Planar Fluence Research Articles

Comparison of Rapid Arc and Intensity Modulated Radiotherapy in a True Beam Linear Accelerator for 6 MV: Application of AAPM TG‐119 tests in treatment planning and quality assurance

AbstractObjectiveWe developed rapid arc (RA) and intensity‐modulated radiotherapy (IMRT) plans based on the American Association of Physicists in Medicine Task Group‐119 (AAPM TG‐119) proposals and compared the planning and quality assurance results.Materials and MethodsTwo treatment plans were used for each study patient: one using 7–9 IMRT fields and the other using the two full‐arc RA methods. Plan optimization and dose calculations were performed using 6 MV photons and EclipseTM with the anisotropic analytical algorithm (AAA). Task group (TG)‐119 described the planning objectives used to evaluate the treatment plans generated for this study. Point dose, planar fluence measurement, and trajectory log file analysis are used for quality assurance.ResultsThe conformity index (CI) for treatment plans varied between 0.76–0.91 when using IMRT and 0.75–0.93 when using RA. The homogeneity index (HI) was approximately 0.10–0.24 (IMRT) and 0.07–0.23 (RA). The ratio of the total number of monitor units required for IMRT to that required for RA was between 0.87 and 2.14. The treatment log files exhibited higher gamma passing with RA than with IMRT.ConclusionRA plans were more effective than IMRT plans in achieving the test goals. Point dose measurements and electronic portal imaging device (EPID)‐based planar fluence measurements showed statistically insignificant differences between the IMRT and RA plan quality assurance (QA) results. However, the trajectory log file analysis exhibited better gamma‐passing results for RA than for IMRT.

Very high-energy electron dose calculation using the Fermi-Eyges theory of multiple scattering and a simplified pencil beam model.

Very high-energy electrons (VHEE) radiotherapy, in the energy range of 100-200 MeV is currently considered a promising technique for the future of radiation therapy and could benefit from the promises of ultra-high dose rate FLASH therapy. However, to our knowledge, no analytical calculation models have been tested for this type of application and the approximations proposed for multiple scattering with electron beams have not been extensively evaluated at these high energies. In this work, we discuss the derivation of a simple and fast algorithm based on the Fermi-Eyges theory of multiple Coulomb scattering for fast dose calculation for VHEE beams (up to 200 MeV). Similar to the Gaussian pencil beam models used for electron or proton beams, this pencil beam kernel is separated into a central and an off-axis term. Monte Carlo simulations are performed to compare the analytical calculations with simulations and to determine the parametrizations used in the model at the highest electron energies. The normalized electron planar fluence distribution is described in water according to the Fermi-Eyges theory of multiple Coulomb scattering and a double Gaussian distribution model. The main quantities used in the model and their calculation (mass angular scattering power, mean energy, range straggling) are discussed and tested for electron energies up to 200 MeV. The TOPAS/Geant4 Monte Carlo (MC) toolkit is used to compare analytical calculations with MC simulations for a theoretical pencil beam irradiation and to find the best parameters describing the range straggling. The model is then tested on a realistic simulation of a pencil beam scanning beamline with treatment field dimensions up to 15×15cm2 and for deep-seated targets. Radial dose distributions of a pencil beam in water were calculated with the model and compared with the results of a complete Monte Carlo simulation. A good agreement (within 2%/2mm gamma passing rate superior to 90%, and a mean deviation between calculated and simulated pencil beam radial spread smaller than 0.6mm) was observed between analytical dose distributions and simulations for energies up to 200 MeV and field sizes up to 15×15cm2 . A parameterization of an electron source and an analytical pencil beam model were proposed in this work, thereby allowing a suitable reproduction of the lateral fluence of a VHEE beam and good agreement between calculations and simulated data. Further improvement of the method would require the consideration of a model describing the large-angle scattering of the electrons. The results of this work could support future research into VHEE radiotherapy and might be of interest for use together with VHEE broad beams produced by scanned narrow pencil beams.

