Total scatter factors of small beams: a multidetector and Monte Carlo study

The scope of this study was to estimate total scatter factors (S(c,p)) of the three smallest collimators of the Cyberknife radiosurgery system (5-10 mm in diameter), combining experimental measurements and Monte Carlo simulation. Two microchambers, a diode, and a diamond detector were used to collect experimental data. The treatment head and the detectors were simulated by means of a Monte Carlo code in order to calculate correction factors for the detectors and to estimate total scatter factors by means of a consistency check between measurement and simulation. Results for the three collimators were: S(c,p) (5 mm) = 0.677 +/- 0.004, S(c,p) (7.5 mm) = 0.820 +/- 0.008, S(c,p) (10 mm) = 0.871 +/- 0.008, all relative to the 60 mm collimator at 80 cm source-to-detector distance. The method also allows the full width at half maximum of the electron beam to be estimated; estimations made with different collimators and different detectors were in excellent agreement and gave a value of 2.1 mm. Correction factors to be applied to the detectors for the measurement of S(c,p) were consistent with a prevalence of volume effect for the microchambers and the diamond and a prevalence of scattering from high-Z material for the diode detector. The proposed method is more sensitive to small variations of the electron beam diameter with respect to the conventional method used to commission Monte Carlo codes, i.e., by comparison with measured percentage depth doses (PDD) and beam profiles. This is especially important for small fields (less than 10 mm diameter), for which measurements of PDD and profiles are strongly affected by the type of detector used. Moreover, this method should allow S(c,p) of Cyberknife systems different from the unit under investigation to be estimated without the need for further Monte Carlo calculation, provided that one of the microchambers or the diode detector of the type used in this study are employed. The results for the diamond are applicable only to the specific detector that was investigated due to excessive variability in manufacturing.     

A method for photon beam Monte Carlo multileaf collimator particle transport

Monte Carlo (MC) algorithms are recognized as the most accurate methodology for patient dose assessment. For intensity-modulated radiation therapy (IMRT) delivered with dynamic multileaf collimators (DMLCs), accurate dose calculation, even with MC, is challenging. Accurate IMRT MC dose calculations require inclusion of the moving MLC in the MC simulation. Due to its complex geometry, full transport through the MLC can be time consuming. The aim of this work was to develop an MLC model for photon beam MC IMRT dose computations. The basis of the MC MLC model is that the complex MLC geometry can be separated into simple geometric regions, each of which readily lends itself to simplified radiation transport. For photons, only attenuation and first Compton scatter interactions are considered. The amount of attenuation material an individual particle encounters while traversing the entire MLC is determined by adding the individual amounts from each of the simplified geometric regions. Compton scatter is sampled based upon the total thickness traversed. Pair production and electron interactions (scattering and bremsstrahlung) within the MLC are ignored. The MLC model was tested for 6 MV and 18 MV photon beams by comparing it with measurements and MC simulations that incorporate the full physics and geometry for fields blocked by the MLC and with measurements for fields with the maximum possible tongue-and-groove and tongue-or-groove effects, for static test cases and for sliding windows of various widths. The MLC model predicts the field size dependence of the MLC leakage radiation within 0.1% of the open-field dose. The entrance dose and beam hardening behind a closed MLC are predicted within +/- 1% or 1 mm. Dose undulations due to differences in inter- and intra-leaf leakage are also correctly predicted. The MC MLC model predicts leaf-edge tongue-and-groove dose effect within +/- 1% or 1 mm for 95% of the points compared at 6 MV and 88% of the points compared at 18 MV. The dose through a static leaf tip is also predicted generally within +/- 1% or 1 mm. Tests with sliding windows of various widths confirm the accuracy of the MLC model for dynamic delivery and indicate that accounting for a slight leaf position error (0.008 cm for our MLC) will improve the accuracy of the model. The MLC model developed is applicable to both dynamic MLC and segmental MLC IMRT beam delivery and will be useful for patient IMRT dose calculations, pre-treatment verification of IMRT delivery and IMRT portal dose transmission dosimetry.     

