Comparison of measured electron energy spectra for six matched, radiotherapy accelerators

Abstract This study compares energy spectra of the multiple electron beams of individual radiotherapy machines, as well as the sets of spectra across multiple matched machines. Also, energy spectrum metrics are compared with central‐axis percent depth‐dose (PDD) metrics. Methods A lightweight, permanent magnet spectrometer was used to measure energy spectra for seven electron beams (7–20 MeV) on six matched Elekta Infinity accelerators with the MLCi2 treatment head. PDD measurements in the distal falloff region provided R 50 and R 80–20 metrics in Plastic Water®, which correlated with energy spectrum metrics, peak mean energy (PME) and full‐width at half maximum (FWHM). Results Visual inspection of energy spectra and their metrics showed whether beams on single machines were properly tuned, i.e., FWHM is expected to increase and peak height decrease monotonically with increased PME. Also, PME spacings are expected to be approximately equal for 7–13 MeV beams (0.5‐cm R90 spacing) and for 13–16 MeV beams (1.0‐cm R90 spacing). Most machines failed these expectations, presumably due to tolerances for initial beam matching (0.05 cm in R 90; 0.10 cm in R 80–20) and ongoing quality assurance (0.2 cm in R 50). Also, comparison of energy spectra or metrics for a single beam energy (six machines) showed outlying spectra. These variations in energy spectra provided ample data spread for correlating PME and FWHM with PDD metrics. Least‐squares fits showed that R 50 and R 80–20 varied linearly and supralinearly with PME, respectively; however, both suggested a secondary dependence on FWHM. Hence, PME and FWHM could serve as surrogates for R 50 and R 80–20 for beam tuning by the accelerator engineer, possibly being more sensitive (e.g., 0.1 cm in R 80–20 corresponded to 2.0 MeV in FWHM). Conclusions Results of this study suggest a lightweight, permanent magnet spectrometer could be a useful beam‐tuning instrument for the accelerator engineer to (a) match electron beams prior to beam commissioning, (b) tune electron beams for the duration of their clinical use, and (c) provide estimates of PDD metrics following machine maintenance. However, a real‐time version of the spectrometer is needed to be practical.

contains a dipole, neodymium permanent magnet with a 1.43 cm air separation, producing a 0.54 T field. The magnetic field disperses the energy distributed electrons onto a computed radiography (CR) strip, whose measured spatial distribution transforms to an energy spectrum (cf Fig. 1).
Potential clinical applications of a real-time version of such a device include, but are not limited to, beam tuning, beam matching, and quality assurance. The aims of the present study were to (a) demonstrate its potential utility for beam matching by comparing electron energy spectra for six matched Elekta accelerators and (b) study the correlation of measured energy spectra metrics with percent depth-dose curve metrics, showing the potential of the former for estimating percent depth-dose metrics for quality assurance.
Results are reported for a set of seven electron beams on six Elekta Infinity radiotherapy accelerators with the MLCi2 treatment head.
Our institution utilizes matched electron beams, which allow patient treatments to be planned using data for a single machine commissioned on our Pinnacle 3 (Philips Healthcare, Cambridge, MA) treatment planning system (TPS) and to be treated on any other matched Elekta accelerator. This provides efficiency of medical physicist beam commissioning effort, flexibility in patient machine assignments, and decreased opportunity for treatment error. Our Elekta accelerators, specifically configured for our institution, have seven nominal beam energies (7,9,10,11,13,16,and 20 MeV) tuned to have R 90 values of 2.0, 2.5, 3.0, 3.5, 4.0, 5.0, and 6.0 cm (AE0.1 cm), which differ slightly from factory-standard beam tunes.