Implementation of pencil beam redefinition algorithm (PBRA) for intraoperative electron radiation therapy (IOERT) treatment planning

PurposeSimilar to other radiation therapy techniques, intraoperative electron radiation therapy (IOERT) can benefit from an online treatment planning system (TPS). Among all the analytical electron dose calculation algorithms, pencil beam redefinition algorithm (PBRA) has shown an acceptable accuracy in inhomogeneities. The input dataset for PBRA includes electron planar fluence, mean direction and root mean square (RMS) spread about the mean direction which had been introduced based on the conventional linear accelerator geometry in former studies. Herein, three methods for implementing PBRA for IOERT system are presented. MethodsThe initialization parameters were identified using Monte Carlo (MC) simulation of a dedicated IOERT system equipped with a cylindrical 10 cm applicator, irradiating a water phantom. Phase space distribution of electrons was recorded on a plane below the applicator. The input dataset was extracted for 2 × 2 mm2 pixels and energy bin width of 1 MeV. ResultsPBRA was implemented with three initialization methods and compared to MC. The 3D gamma analysis of the algorithm with the Formula method, which was in best agreement with MC in a simple water phantom, showed passing rates of more than 99 % for all nominal energies and it was 97.1 % for 8 MeV in the presence of protecting disk and irregular surface. Implementing PBRA on CUDA C++ resulted in 5 s run time for 8 MeV nominal energy in a water phantom. ConclusionsThe agreement between PBRA dose calculation and MC is promising for the development of an intraoperative TPS for IOERT.

Evaluating the dosimetric consequences of MLC leaf positioning errors in dynamic IMRT treatments

AbstractPurposeThe purpose of this study was to evaluate the dosimetric impact of multileaf collimator (MLC) positional errors on dynamic intensity-modulated radiotherapy (IMRT) treatments through planning simulation. Secondly the sensitivity of IMRT MatriXX device for detecting the MLC leaf positional errors was also evaluated.Materials and methodsIn this study five dynamic IMRT plans, each for brain and head–neck (HN), were retrospectively included. An in-house software was used to introduce random errors (uniform distribution between −2·0 and +2·0 mm) and systematic errors [±0·5, ±0·75, ±1·0 and ±2·0 mm (+: open MLC error and −: close MLC error)]. The error-introduced MLC files were imported into the treatment planning system and new dose distributions were calculated. Furthermore, the dose–volume histogram files of all plans were exported to in-house software for equivalent uniform dose (EUD), tumour control probability and normal tissue complication probability calculations. The error-introduced plans were also delivered on LINAC, and the planar fluences were measured by IMRT MatriXX. Further, 3%/3 mm and 2%/2 mm γ-criteria were used for analysis.ResultsIn planning simulation study, the impact of random errors was negligible and ΔEUD was <0·5±0·7%, for both brain and HN. The impact of systematic errors was substantial, and on average, the maximum change in EUD for systematic errors (close 2 mm) was −10·7±3·1% for brain and −15·5±2·6% for HN.ConclusionsIt can be concluded that the acceptable systematic error was 0·4 mm for brain and 0·3 mm for HN. Furthermore, IMRT MatriXX device was able to detect the MLC errors ≥2 mm in HN and >3 mm errors in brain with 2%/2 mm γ-criteria.

Monte Carlo calculations of an Elekta Precise SL-25 photon beam model

AbstractBackgroundMonte Carlo (MC) simulations have been used extensively for benchmarking photon dose calculations in modern radiotherapy using linear accelerators (linacs). Moreover, a major barrier to widespread clinical implementation of MC dose calculation is the difficulty in characterising the radiation source using data reported from manufacturers.PurposeThis work aims to develop a generalised full MC histogram source model of an Elekta Precise SL-25 linac (electron exit window, target, flattening filter, monitor chambers and collimators) for 6 MV photon beams used in standard therapies. The inclusion of many different probability processes such as scatter, nuclear reactions, decay, capture cross-sections and more led to more realistic dose calculations in treatment planning and quality assurance.Materials and methodsTwo different codes, MCNPX 2·6 and EGSr-BEAM, were used for the calculation of particle transport, first in the geometry of the internal/external accelerator source, and then followed by tracking the transport and energy deposition in phantom-equivalent tissues. A full phase space file was scored directly above the upper multilayer collimator’s jaws to derive the beam characteristics such as planar fluence, angular distribution and energy spectrum. To check the quality of the generated photon beam, its depth dose curves and cross-beam profiles were calculated and compared with measured data.ResultsIn-field dose distributions calculated using the accelerator models were tuned to match measurement data with preliminary calculations performed using the accelerator information provided by the manufacturer. Field sizes of 3×3, 5×5, 10×10, 15×15 and 20×20 cm2were analysed. Local differences between calculated and measured curve doses beneath 2% were obtained for all the studied field sizes. Higher discrepancies were obtained in the air–water interface, where measurements of dose distributions with the ionisation chamber need to be shifted for the effective point of measurement.ConclusionThe agreements between MC-calculated and measured dose distributions were excellent for both codes, showing the strength and stability of the proposed model. Beam reconstruction methods as direct input to dose-calculation codes using the recorded histograms can be implemented for more accurate patient dose estimation.