Photon penetration and scatter in micro-pinhole imaging: a Monte Carlo investigation

Pinhole SPECT is rapidly gaining popularity for imaging laboratory animals using gamma-emitting molecules. Penetration and scattering of gamma radiation in the pinhole edge material can account for a significant fraction of the total number of photons detected, particularly if the pinholes have small diameters. This study characterizes the effects of penetration and scatter with micro-pinholes made of lead, tungsten, gold and platinum. Monte Carlo simulations are performed for 1-125 (27-35 keV) and Tc-99m (140 keV) point sources with pinhole diameters ranging from 50 to 500 microm. The simulations account for the effects of photo-electric interaction, Rayleigh scattering, Compton scattering, ionization, bremsstrahlung and electron multiple scattering. As a typical example, in the case of a Tc-99m point source and pinholes with a diameter of 300 microm in gold or platinum, approximately 55% of the photons detected resulted from penetration and approximately 3% from scatter. For pinhole diameters ranging from 100 to 500 microm, the penetration fraction for tungsten and lead was approx a factor of 1.0 to 1.6 higher and the scatter fraction was 1.0 to 1.8 times higher than in case of gold or platinum. Using I-125 instead of Tc-99m decreases the penetration fraction by a factor ranging from 3 to 11 and the scatter fraction by a factor ranging from 12 to 40. For all materials studied, the total amounts of penetrated and scattered photons changed approximately linearly with respect to the pinhole diameter.     

Monte Carlo simulation of diagnostic x-ray scatter

A Monte Carlo method was developed and implemented to simulate x-ray photon transport. Simulations consisted of a pencil beam of monoenergetic photons with energies from 50 to 110 keV incident on water and aluminum slabs. The dependence of scatter fraction and multiple scattering on x-ray energy, scatterer thickness, and material is reported in both number and energy fluence. The average energy of scattered photons reaching the detector plane is also reported. Comparisons are made to previous x-ray scatter computations.     

Monte Carlo study of neutron dose equivalent during passive scattering proton therapy

Stray radiation exposures are of concern for patients receiving proton radiotherapy and vary strongly with several treatment factors. The purposes of this study were to conservatively estimate neutron exposures for a contemporary passive scattering proton therapy system and to understand how they vary with treatment factors. We studied the neutron dose equivalent per therapeutic absorbed dose (H/D) as a function of treatment factors including proton energy, location in the treatment room, treatment field size, spread-out Bragg peak (SOBP) width and snout position using both Monte Carlo simulations and analytical modeling. The H/D value at the isocenter for a 250 MeV medium field size option was estimated to be 20 mSv Gy(-1). H/D values generally increased with the energy or penetration range, fell off sharply with distance from the treatment unit, decreased modestly with the aperture size, increased with the SOBP width and decreased with the snout distance from the isocenter. The H/D values from Monte Carlo simulations agreed well with experimental results from the literature. The analytical model predicted H/D values within 28% of those obtained in simulations; this value is within typical neutron measurement uncertainties.     

质子束流蒙特卡罗模型的建立及对脊形滤波器的探究

目的:探究脊形滤波器结构对质子束流展宽的影响。方法:利用蒙特卡罗程序FLUKA建立质子束流模型，并进行验证。模拟质子束流通过三棱柱型（A型）和金字塔型（B型）两种脊形滤波器，比较使用和不使用脊形滤波器的模拟值:束流前端最大剂量50%到束流末端最大剂量50%的宽度（E50-D50）、束流前端80%到束流末端80%的宽度（E80-D80）及束流末端80%到束流末端20%的宽度（D80-D20）。结果:根据模型计算出的121.1 MeV质子对应的模拟值绘制的积分深度剂量曲线与实际测量的积分深度剂量曲线，E50、E70和D80位置偏差不超过0.06 mm；A型相比B型将E50-D50平均多展宽了0.80 mm，将E80-D80 平均多展宽了0.27 mm，将D80-D20 平均多展宽了0.08 mm。结论:建立的质子束流蒙特卡罗模型合理，三棱柱型（A型）脊形滤波器展宽质子束流的效果更好。     

Initial beam size study for passive scatter proton therapy. I. Monte Carlo verification

The purpose of this work was to provide an initial validation of a Monte Carlo (MC) model of the passive scattering treatment nozzle at the University of Texas M. D. Anderson Cancer Center Proton Therapy Center. The MC model included a detailed definition of each beam-modifying element in the nozzle, and calculations accounted for interactions of the beam with the rotating modulator wheel used to create the spread out Bragg peak. In this work we show comparisons of calculated dose and fluence profiles with measured data from the nozzle for the 250 and 180 MeV beam energies used for patient treatments. Agreement to within 1.5 mm of measured data was observed for all MC calculations. The high level of agreement between the measurements and the MC model for the two beam energies studied provides validation for use of the model in a study of the dosimetric effects of the proton beam size and shape at the nozzle entrance.     

