Determination of effective bremsstrahlung spectra and electron contamination for photon dose calculations

Estimation of the lateral variation of photon beam energy spectra using the percentage depth dose reconstruction method

In photon-collapsed cone convolution (pCCC) algorithm of the Monaco treatment planning system (TPS), the central-axis energy spectrum is assumed constant throughout the entire irradiation area. To consider lateral variations, an off-axis softening factor is applied to attenuation coefficients during the total energy released per unit mass calculation. We evaluated this method through comparison studies of percentage depth doses (PDDs) and off-axis ratios (OARs) calculated by Monaco and measured for a 6 MV photon beam at various off-axis angles and depths. Significant differences were observed, with relative differences exceeding ± 1%. Therefore, this method may not accurately represent lateral variations of energy spectra. We propose directly implementing energy spectra on both central-axis and off-axis to improve dose calculation accuracy for large field. To this end, we introduce reconstruction of PDDs from monoenergetic depth doses (MDDs) along off-axis angles, thereby estimating energy spectra as functions of radial distance. This method derives energy spectra quickly without significantly increasing the beam modeling time. MDDs were computed through Monte Carlo simulations (DOSRZnrc). The variances between reconstructed and measured PDDs were minimized using the generalized-reduced-gradient method to optimize energy spectra. Reconstructed PDDs along off-axis angles of 0°, 1.15°, 2.29°, 3.43°, 4.57°, 5.71°, 6.84°, 7.97°, 9.09°, 10.2° to estimate energy spectra at radial distances of 0-18 cm in 2 cm increments and OARs calculated using estimated energy spectra at 5, 10, and 20 cm depths, well agreed with measurement (relative differences within ± 0.5%). In conclusion, our proposed method accurately estimates lateral energy spectrum variation, thereby improving dose calculation accuracy of pCCC algorithm.

Monte Carlo methods for device simulations in radiation therapy

Monte Carlo (MC) simulations play an important role in radiotherapy, especially as a method to evaluate physical properties that are either impossible or difficult to measure. For example, MC simulations (MCSs) are used to aid in the design of radiotherapy devices or to understand their properties. The aim of this article is to review the MC method for device simulations in radiation therapy. After a brief history of the MC method and popular codes in medical physics, we review applications of the MC method to model treatment heads for neutral and charged particle radiation therapy as well as specific in-room devices for imaging and therapy purposes. We conclude by discussing the impact that MCSs had in this field and the role of MC in future device design.

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.

Modification and validation of an analytical source model for external beam radiotherapy Monte Carlo dose calculations

PURPOSE

A dose calculation tool, which combines the accuracy of the dose planning method (DPM) Monte Carlo code and the versatility of a practical analytical multisource model, which was previously reported has been improved and validated for the Varian 6 and 10 MV linear accelerators (linacs). The calculation tool can be used to calculate doses in advanced clinical application studies. One shortcoming of current clinical trials that report dose from patient plans is the lack of a standardized dose calculation methodology. Because commercial treatment planning systems (TPSs) have their own dose calculation algorithms and the clinical trial participant who uses these systems is responsible for commissioning the beam model, variation exists in the reported calculated dose distributions. Today's modern linac is manufactured to tight specifications so that variability within a linac model is quite low. The expectation is that a single dose calculation tool for a specific linac model can be used to accurately recalculate dose from patient plans that have been submitted to the clinical trial community from any institution. The calculation tool would provide for a more meaningful outcome analysis.

METHODS

The analytical source model was described by a primary point source, a secondary extra-focal source, and a contaminant electron source. Off-axis energy softening and fluence effects were also included. The additions of hyperbolic functions have been incorporated into the model to correct for the changes in output and in electron contamination with field size. A multileaf collimator (MLC) model is included to facilitate phantom and patient dose calculations. An offset to the MLC leaf positions was used to correct for the rudimentary assumed primary point source.

RESULTS

Dose calculations of the depth dose and profiles for field sizes 4 × 4 to 40 × 40 cm agree with measurement within 2% of the maximum dose or 2 mm distance to agreement (DTA) for 95% of the data points tested. The model was capable of predicting the depth of the maximum dose within 1 mm. Anthropomorphic phantom benchmark testing of modulated and patterned MLCs treatment plans showed agreement to measurement within 3% in target regions using thermoluminescent dosimeters (TLD). Using radiochromic film normalized to TLD, a gamma criteria of 3% of maximum dose and 2 mm DTA was applied with a pass rate of least 85% in the high dose, high gradient, and low dose regions. Finally, recalculations of patient plans using DPM showed good agreement relative to a commercial TPS when comparing dose volume histograms and 2D dose distributions.

CONCLUSIONS

A unique analytical source model coupled to the dose planning method Monte Carlo dose calculation code has been modified and validated using basic beam data and anthropomorphic phantom measurement. While this tool can be applied in general use for a particular linac model, specifically it was developed to provide a singular methodology to independently assess treatment plan dose distributions from those clinical institutions participating in National Cancer Institute trials.

