Variations in energy spectra and water-to-material stopping-power ratios in three-dimensional conformal and intensity-modulated photon fields

Future directions on low-energy radiation dosimetry

For more than one century, low-energy (< 100 keV) photons (x-rays and gamma) have been widely used in different areas including biomedical research and medical applications such as mammography, fluoroscopy, general radiography, computed tomography, and brachytherapy treatment, amongst others. It has been demonstrated that most of the electrons produced by low photon energy beams have energies below 10 keV. However, the physical processes by which these low energy electrons interact with matter are not yet well understood. Besides, it is generally assumed that all the energy deposited within a dosimeter sensitive volume is transformed into a response. But such an assumption could be incorrect since part of the energy deposited might be used to create defects or damages at the molecular and atomic level. Consequently, the relationship between absorbed dose and dosimeter response can be mistaken. During the last few years, efforts have been made to identify models that allow to understand these interaction processes from a quantum mechanical point of view. Some approaches are based on electron-beam − solid-state-interaction models to calculate electron scattering cross-sections while others consider the density functional theory method to localize low energy electrons and evaluate the energy loss due to the creations of defects and damages in matter. The results obtained so far could be considered as a starting point. This paper presents some methodologies based on fundamental quantum mechanics which can be considered useful for dealing with low-energy interactions.

Track and dose-average LET dependence of Gafchromic EBT3 and MD-V3 films exposed to low-energy photons

Gafchromic films are widely used in radiotherapy using photons, electrons and protons. Dosimetric characteristics of the films in terms of beam-quality is of great importance for a better evaluation of the absorbed-dose in the clinic. In proton-therapy, film’s response has been reported in terms of track-average, L_Δ,T, or dose-average, L_Δ,D, linear energy transfer (LET), concluding that L_Δ,D is a more reliable parameter than L_Δ,T. Nonetheless, in photon-beams, the film’s response is generally scrutinised in terms of photon-energy. This work aimed at investigating, the total (TEF) and secondary (SE) electron fluence produced in EBT3 and MD-V3 films exposed to 20 kV-160 kV x-ray and ⁶⁰Co beams and their corresponding L_Δ,T and L_Δ,D to determine their influence on the film’s relative-efficiency, RE_Film. Regardless the film-model, at energies below 100 keV, L_Δ,D for TEF are about 1.7 to 2.5 times those of L_Δ,T while for SE they are relatively similar (8–29%). For ⁶⁰Co-gamma, L_Δ,D for TEF and SE are approximately 9 and 4 times L_Δ,T, respectively, which implies that L_Δ,D is more important for high-photon energies. Independent of the electron-fluence and film-model, RE_Film is almost constant at low average-LET, rapidly increases and thereafter steadily rises with average-LET. The RE_Film−LET curve indicated that L_Δ,D is more sensitive to small change than L_Δ,T and if it is evaluated for SE, it would even be more appropriate to better describing the dosimeter response induced by photons in terms of ionization-density instead of L_Δ,T for TEF, as generally done. Based on these results, once can conclude that the effect of the average-LET on the film’s response should be considered when use for clinical-dosimetry using photons and not only the energy.

Determining the energy spectrum of clinical linear accelerator using an optimized photon beam transmission protocol

PURPOSE

The complex beam delivery techniques for patient treatment using a clinical linear accelerator (linac) may result in variations in the photon spectra, which can lead to dosimetric differences in patients that cannot be accounted for by current treatment planning systems (TPSs). Therefore, precise knowledge of the fluence and energy spectrum (ES) of the therapeutic beam is very important. However, owing to the high energy and flux of the beam, the ES cannot be measured directly, and validation of the spectrum modeled in the TPS is difficult. The aim of this study is to develop an efficient beam transmission measurement procedure for accurately reconstructing the ES of a therapeutic x-ray beam generated by a clinical linac.

METHODS

The attenuation of a 6 MV photon beam from an Elekta Synergy Platform clinical linac through different thicknesses of graphite and lead was measured using an ion chamber. The response of the ion chamber as a function of photon energy was obtained using the Monte Carlo (MC) method in the Geant4 simulation code. Using the curves obtained in the photon beam transmission measurements and the ion chamber energy response, the ES was reconstructed using an iterative algorithm based on a mathematical model of the spectrum. To evaluate the accuracy of the spectrum reconstruction method, the reconstructed ES (ES_recon ) was compared to that determined by the MC simulation (ES_MC ).

RESULTS

The ion chamber model in the Geant4 simulation was well validated by comparing the ion chamber perturbation factors determined by the TRS-398 calibration protocol and EGSnrc; the differences were within 0.57%. The number of transmission measurements was optimized to 10 for efficient spectrum reconstruction according to the rate of increase in the spectrum reconstruction accuracy. The distribution of ES_recon obtained using the measured transmission curves was clearly similar to the reference, ES_MC , and the dose distributions in water calculated using ES_recon and ES_MC were similar within a 2% local difference. However, in a heterogeneous medium, the dose discrepancy between them was >5% when a complex beam delivery technique composed of 171 control points was used.

CONCLUSIONS

The proposed measurement procedure required a total time of approximately 1 h to obtain and analyze 20 transmission measurements. In addition, it was confirmed that the transmission curve of high-Z materials influences the accuracy of spectrum reconstruction more than that of low-Z materials. A well-designed transmission measurement protocol suitable for clinical environments could be an essential tool for better dosimetric accuracy in patient treatment and for periodic verification of the beam quality.

