Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy

Monte Carlo (code GEANT) produced 6 and 15 MV phase space (PS) data were used to define several simple photon beam models. For creating the PS data the energy of starting electrons hitting the target was tuned to get correct depth dose data compared to measurements. The modeling process used the full PS information within the geometrical boundaries of the beam including all scattered radiation of the accelerator head. Scattered radiation outside the boundaries was neglected. Photons and electrons were assumed to be radiated from point sources. Four different models were investigated which involved different ways to determine the energies and locations of beam particles in the output plane. Depth dose curves, profiles, and relative output factors were calculated with these models for six field sizes from 5x5 to 40x40cm2 and compared to measurements. Model 1 uses a photon energy spectrum independent of location in the PS plane and a constant photon fluence in this plane. Model 2 takes into account the spatial particle fluence distribution in the PS plane. A constant fluence is used again in model 3, but the photon energy spectrum depends upon the off axis position. Model 4, finally uses the spatial particle fluence distribution and off axis dependent photon energy spectra in the PS plane. Depth dose curves and profiles for field sizes up to 10x10cm2 were not model sensitive. Good agreement between measured and calculated depth dose curves and profiles for all field sizes was reached for model 4. However, increasing deviations were found for increasing field sizes for models 1-3. Large deviations resulted for the profiles of models 2 and 3. This is due to the fact that these models overestimate and underestimate the energy fluence at large off axis distances. Relative output factors consistent with measurements resulted only for model 4.     

光子射野剂量计算参数研究

目的：介绍医用加速器常规光子射线的机器数据测量方法及剂量计算模型中基本参数的计算过程。以百分深度剂量与散射因子为基础数据,根据原散射线模型通过测量数据推导出原射线组织最大剂量比、散射最大剂量比、原射线在水中线性衰减系数、能量注量等,为进一步还原射野在水模体中的剂量分布提供方法与理论。方法：用Blue Phantom三维水箱在医科达Synergy加速器上测量6MV光子线的百分深度剂量、离轴比剂量、总散射因子、准直器散射因子,先从测量的百分深度剂量曲线中按照原散射模型剥离出原射线百分深度剂量,然后在Matlab软件中拟合处理测量的散射因子数据,外推出零野的模体散射因子,从而按照给定公式计算出组织最大剂量比、散射最大剂量比。按照离轴比剂量,利用平方反比规律推出最大开野在模体表面的能量注量。结果：计算出准直器散射因子、总散射因子的拟合公式,外推零野模体散射因子（s。）、根据原射线的百分深度剂量曲线计算出原射线在水中线性衰减系数,组织最大剂量比（TMR）、散射最大剂量比（SMR）、以及射野能量注量分布（Fluence Matrix）。结论：这些基本参数是剂量计算建模的关键,也是进一步研究各种剂量计算模型的基础。     

A two-dimensional pencil-beam algorithm for calculation of arc electron dose distributions

A two-dimensional pencil-beam algorithm is presented for the calculation of arc electron dose distributions in any plane that is perpendicular to the axis of rotation. The dose distributions are calculated by modelling the arced beam as a single broad beam defined by the irradiated surface of the patient. The algorithm is two-dimensional in that the anatomical cross section of the patient and the skin collimators are assumed identical in parallel planes outside the plane of calculation. The broad beam is modelled as a collection of strip beams, each strip beam being characterised by its planar fluence, mean projected angular direction and a root-mean-square spread about the mean direction. Using these parameters, the dose distribution is calculated using pencil-beam theory. Examples of strip-beam parameters and resulting dose distributions for patient geometries are presented. Features of the algorithm, which include (1) incorporation of pencil-beam theory for the calculation of dose in heterogeneous tissue, (2) run times of only about twice that of comparable-sized fixed electron fields and (3) the input requirement of only a single depth dose and four off-axis dose profiles of measured data, make the algorithm practical for clinical use.     