Technical Note: A Monte Carlo study of magnetic-field-induced radiation dose effects in mice

PURPOSE

Magnetic fields are known to alter radiation dose deposition. Before patients receive treatment using an MRI-linear accelerator (MRI-Linac), preclinical studies are needed to understand the biological consequences of magnetic-field-induced dose effects. In the present study, the authors sought to identify a beam energy and magnetic field strength combination suitable for preclinical murine experiments.

METHODS

Magnetic field dose effects were simulated in a mouse lung phantom using various beam energies (225 kVp, 350 kVp, 662 keV [Cs-137], 2 MV, and 1.25 MeV [Co-60]) and magnetic field strengths (0.75, 1.5, and 3 T). The resulting dose distributions were compared with those in a simulated human lung phantom irradiated with a 6 or 8 MV beam and orthogonal 1.5 T magnetic field.

RESULTS

In the human lung phantom, the authors observed a dose increase of 45% and 54% at the soft-tissue-to-lung interface and a dose decrease of 41% and 48% at the lung-to-soft-tissue interface for the 6 and 8 MV beams, respectively. In the mouse simulations, the magnetic fields had no measurable effect on the 225 or 350 kVp dose distribution. The dose increases with the Cs-137 beam for the 0.75, 1.5, and 3 T magnetic fields were 9%, 29%, and 42%, respectively. The dose decreases were 9%, 21%, and 37%. For the 2 MV beam, the dose increases were 16%, 33%, and 31% and the dose decreases were 9%, 19%, and 30%. For the Co-60 beam, the dose increases were 19%, 54%, and 44%, and the dose decreases were 19%, 42%, and 40%.

CONCLUSIONS

The magnetic field dose effects in the mouse phantom using a Cs-137, 3 T combination or a Co-60, 1.5 or 3 T combination most closely resemble those in simulated human treatments with a 6 MV, 1.5 T MRI-Linac. The effects with a Co-60, 1.5 T combination most closely resemble those in simulated human treatments with an 8 MV, 1.5 T MRI-Linac.

Pencil kernel correction and residual error estimation for quality-index-based dose calculations

Experimental data from 593 photon beams were used to quantify the errors in dose calculations using a previously published pencil kernel model. A correction of the kernel was derived in order to remove the observed systematic errors. The remaining residual error for individual beams was modelled through uncertainty associated with the kernel model. The methods were tested against an independent set of measurements. No significant systematic error was observed in the calculations using the derived correction of the kernel and the remaining random errors were found to be adequately predicted by the proposed method.

Development of a 3-D convolution / superposition algorithm for precise dose calculation in the skull

In this paper an algorithm for calculating 3-D dose distributions within the brain is introduced and adapted to the demands of modem radiosurgery. The dose calculation with this model is based on a 3-D distribution of the primary photon intensity which is calculated with a ray casting algorithm. A prelocated matrix takes into account field sizes as well as modifying elements as collimator positions (MLC), blocks, wedges and compensators. Monte Carlo precalculated monoenergetic kernels from 0.1 MeV to 50 MeV were at our disposal. The components of the spectrum were either determined by deconvoluting depth dose curves measured in water or analyzed with a Ge-Li detector system in the case of 60Co. The calculated fluence distribution has to be superposed to the complete kernel containing the spatial energy deposition. Inhomogeneities and tissue interface phenomena (rhoe, Z) have been investigated. The divergence of the rays and the curved surface of the patient are taken into account. Assuming homogenous media, it is possible to shorten the computation time by using the Fast Fourier Transformation (FFT) delivering a first overview within seconds. The algorithm was evaluated and verified under specific conditions of small fields as used in radiosurgery and compared to dose measurements and Monte Carlo calculations. In using both the fast algorithm (FFT) for mainly homogenous conditions on one hand and the very precise superposition for inhomogeneous cases on the other, this algorithm can be a very helpful instrument especially for critical locations in the skull.

Photon pencil kernel parameterisation based on beam quality index

BACKGROUND AND PURPOSE

New treatment techniques in radiotherapy employ increasing dose calculation complexity in treatment planning. For an adequate check of the results coming from a modern treatment planning system, clinical tools with almost the same degree of generality and accuracy as the planning system itself are needed. To fulfil this need we propose a photon pencil kernel parameterization based on a minimum of input data that can be used for phantom scatter calculations. Through scatter integration the pencil kernel model can calculate common parameters, such as TPR or phantom scatter factors, used in various dosimetric QA (quality assurance) procedures.

MATERIAL AND METHODS

The proposed model originates from an already published radially parameterized pencil kernel. A depth parameterization of the pencil kernel parameters has been introduced, based on a large database containing commissioned beam data for a commercial treatment planning system. The entire pencil kernel model demands only one photon beam quality index, TPR20,10, as input.

