Electron spectra derived from depth dose distributions

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.

Experimental validation of a linac head Geant4 model under a grid computing environment

Background and purpose: This work aims to present the strategy to simulate a clinical linear accelerator based on the geometry provided by the manufacturer and summarize the corresponding experimental validation. Simulations were performed with the Geant4 Monte Carlo code under a grid computing environment. The objective of this contribution is reproducing therapeutic dose distributions in a water phantom with an accuracy less than 2%. Materials and methods: A Geant4 Monte Carlo model of an Elekta Synergy linear accelerator has been established, the simulations were launched in a large grid computing platform. Dose distributions are calculated for a 6 MV photon beam with treatment fields ranging from 5 × 5 cm2 to 20 × 20 cm 2 at a source - surface distance of 100 cm. Results: A high degree of agreement is achieved between the simulation results and the measured data, with dose differences of about 1.03% and 1.96% for the percentage depth dose curves and lateral dose profiles, respectively. This agreement is evaluated by the gamma index comparisons. Over 98% of the points for all simulations meet the restrictive acceptability criteria of 2%/2 mm. Conclusion: We have demonstrated the possibility to establish an accurate linac head Monte Carlo model for dose distribution simulations and quality assurance. Percentage depth dose curves and beam quality indices are in perfect agreement with the measured data with an accuracy of better than 2%.

Beam modeling and beam model commissioning for Monte Carlo dose calculation-based radiation therapy treatment planning: Report of AAPM Task Group 157

Dose calculation plays an important role in the accuracy of radiotherapy treatment planning and beam delivery. The Monte Carlo (MC) method is capable of achieving the highest accuracy in radiotherapy dose calculation and has been implemented in many commercial systems for radiotherapy treatment planning. The objective of this task group was to assist clinical physicists with the potentially complex task of acceptance testing and commissioning MC-based treatment planning systems (TPS) for photon and electron beam dose calculations. This report provides an overview on the general approach of clinical implementation and testing of MC-based TPS with a specific focus on models of clinical photon and electron beams. Different types of beam models are described including those that utilize MC simulation of the treatment head and those that rely on analytical methods and measurements. The trade-off between accuracy and efficiency in the various source-modeling approaches is discussed together with guidelines for acceptance testing of MC-based TPS from the clinical standpoint. Specific recommendations are given on methods and practical procedures to commission clinical beam models for MC-based TPS.

Development of a Monte Carlo multiple source model for inclusion in a dose calculation auditing tool

PURPOSE

The Imaging and Radiation Oncology Core Houston (IROC-H) (formerly the Radiological Physics Center) has reported varying levels of agreement in their anthropomorphic phantom audits. There is reason to believe one source of error in this observed disagreement is the accuracy of the dose calculation algorithms and heterogeneity corrections used. To audit this component of the radiotherapy treatment process, an independent dose calculation tool is needed.

METHODS

Monte Carlo multiple source models for Elekta 6 MV and 10 MV therapeutic x-ray beams were commissioned based on measurement of central axis depth dose data for a 10 × 10 cm² field size and dose profiles for a 40 × 40 cm² field size. The models were validated against open field measurements consisting of depth dose data and dose profiles for field sizes ranging from 3 × 3 cm² to 30 × 30 cm² . The models were then benchmarked against measurements in IROC-H's anthropomorphic head and neck and lung phantoms.

RESULTS

Validation results showed 97.9% and 96.8% of depth dose data passed a ±2% Van Dyk criterion for 6 MV and 10 MV models respectively. Dose profile comparisons showed an average agreement using a ±2%/2 mm criterion of 98.0% and 99.0% for 6 MV and 10 MV models respectively. Phantom plan comparisons were evaluated using ±3%/2 mm gamma criterion, and averaged passing rates between Monte Carlo and measurements were 87.4% and 89.9% for 6 MV and 10 MV models respectively.

CONCLUSIONS

Accurate multiple source models for Elekta 6 MV and 10 MV x-ray beams have been developed for inclusion in an independent dose calculation tool for use in clinical trial audits.