Assessment of a new multileaf collimator concept using GEANT4 Monte Carlo simulations

The aim of the work was to investigate in advance the dosimetric properties of a new multileaf collimator (MLC) concept with the help of Monte Carlo (MC) simulations prior to the production of a prototype. The geometrical design of the MLC was implemented in the MC code GEANT4. For the simulation of a 6 MV treatment beam, an experimentally validated phase space and a virtual spatial Gaussian-shaped model placed in the origin were used. For the simulation of the geometry in GEANT4, the jaws and the two leaf packages were implemented with the help of computer-aided design data. First, transmission values for different tungsten alloys were extracted using the simulation codes GEANT4 and BEAMnrc and compared to experimental measurements. In a second step, high-resolution simulations were performed to detect the leakage at depth of maximum dose. The 20%-80% penumbra along the travel direction of the leaves was determined using 10 x 10 cm2 fields shifted along the x- and y-axis. The simulated results were compared with measured data. The simulation of the transmission values for different tungsten alloys showed a good agreement with the experimental measurements (within 2.0%). This enabled an accurate estimation of the attenuation coefficient for the various leaf materials. Simulations with varying width of the spatial Gaussian distribution showed that the leakage and the penumbra depend very much on this parameter: for instance, for widths of 2 and 4 mm, the interleaf leakage is below 0.3% and 0.75%, respectively. The results for the leakage and the penumbra (4.7+/-0.5 mm) are in good agreement with the measurements. This study showed that GEANT4 is appropriate for the investigation of the dosimetric properties of a multileaf collimator. In particular, a quantification of the leakage, the penumbra, and the tongue-and-groove effect and an evaluation of the influence of the beam parameters such as the width of the Gaussian distribution was possible.     

Photon scatter in intensity modulating filters evaluated by first Compton scatter and Monte Carlo calculations and experiments in broad beams

High-atomic-number materials may be used as intensity modulating filters for inverse radiation treatment planning with photon beams. Such filters, when placed in a bremsstrahlung beam, attenuate the primary fluence, but also produce scattered photons that will reach the patient. To account for such effects in the optimization of photon beam intensities a semiempirical method based on narrow and broad beam transmission measurements was used to quantify the number of scattered photons produced in these filters. The method was verified by performing analytical calculations based on first scatter and a Monte Carlo simulation in 6 and 18 MV photon beams. The resultant experimental transmission ratios agree with calculations by these methods within 2 per cent under the experimental conditions investigated. The semiempirical method can thus be used as a basis for preliminary decision-making to select the proper material for intensity modulating filters and can provide a fast method to perform independent quality checks of the calculation accuracy of dose planning systems. Change in beam penetration is of less concern when treatments of target volumes at smaller depths are of interest. A 10 g cm(-2) thick filter made of low-melting-point alloy produces a change in percentage depth dose of less than 2 per cent for depths larger than 10 cm independent of field size. Similarly the scatter correction modifies the dose distribution by less than 5-10 per cent in most cases.     

A Monte Carlo study of multiple scatter effects in Compton scatter densitometry

The contribution of multiple scatter to the measured signal in x- and gamma-ray Compton scatter densitometry has been investigated theoretically by the use of Monte Carlo techniques to follow individual photon life histories. A three component phantom was employed in the computer model to simulate the patient at three examination sites; the radius/ulna, the femoral neck, and the lumbar spine. Monoenergetic radiation beams of 60- and 100-keV photons and polyenergetic x-ray spectra of 100 and 140 kVp were used. Scattered events were detected over 360 degrees and classified according to their origin and frequency of scatter. The single scatter in bone to multiple scatter ratio was studied as an indication of the signal-to-noise ratio and this was found to vary with phantom size but was independent of photon energy. Correction factors to be used in a clinical densitometer to account for the inclusion of multiple scatter events were computed. These were found to be 0.65-0.58 at the optimum scattering angles for the phantoms considered.     

Dose measurements compared with Monte Carlo simulations of narrow 6 MV multileaf collimator shaped photon beams.