RESULTS

By comparing the dose calculation results to the extensive experimental data set in the database, it has been possible to make a thorough analysis of the resulting accuracy. The errors in calculated doses, normalized to the reference geometry, are in most cases smaller than 2%.

CONCLUSIONS

The investigation shows that a pencil kernel model based only on TPR20,10 can be used for dosimetric verification purposes in megavoltage photon beams at depths below the range of contaminating electrons.

Enhanced bremsstrahlung spectrum reconstruction from depth–dose gradients

We present a technique to significantly improve the accuracy of bremsstrahlung spectra reconstructed from central-axis depth-dose data using inverse methods. While typical approaches directly use the measured depth-dose data, we show the advantage of using the gradient of these data for reconstruction. The inverse problem in terms of gradients is shown to be markedly less ill-conditioned than the usual inverse problem. In each case, a regularization is introduced to alleviate the effects of noise due to measurement and computation. The error in taking derivatives of depth-dose data is demonstrated to be sufficiently controllable as not to overtake the improvements in the conditioning of the inverse problem in a pair of simulated examples.

Beam modeling and verification of a photon beam multisource model

Dose calculations for treatment planning of photon beam radiotherapy require a model of the beam to drive the dose calculation models. The beam shaping process involves scattering and filtering that yield radiation components which vary with collimator settings. The necessity to model these components has motivated the development of multisource beam models. We describe and evaluate clinical photon beam modeling based on multisource models, including lateral beam quality variations. The evaluation is based on user data for a pencil kernel algorithm and a point kernel algorithm (collapsed cone) used in the clinical treatment planning systems Helax-TMS and Nucletron-Oncentra. The pencil kernel implementations treat the beam spectrum as lateral invariant while the collapsed cone involves off axis softening of the spectrum. Both algorithms include modeling of head scatter components. The parameters of the beam model are derived from measured beam data in a semiautomatic process called RDH (radiation data handling) that, in sequential steps, minimizes the deviations in calculated dose versus the measured data. The RDH procedure is reviewed and the results of processing data from a large number of treatment units are analyzed for the two dose calculation algorithms. The results for both algorithms are similar, with slightly better results for the collapsed cone implementations. For open beams, 87% of the machines have maximum errors less than 2.5%. For wedged beams the errors were found to increase with increasing wedge angle. Internal, motorized wedges did yield slightly larger errors than external wedges. These results reflect the increased complexity, both experimentally and computationally, when wedges are used compared to open beams.

Characterization of electron contamination in megavoltage photon beams

The purpose of the present study is to characterize electron contamination in photon beams in different clinical situations. Variations with field size, beam modifier (tray, shaping block) and source-surface distance (SSD) were studied. Percentage depth dose measurements with and without a purging magnet and replacing the air by helium were performed to identify the two electron sources that are clearly differentiated: air and treatment head. Previous analytical methods were used to fit the measured data, exploring the validity of these models. Electrons generated in the treatment head are more energetic and more important for larger field sizes, shorter SSD, and greater depths. This difference is much more noticeable for the 18 MV beam than for the 6 MV beam. If a tray is used as beam modifier, electron contamination increases, but the energy of these electrons is similar to that of electrons coming from the treatment head. Electron contamination could be fitted to a modified exponential curve. For machine modeling in a treatment planning system, setting SSD at 90 cm for input data could reduce errors for most isocentric treatments, because they will be delivered for SSD ranging from 80 to 100 cm. For very small field sizes, air-generated electrons must be considered independently, because of their different energetic spectrum and dosimetric influence.

Calculation of photon energy deposition kernels and electron dose point kernels in water

Effects of changes in the physics of EGSnrc compared to EGS4/PRESTA on energy deposition kernels for monoenergetic photons and on dose point kernels for beta sources in water are investigated. In the diagnostic energy range, Compton binding corrections were found to increase the primary energy fraction up to 4.5% at 30 keV with a corresponding reduction of the scatter component of the kernels. Rayleigh scattered photons significantly increase the scatter component of the kernels and reduce the primary energy fraction with a maximum 12% reduction also at 30 keV where the Rayleigh cross section in water has its maximum value. Sampling the photo-electron angular distribution produces a redistribution of the energy deposited by primaries around the interaction site causing differences of up to 2.7 times in the backscattered energy fraction at 20 keV. Above the pair production threshold, the dose distribution versus angle of the primary dose component is significantly different from the EGS4 results. This is related to the more accurate angular sampling of the electron-positron pair direction in EGSnrc as opposed to using a fixed angle approximation in default EGS4. Total energy fractions for photon beams obtained with EGSnrc and EGS4 are almost the same within 0.2%. This fact suggests that the estimate of the total dose at a given point inside an infinite homogeneous water phantom irradiated by broad beams of photons will be very similar for kernels calculated with both codes. However, at interfaces or near boundaries results can be very different especially in the diagnostic energy range. EGSnrc calculated kernels for monoenergetic electrons (50 keV, 100 keV, and 1 MeV) and beta spectra (32P and 90Y) are in excellent agreement with reported EGS4 values except at 1 MeV where inclusion of spin effects in EGSnrc produces an increase of the effective range of electrons. Comparison at 1 MeV with an ETRAN calculation of the electron dose point kernel shows excellent agreement.