Characterization of an extendable multi-leaf collimator for clinical electron beams

An extendable x-ray multi-leaf collimator (eMLC) is investigated for collimation of electron beams on a linear accelerator. The conventional method of collimation using an electron applicator is impractical for conformal, modulated and mixed beam therapy techniques. An eMLC would allow faster, more complex treatments with potential for reduction in dose to organs-at-risk and critical structures. The add-on eMLC was modelled using the EGSnrc Monte Carlo code and validated against dose measurements at 6-21 MeV with the eMLC mounted on a Siemens Oncor linear accelerator at 71.6 and 81.6 cm source-to-collimator distances. Measurements and simulations at 8.4-18.4 cm airgaps showed agreement of 2%/2 mm. The eMLC dose profiles and percentage depth dose curves were compared with standard electron applicator parameters. The primary differences were a wider penumbra and up to 4.2% reduction in the build-up dose at 0.5 cm depth, with dose normalized on the central axis. At 90 cm source-to-surface distance (SSD)--relevant to isocentric delivery--the applicator and eMLC penumbrae agreed to 0.3 cm. The eMLC leaves, which were 7 cm thick, contributed up to 6.3% scattered electron dose at the depth of maximum dose for a 10 × 10 cm2 field, with the thick leaves effectively eliminating bremsstrahlung leakage. A Monte Carlo calculated wedge shaped dose distribution generated with all six beam energies matched across the maximum available eMLC field width demonstrated a therapeutic (80% of maximum dose) depth range of 2.1-6.8 cm. Field matching was particularly challenging at lower beam energies (6-12 MeV) due to the wider penumbrae and angular distribution of electron scattering. An eMLC isocentric electron breast boost was planned and compared with the conventional applicator fixed SSD plan, showing similar target coverage and dose to critical structures. The mean dose to the target differed by less than 2%. The low bremsstrahlung dose from the 7 cm thick MLC leaves had the added advantage of reducing the mean dose to the whole heart. Isocentric delivery using an extendable eMLC means that treatment room re-entry and repositioning the patient for SSD set-up is unnecessary. Monte Carlo simulation can accurately calculate the fluence below the eMLC and subsequent patient dose distributions. The eMLC generates similar dose distributions to the standard electron applicator but provides a practical method for more complex electron beam delivery.     

Comparison of beam characteristics of a gold x-ray target and a tungsten replacement target

A new W-Cu target was designed to replace the existing Au target on a linear accelerator model in common use in radiotherapy. This work shows that targets of different material composition can be designed to produce beams with the same dosimetric character over a wide range of beam energies without adjusting the beam energy. The target design objective was to improve mechanical robustness, replacing water in the beam path with a Cu heat sink, without altering the beam properties for the nominal clinical energy range of 4-25 MV. The W-Cu could then be installed in place of the Au target without recommissioning. The effect of the target swap was measured in the test cells for 11 different beams ranging in nominal energy from 4 to 25 MV, with focus on open field dose distributions, including diagonal profiles taken for the largest (40x40 cm) field, measured at 4 different gantry angles. Depth dose curves agreed to 0.4% or better, profiles to 1.2% or better. Monte Carlo simulations of the treatment head were done for representative energies of 6 and 18 MV. Calculated and measured dose distributions generally matched within 1%, although dose measured in the build-up region of large fields was significantly more than in the simulations. Calculated spectral distributions on the central axis and angular distributions of energy fluence matched for the two targets, whereas angular distributions of fluence were significantly different. Matching energy fluence gave a more favorable match of dose profiles than matching fluence. The target was further tested on several machines operating in a radiotherapy clinic. Measurements were made for a wide range of open field sizes and with selected wedges and blocks. Dose distributions for the two targets agreed to 1.4% or better, including the dose in wedged fields. Wedge factors changed by no more than 0.5%, transmission through a 4.4 HVL block no more than 1.5%. The response of the monitor chamber was found to change, generally by 1%-2%. Therefore, when the W-Cu target was used to replace the Au target, the output of the machine was measured and adjusted appropriately, but there was no requirement for recommissioning.     