Phase space determination from measured dose data for intraoperative electron radiation therapy

A procedure to characterize beams of a medical linear accelerator for their use in Monte Carlo (MC) dose calculations for intraoperative electron radiation therapy (IOERT) is presented. The procedure relies on dose measurements in homogeneous media as input, avoiding the need for detailed simulations of the accelerator head. An iterative algorithm (EM-ML) has been employed to extract the relevant details of the phase space (PHSP) of the particles coming from the accelerator, such as energy spectra, spatial distribution and angle of emission of particles. The algorithm can use pre-computed dose volumes in water and/or air, so that the machine-specific tuning with actual data can be performed in a few minutes. To test the procedure, MC simulations of a linear accelerator with typical IOERT applicators and energies, have been performed and taken as reference. A solution PHSP derived from the dose produced by the simulated accelerator has been compared to the reference PHSP. Further, dose delivered by the simulated accelerator for setups not included in the fit of the PHSP were compared to the ones derived from the solution PHSP. The results show that it is possible to derive from dose measurements PHSP accurate for IOERT MC dose estimations.

Inference of the optimal pretarget electron beam parameters in a Monte Carlo virtual linac model through simulated annealing

The purpose of this study was to develop an efficient method to determine the optimal intensity distribution of the pretarget electron beam in a Monte Carlo (MC) accelerator model able to most accurately reproduce a set of measured photon field profiles for a given accelerator geometry and nominal photon beam energy. The method has the ability to reduce the number of simulations required to commission a MC accelerator model and has achieved better agreement with measurement than other methods described in literature. The method begins from a cylindrically symmetric pretarget electron beam (radius of 0.5 cm) of uniform intensity. This beam is subdivided into annular regions of fluence for which each region is individually transported through the accelerator head and into a water phantom. A simulated annealing search is then performed to determine the optimal combination of weights of the annular fluences that provide a best match between the measured dose distributions and the weighted sum of annular dose distributions for particular pretarget electron energy. When restricted to Gaussian intensity distributions, the optimization determined an optimal FWHM=1.34 mm for 18.0 MeV electrons, with a RMSE=0.49% on 40 x 40 cm2 lateral profiles. When allowed to deviate from Gaussian intensities a further reduction in RMSE was achieved. For our Clinac 21 EX accelerator MC model (based on the 1996 Varian Oncology Systems, Monte Carlo Project package), the optimal unrestricted intensity distribution was found to be a Gaussian-like solution (18.0 MeV, FWHM= 1.10 mm, 40 x 40 cm2 profile, and RMSE=0.15%) with the presence of an extra focal halo contribution on the order of 10% of the maximum Gaussian intensity. Using the optimally derived intensity, 10 x 10 and 4 x 4 cm2 profiles were found to be in agreement with measurement with a maximum RMSE=0.49%. The optimized Gaussian and unrestricted values of the electron beam FWHM were both within the range of those inferred by focal spot image measurements performed by Jaffray et al. ["X-ray sources of medical linear accelerators: Focal and extra-focal radiation," Med. Phys. 20, 1417-1427 (1993)]. The inference of an extra focal pretarget electron component may be an indicator of a deficiency in the MC model and needs further investigation.

Validation of calculations for electrons modulated with conventional photon multileaf collimators