Geometrical splitting technique to improve the computational efficiency in Monte Carlo calculations for proton therapy

To present the implementation and validation of a geometrical based variance reduction technique for the calculation of phase space data for proton therapy dose calculation. The treatment heads at the Francis H Burr Proton Therapy Center were modeled with a new Monte Carlo tool (TOPAS based on Geant4). For variance reduction purposes, two particle-splitting planes were implemented. First, the particles were split upstream of the second scatterer or at the second ionization chamber. Then, particles reaching another plane immediately upstream of the field specific aperture were split again. In each case, particles were split by a factor of 8. At the second ionization chamber and at the latter plane, the cylindrical symmetry of the proton beam was exploited to position the split particles at randomly spaced locations rotated around the beam axis. Phase space data in IAEA format were recorded at the treatment head exit and the computational efficiency was calculated. Depth-dose curves and beam profiles were analyzed. Dose distributions were compared for a voxelized water phantom for different treatment fields for both the reference and optimized simulations. In addition, dose in two patients was simulated with and without particle splitting to compare the efficiency and accuracy of the technique. A normalized computational efficiency gain of a factor of 10-20.3 was reached for phase space calculations for the different treatment head options simulated. Depth-dose curves and beam profiles were in reasonable agreement with the simulation done without splitting: within 1% for depth-dose with an average difference of (0.2 ± 0.4)%, 1 standard deviation, and a 0.3% statistical uncertainty of the simulations in the high dose region; 1.6% for planar fluence with an average difference of (0.4 ± 0.5)% and a statistical uncertainty of 0.3% in the high fluence region. The percentage differences between dose distributions in water for simulations done with and without particle splitting were within the accepted clinical tolerance of 2%, with a 0.4% statistical uncertainty. For the two patient geometries considered, head and prostate, the efficiency gain was 20.9 and 14.7, respectively, with the percentages of voxels with gamma indices lower than unity 98.9% and 99.7%, respectively, using 2% and 2 mm criteria. The authors have implemented an efficient variance reduction technique with significant speed improvements for proton Monte Carlo simulations. The method can be transferred to other codes and other treatment heads.

Analytic evaluation of diffuse fluence error in multilayer scattering media with discontinuous refractive index

A simple analytic method of estimating the error involved in using an approximate boundary condition for diffuse radiation in two adjoining scattering media with differing refractive indices is presented. The method is based on asymptotic planar fluences and enables the relative error to be readily evaluated without recourse to Monte Carlo simulation. Three examples of its application are considered: (1) evaluating the error in calculating the diffuse fluences at a boundary between two media with differing refractive index and dissimilar scattering properties, (2) the dependence of the relative error in a multilayer medium with discontinuous refractive index on the ratio of the reduced scattering coefficient to the absorption coefficient μ(s)'/μ(a), and (3) the parametric dependence of the error in the radiant flux J(s) at the surface of a three-layer medium. The error is significant for strongly forward-biased scattering media with non-negligible absorption and is cumulative in multilayered media with refractive index increments between layers.

