Benchmarking of Monte Carlo simulation of bremsstrahlung from thick targets at radiotherapy energies

Several Monte Carlo systems were benchmarked against published measurements of bremsstrahlung yield from thick targets for 10-30 MV beams. The quantity measured was photon fluence at 1 m per unit energy per incident electron (spectra), and total photon fluence, integrated over energy, per incident electron (photon yield). Results were reported at 10-30 MV on the beam axis for Al and Pb targets and at 15 MV at angles out to 90 degrees for Be, Al, and Pb targets. Beam energy was revised with improved accuracy of 0.5% using an improved energy calibration of the accelerator. Recently released versions of the Monte Carlo systems EGSNRC, GEANT4, and PENELOPE were benchmarked against the published measurements using the revised beam energies. Monte Carlo simulation was capable of calculation of photon yield in the experimental geometry to 5% out to 30 degrees, 10% at wider angles, and photon spectra to 10% at intermediate photon energies, 15% at lower energies. Accuracy of measured photon yield from 0 to 30 degrees was 5%, 1 s.d., increasing to 7% for the larger angles. EGSNRC and PENELOPE results were within 2 s.d. of the measured photon yield at all beam energies and angles, GEANT4 within 3 s.d. Photon yield at nonzero angles for angles covering conventional field sizes used in radiotherapy (out to 10 degrees), measured with an accuracy of 3%, was calculated within 1 s.d. of measurement for EGSNRC, 2 s.d. for PENELOPE and GEANT4. Calculated spectra closely matched measurement at photon energies over 5 MeV. Photon spectra near 5 MeV were underestimated by as much as 10% by all three codes. The photon spectra below 2-3 MeV for the Be and Al targets and small angles were overestimated by up to 15% when using EGSNRC and PENELOPE, 20% with GEANT4. EGSNRC results with the NIST option for the bremsstrahlung cross section were preferred over the alternative cross section available in EGSNRC and over EGS4. GEANT4 results calculated with the "low energy" physics list were more accurate than those calculated with the "standard" physics list.     

Energy and angular distributions of photons from medical linear accelerators

For accurate three-dimensional treatment planning, new models of dose calculations are being developed which require the knowledge of the energy spectra and angular distributions of the photons incident on the surface of the patient. Knowledge of the spectra is also useful in other applications, including the design of filters and beam modifying devices and determination of factors to convert ionization chamber measurements to dose. We have used Monte Carlo code (EGS) to compute photon spectra for a number of different linear accelerators. Both the target and the flattening filter have been accurately modeled. We find the mean photon energy to have a value lower than the generally perceived value of one-third the maximum energy. As expected, the spectra become softer as the distance from the central axis increases. Verification of the spectra is performed by computing dose distributions and half-value layers in water using the calculated spectra and comparing the results with measured data. We also examined the angular distributions of photons incident on the surface of the phantom. In currently used models of dose computations, it is assumed that the angular distribution of photons with respect to fan lines emanating from the source is negligible. Although the angular spread of photons with respect to the incident direction has been found to be small, its contribution to the diffuseness of the beam boundaries is significant.     

Monte Carlo feasibility study of orthogonal bremsstrahlung beams for improved radiation therapy imaging

The basic characteristics of orthogonal bremsstrahlung beams are studied and the feasibility of improved contrast imaging with such a beam is evaluated. In the context of this work, orthogonal bremsstrahlung beams represent the component of the bremsstrahlung distribution perpendicular to the electron beam impinging on an accelerator target. The BEAMnrc Monte Carlo code was used to study target characteristics, energy spectra and relative fluences of orthogonal beams to optimize target design. The reliability of the simulations was verified by comparing our results with benchmark experiments. Using the results of the Monte Carlo optimization, the targets with various materials and a collimator were designed and built. The primary pencil electron beam from the research port of a Varian Clinac-18 accelerator striking on Al, Pb and C targets was used to create orthogonal beams. For these beams, diagnostic image contrast was tested by placing simple Lucite objects in the path of the beams and comparing image contrast obtained in the orthogonal direction to the one obtained in the forward direction. The simulations for various target materials and various primary electron energies showed that a width of 80% of the continuous-slowing-down approximation range (RCSDA) is sufficient to remove electron contamination in the orthogonal direction. The photon fluence of the orthogonal beam for high Z targets is larger compared to low Z targets, i.e. by a factor of 20 for W compared to Be. For a 6 MeV electron beam, the mean energy for low Z targets is calculated to be 320 keV for Al and 150 keV for Be, and for a high Z target like Pb to be 980 keV. For irradiation times of 1.2 s in an electron mode of the linac, the contrast of diagnostic images created with orthogonal beams from the Al target is superior to that in the forward direction. The image contrast and the beam profile of the bremsstrahlung beams were also studied. Both the Monte Carlo study and experiment showed an improvement of the contrast for lower Z target materials. This study confirms the feasibility, both in terms of intensity and image contrast, of orthogonal bremsstrahlung beams for radiation therapy imaging.     

