Finding mechanisms responsible for the spectral distribution of electron beams produced by a linear accelerator

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

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 R₅₀ 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 R₉₀; 0.10 cm in R_80–20) and ongoing quality assurance (0.2 cm in R₅₀). 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 R₅₀ 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 R₅₀ 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.

Permanent-magnet energy spectrometer for electron beams from radiotherapy accelerators

PURPOSE

The purpose of this work was to adapt a lightweight, permanent magnet electron energy spectrometer for the measurement of energy spectra of therapeutic electron beams.

METHODS

An irradiation geometry and measurement technique were developed for an approximately 0.54-T, permanent dipole magnet spectrometer to produce suitable latent images on computed radiography (CR) phosphor strips. Dual-pinhole electron collimators created a 0.318-cm diameter, approximately parallel beam incident on the spectrometer and an appropriate dose rate at the image plane (CR strip location). X-ray background in the latent image, reduced by a 7.62-cm thick lead block between the pinhole collimators, was removed using a fitting technique. Theoretical energy-dependent detector response functions (DRFs) were used in an iterative technique to transform CR strip net mean dose profiles into energy spectra on central axis at the entrance to the spectrometer. These spectra were transformed to spectra at 95-cm source to collimator distance (SCD) by correcting for the energy dependence of electron scatter. The spectrometer was calibrated by comparing peak mean positions in the net mean dose profiles, initially to peak mean energies determined from the practical range of central-axis percent depth-dose (%DD) curves, and then to peak mean energies that accounted for how the collimation modified the energy spectra (recalibration). The utility of the spectrometer was demonstrated by measuring the energy spectra for the seven electron beams (7-20 MeV) of an Elekta Infinity radiotherapy accelerator.

RESULTS

Plots of DRF illustrated their dependence on energy and position in the imaging plane. Approximately 15 iterations solved for the energy spectra at the spectrometer entrance from the measured net mean dose profiles. Transforming those spectra into ones at 95-cm SCD increased the low energy tail of the spectra, while correspondingly decreasing the peaks and shifting them to slightly lower energies. Energy calibration plots of peak mean energy versus peak mean position of the net mean dose profiles for each of the seven electron beams followed the shape predicted by the Lorentz force law for a uniform z-component of the magnetic field, validating its being modeled as uniform (0.542 ± 0.027 T). Measured Elekta energy spectra and their peak mean energies correlated with the 0.5-cm (7-13 MeV) and the 1.0-cm (13-20 MeV) R90 spacings of the %DD curves. The full-width-half-maximum of the energy spectra decreased with decreasing peak mean energy with the exception of the 9-MeV beam, which was anomalously wide. Similarly, R80-20 decreased linearly with peak mean energy with the exception of the 9 MeV beam. Both were attributed to suboptimal tuning of the high power phase shifter for the recycled radiofrequency power reentering the traveling wave accelerator.

CONCLUSIONS

The apparatus and analysis techniques of the authors demonstrated that an inexpensive, lightweight, permanent magnet electron energy spectrometer can be used for measuring the electron energy distributions of therapeutic electron beams (6-20 MeV). The primary goal of future work is to develop a real-time spectrometer by incorporating a real-time imager, which has potential applications such as beam matching, ongoing beam tune maintenance, and measuring spectra for input into Monte Carlo beam calculations.

Electron beam energy QA - a note on measurement tolerances

Monthly QA is recommended to verify the constancy of high‐energy electron beams generated for clinical use by linear accelerators. The tolerances are defined as 2%/2 mm in beam penetration according to AAPM task group report 142. The practical implementation is typically achieved by measuring the ratio of readings at two different depths, preferably near the depth of maximum dose and at the depth corresponding to half the dose maximum. Based on beam commissioning data, we show that the relationship between the ranges of energy ratios for different electron energies is highly nonlinear. We provide a formalism that translates measurement deviations in the reference ratios into change in beam penetration for electron energies for six Elekta (6‐18 MeV) and eight Varian (6‐22 MeV) electron beams. Experimental checks were conducted for each Elekta energy to compare calculated values with measurements, and it was shown that they are in agreement. For example, for a 6 MeV beam a deviation in the measured ionization ratio of ±15% might still be acceptable (i.e., be within ±2 mm), whereas for an 18 MeV beam the corresponding tolerance might be ±6%. These values strongly depend on the initial ratio chosen. In summary, the relationship between differences of the ionization ratio and the corresponding beam energy are derived. The findings can be translated into acceptable tolerance values for monthly QA of electron beam energies.