Custom beam energies and our stringent flatness requirements (AE3% of central-axis dose along major axes and AE4% along diagonal axes 2 cm inside the beam edges at depths of 2 cm for E > 9 MeV and 1 cm for E ≤ 9 MeV) 2,3 required our matched machines to have dual scattering foils that differ slightly from factory-standard ones. 4 The first four of our six Elekta Infinity accelerators utilized the same, modified dual scattering foil systems; whereas, our fifth and sixth accelerators utilized the same modified dual scattering foil systems for 7-13 MeV beams, but a slightly thicker secondary scattering foil for the 16  Elekta electron beams are of particular interest for this study because of their sensitivity to beam tuning, especially recirculated radiofrequency (RF) power. Unusually shaped, multipeak electron energy spectra were reported by Deasy et al. 6 for a Philips F I G . 1. Schematic diagram of top view of central cross-section of permanent magnet spectrometer. The incident electron beam is collimated into a small circular beam by a Cerrobend â collimator, and a downstream copper aperture defines the circular beam entering the magnet block. The two together create a highly parallel beam and reduce the number of electrons entering the magnet block. The dipole magnetic field (blue), pointing out of the page, bends electrons according to the Lorentz force law, dispersing different energies such that higher energy electrons (E2) travel further downstream than lower energy electrons (E1) before striking the CR strip. The lead x-ray block shields the CR strip from bremsstrahlung x rays emitted by beamline components. Dimensions are to scale. accelerator (Elekta predecessor). Kok and Welleweerd 7 showed how the unusual shape of these spectra can be attributed to the phase of recirculated RF power. Our measurements were a random 'snapshot' of the energy spectra. They indicated that our institution's energy spectra were mostly, but not always, single peaked, apparently a result of good, but not always optimal, beam-tuning procedures and of beam tune drifting. Our experiences are that Elekta electron beams require frequent beam tuning, particularly the higher energy electron beams.
Hence, we believe the availability of a real-time electron energy spectrometer would be of value to the accelerator engineer for beam tuning and matching. Also, it might provide reasonable estimates of central-axis percent depth-dose (PDD) curve metrics, determining them from energy spectra metrics.
Therefore, this work first compares measured electron energy spectra for the seven beam energies on the six matched electron machines at our institution. Second, it reports on the correlation between measured electron beam energy spectra and central-axis percent depth-dose metrics. As energy spectra for most beam energies were closely matched, metrics were used for a more quantitative comparison. We used peak mean energy (PME), full-width at half maximum (FWHM), and their ratio FWHM/PME. PME, as defined by McLaughlin et al., is essentially the mean energy over a 30% energy window around the peak. 1 The precision of energy spectra measurements was estimated by repeating measurements seven consecutive times for the 7, 11, and 16-MeV beams. The resulting spectra, plotted in McLaughlin, 8 closely replicated each other. This is reflected in the comparison of PME and FWHM metrics for each of the seven measurements, which showed a relative uncertainty (one standard deviation) of approximately 0.4% for PME and 1.4% for FWHM.

2.B | Measurement of percent depth-dose metrics
Matched electron beams require energy spectra sufficiently matched to produce matched central-axis percent depth-dose curves. In the present study, we evaluated the agreement between PME and FWHM of the energy spectra necessary for R 50 values to agree within 0.05 cm and R 80À20 ðR 20 À R 80 Þ values to agree within 0.10 cm for matched machines. To minimize the effect of any dayto-day drifting of beam tunes, R 50 and R 80-20 values were measured on the same day that the energy spectra were measured.
R 50 and R 80-20 measurements were made in Plastic Water â phantom slabs (CIRS Inc., Norfolk, VA) to minimize depth inaccuracies due to surface determination in a water phantom and to eliminate the time of setting up a beam scanner and water tank. Our measurement technique paralleled that of our clinic's monthly QA protocol for verifying the constancy of percent depth ionization at a depth near R 50 to within 0.2 cm. 9,10 These measurements (near R 100 and R 50 ) along with additional measurements near depths of 80% and 20% ionization, were used to determine R 50 and R 80-20 .
Relative ionization was measured with a 0.6 cm 3 Farmer chamber (TN 30013, PTW, Freiburg, Germany) having a cavity radius, r cav , of 0.3 cm. Measured ionization values at the four depths were normalized to the maximum ionization. Percent ionization vs effective depth (depth minus 0.5r cav ) points were converted into percent dose (%D) vs depth (d) points following AAPM TG-25 protocol 3 and its TG-70 supplement 11 with TG-51 values for relative stopping powers, 12 as implemented in the IBA data acquisition system (IBA, Louvain-la-Neuve, Belgium). Lastly, R 80 , R 50 , and R 20 were determined from a nonlinear, least-squares fit to the four (%D, d) points in the falloff region using where d is the effective depth, D x is the energy-dependent bremsstrahlung dose percent at R p + 2 cm, erfc is the complimentary error function, and a 1 and a 2 are parameters determined by the fit using the nonlinear, Levenberg-Marquardt algorithm option in MATLAB (Math-Works, Natick, MA). Corrections to %D vs depth due to small differences in stopping and scattering powers between water and Plastic Water ® were ignored in the present study. Resulting differences in R 50 and R 80-20 would be small, but more importantly would vary smoothly with energy, having insignificant impact on our conclusions. For machine B-2, the spectra at 9 and 10 MeV also could have had a slightly narrower width with slightly greater amplitude.