On the existence of low-energy photons (<150 keV) in the unflattened x-ray beam from an ordinary radiotherapeutic target in a medical linear accelerator

Low-energy photons (<150 keV) are essential for obtaining high quality x-ray radiographs. These photons are usually produced in the accelerator target, but are effectively absorbed by the flattening filter and, at least partially, by the target itself. Experimental proof is presented for the existence of low-energy photons in the unflattened x-ray beam produced by a 6 MeV electron beam normally incident on the thinner of the two existing ports of the all-Cu radiotherapeutic target of a Clinac 18 (Varian Associates) linear accelerator. A number of one-shot absorption measurements were carried out with 12 foils of Pb absorbers with thicknesses varying from 0.25 to 3 mm in steps of 0.25 mm arranged symmetrically around the central axis on a 7.2 cm radius circumference. A Kodak ECL film-screen-cassette combination was used as a detector in the absorption measurements, in which optical density was measured as a function of the thickness of the Pb absorbers. Two sets of absorption measurements were carried out: the first one with the Clinac 18 6 MV unflattened beam and the second one with the Clinac 600C 6 MV therapeutic counterpart beam. There is a striking difference between the two sets: the optical density versus Pb-absorber thickness curve shows a sharp increase in optical density at small absorber thicknesses in the case of the unflattened 6 MV x-ray beam as compared with a gently sloping dependence in the case of the 6 MV therapeutic beam. A semi-quantitative assessment of the low-energy photon contribution to the whole optical density/contrast is presented. A 0.85 mm thick Pb absorber intercepting the 6 MV unflattened x-ray beam eliminates almost totally the sharp peak in the optical density curve at small Pb-absorber thicknesses. This constitutes additional evidence for the existence of low-energy photons (<150 keV) in the unflattened 6 MV beam from the Cu therapeutic target.     

Compton-scattering measurement of diagnostic x-ray spectrum using high-resolution Schottky CdTe detector

The analysis of x-ray spectra is important for quality assurance (QA) and quality control (QC) of radiographic systems. The aim of this study is to measure the diagnostic x-ray spectra under clinical conditions using a high-resolution Schottky CdTe detector. Under clinical conditions, the direct measurement of a diagnostic spectrum is difficult because of the high photon fluence rates that cause significant detector photon pile-up. An alternative way of measuring the output spectra from a tube is first to measure the 90 deg Compton scattered photons from a given sample. With this set-up detector, pile-up is not a problem. From the scattered spectrum one can then use an energy correction and the Klein-Nishina function to reconstruct the actual spectrum incident upon the scattering sample. The verification of whether our spectra measured by the Compton method are accurate was accomplished by comparing exposure rates calculated from the reconstructed spectra to those measured with an ionization chamber. We used aluminum (Al) filtration ranging in thickness from 0 to 6 mm. The half value layers (HVLs) obtained for a 70 kV beam were 2.78 mm via the ionization chamber measurements and 2.93 mm via the spectral measurements. For a 100 kV beam we obtained 3.98 and 4.32 mm. The small differences in HVLs obtained by both techniques suggest that Compton scatter spectroscopy with a Schottky CdTe detector is suitable for measuring the diagnostic x-ray spectra and useful for QA and QC of clinical x-ray equipment.     