PACS number(s): 87.55, 87.56

Obtaining the intrinsic electron spectrum of linear accelerators using the relation between the current of the bending magnet and the absorbed dose in water

PURPOSE

To present a novel methodology to model the intrinsic electron spectra of a linear accelerator and its situation with respect to the energy window.

METHODS

The spectra are obtained by fitting the variation of R(50) and the maximum dose rate measured in a water phantom with the bending magnet current. The obtained spectra are verified with a realistic Monte Carlo simulation of the accelerator.

RESULTS

The intrinsic spectra and their relative position with respect to the energy window of the bending magnet have been obtained for a Siemens Mevatron KDS and an ELEKTA SL20 accelerators.

CONCLUSIONS

Using this method in the commissioning and scheduled revisions of the accelerator, the tuning of the current of the bending magnet could be done in such a way that both the quality of the beam and the dose rate would reach a better long-term stability.

A modified simulated annealing algorithm for parameter determination for a hybrid virtual model

In this work we present an algorithm based on the simulated annealing (SA) method for electron beam spectrum reconstruction from central axis PDD data. We use a simulated beam in order to assess the accuracy of the method, and compare it with others usually employed. We found that our modified SA algorithm produced excellent reconstructed PDDs and beam profiles and improved reconstructed spectra. We also tested our method for the simultaneous determination of an electron energy spectrum and the position of a trimmer from central axis PDD data, and found this to be sufficient for the determination of the physical parameters of this hybrid model.

Influence of initial electron beam characteristics on monte carlo calculated absorbed dose distributions for linear accelerator electron beams

The least known parameters in a Monte Carlo simulation of a linear accelerator treatment head are often the properties of the initial electron beam directed onto the exit vacuum window. Several initial beams with different spatial fluence distributions, angular divergences and energy spectra have been transported through the geometry of a scattering foil accelerator. The electron beam characteristics (energy spectrum and angular distribution) at the phantom surface and the subsequent relative absorbed dose distribution in a water phantom were calculated. The dose distribution was found to be insensitive to the geometrical properties of the initial beam. Furthermore, the lateral dose profiles are unaffected by the energy spectrum of the initial beam. The effect on the depth-dose curve is negligible if the initial energy spectrum is symmetric (e.g., Gaussian shaped) and its full width at half maximum (FWHM) is less than approximately 10% of the most probable energy. A larger FWHM will decrease the normalized dose gradient, but will not affect the dose in the build-up region. An asymmetric wedge shaped spectrum with a low-energy extension simultaneously increases the dose in the build-up region and decreases the dose gradient. The relationship between the energy spectral width and the normalized dose gradient is, however, smaller than published analytical expressions indicate. Some well-established energy-range relationships were shown to be accurate for most of the initial beams studied. The energy spectrum at the phantom surface was also derived from a measured depth-dose curve through different methods. The extracted spectrum depends on the beam model and the spectral reconstruction algorithm. Even though the depth-dose curve is fairly independent of initial beam characteristics, a correct description of the low-energy tail of the energy spectrum is important to obtain good agreement between measured and Monte Carlo calculated doses in the build-up region.

Dosimetry characteristics of degraded electron beams investigated by Monte Carlo calculations in a setup for intraoperative radiation therapy

Degraded electron beams, as used for intraoperative radiation therapy (IORT) or similar complicated dosimetric situations, have different characteristics compared to conventional electron therapy beams. If international dosimetry protocols are applied in a direct manner to such degraded beams, uncertainties will be introduced in the absorbed dose determination. The Monte Carlo method has been used to verify experimentally determined relative absorbed dose distributions and output factors in an IORT geometry. Monte Carlo generated dose distributions are mostly within +/-2% or +/-2 mm of measured data. The simulated output variation between the IORT cones (relative output factors) are mostly within 2% of measured values. By comparing IORT and conventional electron beam characteristics (e.g. energy spectra, angular distributions and the contributions of different system components to these quantities) limitations and uncertainties of commonly used dosimetric techniques in IORT electron fields are quantified. The intraoperative treatment field contains a larger amount of scattered electrons, which leads to a broader energy spectrum as well as a wider angular distribution of electrons at the phantom surface. The dose from the scattered electrons can contribute up to 40% of the total dose at a depth of dose maximum, compared to approximately 10% for standard beams. A study of the energy spectra at the reference depth reveals that an uncertainty of the order of 1% can be introduced if ionization chamber based dosimetry is used to determine output factors for the investigated IORT system. We recommend that relative absorbed dose distributions and output factors in IORT electron beams and for similar complicated dosimetric situations should be determined with detectors having a small energy and angular dependence (e.g. diamond detectors or p-Si diodes).