Treating shallow tumors with a homogeneous dose while simultaneously minimizing the dose to distal critical organs remains a challenge in radiotherapy. One promising approach is modulated electron radiotherapy (MERT). Due to the scattering properties of electron beams, the commercially provided secondary and tertiary photon collimation systems are not conducive for electron beam delivery when standard source-to-surface distances are used. Also, commercial treatment planning systems may not accurately model electron-beam dose distributions when collimated without the standard applicators. However, by using the photon multileaf collimators (MLCs) to create segments to modulate electron beams, the quality of superficial tumor dose distributions may improve substantially. The purpose of this study is to develop and evaluate calculations for the narrow segments needed to modulate megavoltage electron beams using photon beam multileaf collimators. Modulated electron radiotherapy (MERT) will be performed with a conventional linear accelerator equipped with a 120 leaf MLC for 6-20 MeV electron beam energies. To provide a sharp penumbra, segments were delivered with short SSDs (70-85 cm). Segment widths (SW) ranging from 1 to 10 cm were configured for delivery and planning, using BEAMnrc Monte Carlo (MC) code, and the DOSXYZnrc MC dose calculations. Calculations were performed with voxel size of 0.2 x 0.2 x 0.1 cm3. Dosimetry validation was performed using radiographic film and micro- or parallel-plate chambers. Calculated and measured data were compared using technical computing software. Beam sharpness (penumbra) degraded with decreasing incident beam energy and field size (FS), and increasing SSD. A 70 cm SSD was found to be optimal. The PDD decreased significantly with decreasing FS. The comparisons demonstrated excellent agreement for calculations and measurements within 3%, 1 mm. This study shows that accurate calculations for MERT as delivered with existing photon MLC are feasible and allows the opportunity to take advantage of the dynamic leaf motion capabilities and control systems, to provide conformal dose distributions.

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.

Reconstruction of electron spectra from depth doses with adaptive regularization

Electron spectral reconstruction of medical accelerators from measured depth doses is a practical method for providing the input initial phase space distribution at the patient surface that is required by Monte Carlo treatment planning systems. The posed inverse problem of spectral reconstruction is ill conditioned and this may lead to nonphysical oscillations in the reconstructed spectra. Use of a variational method of solution with a regularization technique removes the oscillations but tends to smooth the sharp (deltalike) energy peak that is a common feature in electron spectra generated by medical accelerators. Because the sharp peak contains a large percentage of the electrons in the spectrum, an accurate estimate of the peak width, height and position is critical to the success of the technique for spectrum reconstruction with regularization. We propose use of an adaptive regularization term as a special form of the general Tichonov regularization function. The variational method with the adaptive regularization term is applied to reconstruct electron spectra for the 6, 9, and 18 MeV electron beams of a Varian Clinac 2100C accelerator and proves to be a very simple, effective and accurate approach. Results using this variational method with adaptive regularization almost perfectly reconstruct electron spectra from depth dose distributions.

Sensitivity of large-field electron beams to variations in a Monte Carlo accelerator model

Adjustments made to Monte Carlo models during the commissioning of the simulation should be physically realistic and correspond to actual machine characteristics. Large electron fields, with the jaws fully open and the applicator removed, are sensitive to important source and geometry parameters and may provide the most accurate beam models, including those collimated by an applicator. We report on the results of a comprehensive Monte Carlo sensitivity study documenting the response of these large fields to changes in the configuration of a Siemens Primus linear accelerator. The study was performed for 6, 9 12, 15, 18 and 21 MeV configurations, and included variations of thickness, position and lateral alignment of all treatment head components. Variations of electron beam characteristics were also included in the study. Results were classified by their impact on central-axis depth dose distributions, including the bremsstrahlung tail, and on beam profiles near D(max) and in the bremsstrahlung region. Low-energy results show an increased sensitivity to electron beam properties. High-energy bremsstrahlung profiles are shown to be useful in determining misalignments between the beam axis and mechanical isocentre. For all energies, the alignment of the secondary scattering foil and monitor chamber are shown to be critical for correctly modelling beam asymmetries. The results suggest a methodology for commissioning of electron beams using Monte Carlo treatment head simulation.

Monte Carlo simulation of large electron fields

Accurate simulation of large electron fields may lead to improved accuracy in Monte Carlo treatment planning while simplifying the commissioning procedure. We have used measurements made with wide-open jaws and no electron applicator to adjust simulation parameters. Central axis depth dose curves and profiles of 6-21 MeV electron beams measured in this geometry were used to estimate source and geometry parameters, including those that affect beam symmetry: incident beam direction and offset of the secondary scattering foil and monitor chamber from the beam axis. Parameter estimation relied on a comprehensive analysis of the sensitivity of the measured quantities, in the large field, to source and geometry parameters. Results demonstrate that the EGS4 Monte Carlo system is capable of matching dose distributions in the largest electron field to the least restrictive of 1 cGy or 1 mm, with D(max) of 100 cGy, over the full energy range. This match results in an underestimation of the bremsstrahlung dose of 10-20% at 15-21 MeV, exceeding the combined experimental and calculational uncertainty in this quantity of 3%. The simulation of electron scattering at energies of 15-21 MeV in EGS4 may be in error. The recently released EGSnrc/BEAMnrc system may provide a better match to measurement.

