A beam model for focused proton pencil beams.

INTRODUCTION: We present a beam model for Monte Carlo simulations of the IBA pencil beam scanning dedicated nozzle installed at the Skandion Clinic. Within the nozzle, apart from entrance and exit windows and the two ion chambers, the beam traverses vacuum, allowing for a beam that is convergent downstream of the nozzle exit. MATERIALS AND METHODS: We model the angular, spatial and energy distributions of the beam phase space at the nozzle exit with single Gaussians, controlled by seven energy dependent parameters. The parameters were determined from measured profiles and depth dose distributions. Verification of the beam model was done by comparing measured and GATE acquired relative dose distributions, using plan specific log files from the machine to specify beam spot positions and energy. RESULTS: GATE-based simulations with the acquired beam model could accurately reproduce the measured data. The gamma index analysis comparing simulated and measured dose distributions resulted in >95% global gamma index pass rates (3%/2 mm) for all depths. CONCLUSION: The developed beam model was found to be sufficiently accurate for use with GATE e.g. for applications in quality assurance (QA) or patient motion studies with the IBA pencil beam scanning dedicated nozzles.

Modelling lateral beam quality variations in pencil kernel based photon dose calculations.

Standard treatment machines for external radiotherapy are designed to yield flat dose distributions at a representative treatment depth. The common method to reach this goal is to use a flattening filter to decrease the fluence in the centre of the beam. A side effect of this filtering is that the average energy of the beam is generally lower at a distance from the central axis, a phenomenon commonly referred to as off-axis softening. The off-axis softening results in a relative change in beam quality that is almost independent of machine brand and model. Central axis dose calculations using pencil beam kernels show no drastic loss in accuracy when the off-axis beam quality variations are neglected. However, for dose calculated at off-axis positions the effect should be considered, otherwise errors of several per cent can be introduced. This work proposes a method to explicitly include the effect of off-axis softening in pencil kernel based photon dose calculations for arbitrary positions in a radiation field. Variations of pencil kernel values are modelled through a generic relation between half value layer (HVL) thickness and off-axis position for standard treatment machines. The pencil kernel integration for dose calculation is performed through sampling of energy fluence and beam quality in sectors of concentric circles around the calculation point. The method is fully based on generic data and therefore does not require any specific measurements for characterization of the off-axis softening effect, provided that the machine performance is in agreement with the assumed HVL variations. The model is verified versus profile measurements at different depths and through a model self-consistency check, using the dose calculation model to estimate HVL values at off-axis positions. A comparison between calculated and measured profiles at different depths showed a maximum relative error of 4% without explicit modelling of off-axis softening. The maximum relative error was reduced to 1% when the off-axis softening was accounted for in the calculations.

Reply to the comment on 'Monte Carlo calculated microdosimetric spread for cell nucleus-sized targets exposed to brachytherapy 125I and 192Ir sources and 60Co cell irradiation'.

A discrepancy between the Monte Carlo derived relative standard deviation [Formula: see text] (microdosimetric spread) and experimental data was reported by Villegas et al (2013 Phys. Med. Biol. 58 6149-62) suggesting wall effects as a plausible explanation. The comment by Lindborg et al (2015 Phys. Med. Biol. 60 8621-4) concludes that this is not a likely explanation. A thorough investigation of the Monte Carlo (MC) transport code used for track simulation revealed a critical bug. The corrected MC version yielded [Formula: see text] values that are now within experimental uncertainty. Other microdosimetric findings are hereby communicated.

Microdosimetric spread for cell-sized targets exposed to 6°Co, ¹9²Ir and ¹²5I sources.

The magnitude of the spread in specific energy deposition per cell may be a confounding factor in dose-response analysis motivating derivation of explicit data for the most common brachytherapy isotopes (125)I and (192)Ir, and for (60)Co radiation frequently used as reference in RBE studies. The aim of this study is to analyse the microdosimetric spread as given by the frequency distribution of specific energy for a range of doses imparted by (125)I, (192)Ir and (60)Co sources. An upgraded version of the Monte Carlo code PENELOPE was used for scoring energy deposition distributions in liquid water for each of the radiation qualities. Frequency distributions of specific energy were calculated according to the formalism of Kellerer and Chmelevsky. Results indicate that the magnitude of the microdosimetric spread increases with decreasing target size and decreasing energy of the radiation quality. Within the clinical relevant dose range (1 to 100 Gy), the spread does not exceed 4 % for (60)Co, 5 % for (192)Ir and 6 % for (125)I. The frequency distributions can be accurately approximated with symmetrical normal distributions at doses down to 0.2 Gy for (60)Co, 0.1 Gy for (192)Ir and 0.08 Gy for (125)I.