Characteristics of kilovoltage x-ray beams used for cone-beam computed tomography in radiation therapy

The purpose of this investigation is to characterize the beams produced by a kilovoltage (kV) imager integrated into a linear accelerator (Varian on-board imager integrated into the Trilogy accelerator) for acquiring high resolution volumetric cone-beam computed tomography (CBCT) images of the patient on the treatment table. The x-ray tube is capable of generating photon spectra with kVp values between 40 and 125 kV. The Monte Carlo simulations were used to study the characteristics of kV beams and the properties of imaged target scatters. The Monte Carlo results were benchmarked against measurements, and excellent agreements were obtained. We also studied the effect of including the electron impact ionization (EII), and the simulation showed that the characteristic radiation is increased significantly in the energy spectra when EII is included. Although only slight beam hardening is observed in the spectra of all photons after passing through the phantom target, there is a significant difference in the spectra and angular distributions between scattered and primary photons. The results also show that the photon fluence distributions are significantly altered by adding bow tie filters. The results indicate that a combination of large cone-beam field size and large imaged target significantly increases scatter-to-primary ratios for photons that reach the detector panel. For phantoms 10 cm, 20 cm and 30 cm thick of water placed at the isocentre, the scatter-to-primary ratios are 0.94, 3.0 and 7.6 respectively for an open 125 kVp CBCT beam. The Monte Carlo simulations show that the increase of the scatter is proportional to the increase of the imaged volume, and this also applies to scatter-to-primary ratios. This study shows both the magnitude and the characteristics of scattered x-rays. The knowledge obtained from this investigation may be useful in the future design of the image detector to improve the image quality.     

Magnetic collimation and metal foil filtering for electron range and fluence modulation

We investigated the use of magnetically collimated electron beams together with metal filters for electron fluence and range modulation. A longitudinal magnetic field collimation method was developed to reduce skin dose and to improve the electron beam penumbra. Thin metal foils were used to adjust the energies of magnetically collimated electrons. The effects for different types of foils such as Al, Be, Cu, Pb, and Ti were studied using Monte Carlo calculations. An empirical pencil beam dose calculation model was developed to calculate electron dose distributions under magnetic collimation and foil modulation. An optimization method was developed to produce conformal dose distributions for simulated targets such as a horseshoe-shaped target. Our results show that it is possible to produce an electron depth dose enhancement peak using similar techniques of producing a spread-out Bragg peak. In conclusion, our study demonstrates new aspects of using magnetic collimation and foil filtration for producing fluence and range modulated electron dose distributions.     

Inhomogeneity corrections in electron-beam dose planning. Limitations with the semi-infinite slab approximation

An investigation was made of the limitations of the semi-infinite slab approximation used in pencil-beam models for electron-beam dose planning. Comparison of measured and calculated dose distributions were made for one-, two- and three-dimensional air inhomogeneities in water. The two- and three-dimensional air cavities were cylindrical with the axis parallel to the incident beam. The radii of the cavities were between 11 and 46 mm and the incident electron energies between 10 and 20 MeV. The measurements were made with a silicon diode. In the calculations the semi-infinite slab approximation was applied to a Gaussian model of the beam and to a generalised Gaussian model. The latter also takes large-angle single scattering into account. By using an absorber in front of the cavity the different fluence contributions to the central axis dose could be measured separately. The result shows that a doubling of the dose may be obtained along the central axis for narrow deep cavities. The dose contribution from the electron transport into the cavity from the cylindrical wall is shown to be underestimated by the semi-infinite slab approximation. This is shown to give large errors especially at depths where the angular distribution of the electrons is large and the electrons have a long drift space in air.     

Electron beam modeling and commissioning for Monte Carlo treatment planning

A hybrid approach for commissioning electron beam Monte Carlo treatment planning systems has been studied. The approach is based on the assumption that accelerators of the same type have very similar electron beam characteristics and the major difference comes from the on-site tuning of the electron incident energy at the exit window. For one type of accelerator, a reference machine can be selected and simulated with the Monte Carlo method. A multiple source model can be built on the full Monte Carlo simulation of the reference beam. When commissioning electron beams from other accelerators of the same type, the energy spectra in the source model are tuned to match the measured dose distributions. A Varian Clinac 2100C accelerator was chosen as the reference machine and a four-source beam model was established based on the Monte Carlo simulations. This simplified beam model can be used to generate Monte Carlo dose distributions accurately (within 2%/2 mm compared to those calculated with full phase space data) for electron beams from the reference machine with various nominal energies, applicator sizes, and SSDs. Three electron beams were commissioned by adjusting the energy spectra in the source model. The dose distributions calculated with the adjusted source model were compared with the dose distributions calculated using the phase space data for these beams. The agreement is within 1% in most of cases and 2% in all situations. This preliminary study has shown the capability of the commissioning approach for handling large variation in the electron incident energy. The possibility of making the approach more versatile is also discussed.     