An MCNP-based model of a medical linear accelerator x-ray photon beam

The major components in the x-ray photon beam path of the treatment head of the VARIAN Clinac 2300 EX medical linear accelerator were modeled and simulated using the Monte Carlo N-Particle radiation transport computer code (MCNP). Simulated components include x-ray target, primary conical collimator, x-ray beam flattening filter and secondary collimators. X-ray photon energy spectra and angular distributions were calculated using the model. The x-ray beam emerging from the secondary collimators were scored by considering the total x-ray spectra from the target as the source of x-rays at the target position. The depth dose distribution and dose profiles at different depths and field sizes have been calculated at a nominal operating potential of 6 MV and found to be within acceptable limits. It is concluded that accurate specification of the component dimensions, composition and nominal accelerating potential gives a good assessment of the x-ray energy spectra.

Enhanced spectral discrimination through the exploitation of interface effects in photon dose data

The convolution/superposition algorithm for computing dose from photon beams in radiation therapy planning requires knowledge of the energy spectrum. The algorithm can compute the dose for a polyenergetic beam as the weighted sum of the individual dose contributions from monoenergetic beams. In this study we exploit interface effects apparent in the dose distributions to discriminate among spectra of high energy photon beams. We have studied the sensitivity of the depth dose distribution to the energy components using a hypothetical beam for various field sizes and depths in water and water-lung-water media. Six theoretical spectra were simulated. We compared depth dose data from these spectra using three quantitative measures which are inherently free of normalization ambiguities: for homogeneous water, the ratio D20/D10 and a logarithmic derivative in the buildup region LD(build-up) and for inhomogeneous lung/water, the lung correction factor (CF). It was found that the ability of both the CF and the LD(build-up) tests to discriminate between the various theoretical spectra were superior to that of the D20/D10 test. This discriminating power of the CF test decreases with increasing field size due to restored electronic equilibrium. The CF test, though, has some advantages over the LD(build-up) test since it is less prone to electron contamination issues and numerical errors. A practical example with a 15 MV photon beam illustrates the process. Consequently, we suggest that as part of a beam-commissioning methodology, designated electronic disequilibrium test cases be implemented in unambiguously determining the correct energy spectrum to be used.

Experimental verification of convolution/superposition photon dose calculations for radiotherapy treatment planning

This work describes an experimental verification of the two-photon dose calculation engines available on the Helax-TMS (version 6.1) commercial radiotherapy treatment planning system. The performance of the pencil beam convolution and the collapsed cone superposition algorithms was examined for 4, 6, 15 MV beams, under a range of clinically relevant irradiation geometries. Comparisons against measurements were carried out in terms of absolute dose, thus assessment of the accuracy of monitor unit (MU) calculations was also carried out. Results show that both algorithms agree with measurement to acceptable tolerance levels in most cases in homogeneous water-equivalent media irradiated under full scatter conditions. The collapsed cone algorithm slightly overestimates the penumbra width and this is mainly due to discretization effects of the fluence matrix. The accuracy of this algorithm strongly depends on the resolution of the patient density matrix. It is recommended that the density matrix voxel size used for dose calculations is less than 5 x 5 x 5 mm3. The dose in media irradiated under missing tissue geometry, or in the presence of low or high-density heterogeneities, is modelled best with the collapsed cone algorithm. This is of particular clinical interest in treatment planning of the breast and of the thorax. For these treatment sites, a retrospective study of treatment plans indicated in certain cases significant overestimation of the dose to the planning target volume when using the pencil beam convolution model.

Geometrical and dosimetrical characterization of the photon source using a micro-multileaf collimator for stereotactic radiosurgery

A micro-multileaf collimator (microMLC) for stereotactic radiosurgery is used for determination of the spatial intensity distribution of the photon source of a linear accelerator. The method is based on grid field dose measurements using film dosimetry and is easy to perform. Since the microMLC does not allow 'direct' imaging of the photon source, special software has been developed to analyse grid field measurements. Besides the source-density function, grid field analysis yields the position of the focal spot in the room laser coordinate system of the linear accelerator and the position of the treatment head rotation axis and the inclination angle of the leaf bank. Thus the method can be used for base dosimetry and for quality assurance in radiosurgery using a microMLC.

[Improvement of the accuracy of the Laplace transform method for the determination of radiotherapy spectra of clinical linear accelerators]

The present study focused on the reconstruction of the bremsstrahlung spectrum of a clinical linear accelerator from the measured transmission curve, with the aim of improving the accuracy of this method. The essence of the method was the analytic inverse Laplace transform of a parameter function fitted to the measured transmission curve. We tested known fitting functions, however they resulted in considerable fitting inaccuracy, leading to inaccuracies of the bremsstrahlung spectrum. In order to minimise the fitting errors, we employed a linear combination of n equations with 2n-1 parameters. The fitting errors are now considerably smaller. The measurement of the transmission function requires that the energy-dependent detector response is taken into account. We analysed the underlying physical context and developed a function that corrects for the energy-dependent detector response. The factors of this function were experimentally determined or calculated from tabulated values.