Analytic modeling of photon scatter from flattening filters in photon therapy beams.

Analytic models for calculation of scatter distributions from flattening filters in therapy photon beams are presented. It is shown that the amount of scatter with high atomic number filters can vary from 2% in 4-MV beams to 10% for 24-MV beams. The use of low atomic number filters can increase the amount of scatter by a factor of 2. The dependence on the opening angle of the primary collimator is quite large since a larger opening angle requires a thicker filter, which increases the scattered fraction of the filtered beam. The scatter makes the filter act as an extended source of extra-focal radiation. The source distribution for monomedia filters is shown to be almost triangular. Integration in the calculation-point's eye view over the visible part of the filter scatter source yields the scatter fraction of the total energy fluence incident upon the patient. The experimentally well-known "tilt" of dose profiles for asymmetrical fields is explained by the model. For complete modeling of head scatter distributions in treatment planning, the model presented must be combined with models also describing the scatter from the collimators, auxiliary modulators such as wedges and compensating filters, and collimator backscatter to the beam monitor.

Collimator scatter in photon therapy beams.

A model for collimator photon scatter calculations is presented. The scatter from a collimating block is separated into two categories, one being the scatter released from photons entering the block through the surface facing the source, and one from photons striking the block tangentially through the side tangential to the beam. Both sources of scatter are analyzed by means of scatter kernels, defined as the scatter fluence distribution from a narrow line beam striking a collimator block. Kernels for both cases are calculated analytically using first scatter models based on Klein-Nishina cross sections including corrections for binding effects and coherent scattering. For 1-MeV primary photons, Monte Carlo calculations (EGS4) are used to show that the collimator scatter is dominated by first scatter. The kernels for the two types of scattering geometries are shown to be related and thus the total collimator scatter kernel can be derived from the kernel for the photons which have entered the block through the source facing side. Using a set of photon beam spectra, the kernels are parameterized as functions of beam energy in a form suitable for implementation in treatment planning systems. The parameterization is used to derive collimator scatter distributions for broad beam geometries of clinical interest. It is shown that scatter from the primary collimator, due to its location close to the beam source, is a major source of scatter that amounts to several percent of the primary fluence. The scatter from beam shaping collimators, however, generally accounts for less than 1% of the primary fluence. Although the beam-shaping collimators generate little scatter, the model used to calculate the resulting dose component is simple to implement and separates the different sources of scattered photons from the accelerator head. The latter provides generality and accuracy in dose per monitor unit calculations in treatment planning. Due to the low magnitude of collimator scatter it is recommended to use the phrase "head scatter" instead of "collimator scatter" when addressing the overall subject of extra-focal radiation from medical accelerators.

Collapsed cone convolution of radiant energy for photon dose calculation in heterogeneous media.

A method for photon beam dose calculations is described. The primary photon beam is raytraced through the patient, and the distribution of total radiant energy released into the patient is calculated. Polyenergetic energy deposition kernels are calculated from the spectrum of the beam, using a database of monoenergetic kernels. It is shown that the polyenergetic kernels can be analytically described with high precision by (A exp( -ar) + B exp( -br)/r2, where A, a, B, and b depend on the angle with respect to the impinging photons and the accelerating potential, and r is the radial distance. Numerical values of A, a, B, and b are derived and used to convolve energy deposition kernels with the total energy released per unit mass (TERMA) to yield dose distributions. The convolution is facilitated by the introduction of the collapsed cone approximation. In this approximation, all energy released into coaxial cones of equal solid angle, from volume elements on the cone axis, is rectilinearly transported, attenuated, and deposited in elements on the axis. Scaling of the kernels is implicitly done during the convolution procedure to fully account for inhomogeneities present in the irradiated volume. The number of computational operations needed to compute the dose with the method is proportional to the number of calculation points. The method is tested for five accelerating potentials; 4, 6, 10, 15, and 24 MV, and applied to two geometries; one is a stack of slabs of tissue media, and the other is a mediastinum-like phantom of cork and water. In these geometries, the EGS4 Monte Carlo system has been used to generate reference dose distributions with which the dose computed with the collapsed cone convolution method is compared. Generally, the agreement between the methods is excellent. Deviations are observed in situations of lateral charged particle disequilibrium in low density media, however, but the result is superior compared to that of the generalized Batho method.