A silicon diode in a thimble-type mount for measurement of diagnostic x-ray spectra

A silicon detector which can be used like a thimble chamber has been constructed. The silicon diode chip used here is very small (1.7 x 1.7 x 0.1 mm3), and the construction materials of the detector mount are thin and have low atomic numbers. Thus, the characteristic x-rays from the mount give no distortion on the obtained spectra, and the photons incident on the back surface of the silicon chip can be measured. Furthermore, the perturbation of the x-ray field is small. The energy resolution of the detector is 2.0 keV (full width at half maximum) for 59.5 keV photons at room temperature. Bremsstrahlung spectra (60-100 kV, 1-2 mA) have been measured without using a pinhole collimator; the obtained spectra are in good agreement with those obtained with a Ge detector. The spectrum of the radiation in a water phantom irradiated with 90 kV x-rays has also been measured by inserting the detector in the phantom; the obtained scattered spectrum has been corrected for the angular dependence of detector efficiency. The increase in total photon number due to this correction has been found to be below 2%.     

Resolution at oblique incidence angles of a flat panel imager for breast tomosynthesis

Oblique incidence of x rays on an imaging detector causes blurring that reduces spatial resolution. For simple projection imaging this effect is small and often ignored. However, for breast tomosynthesis, the incidence angle can be larger (>20 degrees), leading to increased blur for some of the projections. The modulation transfer function (MTF) is measured for a typical phosphor-coupled flat-panel detector versus angular incidence of the x-ray beam for two x-ray spectra: 26 kV Mo/Mo and 40 kV Rh/Al. At an incidence angle of 40 degrees the MTF at 5 mm(-1) falls by 35% and 40% for each spectrum, respectively (and 65%/80% at 8 mm(-1)). Increasing the detector absorber thickness to achieve improved quantum efficiency will cause the blurring effect due to beam obliquity to become greater. The impact of this blur is likely to cause misregistration and increased relative noise in tomosynthesis reconstructed images.     

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.     

On the significance of very small angle scattered radiation to radiographic imaging at low energies

We have studied the angular distribution of scattered radiation at low energies for angles between 2 degrees and 15 degrees from the outward normal to the exit surface of several phantoms, with 1 degree resolution. A cryogenically cooled germanium detector was used to measure the spectra of the scattered radiation. The differential scattering fluences, or numbers of photons per unit solid angle per unit surface area, exhibit distinct peaks at angles in the vicinity of 5 degrees, with the angular position being only slightly energy dependent but very material dependent. The scattered spectra show large changes as a function of angle, in some cases actually becoming harder than the exit unscattered beam. The significance of this behavior relative to the imaging of targets in mammography examinations is discussed.     

Monte Carlo studies of the exit photon spectra and dose to a metal/phosphor portal imaging screen

The energy spectra and the dose to a Cu plate/Gd2O2S phosphor portal imaging detector were investigated for monoenergetic incident beams of photons (1.25, 2, and 5 MeV). The Monte Carlo method was used to characterize the influence of the patient/detector geometry, detector material and design, and incident beam energy on the spectral distribution and the dose, at the imaging detector plane, of a photon beam scattered from a water phantom. The results show that radiation equilibrium is lost in the air gap and that, for the geometries studied, this effect led to a reduction in the exit dose of up to 40%. The finding that the effects of the air gap and field size are roughly complementary has led to the hypothesis that an equivalent field size concept may be used to account for intensity and spectral changes arising from air gap variations. The copper plate preferentially attenuates the low-energy scattered photons incident on it, while producing additional annihilation, bremsstrahlung, and scattered photons. As a result, the scatter spectra at the copper surface entrance of the detector differs significantly from that at the Cu/phosphor interface. In addition, the mean scattered photon energy at the interface was observed to be roughly 0.4 MeV higher than the corresponding effective energy for 2 MeV incident beams. A comparison of the dose to various detector materials showed that exit dosimetry errors of up to 24% will occur if it is assumed that the Cu plate/Gd2O2S phosphor detector is water equivalent.     