Validation of a pencil beam model-based treatment planning system for fast neutron therapy

Treatment planning systems (TPSs) are used to compute dose delivered to the patient. In the case of fast neutron therapy, TPSs are mostly not of general purpose but are dedicated to one facility. This is due to the few fast neutron facilities worldwide and due to the high variation in the neutron energy distributions. Efforts have been undertaken to develop a new TPS that could be applied to all the existing fast neutron facilities. The University Hospital of Essen operates a d (14 MeV) + Be fast neutron beam and the TPS used is based on an empirical model. In a previous study, the empirical model has been evolved to a pencil beam model of 35 monoenergetic neutron beams. Monte Carlo techniques have been utilized to compute distributions of the energy deposition due to primary and scattered neutrons in a simple geometry water phantom. The experimental validation of the method is now presented. Depth dose curves in water of monoenergetic neutrons have been derived from the distributions of energy deposition. The resultant depth dose curves have been utilized in order to determine the depth dose curves of the fast neutron beam of the Essen facility for the 14 radiation field sizes available in this facility. This determination requires the initial neutron spectrum. As this spectrum could not be measured at the Essen facility, the initial neutron spectrum of the Physikalisch Technische Bundesanstalt, Braunschweig, Germany, which operates the same cyclotron, was used. The calculated depth dose curves were compared to experimental depth dose curves that have been obtained in water at the University Hospital of Essen. The comparison between calculated and experimental depth dose curves showed significant deviations in the case of large radiation fields and of depth less than 5 cm. In the case of radiation field areas less than 150 cm2 and depth more than 5 cm (usual clinical situation), the measured and calculated values are in a good agreement. In the case of clinical situation, the dependence on the radiation field size is relatively well taken into account by the model presented here.     

Calculation of a pencil beam kernel from measured photon beam data

Usually, pencil beam kernels for photon beam calculations are obtained by Monte Carlo calculations. In this paper, we present a method to derive a pencil beam kernel from measured beam data, i.e. central axis depth doses, phantom scatter factors and off-axis ratios. These data are usually available in a radiotherapy planning system. The differences from other similar works are: (a) the central part of the pencil beam is derived from the measured penumbra of large fields and (b) the dependence of the primary photon fluence on the depth caused by beam hardening in the phantom is taken into account. The calculated pencil beam will evidently be influenced by the methods and instruments used for measurement of the basic data set. This is of particular importance for an accurate prediction of the absorbed dose delivered by small fields. Comparisons with measurements show that the accuracy of the calculated dose distributions fits well in a 2% error interval in the open part of the field, and in a 2 mm isodose shift in the penumbra region.     

A multiple source model for 6 MV photon beam dose calculations using Monte Carlo

A multiple source model (MSM) for the 6 MV beam of a Varian Clinac 2300 C/D was developed by simulating radiation transport through the accelerator head for a set of square fields using the GEANT Monte Carlo (MC) code. The corresponding phase space (PS) data enabled the characterization of 12 sources representing the main components of the beam defining system. By parametrizing the source characteristics and by evaluating the dependence of the parameters on field size, it was possible to extend the validity of the model to arbitrary rectangular fields which include the central 3 x 3 cm2 field without additional precalculated PS data. Finally, a sampling procedure was developed in order to reproduce the PS data. To validate the MSM, the fluence, energy fluence and mean energy distributions determined from the original and the reproduced PS data were compared and showed very good agreement. In addition, the MC calculated primary energy spectrum was verified by an energy spectrum derived from transmission measurements. Comparisons of MC calculated depth dose curves and profiles, using original and PS data reproduced by the MSM, agree within 1% and 1 mm. Deviations from measured dose distributions are within 1.5% and 1 mm. However, the real beam leads to some larger deviations outside the geometrical beam area for large fields. Calculated output factors in 10 cm water depth agree within 1.5% with experimentally determined data. In conclusion, the MSM produces accurate PS data for MC photon dose calculations for the rectangular fields specified.     