Modeling transmission and scatter for photon beam attenuators.

The development of treatment planning methods in radiation therapy requires dose calculation methods that are both accurate and general enough to provide a dose per unit monitor setting for a broad variety of fields and beam modifiers. The purpose of this work was to develop models for calculation of scatter and transmission for photon beam attenuators such as compensating filters, wedges, and block trays. The attenuation of the beam is calculated using a spectrum of the beam, and a correction factor based on attenuation measurements. Small angle coherent scatter and electron binding effects on scattering cross sections are considered by use of a correction factor. Quality changes in beam penetrability and energy fluence to dose conversion are modeled by use of the calculated primary beam spectrum after passage through the attenuator. The beam spectra are derived by the depth dose effective method, i.e., by minimizing the difference between measured and calculated depth dose distributions, where the calculated distributions are derived by superposing data from a database for monoenergetic photons. The attenuator scatter is integrated over the area viewed from the calculation point of view using first scatter theory. Calculations are simplified by replacing the energy and angular-dependent cross-section formulas with the forward scatter constant r2(0) and a set of parametrized correction functions. The set of corrections include functions for the Compton energy loss, scatter attenuation, and secondary bremsstrahlung production. The effect of charged particle contamination is bypassed by avoiding use of dmax for absolute dose calibrations. The results of the model are compared with scatter measurements in air for copper and lead filters and with dose to a water phantom for lead filters for 4 and 18 MV. For attenuated beams, downstream of the buildup region, the calculated results agree with measurements on the 1.5% level. The accuracy was slightly less in situations where the scatter component is very large, as for very large fields with very short filter to detector distances. The implementation of the model into treatment planning systems is discussed.

A pencil beam model for photon dose calculation.

A method for photon dose calculation in radio therapy planning using pencil beam energy deposition kernels is presented. It is designed to meet the requirements of an algorithm for 3-D treatment planning that is general enough to handle irregularly shaped radiation fields incident on a heterogeneous patient. It is point oriented and thus faster than a full 3-D convolution algorithm and uses the same physical data base to characterize a clinical beam as a full 3-D convolution algorithm. It is shown that photon therapy beams can be characterized with great accuracy from a combination of precalculated Monte Carlo energy deposition kernels and dose distributions measured in a water phantom. The data are used to derive analytical pencil beam kernels that are approximately partitionated into the dose from (i) primary released electrons and positrons, (ii) scattered, bremsstrahlung, and annihilation photons, (iii) contaminating photons, and (iv) charged particles from the collimator head. A semianalytical integration method, based on triangulation of the field, is developed for dose calculation using the analytical kernels. Dose is calculated in units normalized to the incident energy fluence which facilitates output factor calculation. For application in heterogeneous media, a scatter correction factor is derived using monodirectional convolution along the ray path. In homogeneous media results are compared with measurements and in heterogeneous media with Monte Carlo calculations and the Batho method.

Application of the convolution method for calculation of output factors for therapy photon beams.

The output factor for a therapy photon beam is defined as the dose per monitor unit relative to the dose per monitor unit in a reference field. Convolution models for photon dose calculations yield the dose in units normalized to the incident energy fluence with phantom scatter intrinsically modeled. Output factors calculated with the convolution method as the dose per unit energy fluence relative to the calculated dose per unit energy fluence in a reference field could deviate as much as 5% if corrections are not made for perturbations due to treatment head scatter. Significant perturbations are particles backscattered from the collimators to the monitor and photons forward scattered from the filter and collimators in the treatment head. The forward scatter adds an "unmonitored" contribution to the total energy fluence of the beam. A model is developed that describes the field size dependence of these perturbations for conversion of output factors, calculated with the convolution method, to machine output factors as an integrated part in treatment planning. The necessary machine characteristics are derived from measurements of the output in air for a limited set of field sizes. The method has been tested using five different multileaf collimated irregular fields at 6 MV and for a large set of rectangular fields at 5, 6, and 18 MV and found to predict output factors with an accuracy better than 1%.

The collapsed cone superposition algorithm applied to scatter dose calculations in brachytherapy.

Methods for scatter dose calculations in brachytherapy have been developed based on the collapsed cone superposition algorithm. The methods account for effects on the scatter dose caused by the three-dimensional distribution of heterogeneities in the irradiated volume and are considerably faster than methods based on straightforward superposition of kernels or direct Monte Carlo simulations. Use of a successive-scattering approach, in which the dose contribution from once- and multiply scattered photons are calculated separately, was found superior to conventional superposition using a single point kernel for all scatter generations. Use of the successive-scattering approach significantly reduces artifacts stemming from steep fluence gradients, typical of the brachytherapy geometry and critical for the collapsed cone approximation. The algorithm is tested versus Monte Carlo simulations for point sources of energies 28.4, 100, 350, and 662 keV. Results agree well for both a homogeneous water phantom and an air-water half-phantom.

