On the initial angular variances of clinical electron beams

Electron beam radiotherapy treatment planning systems need to be fed with the characteristics of the high-energy electron beams (4-50 MeV) from the specifically applied accelerator. Beams can be characterized by their mean initial energy, effective initial angular variance, virtual source position and the resulting central axis depth dose distribution in water. This information is the only input to pencil beam dose calculation models. Newer calculation models like macro Monte Carlo, voxel Monte Carlo and phase space evolution require as input the full initial phase space or a parametrization of that initial phase space, generally consisting of a primary beam component and one or more scatter components. This primary beam component is often characterized by initial energy, primary beam initial angular variance and virtual source distance. The purpose of the present investigation was to investigate to what extent standard values can be used both for the effective initial angular variance as input to pencil beam models and for the primary beam initial angular variance. Comprehensive benchmark data were obtained on the initial angular variance of various types of accelerator, for various energies and field sizes. The initial angular variance sigma2theta(x) has been derived from penumbra measurements in air by means of film dosimetry at various distances from the lower collimator. For the types of accelerator used in radiotherapy nowadays the measurements show values for sigma2theta(x)/T(E) of around 13 cm where T(E) is the ICRU-35 linear angular scattering power in air. This value can be chosen as standard value for the primary beam initial angular variance, only slightly compromising the dose calculation accuracy. As input to pencil beam models, an effective sigma2theta(x)/T(E) should be used incorporating the scatter from the lower collimator. For the case that the air gaps between lower collimator and patient are small (5-10 cm) an effective sigma2theata(x)/T(E) of 20 cm has been found and is recommended as the standard input for pencil beam models. Of the accelerators investigated, a different value was found only for the Elekta SL15, i.e. 50% higher for the effective sigma2theta(x)/T(E).     

The effect of angular spread on the intensity distribution of arbitrarily shaped electron beams

Knowledge of the relative intensity distribution at the patient's surface is essential for pencil beam calculations of three-dimensional dose distributions for arbitrarily shaped electron beams. To calculate the relative intensity distribution, the spatial spread resulting from angular spread is convolved with a two-dimensional step function whose shape corresponds to the applicator aperture. Two different approaches to obtain angular spread or the equivalent spatial spread are investigated. In the first method, the pencil beam angular spread is assumed to be Gaussian in shape. The angular spread constants (sigma theta) are then obtained from the slopes of measured intensity profiles. In the second method, the angular spread, in the form of an array of numerical values, is obtained by the deconvolution of measured intensity profiles. After obtaining the angular spread, the calculation for convolution is done in a number of parallel planes normal to the central axis at various distances from the electron collimator. Intensity at any arbitrary point in space is computed by interpolating between intensity distributions in adjacent planes on either side of the point. The effects of variations in angular spread as a function of field size for two treatment machines, one with a scanned electron beam and the other with a scattering foil, have been studied. The consequences of assuming angular spread to be of Gaussian shape are also examined. The electron intensity calculation techniques described in this paper apply primarily to methods of dose calculations that employ pencil beams generated using Monte Carlo simulations.     

Collimated electron beams and their associated penumbra widths

The Fermi-Eyges multiple-scattering theory for electrons is applied to calculate profiles of collimated electron beams. The dose profile below the collimator is a convolution of the intensity distribution of the electrons at the level of the collimator and the distribution arising from the propagation of a Gaussian point source from the collimator to the level of the calculation. The electrons at the level of the collimator possess an angular distribution characteristic of the configuration of the electron beam at the vacuum window. Hence, the dose profile and its associated penumbra width can be expressed in terms of the angular moments of the distribution of the electrons at the collimator. The dependence of the penumbra width on the configuration-dependent angular spread of the electrons at the collimator accounts for differences in the size of the penumbra between two broad-beam configurations. These differences are also seen experimentally. We have also studied the dependence of the angular moments of the electrons upon scattering foils present above the collimator and the position of the beam-broadening device in the accelerator head.     