Validation of intensity modulation on a commercial treatment planning system

For two years now, a study on intensity modulated radiotherapy (IMRT) has been in progress at the Antoine Lacassagne Hospital Center for Cancer Therapy (in Nice) in collaboration with the University of Nice-Sophia Antipolis. The kind of intensity modulation that was used is the "step and shoot" technique in which the modulated beam is created both by adding andjoining elementary fields. Before carrying out clinical tests, several problems regarding the production of modulated beams has to be mastered. The current developments of our study enable us to dosimetrically produce (in water phantom and in the PMMA phantom) complexmodulated whose segmentation was calculated by one commercial treatment planning system (TPS). Nevertheless, we showed and studied some critical discrepancies between standard clinical calculations and the calculations using field segmentation. We showed that with nonoptimal conditions of segmentation the discrepancies, which are due to the type of algorithm used, could bring about significant errors inside the field of up to 10% of maximum dose. Another point of our study is the quantification and resolution of differences between measurements and calculations due to the internal segmentation of calculated modulated fields and their realization on Linac. Once again, in none optimal conditions of segmentation and inside the field we obtained discrepancies up to 20% of maximum dose between calculations using field segmentation and measurements. That was mainly due to the tongue and groove effect and penumbra phenomena. This study allows us to show that the discrepancies between segmentation calculations and standard clinical calculations should be solved by the use of penumbra models during segmentation calculations. We will introduce both the study and its near-future perspectives.

[Dose distribution of asymmetric fields: comparison of the Helax-TMS with our developed 2D-program ASYMM]

The purpose of this investigation was to compare the commercial 3D-treatment planning system Helax TMS to a simple 2D program ASYMM, concerning the calculation of dose distributions for asymmetric fields. The dose calculation algorithm in Helax-TMS is based on the polyenergetic pencil beam model of Ahnesjö. Our own developed 2D treatment planning program ASYMM, based on the Thomas and Thomas method for asymmetric open fields, has been extended to calculate the dose distributions for open and wedged fields. Using both methods, dose distributions for various asymmetric open and wedged fields of a 4-MV Linear accelerator were calculated and compared with measured data in water. The agreement of the Helax-TMS and the ASYMM with the experiment was good, whereas ASYMM showed a better accuracy for larger asymmetric angles. The explanation for this result is based on the consideration of beam hardening within the flattening filter and edges for different asymmetric settings in ASYMM algorithm. The TMS, however, owns the diverse possibilities that the 3D calculation and corresponding representation provide and holds better application opportunities in clinical routine.

A simple method for bremsstrahlung spectra reconstruction from transmission measurements

A new method for evaluation of bremsstrahlung spectra from transmission measurements has been developed. In this method some very well known facts relating to thick target bremsstrahlung spectra are a priori included in the calculation procedure. Some characteristics of the method are preliminarily illustrated on a 6 MV therapy linear accelerator.

Monte Carlo calculation of nine megavoltage photon beam spectra using the BEAM code

A recent paper analyzed the sensitivity to various simulation parameters of the Monte Carlo simulations of nine beams from three major manufacturers of commercial medical linear accelerators, ranging in energy from 4-25 MV. In this work the nine models are used: to calculate photon energy spectra and average energy distributions and compare them to those published by Mohan et al. [Med. Phys. 12, 592-597 (1985)]; to separate the spectra into primary and scatter components from the primary collimator, the flattening filter and the adjustable collimators; and to calculate the contaminant-electron fluence spectra and the electron contribution to the depth-dose curves. Notwithstanding the better precision of the calculated spectra, they are similar to those calculated by Mohan et al. The three photon spectra at 6 MV from the machines of three different manufacturers show differences in their shapes as well as in the efficiency of bremsstrahlung production in the corresponding target and filter combinations. The contribution of direct photons to the photon energy fluence in a 10 x 10 field varies between 92% and 97%, where the primary collimator contributes between 0.6% and 3.4% and the flattening filter contributes between 0.6% and 4.5% to the head-scatter energy fluence. The fluence of the contaminant electrons at 100 cm varies between 5 x 10(-9) and 2.4 x 10(-7) cm(-2) per incident electron on target, and the corresponding spectrum for each beam is relatively invariant inside a 10 x 10 cm2 field. On the surface the dose from electron contamination varies between 5.7% and 11% of maximum dose and, at the depth of maximum dose, between 0.16% and 2.5% of maximum dose. The photon component of the percentage depth-dose at 10 cm depth is compared with the general formula provided by AAPM's task group 51 and confirms the claimed accuracy of 2%.