Measurement of diagnostic x-ray spectra using a silicon photodiode

Diagnostic x-ray spectra (66-103 kV, 1-2 mA) were measured without pinhole collimator or liquid nitrogen cooling by using a silicon p-i-n photodiode. An x-ray count rate was low (approximately 400 photons/s) at distances of 2-3 m away from an x-ray target, because the i layer of the photodiode was very small (1.5 mm2 in area and 75 microns in thickness). The junction reverse current of the photodiode was 50-70 pA at room temperature and energy resolution for 59.5-keV gamma rays was 2.0 keV (full width at half-maximum), which was limited by the electric noise of a preamplifier. Measured spectra were corrected for detector distortion. The corrected spectra were similar to those determined with a Ge detector. The i-layer thickness of the photodiode was an important parameter for the correction. In particular, when the thickness was thin, the fraction of photoelectron escape became large; this fraction was estimated analytically for various i-layer thicknesses. The angular dependence of the full-energy peak efficiency was measured; for the photons whose energies were above 17.8 keV the angular dependence was isotropic except for angles greater than 60 degrees off the photodiode axis. This method is therefore applicable to the measurement of scattered x rays.     

Feasibility study on epithermal neutron field for cyclotron-based boron neutron capture therapy

To realize the accelerator-based boron neutron capture therapy (BNCT) at the Cyclotron and Radioisotope Center of Tohoku University, the feasibility of a cyclotron-based BNCT was evaluated. This study focuses on optimizing the epithermal neutron field with an energy spectrum and intensity suitable for BNCT for various combinations of neutron-producing reactions and moderator materials. Neutrons emitted at 90 degrees from a thick (stopping-length) Ta target, bombarded by 50 MeV protons of 300 microA beam current, were selected as a neutron source, based on the measurement of angular distributions and neutron energy spectra. As assembly composed of iron, AlF3/Al/6LiF, and lead was chosen as moderators, based on the simulation trials using the MCNPX code. The depth dose distributions in a cylindrical phantom, calculated with the MCNPX code, showed that, within 1 h of therapeutic time, the best moderator assembly, which is 30-cm-thick iron, 39-cm-thick AlF3/Al/6LiF, and 1-cm-thick lead, provides an epithermal neutron flux of 0.7 x 10(9) [n cm(-2) s(-1)]. This results in a tumor dose of 20.9 Gy-eq at a depth of 8 cm in the phantom, which is 6.4 Gy-eq higher than that of the Brookhaven Medical Research Reactor at the equivalent condition of maximum normal tissue tolerance. The beam power of the cyclotron is 15 kW, which is much lower than other accelerator-based BNCT proposals.     

Slit x-ray beam primary dose profiles determined by analytical transport of Compton recoil electrons

Accurate measurement of radiation beam penumbras is essential for conformal radiotherapy. For this purpose a detailed knowledge of the dosimeter's spatial response is required. However, experimental determination of detector spatial response is cumbersome and restricted to the specific detector type and beam spectrum used. A model has therefore been developed to calculate in slit beam geometry both dose profiles and detector response profiles. Summations over representative photon beam spectra yield profiles for polyenergetic beams. In the present study the model is described and resulting dose profiles verified. The model combines Compton scattering of incident photons, transport of resulting electrons by Fermi-Eyges small-angle multiple scattering theory, and functions to limit electron transport. This analytic model thus yields line spread kernels of primary dose in a water phantom. It is shown that the spatial response of an ideal point detector to a primary photon beam can be well described by the model; the calculations are verified by measurements with a diamond detector in a telescopic slit geometry in which all dose contributions except for the primary dose can be excluded. Effects of photon detector behavior, source size of the linear accelerator (linac) and detector size are studied. Measurements show that slit dose profiles calculated by means of the kernel are accurate within 0.1 mm of the full-width at half-maximum. For a theoretical point source and point detector combined with a 0.2 mm wide slit, the full-width half-maximum values of the slit beam dose profiles are calculated as 0.37 mm and 0.42 mm in a 6 MV and 25 MV x-ray beam, respectively. The present study shows that the model is adequate to calculate local dose effects that are dominated by approximately mono-directional, primary photon fluence. The analytic model further provides directional electron fluence information and is designed to be applied to various detectors and linac beam spectra.     

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.     