Optimization of dual electron multileaf collimator materials by use of EGSnrc

A dual electron multileaf collimator (eMLC) has recently been proposed and ascertained to be effective in the collimation of therapy electron beams. The EGSnrc Monte Carlo code has been used in the optimization of the dual eMLC by simulation of the Varian 2100C medical linear accelerator with the applicator completely replaced by the dual eMLC, and calculation of the dose distributions in a water phantom. The planar fluence results showed that the material combination of 2-cm-thick brass and 2-cm-thick tungsten (eMLCT1) as upper and lower eMLCs, respectively, offers minimal radiation leakage outside the treatment field. Dose calculation results used in estimation of the maximum dose, depth of the maximum dose, surface dose, bremsstrahlung background, and penumbra indicate that eMLCT1 offers better beam qualities than do the other dual eMLCs that were considered. Maximum optimization was obtained with the dual eMLC designed such that the material of the lower eMLC had a higher density than that of the upper eMLC.

Fast, accurate photon beam accelerator modeling using BEAMnrc: A systematic investigation of efficiency enhancing methods and cross‐section data

In this work, an investigation of efficiency enhancing methods and cross-section data in the BEAMnrc Monte Carlo (MC) code system is presented. Additionally, BEAMnrc was compared with VMC++, another special-purpose MC code system that has recently been enhanced for the simulation of the entire treatment head. BEAMnrc and VMC++ were used to simulate a 6 MV photon beam from a Siemens Primus linear accelerator (linac) and phase space (PHSP) files were generated at 100 cm source-to-surface distance for the 10 x 10 and 40 x 40 cm2 field sizes. The BEAMnrc parameters/techniques under investigation were grouped by (i) photon and bremsstrahlung cross sections, (ii) approximate efficiency improving techniques (AEITs), (iii) variance reduction techniques (VRTs), and (iv) a VRT (bremsstrahlung photon splitting) in combination with an AEIT (charged particle range rejection). The BEAMnrc PHSP file obtained without the efficiency enhancing techniques under study or, when not possible, with their default values (e.g., EXACT algorithm for the boundary crossing algorithm) and with the default cross-section data (PEGS4 and Bethe-Heitler) was used as the "base line" for accuracy verification of the PHSP files generated from the different groups described previously. Subsequently, a selection of the PHSP files was used as input for DOSXYZnrc-based water phantom dose calculations, which were verified against measurements. The performance of the different VRTs and AEITs available in BEAMnrc and of VMC++ was specified by the relative efficiency, i.e., by the efficiency of the MC simulation relative to that of the BEAMnrc base-line calculation. The highest relative efficiencies were approximately 935 (approximately 111 min on a single 2.6 GHz processor) and approximately 200 (approximately 45 min on a single processor) for the 10 x 10 field size with 50 million histories and 40 x 40 cm2 field size with 100 million histories, respectively, using the VRT directional bremsstrahlung splitting (DBS) with no electron splitting. When DBS was used with electron splitting and combined with augmented charged particle range rejection, a technique recently introduced in BEAMnrc, relative efficiencies were approximately 420 (approximately 253 min on a single processor) and approximately 175 (approximately 58 min on a single processor) for the 10 x 10 and 40 x 40 cm2 field sizes, respectively. Calculations of the Siemens Primus treatment head with VMC++ produced relative efficiencies of approximately 1400 (approximately 6 min on a single processor) and approximately 60 (approximately 4 min on a single processor) for the 10 x 10 and 40 x 40 cm2 field sizes, respectively. BEAMnrc PHSP calculations with DBS alone or DBS in combination with charged particle range rejection were more efficient than the other efficiency enhancing techniques used. Using VMC++, accurate simulations of the entire linac treatment head were performed within minutes on a single processor. Noteworthy differences (+/- 1%-3%) in the mean energy, planar fluence, and angular and spectral distributions were observed with the NIST bremsstrahlung cross sections compared with those of Bethe-Heitler (BEAMnrc default bremsstrahlung cross section). However, MC calculated dose distributions in water phantoms (using combinations of VRTs/AEITs and cross-section data) agreed within 2% of measurements. Furthermore, MC calculated dose distributions in a simulated water/air/water phantom, using NIST cross sections, were within 2% agreement with the BEAMnrc Bethe-Heitler default case.