Sensitivity of megavoltage photon beam Monte Carlo simulations to electron beam and other parameters

The BEAM code is used to simulate nine photon beams from three major manufacturers of medical linear accelerators (Varian, Elekta, and Siemens), to derive and evaluate estimates for the parameters of the electron beam incident on the target, and to study the effects of some mechanical parameters like target width, primary collimator opening, flattening filter material and density. The mean energy and the FWHM of the incident electron beam intensity distributions (assumed Gaussian and cylindrically symmetric) are derived by matching calculated percentage depth-dose curves past the depth of maximum dose (within 1% of maximum dose) and off-axis factors (within 2sigma at 1% statistics or less) with measured data from the AAPM RTC TG-46 compilation. The off-axis factors are found to be very sensitive to the mean energy of the electron beam, the FWHM of its intensity distribution, its angle of incidence, the dimensions of the upper opening of the primary collimator, the material of the flattening filter and its density. The off-axis factors are relatively insensitive to the FWHM of the electron beam energy distribution, its divergence and the lateral dimensions of the target. The depth-dose curves are sensitive to the electron beam energy, and to its energy distribution, but they show no sensitivity to the FWHM of the electron beam intensity distribution. The electron beam incident energy can be estimated within 0.2 MeV when matching either the measured off-axis factors or the central-axis depth-dose curves when the calculated uncertainties are about 0.7% at the 1 sigma level. The derived FWHM (+/-0.1 mm) of the electron beam intensity distributions all fall within 1 mm of the manufacturer specifications except in one case where the difference is 1.2 mm.

Dosimetric verification of modulated photon fields by means of compensators for a kernel model

The approach in treatment planning of applying beam quality correction factors to model compensator-induced depth-hardening effects is investigated and the present work comprises a dosimetric verification of the model for a common compensator material. Lead sheet modulators for four different phantom shapes were designed using a treatment planning system based on the model. The modulators were designed to yield homogeneous dose in a plane. The calculated modulation created by the lead sheets was re-imported into the treatment planning system and applied to a water phantom geometry for verification purposes. Comparing measurements, a total of 31 different geometries were measured, with calculations in this geometry showing good agreement for depth doses, dose profiles and output data with a maximum deviation of 4% except locally in the penumbra region and close to the edges of the cut lead sheets.

Detector line spread functions determined analytically by transport of Compton recoil electrons

To achieve the maximum benefit of conformal radiation therapy it is necessary to obtain accurate knowledge of radiation beam penumbras based on high-resolution relative dosimetry of beam profiles. For this purpose there is a need to perform high-resolution dosimetry with well-established routine dosimeters, such as ionization chambers or diodes. Profiles measured with these detectors must be corrected for the dosimeter's nonideal response, caused by finite dimensions and, in the case of an ionization chamber, the alteration of electron transport and a contribution of electrons recoiled in the chamber wall and the central electrode. For this purpose the line spread function (LSF) of the detector is needed. The experimental determination of LSFs is cumbersome and restricted to the specific detector and beam energy spectrum used. Therefore, a previously reported analytical model [Med. Phys. 27, 923-934 (2000)] has been extended to determine response profiles of routine dosimeters: shielded diodes and, in particular, ionization chambers, in primary dose slit beams. The model combines Compton scattering of incident photons, the transport of recoiled electrons by Fermi-Eyges small-angle multiple scattering theory, and functions to limit electron transport. It yields the traveling direction and the energy of electrons upon incidence on the detector surface. In the case of ionization chambers, geometrical considerations are then sufficient to calculate the relative amount of ionization in chamber air, i.e., the detector response, as a function of the detector location in the slit beam. In combination with the previously reported slit beam dose profiles, the LSF can then readily be derived by reconstruction techniques. Since the spectral contributions are preserved, the LSF of a dosimeter is defined for any beam for which the effective spectrum is known. The detector response profiles calculated in this study have been verified in a telescopic slit beam geometry, and were found to correspond to experimental profiles within 0.2 and 0.3 mm (full width at half-maximum) for a Wellhoefer IC15 chamber in a 6 and 25 MV-X x-ray beam, respectively. For a shielded diode these figures were found to be 0.2 and 0.1 mm, respectively. It is shown that a shielded diode in a primary beam needs only a small size-based correction of measured profiles. The effect of the LSF of an IC15 chamber on penumbra width has been determined for a set of model penumbras. The LSFs calculated by the application of the analytical model yield a broadening by 2 mm of a 3 mm wide penumbra (20%-80%). This is 0.5 mm (6 MV-X) to 1 mm (25 MV-X) smaller than found with the experimental LSFs. With a spatial correction based on the LSFs that were determined in this study, this broadening of up to 2 mm is eliminated, so that ionization chambers like the IC15 can be used for high-resolution relative dosimetry on a routine basis.