Determination of three parameters describing the uncollimated electron beam in air

The parameters that describe the electron dose distribution phi (r, theta, z) produced in air by an uncollimated clinical electron beam are accurately determined. For the determination of these parameters the multiple scattering theory of Fermi is assumed. A new method which determines the angular variance at the phantom surface is introduced and the results appear to be in good agreement with the multiple scattering theory. Knowledge of the values of these parameters is essential for a numerical determination of the dose distribution in air and in the patient.     

Electron beam characteristics of the 50-MeV racetrack microtron.

Electron beams in the MM50 racetrack microtron are generated by computer controlled scanning of a well-focused electron pencil beam. The treatment head is optimized to give a minimum of scatter between the source position and the collimator plane by a general minimization of all scattering material in the beam and by replacement of the air in the treatment head by helium, which has a much lower linear scattering power than air. A double-focused multileaf collimator with a 31-cm collimator to patient distance is used both for electron and photon collimation. In general, no extra electron collimation is needed for the standard SSD of 100 cm. To make irregular field collimation at a distance this far from the patient possible, a number of requirements have to be fulfilled regarding the virtual source position and the spatial and angular distribution of the initial electron beam. The virtual source position has been found to be at a fixed position for different irradiation parameters. This is important for the use of the light field in electron beam treatment but also for achieving a high degree of accuracy in the dosimetry. Scatter from the multileaf collimator has not been found to give any significant contribution to the radiation field or to the monitor output factor of the MM50. Experimental dose distribution data on the MM50 have been compared to data both from other types of treatment units and to Monte Carlo simulations.     

The mass angular scattering power method for determining the kinetic energies of clinical electron beams.

A method for determining the kinetic energy of clinical electron beams is described. The method is based on the measurement in air of the spatial spread of a pencil electron beam which is produced from the broad clinical electron beam. As predicted by the Fermi-Eyges theory, the dose distribution measured in air on a plane, perpendicular to the incident direction of the initial pencil electron beam, is Gaussian. The square of its spatial spread is related to the mass angular scattering power which in turn is related to the kinetic energy of the electron beam. The measured spatial spread may thus be used to determine the mass angular scattering power, which is then used to determine the kinetic energy of the electron beam from the known relationship between mass angular scattering power and kinetic energy. Energies obtained with the mass angular scattering power method agree with those obtained with the electron range method. The angular scattering power method is relatively cumbersome, but allows us to determine the kinetic energies of electron beams from first principles, in contrast to the empirical methods based on range measurements in water.     

Electron contamination from different materials in high energy photon beams

Relative lateral electron surface dose distributions from filters and air in high energy photon beams were determined using the Fermi-Eyges theory of multiple scattering. The model includes transmission and angular scattering in materials and in air. Backscatter from the phantom was also estimated. The variation of surface dose with different parameters such as atomic number, thickness and position of material, field size and photon energy was investigated. The calculated data show good agreement with experiment. For 60Co gamma rays, electron filters of medium atomic number give the lowest surface dose, whereas for higher energies a low to medium atomic number material should be used, especially for short material-phantom distances and large field sizes. The contribution to surface dose can be reduced by over 30% by placing a thin foil of high atomic number after a low to medium atomic number filter, thus scattering some electrons from the beam. For 60Co gamma rays the air is often the dominant source of contaminating electrons because of high multiple scatter loss at this energy, while for higher photon energies the beam flattening filter is the main electron source because of the small emission angle of the electrons and the small scattering power at high energies.     

The impact of MLC transmitted radiation on EPID dosimetry for dynamic MLC beams

The purpose of this study was to experimentally quantify the change in response of an amorphous silicon (a-Si) electronic portal imaging device (EPID) to dynamic multileaf collimator (dMLC) beams with varying MLC-transmitted dose components and incorporate the response into a commercial treatment planning system (TPS) EPID prediction model. A combination of uniform intensity dMLC beams and static beams were designed to quantify the effect of MLC transmission on EPID response at the central axis of 10 x 10 cm2 beams, at off-axis positions using wide dMLC beam profiles, and at different field sizes. The EPID response to MLC transmitted radiation was 0.79 +/- 0.02 of the response to open beam radiation at the central axis of a 10 x 10 cm2 field. The EPID response to MLC transmitted radiation was further reduced relative to the open beam response with off-axis distance. The EPID response was more sensitive to field size changes for MLC transmitted radiation compared to open beam radiation by a factor of up to 1.17 at large field sizes. The results were used to create EPID response correction factors as a function of the fraction of MLC transmitted radiation, off-axis distance, and field size. Software was developed to apply the correction factors to each pixel in the TPS predicted EPID image. The corrected images agreed more closely with the measured EPID images in areas of intensity modulated fields with a large fraction of MLC transmission and, as a result the accuracy of portal dosimetry with a-Si EPIDs can be improved. Further investigation into the detector response function and the radiation source model are required to achieve improvements in accuracy for the general case.     