Total skin electron therapy treatment verification: Monte Carlo simulation and beam characteristics of large non-standard electron fields

Total skin electron therapy (TSET) is a complex technique which requires non-standard measurements and dosimetric procedures. This paper investigates an essential first step towards TSET Monte Carlo (MC) verification. The non-standard 6 MeV 40 x 40 cm2 electron beam at a source to surface distance (SSD) of 100 cm as well as its horizontal projection behind a polymethylmethacrylate (PMMA) screen to SSD = 380 cm were evaluated. The EGS4 OMEGA-BEAM code package running on a Linux home made 47 PCs cluster was used for the MC simulations. Percentage depth-dose curves and profiles were calculated and measured experimentally for the 40 x 40 cm2 field at both SSD = 100 cm and patient surface SSD = 380 cm. The output factor (OF) between the reference 40 x 40 cm2 open field and its horizontal projection as TSET beam at SSD = 380 cm was also measured for comparison with MC results. The accuracy of the simulated beam was validated by the good agreement to within 2% between measured relative dose distributions, including the beam characteristic parameters (R50, R80, R100, Rp, E0) and the MC calculated results. The energy spectrum, fluence and angular distribution at different stages of the beam (at SSD = 100 cm, at SSD = 364.2 cm, behind the PMMA beam spoiler screen and at treatment surface SSD = 380 cm) were derived from MC simulations. Results showed a final decrease in mean energy of almost 56% from the exit window to the treatment surface. A broader angular distribution (FWHM of the angular distribution increased from 13 degrees at SSD = 100 cm to more than 30 degrees at the treatment surface) was fully attributable to the PMMA beam spoiler screen. OF calculations and measurements agreed to less than 1%. The effect of changing the electron energy cut-off from 0.7 MeV to 0.521 MeV and air density fluctuations in the bunker which could affect the MC results were shown to have a negligible impact on the beam fluence distributions. Results proved the applicability of using MC as a treatment verification tool for complex radiotherapy techniques.     

Application of the electron pencil beam redefinition algorithm to electron arc therapy

This project investigated the potential of summing fixed-beam dose distributions calculated using the pencil-beam redefinition algorithm (PBRA) at small angular steps (1 degree) to model an electron arc therapy beam. The PRBA, previously modified to model skin collimation, was modified further by incorporating two correction factors. One correction factor that is energy, SSD (source-to-surface distance), and field-width dependent constrained the calculated dose output to be the same as the measured dose output for fixed-beam geometries within the range of field widths and SSDs encountered in arc therapy. Another correction factor (single field-width correction factor for each energy) compensated for large-angle scattering not being modeled, allowing a more accurate calculation of dose output at mid arc. The PBRA was commissioned to accurately calculate dose in a water phantom for fixed-beam geometries typical of electron arc therapy. Calculated central-axis depth doses agreed with measured doses to within 2% in the low-dose gradient regions and within 1-mm in the high-dose gradient regions. Off-axis doses agreed to within 2 mm in the high-dose gradient regions and within 3% in the low-dose gradient regions. Arced-beam calculations of dose output and depth dose at mid arc were evaluated by comparing to data measured using two cylindrical water phantoms with radii of 12 and 15 cm at 10 and 15 MeV. Dose output was measured for all combinations of phantom radii of curvature, collimator widths (4, 5, and 6 cm), and arc angles (0 degrees, 20 degrees, 40 degrees, 60 degrees, 80 degrees, and 90 degrees) for both beam energies. Results showed the calculated mid-arc dose output to agree within 2% of measurement for all combinations. For a 90 degree arc angle and 5 x 20 cm2 field size, the calculated mid-arc depth dose in the low-dose gradient region agreed to within 2% of measurement for all depths at 10 MeV and for depths greater than depth of dose maximum R100 at 15 MeV. For depths in the buildup region at 15 MeV the calculations overestimated the measured dose by as much as 3.4%. Mid-arc depth dose in the high-dose gradient region agreed to within 2.2 mm of measured dose. Calculated two-dimensional relative dose distributions in the plane of rotation were compared to dose measurements using film in a cylindrical polystyrene phantom for a 90 degree arc angle and field widths of 4, 5, and 6 cm at 10 and 15 MeV. Results showed that off-axis dose at the ends of arc (without skin collimation) agreed to within 2% in the low-dose gradient region and to within 1.2 mm in the high-dose gradient region. This work showed that the accuracy of the PBRA arced-beam dose model met the criteria specified by Van Dyk et al. [Int. J. Radiat. Oncol. Biol. Phys. 26, 261-273 (1993)] with the exception of the buildup region of the 15 MeV beam. Based on the present results, results of a previous study showing acceptable accuracy in the presence of skin collimation, and results of a previous study showing acceptable accuracy in the presence of internal heterogeneities, it is concluded that the PBRA arced-beam dose model should be adequate for planning electron arc therapy.