Verification and implementation of dynamic wedge calculations in a treatment planning system based on a dose-to-energy-fluence formalism.

The use of dynamic movements on linear accelerators during irradiation has found a revised interest lately due to the integration of computers to control the accelerator. In this paper, dynamic wedge fields that are produced by moving one of the collimator blocks during irradiation are studied. Since these wedge fields differ from those of mechanical wedges, certain requirements are to be met on the treatment planning system. A pencil-beam-based treatment planning system that uses the resultant energy fluence distribution from the dynamic collimator movement has been extensively reviewed. In calculations, the system treats the dynamic collimated field as a single, modulated field that yields calculation times close to those for open beams. Details are given on the theoretical model used for the calculation of dynamically generated dose distributions. Measurements of depth doses, profiles, and output factors in dynamic wedge fields indicate that calculations accurately predict the outcome from dynamic wedges without any additional measurements other than those used for characterization of static open beams.

Determination of effective bremsstrahlung spectra and electron contamination for photon dose calculations.

A method is described for determining an effective, depth dose consistent bremsstrahlung spectra for high-energy photon beams using depth dose curves measured in water. A simple, analytical model with three parameters together with the nominal accelerating potential is used to characterise the bremsstrahlung spectra. The model is used to compute weights for depth dose curves from monoenergetic photons. These monoenergetic depth doses, calculated with the convolution method from Monte Carlo generated point spread functions (PSF), are added to yield the pure photon depth dose distribution. The parameters of the analytical spectrum model are determined using an iterative technique to minimise the difference between calculated and measured depth dose curves. The influence from contaminant electrons is determined from the difference between the calculated and the measured depth dose.

Dose calculation in brachytherapy for a 192Ir source using a primary and scatter dose separation technique.

A dose calculation algorithm for brachytherapy is presented that reduces errors in absolute dose calculation and facilitates new techniques for modelling heterogeneity effects from tissues, internal shields and superficially positioned sources. The algorithm is based on Monte Carlo simulations for specific source and applicator combinations. The dose is scored separately, in absolute units, for the primary and different categories of scatter according to the photon scatter generation. Radial dose distributions for the primary dose and the total scatter dose are parametrized using functions based on simple one-dimensional transport theory. The fitted radial parameters are functions of the angle to the long axis of the source to account for the anisotropy of the dose distribution. The kerma in air at the reference point 1 m from the source is also simulated using Monte Carlo techniques and both the dose and kerma are normalized per source emitted radiant energy. The calculated kerma per radiant energy is used together with the measured reference air kerma rate and the ratio of the dose to the kerma to calibrate the calculated absolute dose rate. Data are presented for an 192Ir cylindrical source, in combination with water, nylon and stainless steel applicators. Values of the radial dose profiles, specific dose rate constants and corrections to the air kerma for attenuation and scatter in air are calculated. Anisotropy functions for the 192Ir source and a water-equivalent applicator are compared to published values. The effects of the applicator wall material on the radial dose distribution are also discussed.

Build-up cap materials for measurement of photon head-scatter factors.

The suitability of high-Z materials as build-up caps for head-scatter measurements has been investigated. Build-up caps are often used to enable characterization of fields too small for a mini-phantom. We have studied lead and brass build-up caps with sufficiently large wall thicknesses, as compared to the range of contaminating electrons originating in the accelerator head, and compared them with build-up caps made of ionization chamber equivalent materials, i.e. graphite. The results were also compared with measurements taken using square and cylindrical polystyrene mini-phantoms. Field sizes ranging from 3 cm x 3 cm up to 40 cm x 40 cm were studied for nominal photon energies of 4, 6, 10 and 18 MV. The results show that the use of lead and brass build-up caps produces normalized head-scatter data slightly different from graphite build-up caps for large fields at high photon energies. At lower energies, however, no significant differences were found. The intercomparison between the two different plastic mini-phantoms and graphite caps showed no differences.

Point kernels and superposition methods for scatter dose calculations in brachytherapy.