A comparison of Monte Carlo and Fermi-Eyges-Hogstrom estimates of heart and lung dose from breast electron boost treatment

PURPOSE

Electrons are commonly used in the treatment of breast cancer primarily to deliver a tumor bed boost. We compared the use of the Monte Carlo (MC) method and the Fermi-Eyges-Hogstrom (FEH) algorithm to calculate the dose distribution of electron treatment to normal tissues.

METHODS AND MATERIALS

Ten patients with left-sided breast cancer treated with breast-conservation therapy at the University of California, San Francisco, were included in this study. Each patient received an electron boost to the surgical bed to a dose of 1,600 cGy in 200 cGy fractions prescribed to 80% of the maximum. Doses to the left ventricle (LV) and the ipsilateral lung (IL) were calculated using the EGS4 MC system and the FEH algorithm implemented on the commercially available Pinnacle treatment planning system. An anthromorphic phantom was irradiated with radiochromic film in place to verify the accuracy of the MC system.

RESULTS

Dose distributions calculated with the MC algorithm agreed with the film measurements within 3% or 3 mm. For all patients in the study, the dose to the LV and IL was relatively low as calculated by MC. That is, the maximum dose received by up to 98% of the LV volume was < 100 cGy/day. Less than half of the IL received a dose in excess of 30 cGy/day. When compared with MC, FEH tended to show reduced penetration of the electron beam in lung, and FEH tended to overestimate the bremsstrahlung dose in regions well beyond the electron practical range. These differences were clinically likely to be of little significance, comprising differences of less than one-tenth of the LV and IL volume at doses > 30 cGy and differences in maximum dose of < 35 cGy/day to the LV and 80 cGy/day to the IL.

CONCLUSIONS

From our series, using clinical judgment to prescribe the boost to the surgical bed after breast-conserving treatment results in low doses to the underlying LV and IL. When calculated dose distributions are desired, MC is the most accurate, but FEH can still be used.

Angular correction in reconstruction of electron spectra from depth dose distributions

Techniques for reconstruction of electron spectra from the depth-dose curves used to date have ignored the angular distribution of incident electrons scattered at large angles. The approximation adopted is to employ a database of monoenergetic depth-dose curves generated for normal incidence of electrons at the surface. This approximation is acceptable for direct electrons with small angular spread. However, electrons scattered from the treatment head and collimating system may have large average angles of incidence which affects the depth-dose distribution significantly at shallow depths by increasing energy deposition close to the surface. We show that ignoring the electron incident angular distribution leads to systematic errors in the low energy region of reconstructed electron spectra. We propose a simple 1-D model to correct for these systematic errors using only electron angular distribution at the central beam axis. This model provides reconstructed spectra in excellent agreement with Monte Carlo simulation in the low energy region.

Three-dimensional electron dose calculation using an improved hybrid pencil beam model

An improved hybrid-pencil beam model (HPBM) for electron-beam three-dimensional dose calculation has been studied. The model is based on the fact that away from the edges of a large field, the electron distribution function exactly equals that for an infinitely wide electron beam. In the present model, we use the bipartition model to calculate the longitudinal part of the pencil-beam distribution function, and Fermi-Eyges multiple-scattering theory to calculate its transverse part. In order to describe the electron beam characteristics accurately, we introduce a new parameter, which is extracted from measured profile data near the surface of a water phantom, to correct the transverse distribution determined by the Fermi-Eyges theory. Furthermore, we introduce an effective energy spectrum to describe the effect on the collimated electron beam of the accelerator head. The dose distributions calculated with the improved HPBM were compared with the experimental data, and the agreement was within 1% in most of cases. This preliminary study has demonstrated the potential for use of the model in the clinical therapy.

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.