Ideally, each spectrum should appear as a single, asymmetric peak, 13 which is approximately Gaussian-shaped on the high energy side of the peak and Lorentzian-shaped on the low energy side.
However, it is well known that the energy spectrum can be multipeaked if the recirculated RF power is not in proper phase. 7 Inspection of our data shows that only a few spectra hinted at being multipeaked, e.g., 7 and 10 MeV for machine A-1, 9 MeV for machine A-2, 13 MeV for machines A-2 and A-3, and 20 MeV for Because most beams were well matched, a more quantitative comparison that utilizes previously defined peak mean energy (PME), full-width at half maximum (FWHM), and their ratio (FWHM/PME) is given in Table 1. Ideally, the matching energy spectra from different machines would be identical; such is not the case, because (a) each accelerator will tune slightly differently and (b) quality assurance standards 9,10 allow R 50 to vary AE0.2 cm in water, corresponding to approximately AE0.5 MeV in PME. Hence, peak mean energies should fall within a band of 1.0 MeV. Variations in the PME from the six T A B L E 1 Comparison of energy spectra metrics from the six matched Elekta Infinity accelerators for each of the seven beam energies. Metrics are peak mean energy (PME), full-width at half maximum (FWHM), and relative width (FWHM/PME). Far right column lists the difference (D) in maximum and minimum values for PME and FWHM for the six matched machines.
In matching electron beams, our criterion for R 50 is 0.05 cm; therefore, if matching the beam using the measured energy spectrum, the PME value should agree to within 0.  Fig. 5. A second-order polynomial, least-squares fit to these data demonstrates that R 80-20 is primarily governed by the incident PME, increasing supralinearly with increasing PME values. This is attributed to increased range straggling with increasing PME. However, variations among the six data points for each of the seven nominal energies indicate an additional, second-order dependence on another factor, which almost certainly is the difference in the widths of the energy spectra (FWHM). This is also evident for the Atomic Energy of Canada Limited (AECL) Therac 20 and 25 scanned electron beams, which having a much narrower energy spectra (smaller FWHM), have substantially smaller values for R 80-20 (cf ICRU 35, 13 Pfalzner and Clarke, 16 O'Brien et al. 17 ). Beam Metric Hence, these data confirm that the FWHM of the energy spectra plays a minor, but important role in beam matching. Variations from a straight line fit at each energy were due in part to variations in PME values for all six accelerators at the same nominal energy. To better understand these data, they were fit to a theory that relates the slope of the dose falloff region with PME and FWHM. The theory used to relate R 80-20 to PME and FWHM was a modified version of eq. (6.35) in ICRU 35), 13,18 i.e., R 80À20 ðPME; FWHMÞ ¼ R 80À20 ðPME; 0Þ 1 þ c 1 Á FWHM PME ; where R 80-20 at PME for FWHM = 0 is modeled by The  Table 1 and the corresponding R 80-20 values in Table 2   Utilizing these results, it is possible to correlate matching criteria comparing FWHM with the clinical value of 0.1 cm for R 80-20 , i.e., DFWHM ¼ DR 80À20 dR 80À20 ðPME; FWHMÞ dFWHM À1 ; ¼ DR 80À20 c 1 Á R 80À20 ðPME; 0Þ PME À1 ;

| SUMMARY AND RE COMMENDATIONS
Based on the results of the present study, we conclude that a lightweight, permanent magnet spectrometer 1 is a useful tool for measuring energy spectra of matched therapeutic electron beams, allowing their comparison and evaluation, both qualitatively and quantitatively. Comparison of energy spectra for all beams on a single accelerator in most cases showed that the PME and FWHM of the energy spectra did not always smoothly vary monotonically with beam energy, as otherwise expected. If improperly tuned, the accelerator produced a beam energy spectrum with an inappropriate value for the peak mean (PME) energy; also, suboptimal tuning of recirculated RF power can broaden the spectrum from its minimal FWHM. 7 Suboptimal tuning was clearly visible in the shapes of energy spectra within the set for individual accelerators, which was supported by metrics such as PME and FWHM. Also, a comparison of energy spectra for a single beam energy on multiple matched machines showed unacceptably large variations in PME and FWHM.