A simple magnetic spectrometer for radiotherapy electron beams

Optimization of the regularization parameter in the Dual Annealing method used for the reconstruction of energy spectrum of electron beam generated by the AQURE mobile accelerator

INTRODUCTION

The shape of the energy spectrum is an essential component of any electron beam Monte Carlo model. Due to specialized equipment and the long measurement time for the direct methods for determining the energy spectrum, attractive alternatives are backward spectrum reconstructions from the measured data. One such approach is solving the first-degree Fredholm integral equation with appropriate regularization. It makes it possible to calculate the depth distribution as the sum of the distributions from monoenergetic beams. This study aims to determine the optimal value of the regularization parameter for the problem of determining the spectrum of the electron beam produced by a mobile accelerator used during intraoperative radiotherapy.

MATERIAL AND METHODS

The Geant4 package was used to generate the distributions of deep doses for monoenergetic beams for two models with different degrees of complexity, i.e. simple (theoretical) and full (for the mobile accelerator). The dose distributions for four different shapes of energy spectrum (for each model) were obtained similarly. They were established as the reference data for further calculations. The Dual Annealing optimization method was used to obtain the reconstructed spectrum. The multiple optimizations that differ by the regularization parameter (ranging from 0 to 1) were performed. For each reconstruction, similarity indicators of the energy spectrum and the dose distribution to the referenced data were calculated to determine the optimal regularization parameters.

RESULTS

Optimal regularization parameters determined by similarity indicators for the spectrum and the dose distribution differ for geometry models considered in the study. The regularization parameter for the simple geometry ranged from 0.03 to 0.05, while for full geometry, they were from 0.05 to 0.06. The results for conventional linear accelerators found in the literature range from 0.5 to 1.1.

CONCLUSION

The Dual Annealing optimization method can be effectively used to solve the Fredholm equation with Tikhonov regularization to reconstruct an electron beam's energy spectrum. The regularization parameter value depends on the beam-forming system. Its value for the mobile accelerator considered in the study ranges from 0.05 to 0.06, depending on the nominal beam energy value.

Monitoring electron energies during FLASH irradiations

When relativistic electrons are used to irradiate tissues, such as during FLASH pre-clinical irradiations, the electron beam energy is one of the critical parameters that determine the dose distribution. Moreover, during such irradiations, linear accelerators (linacs) usually operate with significant beam loading, where a small change in the accelerator output current can lead to beam energy reduction. Optimisation of the tuning of the accelerator's radio frequency system is often required. We describe here a robust, easy-to-use device for non-interceptive monitoring of potential variations in the electron beam energy during every linac macro-pulse of an irradiation run. Our approach monitors the accelerated electron fringe beam using two unbiased aluminium annular charge collection plates, positioned in the beam path and with apertures (5 cm in diameter) for the central beam. These plates are complemented by two thin annular screening plates to eliminate crosstalk and equalise the capacitances of the charge collection plates. The ratio of the charge picked up on the downstream collection plate to the sum of charges picked up on the both plates is sensitive to the beam energy and to changes in the energy spectrum shape. The energy sensitivity range is optimised to the investigated beam by the choice of thickness of the first plate. We present simulation and measurement data using electrons generated by a nominal 6 MeV energy linac as well as information on the design, the practical implementation and the use of this monitor.

New algorithm using L1 regularization for measuring electron energy spectra

Retrieving the spectrum of physical radiation from experimental measurements typically involves using a mathematical algorithm to deconvolve the instrument response function from the measured signal. However, in the field of signal processing known as "Source Separation" (SS), which refers to the process of computationally retrieving the separate source components that generate an overlapping signal on the detector, the deconvolution process can become an ill-posed problem and crosstalk complicates the separation of the individual sources. To overcome this problem, we have designed a magnetic spectrometer for inline electron energy spectrum diagnosis and developed an analysis algorithm using techniques applicable to the problem of SS. An unknown polychromatic electron spectrum is calculated by sparse coding using a Gaussian basis function and an L1 regularization algorithm with a sparsity constraint. This technique is verified by using a specially designed magnetic field electron spectrometer. We use Monte Carlo simulations of the detector response to Maxwellian input energy distributions with electron temperatures of 5.0 MeV, 10.0 MeV, and 15.0 MeV to show that the calculated sparse spectrum can reproduce the input spectrum with an optimum energy bin width automatically selected by the L1 regularization. The spectra are reproduced with a high accuracy of less than 4.0% error, without an initial value. The technique is then applied to experimental measurements of intense laser accelerated electron beams from solid targets. Our analysis concept of spectral retrieval and automatic optimization of energy bin width by sparse coding could form the basis of a novel diagnostic method for spectroscopy.

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.

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.

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

The measured electron spectra of linear accelerators from several manufacturers differ in comparison to the spectral form and width. As part of our investigations of linac performance and stability, we analyzed the electron spectra of our linacs. After building a spectrometer the electron spectra were measured. The measured spectral widths were comparable with the results published in the literature. It appeared that the phase of the recycled radio pulse in combination with the limited bandwidth of the bending magnet are responsible for unusual (multipeak) electron spectra. The scatter filters only have a relatively small widening effect on the spectrum. There was no indication that multipeak or wide spectra are related to linac instabilities.