Point kernels have been generated and applied for calculation of scatter dose distributions around monoenergetic point sources for photon energies ranging from 28 to 662 keV. Three different approaches for dose calculations have been compared: a single-kernel superposition method, a single-kernel superposition method where the point kernels are approximated as isotropic and a novel 'successive-scattering' superposition method for improved modelling of the dose from multiply scattered photons. An extended version of the EGS4 Monte Carlo code was used for generating the kernels and for benchmarking the absorbed dose distributions calculated with the superposition methods. It is shown that dose calculation by superposition at and below 100 keV can be simplified by using isotropic point kernels. Compared to the assumption of full in-scattering made by algorithms currently in clinical use, the single-kernel superposition method improves dose calculations in a half-phantom consisting of air and water. Further improvements are obtained using the successive-scattering superposition method, which reduces the overestimates of dose close to the phantom surface usually associated with kernel superposition methods at brachytherapy photon energies. It is also shown that scatter dose point kernels can be parametrized to biexponential functions, making them suitable for use with an effective implementation of the collapsed cone superposition algorithm.

Dose calculations for external photon beams in radiotherapy.

Dose calculation methods for photon beams are reviewed in the context of radiation therapy treatment planning. Following introductory summaries on photon beam characteristics and clinical requirements on dose calculations, calculation methods are described in order of increasing explicitness of particle transport. The simplest are dose ratio factorizations limited to point dose estimates useful for checking other more general, but also more complex, approaches. Some methods incorporate detailed modelling of scatter dose through differentiation of measured data combined with various integration techniques. State-of-the-art methods based on point or pencil kernels, which are derived through Monte Carlo simulations, to characterize secondary particle transport are presented in some detail. Explicit particle transport methods, such as Monte Carlo, are briefly summarized. The extensive literature on beam characterization and handling of treatment head scatter is reviewed in the context of providing phase space data for kernel based and/or direct Monte Carlo dose calculations. Finally, a brief overview of inverse methods for optimization and dose reconstruction is provided.

Limitations of a pencil beam approach to photon dose calculations in lung tissue.

A common limitation in treatment planning systems for photon dose calculation is to ignore the impact on electron transport and photon scatter from patient heterogeneities. The heterogeneity correlation is often based on scaling operations along beam rays as for the method according to Batho or the more novel approach of 1D convolutions along beam paths applied in pencil-beam-based systems. The effects of the limitation have been studied in a mediastinum geometry for a wide range of beam qualities by comparing the results from a pencil-beam-based treatment planning system with the results from Monte Carlo calculations. As expected, the deviations within unit-density volumes are small while deviations in low-density volumes increase with increasing beam energy from approximately 3% for 4 MV to 14% for 18 MV x-rays as a result of increased electron disequilibrium.

Implementation of pencil kernel and depth penetration algorithms for treatment planning of proton beams.

The implementation of two algorithms for calculating dose distributions for radiation therapy treatment planning of intermediate energy proton beams is described. A pencil kernel algorithm and a depth penetration algorithm have been incorporated into a commercial three dimensional treatment planning system (Helax-TMS, Helax AB, Sweden) to allow conformal planning techniques using irregularly shaped fields, proton range modulation, range modification and dose calculation for non-coplanar beams. The pencil kernel algorithm is developed from the Fermi Eyges formalism and Molière multiple-scattering theory with range straggling corrections applied. The depth penetration algorithm is based on the energy loss in the continuous slowing down approximation with simple correction factors applied to the beam penumbra region and has been implemented for fast, interactive treatment planning. Modelling of the effects of air gaps and range modifying device thickness and position are implicit to both algorithms. Measured and calculated dose values are compared for a therapeutic proton beam in both homogeneous and heterogeneous phantoms of varying complexity. Both algorithms model the beam penumbra as a function of depth in a homogeneous phantom with acceptable accuracy. Results show that the pencil kernel algorithm is required for modelling the dose perturbation effects from scattering in heterogeneous media.

The conceptual design of a radiation oncology planning system.

The conceptual design of a three-dimensional, radiation oncology planning system is described. To assure that clinical needs were met, the working routines in two major Swedish radiation oncology departments were analysed in detail. Generic work flow was identified and mapped and compared to those in other institutions. The flow was partitioned into a number of nodes that together formed a basis for the design of the system handling logistics. The design criteria of this system emphasised accommodation of current clinical practice and traditional treatment modalities, and facilitated means to validate the computational techniques. The system should also allow for new procedures and was based on the analysis of current practice and a synthetic idea of how 3D treatment planning should be done. The final product supports the treatment planning work in its entirety. It is believed that the techniques followed are of interest to those engaged in computer systems of similar purposes and complexities.