Reconstruction of electron spectra using singular component decomposition

Reconstruction of electron spectra of medical accelerators from measured depth dose distributions is an attractive tool for commissioning of a Monte Carlo treatment planning system. However, the reconstruction method is an inverse radiation transport problem which is poorly conditioned, in the sense it may become unstable due to small perturbations in the input data. Predicting the sharp (delta-like) peak in the electron spectrum provides an additional challenge for the numerical reconstruction technique. To improve efficiency and robustness of the reconstruction technique, we developed an algorithm based on a separation of the electron spectrum into singular and regular components. We approximate the singular peak of the spectrum by a narrow weighted Gaussian function. The parameters of this Gaussian function are sought using only the fall-off and toe regions of the depth-dose curve. Analytical representation of the spectral peak by a Gaussian has benefit since only one weight and the mean and variance must be derived from the depth-dose curve instead of multiple spectra weights. The regular part of the spectrum is reconstructed from the residual depth-dose distribution using a variational method combined with a regularization technique to avoid the nonphysical oscillations. The effectiveness of the method is demonstrated by comparing predictions to "benchmark" spectra and depth-dose distributions from Monte Carlo simulation of medical accelerators.

Derivation of electron and photon energy spectra from electron beam central axis depth dose curves

A method for deriving the electron and photon energy spectra from electron beam central axis percentage depth dose (PDD) curves has been investigated. The PDD curves of 6, 12 and 20 MeV electron beams obtained from the Monte Carlo full phase space simulations of the Varian linear accelerator treatment head have been used to test the method. We have employed a 'random creep' algorithm to determine the energy spectra of electrons and photons in a clinical electron beam. The fitted electron and photon energy spectra have been compared with the corresponding spectra obtained from the Monte Carlo full phase space simulations. Our fitted energy spectra are in good agreement with the Monte Carlo simulated spectra in terms of peak location, peak width, amplitude and smoothness of the spectrum. In addition, the derived depth dose curves of head-generated photons agree well in both shape and amplitude with those calculated using the full phase space data. The central axis depth dose curves and dose profiles at various depths have been compared using an automated electron beam commissioning procedure. The comparison has demonstrated that our method is capable of deriving the energy spectra for the Varian accelerator electron beams investigated. We have implemented this method in the electron beam commissioning procedure for Monte Carlo electron beam dose calculations.

Comparison of measured and Monte Carlo calculated dose distributions from the NRC linac

We have benchmarked photon beam simulations with the EGS4 user code BEAM [Rogers et al., Med. Phys. 22, 503-524 (1995)] by comparing calculated and measured relative ionization distributions in water from the 10 and 20 MV photon beams of the NRC linac. Unlike previous calculations, the incident electron energy is known independently to 1%, the entire extra-focal radiation is simulated, and electron contamination is accounted for. The full Monte Carlo simulation of the linac includes the electron exit window, target, flattening filter, monitor chambers, collimators, as well as the PMMA walls of the water phantom. Dose distributions are calculated using a modified version of the EGS4 user code DOSXYZ which additionally allows scoring of average energy and energy fluence in the phantom. Dose is converted to ionization by accounting for the (L/rho)water(air) variation in the phantom, calculated in an identical geometry for the realistic beams using a new EGS4 user code, SPRXYZ. The variation of (L/rho)water(air) with depth is a 1.25% correction at 10 MV and a 2% correction at 20 MV. At both energies, the calculated and the measured values of ionization on the central axis in the buildup region agree within 1% of maximum ionization relative to the ionization at 10 cm depth. The agreement is well within statistics elsewhere. The electron contamination contributes 0.35(+/- 0.02) to 1.37(+/- 0.03)% of the maximum dose in the buildup region at 10 MV and 0.26(+/- 0.03) to 3.14(+/- 0.07)% of the maximum dose at 20 MV. The penumbrae at 3 depths in each beam (in g/cm2), 1.99 (dmax, 10 MV only), 3.29 (dmax, 20 MV only), 9.79 and 19.79, agree with ionization chamber measurements to better than 1 mm. Possible causes for the discrepancy between calculations and measurements are analyzed and discussed in detail.