Tissue equivalence in clinical neutron dosimetry: comparison of dose distributions in nine tissue substitutes for a d(14)Be neutron beam

Depth dose distributions for a d(14)Be neutron beam, measured separately for total and gamma absorbed dose, are presented for nine tissue substitutes and for two field sizes. These data are used to examine methods to transform depth dose curves from one material to another. Best results are found when the local depths are transformed by constant empirical factors which are independent of depth and field size. As a physical interpretation of the empirical factors, kerma-weighted mean-free-path lengths are calculated for the interaction of the Essen neutron beam with the materials. The ratios of these free path lengths agree with the empirical factors within +/- 10%. However, for clinical dosimetry, a direct comparability of spatial absorbed dose distributions measured in two different phantom materials is only given if their corresponding transformation factor is near unity.     

A topographic leaf-sequencing algorithm for delivering intensity modulated radiation therapy

Topographic treatment is a radiation therapy delivery technique for fixed-gantry (nonrotational) treatments on a helical tomotherapy system. The intensity-modulated fields are created by moving the treatment couch relative to a fan-beam positioned at fixed gantry angles. The delivered dose distribution is controlled by moving multileaf collimator (MLC) leaves into and out of the fan beam. The purpose of this work was to develop a leaf-sequencing algorithm for creating topographic MLC sequences. Topographic delivery was modeled using the analogy of a water faucet moving over a collection of bottles. The flow rate per unit length of the water from the faucet represented the photon fluence per unit length along the width of the fan beam, the collection of bottles represented the pixels in the treatment planning fluence map, and the volume of water collected in each bottle represented the delivered fluence. The radiation fluence per unit length delivered to the target at a given position is given by the convolution of the intensity distribution per unit length over the width of the beam and the time per unit distance along the direction of travel that an MLC leaf is open. The MLC opening times for the desired dose profiles were determined using a technique based on deconvolution using a genetic algorithm. The MLC opening times were expanded in terms of a Fourier series, and a genetic algorithm was used to find the best expansion coefficients for a given dose distribution. A series of wedge shapes (15, 30, 45, and 60 deg) and "dose well" test fluence maps were created to test the algorithm's ability to generate topographic leaf sequences. The accuracy of the leaf-sequencing algorithm was measured on a helical tomotherapy system using radiographic film placed at depth in water equivalent material. The measured dose profiles were compared with the desired dose distributions. The agreement was within +/- 2% or 2 mm distance-to-agreement (DTA) in the high dose gradient regions for all test cases. The central axis measured dose was between 3.6% and 4.2% higher than the expected dose for the wedge cases. For the "dose well" test cases, the calculated and measured doses agreed to within +/- 0.5% at the peak and within +/- 1.6% in the "dose well." The topographic leaf-sequencing algorithm produced deliverable dose distributions that agreed well with the calculated dose distributions. This delivery technique could be used for treatment of whole intact breast. However, additional work is needed to further improve the algorithm in order to get better agreement between the calculated, deliverable, and measured dose distributions.     

Commissioning 6 MV photon beams of a stereotactic radiosurgery system for Monte Carlo treatment planning