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.     

Description of the uncollimated electron beam in air by means of a directional pencil beam model

The dose distribution of an uncollimated electron beam in air, described by phi(theta x, x, z), is shown to be mathematically equivalent to a directional pencil beam model. In this model the multiple scattering theory of Fermi is assumed. After implementation of the model by using a computer program, dose distributions of electron fields of various shapes were calculated and compared with dose distributions obtained by experiment. In general, the distributions appear to agree well, but in some situations noticeable differences can be observed, which is probably due to the fact that large-angle scattered electrons are not considered in this model.     

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.     

A restricted angular scattering model for electron penetration in dense media

A restricted angular scattering model for electron penetration in dense media is presented. In the model, the Fermi-Eyges transport equation is modified through the addition of an extra term which may be interpreted as representing an apparent force opposing the scattering of electrons into wider angles. The introduction of this extra term allows the modeling of the measured saturation in the mean square angular spread of electrons with depth. The restricted scattering model retains the Gaussian features of the Fermi-Eyges model and, therefore, may be readily incorporated into existing dose computation algorithms. Good agreement is obtained with measured angular electron distribution data for a point monodirectional beam over a wide range of incident electron energies (5-20 MeV) and scattering media (atomic numbers of 6 to 82). Also, a comparison of the restricted scattering model predictions with measurements of the lateral pencil beam spread shows an improvement over the predictions of Fermi-Eyges model close to the end of the electron range. Broad beam profiles were generated using both the Fermi-Eyges and restricted scattering models. A comparison of predicted and measured beam profiles shows that the restricted scattering model is a significant improvement over the Fermi-Eyges model for the prediction of beam penumbra shape in homogeneous media.     

Dual scattering foil design for poly-energetic electron beams

The laser wakefield acceleration (LWFA) mechanism can accelerate electrons to energies within the 6-20 MeV range desired for therapy application. However, the energy spectrum of LWFA-generated electrons is broad, on the order of tens of MeV. Using existing laser technology, the therapeutic beam might require a significant energy spread to achieve clinically acceptable dose rates. The purpose of this work was to test the assumption that a scattering foil system designed for a mono-energetic beam would be suitable for a poly-energetic beam with a significant energy spread. Dual scattering foil systems were designed for mono-energetic beams using an existing analytical formalism based on Gaussian multiple-Coulomb scattering theory. The design criterion was to create a flat beam that would be suitable for fields up to 25 x 25 cm2 at 100 cm from the primary scattering foil. Radial planar fluence profiles for poly-energetic beams with energy spreads ranging from 0.5 MeV to 6.5 MeV were calculated using two methods: (a) analytically by summing beam profiles for a range of mono-energetic beams through the scattering foil system, and (b) by Monte Carlo using the EGS/BEAM code. The analytic calculations facilitated fine adjustments to the foil design, and the Monte Carlo calculations enabled us to verify the results of the analytic calculation and to determine the phase-space characteristics of the broadened beam. Results showed that the flatness of the scattered beam is fairly insensitive to the width of the input energy spectrum. Also, results showed that dose calculated by the analytical and Monte Carlo methods agreed very well in the central portion of the beam. Outside the useable field area, the differences between the analytical and Monte Carlo results were small but significant, possibly due to the small angle approximation. However, these did not affect the conclusion that a scattering foil system designed for a mono-energetic beam will be suitable for a poly-energetic beam with the same central energy. Further studies of the dosimetric properties of LWFA-generated electron beams will be done using Monte Carlo methods.     