Implementation and validation of a fluence pencil kernels model for GaN-based dosimetry in photon beam radiotherapy

Gallium nitride (GaN), a direct-gap semiconductor that is radioluminescent, can be used as a transducer yielding a high signal from a small detecting volume and thus potentially suitable for use in small fields and for high dose gradients. A common drawback of semiconductor dosimeters with effective atomic numbers higher than soft tissues is that their responses depend on the presence of low energy photons for which the photoelectric cross section varies strongly with atomic number, which may affect the accuracy of dosimetric measurements. To tackle this 'over-response' issue, we propose a model for GaN-based dosimetry with readout correction. The local photon spectrum is calculated by convolving fluence pencil kernel spectra with the beam aperture fluence distribution. The response of a GaN detector is modelled by combining large cavity theory and small cavity theory for the low and high energy components of the local spectrum. Monte Carlo simulations are employed for determination of specific correction factors for different GaN transducer sizes and irradiation conditions. Some model parameters such as the cut-off energy and partitioning energy are discussed. The accuracy of the GaN dosimetric response model has been evaluated for tissue phantom ratio experiments along the central axis. These experiments have shown that calculated and measured GaN responses stay within ±3% at all depths beyond the build-up depth. The calculated GaN response factor is also in good agreement with measured data (±2.5%). The validated model with response compensation improves significantly the accuracy of dosimetric measurements: below 2.5% deviation as compared to 13% without compensation, for a 10 × 10 cm(2) field, at depth from 1.5 to 22 cm.

Beam quality and dose perturbation of 6 MV flattening-filter-free linac

The aim of this study is twofold: (a) determination of the spectral differences for flattening-filter-free (FFF) versus standard (STD) linac under various clinical conditions, (b) based on an extensive list of clinically important beam configurations, identification of clinical scenarios that lead to higher macroscopic dose perturbations due to the presence of high-Z material. The focus is on dose enhancement due to contrast agents including high-Z elements such as gold or gadolinium. EGSnrc was used to simulate clinical beams under various irradiation conditions: open/IMRT/spit-IMRT fields, in/out-off-field areas, different depths and field sizes. Spectra were calculated and analyzed for about 80 beams and for a total of 480 regions. Quantitative differential effects in beam quality were characterized using energy-dependent and cumulative dose perturbation metrics. Analysis of the spectral database showed that even though the general trends for both linacs (FFF/STD) were the same, there were crucial differences. In general, the relative changes between different conditions were smaller for FFF spectra. This was because of the higher component of low-energy photons of the FFF linac, which already lead to higher dose enhancement than for the STD linac (photon energies were more "uniformly" distributed for FFF spectra and henceforth their perturbation resulted in lesser relative changes). For out-of-field FFF spectra and split-IMRT fields the strongest enhancement were observed (∼25 and ∼5 respectively). Different spectral scenarios lead to different dose enhancements, however, they scale with the higher effective-Z of the materials and were directly related to the lower range of the spectra (<200 keV).

Variations in photon energy spectra of a 6 MV beam and their impact on TLD response

PURPOSE

Measurement of the absorbed dose from radiotherapy beams is an essential component of providing safe and reproducible treatment. For an energy-dependent dosimeter such as thermoluminescent dosimeters (TLDs), it is generally assumed that the energy spectrum is constant throughout the treatment field and is unperturbed by field size, depth, field modulation, or heterogeneities. However, this does not reflect reality and introduces error into clinical dose measurements. The purpose of this study was to evaluate the variability in the energy spectrum of a Varian 6 MV beam and to evaluate the impact of these variations in photon energy spectra on the response of a common energy-dependent dosimeter, TLD.

METHODS

Using Monte Carlo methods, we calculated variations in the photon energy spectra of a 6 MV beam as a result of variations of treatment parameters, including field size, measurement location, the presence of heterogeneities, and field modulation. The impact of these spectral variations on the response of the TLD is largely based on increased photoelectric effect in the dosimeter, and this impact was calculated using Burlin cavity theory. Measurements of the energy response were also made to determine the additional energy response due to all intrinsic and secondary effects.

RESULTS

For most in-field measurements, regardless of treatment parameter, the dosimeter response was not significantly affected by the spectral variations (<1% effect). For measurement points outside of the treatment field, where the spectrum is softer, the TLD over-responded by up to 12% due to an increased probability of photoelectric effect in the TLD material as well as inherent ionization density effects that play a role at low photon energies.

CONCLUSIONS

It is generally acceptable to ignore the impact of variations in the photon spectrum on the measured dose for locations within the treatment field. However, outside the treatment field, the spectra are much softer, and a correction factor is generally appropriate. The results of this work have determined values for this factor, which range from 0.88 to 0.99 depending on the specific irradiation conditions.

Comparison of two methods to compute the absorbed dose to water for photon beams

Cross-validation was performed between an in-house dose-to-water (D(water)) calculation method used at Virginia Commonwealth University and the VMC++ D(water) calculation during particle transport. The effect of Monte Carlo statistical precision was observed. The results of the two calculations on homogeneous phantoms with densities varying from 0.3 g cm(-3) to 2.95 g cm(-3) were compared. Depth and field size dependence were tested. D(water) calculations were compared in a bone-lung-bone phantom to observe how the calculations differed in steep density gradients. The methods were compared for five prostate and five head-and-neck (H/N) patient cases as well. In all phantom tests, the differences between the two D(water) calculations were less than 1%. The largest differences in patient cases was a prostate case in which 1% of the voxels with doses greater than 50% of the maximum dose had a systematic difference corresponding to 1.16% of the maximum dose. All differences were clinically insignificant.