The goal of this work is to implement a beam commissioning procedure to generate a multiple source model using a set of standard measurement data for possible Monte Carlo treatment planning in the clinic for a Cyberknife stereotactic radiosurgery system. The required measurement data include the central axis depth dose curve (PDD), the dose profile at dmax(= 1.5 cm) of 60 mm cone at 80 cm source-to-surface distance (SSD), and the cone output factors for cones of 5 mm to 60 mm at 80 cm source-to-axis distance (SAD). The employed dual source model has the same structure as the one that has been studied in our previous work while most of the parameters of each source are extracted from the measurement data rather than the beam phase space. The energy spectra will be extracted from the central axis PDD, the fluence distributions will be deconvoluted from the dose profile at dmax, and the source distributions will be determined from the measured cone output factors. Monte Carlo dose calculations in various water phantoms have been performed to verify the beam commissioning procedure. The agreement between the measurements and the commissioning results was within 2%/1 mm for the central axis PDDs and the dose profiles at various depths when an IC-3 chamber was used and within 2% for the cone output factors for various collimator sizes of 5 to 60 mm. Largest difference (9.5%) was observed for the 7.5 mm cone when an IC-10 chamber was used. The large differences can be attributed to the volumetric averaging effect of the IC-10 chamber, whose dimension is comparable to the field of the small cones. The overall agreement between the measurements and the commissioning results is clinically acceptable, which implies that our commissioning tool is adequate for clinical applications of Monte Carlo dose calculations for the Cyberknife stereotactic radiosurgery system.     

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

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

A virtual photon energy fluence model for Monte Carlo dose calculation

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is also useful for IMRT applications because a full Monte Carlo simulation of the treatment head would be too time-consuming for many small fields.     

Electron spectra derived from depth dose distributions

The technique of extracting electron energy spectra from measured distributions of dose along the central axis of clinical electron beams is explored in detail. Clinical spectra measured with this simple spectroscopy tool are shown to be sufficient in accuracy and resolution for use in Monte Carlo treatment planning. A set of monoenergetic depth dose curves of appropriate energy spacing, precalculated with Monte Carlo for a simple beam model, are unfolded from the measured depth dose curve. The beam model is comprised of a point electron and photon source placed in vacuum with a source-to-surface distance of 100 cm. Systematic error introduced by this model affects the calculated depth dose curve by no more than 2%/2 mm. The component of the dose due to treatment head bremsstrahlung, subtracted prior to unfolding, is estimated from the thin-target Schiff spectrum within 0.3% of the maximum total dose (from electrons and photons) on the beam axis. Optimal unfolding parameters are chosen, based on physical principles. Unfolding is done with the public-domain code FERDO. Comparisons were made to previously published spectra measured with magnetic spectroscopy and to spectra we calculated with Monte Carlo treatment head simulation. The approach gives smooth spectra with an average resolution for the 27 beams studied of 16+/-3% of the mean peak energy. The mean peak energy of the magnetic spectrometer spectra was calculated within 2% for the AECL T20 scanning beam accelerators, 3% for the Philips SL25 scattering foil based machine. The number of low energy electrons in Monte Carlo spectra is estimated by unfolding with an accuracy of 2%, relative to the total number of electrons in the beam. Central axis depth dose curves calculated from unfolded spectra are within 0.5%/0.5 mm of measured and simulated depth dose curves, except near the practical range, where 1%/1 mm errors are evident.     

A beam source model for scanned proton beams

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

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.     

A computational study into the use of polyacrylamide gel and A-150 plastic as brain tissue substitutes for boron neutron capture therapy

A precise evaluation of the dosimetric performance of epithermal neutron beams designed for boron neutron capture theory of brain tumours requires the use of a phantom material that closely matches brain tissue. The aim of this study was to investigate how well polyacrylamide gel (or PAG) and A- 150 plastic performed as substitutes for brain tissue compared with standard phantom materials such as water and polymethyl-methacrylate (or PMMA). Thermal neutron fluence, photon dose and epithermal neutron dose distributions were calculated for the epithermal neutron beam available at the University of Birmingham. The results presented in this paper show that the PAG provides a good simulation of radiation transport in the brain with differences from the real brain of +9.4%, - 10.8% and +5.1% at a depth of 50 mm for thermal neutron fluence, gamma dose and epithermal neutron dose distributions respectively. The polyacrylamide gel presented is therefore a promising substitute for brain tissue that can, as a dosimeter, provide a three-dimensional map of the absorbed dose delivered by the epithermal neutron beam. However, this study does not investigate the agreement between doses derived from magnetic resonance and physical doses for such gels. A- 150 plastic was shown to be a better substitute for brain tissue than PMMA, with differences from brain of -1.9%, -12.4% and - 13.2% at a depth of 50 mm for thermal neutron fluence, gamma dose and epithermal neutron dose distributions respectively, against +21.1%, -16.2% and +19.2% for PMMA. A-150 plastic should therefore be the material of choice for solid phantoms.     