Measurements of dose distributions in small beams of 6 MV x-rays

Dose distributions produced by small circular beams of 6 MV x-rays have been measured using ionisation chambers of small active volume. Specific quantities measured include tissue maximum ratios (TMR), total scatter correction factors (St), collimator scatter correction factors (Sc) and off-axis ratios (OAR). Field sizes ranged from 12.5 to 30 mm diameter, and were defined by machined auxiliary collimators with the movable jaws set for a 4 cm x 4 cm field size. Due to the lack of complete lateral electronic equilibrium for these small fields, the accuracy of the measurements was also investigated. This was accomplished by studying dose response as a function of detector size. Uncertainties of 2.5% were observed for the central axis dose in the 12.5 mm field when measuring with an ionisation chamber with a diameter of 3.5 mm. The total scatter correction factor exhibits a strong field size dependence for fields below 20 mm diameter, while the collimator scatter correction factor is constant and is defined by the setting of the movable jaws. Off-axis ratio measurements show larger dose gradients at the beam edges than those achieved with conventional collimator systems. Corrected profiles measured with an ionisation chamber are compared with measurements made with photographic film and LiF thermoluminescent dosemeters.     

Dose properties of x-ray beams produced by laser-wakefield-accelerated electrons

Given that laser wakefield acceleration (LWFA) has been demonstrated experimentally to accelerate electron beams to energies beyond 25 MeV, it is reasonable to assess the ability of existing LWFA technology to compete with conventional radiofrequency linear accelerators in producing electron and x-ray beams for external-beam radiotherapy. We present calculations of the dose distributions (off-axis dose profiles and central-axis depth dose) and dose rates of x-ray beams that can be produced from electron beams that are generated using state-of-the-art LWFA. Subsets of an LWFA electron energy distribution were propagated through the treatment head elements (presuming an existing design for an x-ray production target and flattening filter) implemented within the EGSnrc Monte Carlo code. Three x-ray energy configurations (6 MV, 10 MV and 18 MV) were studied, and the energy width deltaE of the electron-beam subsets varied from 0.5 MeV to 12.5 MeV. As deltaE increased from 0.5 MeV to 4.5 MeV, we found that the off-axis and central-axis dose profiles for x-rays were minimally affected (to within about 3%), a result slightly different from prior calculations of electron beams broadened by scattering foils. For deltaE of the order of 12 MeV, the effect on the off-axis profile was of the order of 10%, but the central-axis depth dose was affected by less than 2% for depths in excess of about 5 cm beyond d(max). Although increasing deltaE beyond 6.5 MeV increased the dose rate at d(max) by more than 10 times, the absolute dose rates were about 3 orders of magnitude below those observed for LWFA-based electron beams at comparable energies. For a practical LWFA-based x-ray device, the beam current must be increased by about 4-5 orders of magnitude.     

Photon beam characterization and modelling for Monte Carlo treatment planning

Photon beams of 4, 6 and 15 MV from Varian Clinac 2100C and 2300C/D accelerators were simulated using the EGS4/BEAM code system. The accelerators were modelled as a combination of component modules (CMs) consisting of a target, primary collimator, exit window, flattening filter, monitor chamber, secondary collimator, ring collimator, photon jaws and protection window. A full phase space file was scored directly above the upper photon jaws and analysed using beam data processing software, BEAMDP, to derive the beam characteristics, such as planar fluence, angular distribution, energy spectrum and the fractional contributions of each individual CM. A multiple-source model has been further developed to reconstruct the original phase space. Separate sources were created with accurate source intensity, energy, fluence and angular distributions for the target, primary collimator and flattening filter. Good agreement (within 2%) between the Monte Carlo calculations with the source model and those with the original phase space was achieved in the dose distributions for field sizes of 4 cm x 4 cm to 40 cm x 40 cm at source surface distances (SSDs) of 80-120 cm. The dose distributions in lung and bone heterogeneous phantoms have also been found to be in good agreement (within 2%) for 4, 6 and 15 MV photon beams for various field sizes between the Monte Carlo calculations with the source model and those with the original phase space.     