Analytical theory for the fluence, planar fluence, energy fluence, planar energy fluence and absorbed dose of primary particles and their fragments in broad therapeutic light ion beams

The purpose of the present work is to develop analytical expressions for the depth variation of the fluence, planar fluence, the energy fluence, planar energy fluence, the mean energy and absorbed dose of primary ions and their associated fragments in tissue-like media with ranges of clinical interest. The analytical expressions of the primary ions and associated fragments take into account nuclear interactions, energy losses, range straggling and multiple scattering. The analytical models of the radiation field quantities were compared with the results of the modified Monte Carlo (MC) code SHIELD-HIT +. The results show that the shape of the depth absorbed dose distribution of the primary particles is characterized by an increasingly steep exponential fluence decrease with depth as the charge and atomic weight increase. This is accompanied by a compensating increased energy loss towards the Bragg peak as the charge of the ion increases. These largely compensating mechanisms are the main reason that the depth absorbed dose curve of all light ions is surprisingly similar. In addition, a rather uniform dose in the plateau region is obtained since the increasing fragment production almost precisely compensates the loss of primaries. The dominating light fragments such as protons and alpha particles are characterized by longer ranges than the primaries and their depth dose curves to some extent coincide well with the depth fluence curves due to a rather slow variation of mean stopping powers. In contrast, the heavier fragments are characterized by the build up of a slowing down spectrum similar to that of the primaries but with initially slightly shorter or longer ranges depending on their mass to atomic number ratio. The presented analytical theory for the light ion penetration in matter agree quite well with the MC and experimental data and may be very useful for fast analytical calculations of quantities like mean energy, fluence, energy fluence, absorbed dose, and LET.

Characteristics of elliptical sources in BEAMnrc Monte Carlo system: Implementation and application

Recently, several papers noticed that the electron focal spot of a linear accelerator (linac) could be elliptical which would cause dosimetric discrepancies between measurements and Monte Carlo simulations. To resolve the mismatch, two elliptical source models were developed in BEAMnrc code. The first was a parallel beam elliptical source with uniform distribution where the shape of the source was primarily considered. The other was a parallel beam elliptical source with Gaussian distribution whose source distribution follows the normal distribution. To validate the elliptical source models, uniform and Gaussian electron beams were impinged on a thin air target. Both models successfully reproduced the elliptical shapes and source distributions. Then, this study investigated the characteristics of the elliptical Gaussian source for a 6 MV photon beam in a Varian 21EX linac. The linac head model was implemented in the BEAMnrc/EGSnrc system and commissioned by comparing the lateral and depth dose profiles to the ion chamber measurements acquired from the annual quality assurance (QA). It was found that the circular Gaussian beam with 6 MeV/0.2 cm full width half maximum (FWHM) produces the best matches to the QA data. To explore the characteristics of the elliptical Gaussian source, this study employed an elliptical Gaussian electron source with 0.1 cm FWHM in the x axis and 0.2 cm FWHM in the y axis which was incident on the target of the linac head. Two circular Gaussian beams with 0.1 and 0.2 cm FWHM were employed to compare the differences between circular and elliptical sources. For all the sources, planar and energy fluences were acquired and analyzed. This study also compared the lateral and depth dose profiles in a water phantom by using a DOSXYZnrc user code. In results, a constricted shoulder effect was observed in both planar and energy fluence plots when the FWHM value was increased and the field size is larger than 30 x 30 cm2. The same effect was also noticed in the lateral dose profiles, while the depth dose profile did not vary much.