A virtual linear accelerator for verification of treatment planning systems

A virtual linear accelerator is implemented into a commercial pencil-beam-based treatment planning system (TPS) with the purpose of investigating the possibility of verifying the system using a Monte Carlo method. The characterization set for the TPS includes depth doses, profiles and output factors, which is generated by Monte Carlo simulations. The advantage of this method over conventional measurements is that variations in accelerator output are eliminated and more complicated geometries can be used to study the performance of a TPS. The difference between Monte Carlo simulated and TPS calculated profiles and depth doses in the characterization geometry is less than +/-2% except for the build up region. This is of the same order as previously reported results based on measurements. In an inhomogeneous, mediastinum-like case, the deviations between TPS and simulations are small in the unit-density regions. In low-density regions, the TPS overestimates the dose, and the overestimation increases with increasing energy from 3.5% for 6 MV to 9.5% for 18 MV. This result points out the widely known fact that the pencil beam concept does not handle changes in lateral electron transport, nor changes in scatter due to lateral inhomogeneitics. It is concluded that verification of a pencil-beam-based TPS with a Monte Carlo based virtual accelerator is possible, which facilitates the verification procedure.

Slit x-ray beam primary dose profiles determined by analytical transport of Compton recoil electrons

Accurate measurement of radiation beam penumbras is essential for conformal radiotherapy. For this purpose a detailed knowledge of the dosimeter's spatial response is required. However, experimental determination of detector spatial response is cumbersome and restricted to the specific detector type and beam spectrum used. A model has therefore been developed to calculate in slit beam geometry both dose profiles and detector response profiles. Summations over representative photon beam spectra yield profiles for polyenergetic beams. In the present study the model is described and resulting dose profiles verified. The model combines Compton scattering of incident photons, transport of resulting electrons by Fermi-Eyges small-angle multiple scattering theory, and functions to limit electron transport. This analytic model thus yields line spread kernels of primary dose in a water phantom. It is shown that the spatial response of an ideal point detector to a primary photon beam can be well described by the model; the calculations are verified by measurements with a diamond detector in a telescopic slit geometry in which all dose contributions except for the primary dose can be excluded. Effects of photon detector behavior, source size of the linear accelerator (linac) and detector size are studied. Measurements show that slit dose profiles calculated by means of the kernel are accurate within 0.1 mm of the full-width at half-maximum. For a theoretical point source and point detector combined with a 0.2 mm wide slit, the full-width half-maximum values of the slit beam dose profiles are calculated as 0.37 mm and 0.42 mm in a 6 MV and 25 MV x-ray beam, respectively. The present study shows that the model is adequate to calculate local dose effects that are dominated by approximately mono-directional, primary photon fluence. The analytic model further provides directional electron fluence information and is designed to be applied to various detectors and linac beam spectra.

Implementation of FFT convolution and multigrid superposition models in the FOCUS RTP system

In radiotherapy treatment planning, convolution/superposition algorithms currently represent the best practical approach for accurate photon dose calculation in heterogeneous tissues. In this work, the implementation, accuracy and performance of the FFT convolution (FFTC) and multigrid superposition (MGS) algorithms are presented. The FFTC and MGS models use the same 'TERMA' calculation and are commissioned using the same parameters. Both models use the same spectra, incorporate the same off-axis softening and base incident lateral fluence on the same measurements. In addition, corrections are explicitly applied to the polyenergetic and parallel kernel approximations, and electron contamination is modelled. Spectra generated by Monte Carlo (MC) modelling of treatment heads are used. Calculations using the MC spectra were in excellent agreement with measurements for many linear accelerator types. To speed up the calculations, a number of calculation techniques were implemented, including separate primary and scatter dose calculation, the FFT technique which assumes kernel invariance for the convolution calculation and a multigrid (MG) acceleration technique for the superposition calculation. Timing results show that the FFTC model is faster than MGS by a factor of 4 and 8 for small and large field sizes, respectively. Comparisons with measured data and BEAM MC results for a wide range of clinical beam setups show that (a) FFTC and MGS doses match measurements to better than 2% or 2 mm in homogeneous media; (b) MGS is more accurate than FFTC in lung phantoms where MGS doses are within 3% or 3 mm of BEAM results and (c) FFTC overestimates the dose in lung by a maximum of 9% compared to BEAM.

Determining clinical photon beam spectra from measured depth dose with the Cimmino algorithm

A method to determine the spectrum of a clinical photon beam from measured depth-dose data is described. At shallow depths, where the range of Compton-generated electrons increases rapidly with photon energy, the depth dose provides the information to discriminate the spectral contributions. To minimize the influence of contaminating electrons, small (6 x 6 cm2) fields were used. The measured depth dose is represented as a linear combination of basis functions, namely the depth doses of monoenergetic photon beams derived by Monte Carlo simulations. The weights of the basis functions were obtained with the Cimmino feasibility algorithm, which examines in each iteration the discrepancy between predicted and measured depth dose. For 6 and 15 MV photon beams of a clinical accelerator, the depth dose obtained from the derived spectral weights was within about 1% of the measured depth dose at all depths. Because the problem is ill conditioned, solutions for the spectrum can fluctuate with energy. Physically realistic smooth spectra for these photon beams appeared when a small margin (about +/- 1%) was attributed to the measured depth dose. The maximum energy of both derived spectra agreed with the measured energy of the electrons striking the target to within 1 MeV. The use of a feasibility method on minimally relaxed constraints provides realistic spectra quickly and interactively.