Energy- and intensity-modulated electron beams for radiotherapy

This work investigates the feasibility of optimizing energy- and intensity-modulated electron beams for radiation therapy. A multileaf collimator (MLC) specially designed for modulated electron radiotherapy (MERT) was investigated both experimentally and by Monte Carlo simulations. An inverse-planning system based on Monte Carlo dose calculations was developed to optimize electron beam energy and intensity to achieve dose conformity for target volumes near the surface. The results showed that an MLC with 5 mm leaf widths could produce complex field shapes for MERT. Electron intra- and inter-leaf leakage had negligible effects on the dose distributions delivered with the MLC, even at shallow depths. Focused leaf ends reduced the electron scattering contributions to the dose compared with straight leaf ends. As anticipated, moving the MLC position toward the patient surface reduced the penumbra significantly. There were significant differences in the beamlet distributions calculated by an analytic 3-D pencil beam algorithm and the Monte Carlo method. The Monte Carlo calculated beamlet distributions were essential to the accuracy of the MERT dose distribution in cases involving large air gaps, oblique incidence and heterogeneous treatment targets (at the tissue-bone and bone-lung interfaces). To demonstrate the potential of MERT for target dose coverage and normal tissue sparing for treatment of superficial targets, treatment plans for a hypothetical treatment were compared using photon beams and MERT.     

Design and evaluation of a variable aperture collimator for conformal radiotherapy of small animals using a microCT scanner

Treatment of small animals with radiation has in general been limited to planar fields shaped with lead blocks, complicating spatial localization of dose and treatment of deep-seated targets. In order to advance laboratory radiotherapy toward what is accomplished in the clinic, we have constructed a variable aperture collimator for use in shaping the beam of microCT scanner. This unit can image small animal subjects at high resolution, and is capable of delivering therapeutic doses in reasonable exposure times. The proposed collimator consists of two stages, each containing six trapezoidal brass blocks that move along a frame in a manner similar to a camera iris producing a hexagonal aperture of variable size. The two stages are offset by 30 degrees and adjusted for the divergence of the x-ray beam so as to produce a dodecagonal profile at isocenter. Slotted rotating driving plates are used to apply force to pins in the collimator blocks and effect collimator motion. This device has been investigated through both simulation and measurement. The collimator aperture size varied from 0 to 8.5 cm as the driving plate angle increased from 0 to 41 degrees. The torque required to adjust the collimator varied from 0.5 to 5 N x m, increasing with increasing driving plate angle. The transmission profiles produced by the scanner at isocenter exhibited a penumbra of approximately 10% of the collimator aperture width. Misalignment between the collimator assembly and the x-ray source could be identified on the transmission images and corrected by adjustment of the collimator location. This variable aperture collimator technology is therefore a feasible and flexible solution for adjustable shaping of radiation beams for use in small animal radiotherapy as well as other applications in which beam shaping is desired.     

Collimator scatter in modeling radiation beam profiles

In computer dose calculations using scatter-air ratio sector summation algorithms, the primary dose from the target to points away from the central axis of a beam is computed using an exponential intensity model of the source and a transmission parameter for the collimator. This model works well inside the beam and near edges but is inaccurate outside the beam at distances of more than 1-2 cm from beam edges. We have modified the standard beam profile model to include a dose contribution representing photon radiation scattered from the collimators. Collimator edges are treated mathematically as line sources and an adjustable parameter is introduced which represents the activity per unit length of the collimator edges. Dose from the collimator edges is assumed to decrease purely geometrically as the inverse of the square of the distance and no modification is made for tissue attenuation. With these assumptions, the total collimator scatter dose to a point is most accurately computed by a line integral over the edges of the beam outline. This modification fits naturally into the standard scatter-air ratio sector summation computer algorithm but adds significantly to dose computation time. Some approximations eliminate the line integration and lead to a collimator scatter term which is proportional to field perimeter and independent of off-axis distance. The modified dose model was tested by comparing measured dose profiles with computed ones using x-ray beams from Philips (6 and 15 MV) and Varian (4 and 6 MV) accelerators. There was significant improvement in fit compared to the standard beam model for points outside the radiation beam.