Small fields where electronic equilibrium is not achieved are becoming increasingly important in clinical practice. These complex situations give rise to problems and inaccuracies in both dosimetry and analytical/empirical dose calculation, and therefore require other than conventional methods. A natural diamond detector and a Markus parallel plate ionization chamber have been selected for clinical dosimetry in 6 MV photon beams. Results of simulations using the Monte Carlo system BEAM/EGS4 to model the beam geometry have been compared with dose measurements. A modification of the existing component module for multileaf collimators (MLCs) allowed the modeling of a linear accelerator SL 25 (Elekta Oncology Systems) equipped with a MLC with curved leaf-ends. A mechanical measurement method with spacer plates and a light-field edge detection technique are described as methods to obtain geometrical data of collimator openings for application in the Monte Carlo system. Generally a good agreement is found between measurements and calculations of depth dose distributions and deviations are typically less than 1%. Calculated lateral dose profiles slightly exceed measured dose distributions near the higher level of the penumbras for a 10x2 cm2 field, but agree well with the measurements for all other cases. The simulations are also able to predict variations of output factors and ratios of output factors as a function of field width and field-offset. The Monte Carlo results demonstrate that qualitative changes in energy spectra are too small to explain these variations and that especially geometrical factors affect the output factors and depth dose curves and profiles.     

Convolution/superposition using the Monte Carlo method

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

Energy and spatial distribution of multiple order Compton scatter in SPECT: a Monte Carlo investigation

Energy and spatial projection distributions were simulated for gamma camera imaging of multiple order Compton scattered photons. SPECT imaging of a line source of radioactivity located in a water filled cylindrical phantom was modelled using Monte Carlo techniques. Photon trajectories were followed from emission to detection including the effects of all physical interactions and the resulting energy spectra and spatial projections were sorted as a function of the number of times the photon underwent Compton scattering before detection. Analysis of energy spectra demonstrates that Compton events up to second order overlap with the non-scattered events and distributions are peaked at lower energies as the scattering order increases. Analysis of spatial projections shows that, with increasing order, Compton events produce tails on the line spread function which progress from roughly exponential to nearly flat distributions. The use of Monte Carlo modelling thus allows a detailed investigation of the spatial and energy distribution of Compton scatter which could not be performed using present experimental techniques.     

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.     

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.     

Benchmarking of the dose planning method (DPM) Monte Carlo code using electron beams from a racetrack microtron

A comprehensive set of measurements and calculations has been conducted to investigate the accuracy of the Dose Planning Method (DPM) Monte Carlo code for dose calculations from 10 and 50 MeV scanned electron beams produced from a racetrack microtron. Central axis depth dose measurements and a series of profile scans at various depths were acquired in a water phantom using a Scanditronix type RK ion chamber. Source spatial distributions for the Monte Carlo calculations were reconstructed from in-air ion chamber measurements carried out across the two-dimensional beam profile at 100 cm downstream from the source. The in-air spatial distributions were found to have full width at half maximum of 4.7 and 1.3 cm, at 100 cm from the source, for the 10 and 50 MeV beams, respectively. Energy spectra for the 10 and 50 MeV beams were determined by simulating the components of the microtron treatment head using the code MCNP4B. DPM calculations are on average within +/- 2% agreement with measurement for all depth dose and profile comparisons conducted in this study. The accuracy of the DPM code illustrated in this work suggests that DPM may be used as a valuable tool for electron beam dose calculations.     

Uncertainties and correction methods when modeling passive scattering proton therapy treatment heads with Monte Carlo

Nowadays, Monte Carlo models of proton therapy treatment heads are being used to improve beam delivery systems and to calculate the radiation field for patient dose calculations. The achievable accuracy of the model depends on the exact knowledge of the treatment head geometry and time structure, the material characteristics, and the underlying physics. This work aimed at studying the uncertainties in treatment head simulations for passive scattering proton therapy. The sensitivities of spread-out Bragg peak (SOBP) dose distributions on material densities, mean ionization potentials, initial proton beam energy spread and spot size were investigated. An improved understanding of the nature of these parameters may help to improve agreement between calculated and measured SOBP dose distributions and to ensure that the range, modulation width, and uniformity are within clinical tolerance levels. Furthermore, we present a method to make small corrections to the uniformity of spread-out Bragg peaks by utilizing the time structure of the beam delivery. In addition, we re-commissioned the models of the two proton treatment heads located at our facility using the aforementioned correction methods presented in this paper.     

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.