Calculation of a pencil beam kernel from measured photon beam data

Usually, pencil beam kernels for photon beam calculations are obtained by Monte Carlo calculations. In this paper, we present a method to derive a pencil beam kernel from measured beam data, i.e. central axis depth doses, phantom scatter factors and off-axis ratios. These data are usually available in a radiotherapy planning system. The differences from other similar works are: (a) the central part of the pencil beam is derived from the measured penumbra of large fields and (b) the dependence of the primary photon fluence on the depth caused by beam hardening in the phantom is taken into account. The calculated pencil beam will evidently be influenced by the methods and instruments used for measurement of the basic data set. This is of particular importance for an accurate prediction of the absorbed dose delivered by small fields. Comparisons with measurements show that the accuracy of the calculated dose distributions fits well in a 2% error interval in the open part of the field, and in a 2 mm isodose shift in the penumbra region.

Dose calculations for external photon beams in radiotherapy

Dose calculation methods for photon beams are reviewed in the context of radiation therapy treatment planning. Following introductory summaries on photon beam characteristics and clinical requirements on dose calculations, calculation methods are described in order of increasing explicitness of particle transport. The simplest are dose ratio factorizations limited to point dose estimates useful for checking other more general, but also more complex, approaches. Some methods incorporate detailed modelling of scatter dose through differentiation of measured data combined with various integration techniques. State-of-the-art methods based on point or pencil kernels, which are derived through Monte Carlo simulations, to characterize secondary particle transport are presented in some detail. Explicit particle transport methods, such as Monte Carlo, are briefly summarized. The extensive literature on beam characterization and handling of treatment head scatter is reviewed in the context of providing phase space data for kernel based and/or direct Monte Carlo dose calculations. Finally, a brief overview of inverse methods for optimization and dose reconstruction is provided.

Transmission measurements in air using the ESTRO mini-phantom

The aim of this work is to study the possibility of using the ESTRO mini-phantom for transmission measurements of primary kerma in water at a point free in air. We discuss in-air measurements in general, with special attention given to in-air equivalent measurements using a water equivalent mini-phantom. The study includes four different photon energies (4, 6, 10 and 18 MV), where scoring of dose and primary kerma inside a mini-phantom in narrow beam geometry is performed with the Monte Carlo code EGS4. The results reveal that relative measurements (i.e. with and without a water absorber present) at 10 cm depth in a mini-phantom do not represent the variation of primary kerma in water at a point free in air (deviations as large as 7% at 4 MV are observed). Minimum deviations are obtained at depths somewhat larger than the depth of dose maximum. The observed deviations are due to a considerable beam hardening in the water absorber, which changes the amount of attenuation and scatter inside the mini-phantom.

Composite energy deposition kernels for focused point monodirectional photon beams

A 3D volume overlap algorithm has been developed for converting energy deposition kernels between arbitrary 2D and 3D irradiation geometries. The kernels can be used as convolution kernels in inverse radiation therapy planning and as accurate descriptions of the dose distributions for clinically important beam geometries. The new method of dose calculation combining Monte Carlo and analytical methods has introduced an improved accuracy in dose calculation on the fractional per cent level. The comparisons are also made for a wide range of photon spectra and irradiation geometries from narrow point monodirectional pencil beams to finite uniform beams, 4pi steradians isotropically converging beams and divergent beams from isotropic point sources. It is seen that the photon scatter penumbra is highest at low photon energies whereas the secondary electron penumbra is widest at high photon energies, making low energy beams more interesting for small targets and high energy beams most useful for large deep-seated targets.

An MCNP-based model of a linear accelerator x-ray beam

The Monte Carlo N-Particle radiation transport computer code (MCNP) has been employed on a personal computer to develop a simple model simulating the major components within the beam path of a linear accelerator radiation head, namely the electron target, primary conical collimator, beam flattening filter, wedge filter and the secondary collimators. The model was initially used to calculate the energy spectra and angular distributions of the x-ray beam for the Philips SL 75/5 linear accelerator, in a plane immediately beneath the flattening filter. These data were subsequently used as a 'source' of x-rays at the target position, to assess the emergent beam from the secondary collimators. The depth dose distributions and dose profiles at constant depth for various field sizes have been calculated for a nominal operating potential of 4 MV and found to be within acceptable limits. It is concluded that the technique may be used to calculate the energy spectra of any linear accelerator upon specification of the component dimensions, materials and nominal accelerating potential. It is anticipated that this work will serve as the basis of a quality control tool for linear accelerators and treatment planning systems.