Dynamic wedge versus physical wedge: a Monte Carlo study

The purpose of this study is to analyze the characteristics of dynamic wedges (DW) and to compare DW to physical wedges (PW) in terms of their differences in affecting beam spectra, energy fluence, angular distribution, contaminated electrons, and dose distributions. The EGS4/BEAM Monte Carlo codes were used to simulate the exact geometry of a 6 MV beam and to calculate 3-D dose distributions in phantom. The DW was simulated in accordance with the segmented treatment tables (STT). The percentage depth dose curves and beam profiles for PW, DW, and open fields were measured and used to verify the Monte Carlo simulations. The Monte Carlo results were found to agree within 2% with the measurements performed using film and ionizing chambers in a water phantom. The present EGS4 calculation reveals that the effects of a DW on beam spectral and angular distributions, as well as electron contamination, are much less significant than those for a PW. For the 6 MV photon beam, a 45 degrees PW can result in a 30% increase in mean photon energy due to the effect of beam hardening. It can also introduce a 5% dose reduction in the build-up region due to the reduction of contaminated electrons by the PW. Neither this mean-energy increase nor such dose reduction is found for a DW. Compared to a DW, a PW alters the photon-beam spectrum significantly. The dosimetric differences between a DW and a PW are significant and clearly affect the clinical use of these beams. The data presented may be useful for DW commissioning.     

Optimization of photon beam flatness for radiation therapy

In this work, we investigate the relation between lateral fluence/dose distributions and photon beam uniformity, possibly identifying ways to improve these characteristics. The calculations included treatment head scatter properties associated with three common types of linear accelerators in order to study their impact on the results. For 6 and 18 MV photon beams the lateral fluence distributions were optimized with respect to the resulting calculated flatness, as defined by the International Electrotechnical Commission (IEC), at 10 cm depth in six different field sizes. The limits proposed by IEC for maximum dose ratios ('horns') at the depth of dose maximum have also been accounted for in the optimization procedure. The conclusion was that typical head scatter variations among different types of linear accelerators have a very limited effect on the optimized results, which implies that the existing differences in measured off-axis dose distributions are related to non-equivalent optimization objectives. Finally, a comparison between the theoretically optimized lateral dose distributions and corresponding dose measurements for the three investigated accelerator types was performed. Although the measured data generally fall within the IEC requirements the optimized distributions show better results overall for the evaluated uniformity parameters, indicating that there is room for improved flatness performance in clinical photon beams.     

Application of measured pencil beam parameters for electron beam model evaluation

Most current electron beam models, as are used in commercial treatment planning systems, combine measured broad beam central axis depth dose data with measured or modeled functions to approximate radial scatter and heterogeneity effects. In this paper, we extend a recently developed pencil beam model to calculate doses outside the field edge and doses in heterogeneous media. We have also explored use of this model as a tool for evaluating commercial electron planning programs. The algorithm we have developed, based on the concept of the lateral buildup ratio (LBR), enables calculation of dose at any point in an irregular electron field, and is capable of generating both on- and off-axis depth dose curves and isodose profiles. This model includes the effects of density and mass-angular scattering power in measured broad beam central axis depth dose data, which when combined with small field reference data, can be used to generate LBR ratios. From these ratios one can infer the depth dependent, effective pencil beam radial spread parameter a in water or other materials, which can be used to model any arbitrary field. We have used this approach to calculate fractional depth doses for small fields incident on aluminum and cork, which we have then compared against measurements and the calculations of several commercial planning systems.