space plane (at the downstream end of the applicator) obtained from both simulation codes are similar, although significant differences do appear in some cases. These differences, however, are shown to have a negligible effect on the calculated dose distributions. Various practical aspects of the simulations, such as the calculation of statistical uncertainties and the effect of the 'latent' variance in the phase-space file, are discussed in detail.

Accurate measurement of exposure rate from a 60Co teletherapy source: deviations from the inverse-square law

A cylindrical gamma-ray 60Co source of activity alpha is predicted to produce an exposure rate X at a distance d in vacuum, given by X = gamma(T)(alpha/d2), where gamma(T) is the specific gamma-ray constant. It has been documented that this formula may be used to approximate X with an accuracy of 1% from a source of length l, provided that d/l > or = 5. It is shown that the formula is accurate to 0.1% under these conditions, provided that the distance is measured from the centre of the source. When absorption in the source and scattering in the collimator are considered, the position of the origin d = 0 can shift by a distance of the order of centimetres. Absorption in air between the source and the ionization chamber adds an exponential factor to the formula. It is shown that even when these modifications are included the discrepancy in the results, although generally less than 1%, is still large compared with the measurement errors. Some suggestions are made for the origin of this discrepancy.

Use of Monte Carlo computation in benchmarking radiotherapy treatment planning system algorithms

Radiotherapy treatments are becoming more complex, often requiring the dose to be calculated in three dimensions and sometimes involving the application of non-coplanar beams. The ability of treatment planning systems to accurately calculate dose under a range of these and other irradiation conditions requires evaluation. Practical assessment of such arrangements can be problematical, especially when a heterogeneous medium is used. This work describes the use of Monte Carlo computation as a benchmarking tool to assess the dose distribution of external photon beam plans obtained in a simple heterogeneous phantom by several commercially available 3D and 2D treatment planning system algorithms. For comparison, practical measurements were undertaken using film dosimetry. The dose distributions were calculated for a variety of irradiation conditions designed to show the effects of surface obliquity, inhomogeneities and missing tissue above tangential beams. The results show maximum dose differences of 47% between some planning algorithms and film at a point 1 mm below a tangentially irradiated surface. Overall, the dose distribution obtained from film was most faithfully reproduced by the Monte Carlo N-Particle results illustrating the potential of Monte Carlo computation in evaluating treatment planning system algorithms.

Monte Carlo validation in diagnostic radiological imaging

Monte Carlo analysis in the radiological sciences has been used for several decades, however with the ever-increasing power of desktop computers, the utility of Monte Carlo simulation is increasing. A Monte Carlo code called the Simple Investigative Environment for Radiological Research Applications (SIERRA) is described mathematically, and is then compared against an array of published and unpublished results determined by other means. A series of 32 comparisons between data sets, 22 from independent Monte Carlo simulations and 10 from physically measured data, were assessed. The compared parameters included depth dose curves, lateral energy scattering profiles, scatter to primary ratios, normalized glandular doses, angular scattering distributions, and computed tomography dose index (CTDI) values. Three of the 32 comparison data sets were excluded as they were identified as outliers. Of the remaining 29 data sets compared, the mean differences ranged from -14.8% to +17.2%, and the average of the mean differences was 0.12% (sigma = 1.64%), and the median difference was 1.57%. Fifty percent of the comparisons showed mean differences of approximately 5% or less, and 93% of the comparisons showed mean differences of 12% or less. We conclude that for research applications in diagnostic radiology, the SIERRA Monte Carlo code demonstrates accuracy and precision to well within acceptable levels.

Monte Carlo modelling of electron beams from medical accelerators

Monte Carlo simulation of radiation transport is considered to be one of the most accurate methods of radiation therapy dose calculation. With the rapid development of computer technology, Monte Carlo based treatment planning for radiation therapy is becoming practical. A basic requirement for Monte Carlo treatment planning is a detailed knowledge of the radiation beams from medical accelerators. A practical approach to obtain the above is to perform Monte Carlo simulation of radiation transport in the medical accelerator. Additionally, Monte Carlo modelling of the treatment machine head can also improve our understanding of clinical beam characteristics, help accelerator design and improve the accuracy of clinical dosimetry by providing more realistic beam data. This paper summarizes work over the past two decades on Monte Carlo simulation of clinical electron beams from medical accelerators.

Comparison of EGS4 and MCNP4b Monte Carlo codes for generation of photon phase space distributions for a Varian 2100C

Monte Carlo based dose calculation algorithms require input data or distributions describing the phase space of the photons and secondary electrons prior to the patient-dependent part of the beam-line geometry. The accuracy of the treatment plan itself is dependent upon the accuracy of this distribution. The purpose of this work is to compare phase space distributions (PSDs) generated with the MCNP4b and EGS4 Monte Carlo codes for the 6 and 18 MV photon modes of the Varian 2100C and determine if differences relevant to Monte Carlo based patient dose calculations exist. Calculations are performed with the same energy transport cut-off values. At 6 MV, target bremsstrahlung production for MCNP4b is approximately 10% less than for EGS4, while at 18 MV the difference is about 5%. These differences are due to the different bremsstrahlung cross sections used in the codes. Although the absolute bremsstrahlung production differs between MCNP4b and EGS4, normalized PSDs agree at the end of the patient-independent geometry (prior to the jaws), resulting in similar dose distributions in a homogeneous phantom. EGS4 and MCNP4b are equally suitable for the generation of PSDs for Monte Carlo based dose computations.