SU‐FF‐T‐76: Analysis of a Novel Method of IMRT QA Using EPID‐Acquired QA Planes

Purpose: To assess the efficacy and quantify the accuracy of a novel method for IMRT QA in which the measured dose plane is derived from an EPID image. Method and Materials: aSi EPID data was acquired and converted using a novel method based on a machine‐specific beam model to estimate QA dose planes from mega voltage (MV) EPID images. Dose planes were calculated in a homogeneous, water‐equivalent QA phantom using the model and an acquired MV EPID image with no additional buildup required on the EPID.Specific parameters, such as field size output dependency, dose redistribution kernel, potential off‐axis corrections and absolute dose calibration, were measured to create the model that is based on the raw EPID files.QA dose planes were compared to ion chamber measurements, MapCHECK® measurements, and planar fluences generated by ADAC Pinnacle3® TPS. MapCHECK® and ion chamber (IC) measurements were taken at multiple depths at a source to detector distance (SDD) of 100cm. Dose planes in homogenous media were estimated using EPID images acquired at a distance of 140cm SDD. Data was collected for both 6 MV and 10 MV energies to determine the accuracy of the model for these two energies. Results: Preliminary sample analysis demonstrates that the dose planes estimated by the model using EPID images of complex IMRT fields result in >98% pass rate of all point measurements from MapCHECK®, employing a 3% dose or a 2mm distance to agreement criterion. Agreement between MapCHECK® and IC measurements were within 1%. Conclusion: This novel method shows promise as a tool for IMRT QA with reasonable accuracy. Setup, acquisition and analysis can be performed in a more time efficient manner than is possible with current methods of IMRT QA. Conflict of Interest: This work was partially funded by Sun‐Nuclear Co.® and Canis Lupus LLC.

SU-FF-T-43: A Planar Dose Calculation Algorithm for IMRT Quality Assurance

Purpose: To develop a fast algorithm for independent planar dose verification of IMRT plans delivered with an MLC as part of the IMRT quality assurance procedure. Methods and Materials: A fast empirical IMRT planner dose calculation algorithm was implemented. In-air output factors were used to model the source distribution, which is used to calculate the planar fluence at the detector plane based on the projected source integration on the source plane shaped by the combined positions of the jaws and MLC. The planner dose is obtained by convolving the planner fluence with a kernel, which is modified from the published kernel by fitting to standard field profiles at the specified depth. MLC-introduced dosimetric effects, such as leaf transmission, rounded leaf end, and tongue-and-groove effects were accounted for explicitly by empirical fits to measured data. The algorithm was applied to two linac models with completely different head designs: a Varian 2100 C/D with 120-leaf MLC and an Elekta Synergy S with Beam Modulator (40-leaf MLC with no backup jaws). The calculated planner dose distributions were compared with both the MapCHECK measurements and with calculations using a commercial planning system (Pinnacle3, version 7.6) for several clinical cases. Comparison was done using the MapCHECK software in absolute dose mode with 3% dose error and 3-mm distance-to-agreement criteria. Results: The passing rate for most of the cases is above 95% with most of the failing points in the field edges. The calculation time for each field is about 5 sec using a personal laptop computer and is independent of field size. Conclusions: A fast algorithm has been developed for independent planar dose verification of IMRT plans as part of the IMRT quality assurance procedure. The algorithm was applied to two linac models with excellent results. Research sponsored by Sun Nuclear Corp.

TU‐C‐T‐6E‐02: A Computational Algorithm for Independent Planar Dose Verification of IMRT

Purpose: The purpose of this work is to develop a computational algorithm for independent planar dose verification of IMRT plans delivered with an MLC as part of the IMRT quality assurance procedure. Method and Materials: A pencil beam convolution method was adopted for the algorithm. The general scheme of the calculation consists of three parts. The first part calculates the delivered fluence in air based on the positions of the leaves and jaws specified in the RTP file. We employed a modified three‐source model to obtain the planar fluence at the detector plane based on the projected source integration on the source plane shaped by the combined positions of the jaws and MLC. In the second part, dose kernel in phantom was determined by fitting the convolution results with a series of square‐field profiles. Thirdly, the mid‐leaf and interleaf transmissions, rounded leaf end, and tongue‐and‐groove effects were considered to improve the accuracy of the algorithm. All of these effects were taken into account by semi‐empirical methodology and the parameters were obtained by fits to measured data. To verify the accuracy of the algorithm, we compared the calculation results with the MapCHECK measurements. Results: The accuracy of the algorithm was verified by comparing the calculations with the MapCHECK measurements for several head‐and‐neck cases. The passing rate for most of the cases is above 95% with the 2% in absolute dose or 2‐mm distance‐to‐agreement criteria. The agreement was better than the agreement between the results from a commercial planning system (Pinnacle3, version 7.0g) and MapCHECK measurements for all the cases tested. Conclusion: An algorithm has been developed for independent planar dose verification of IMRT plans as part of the IMRT quality assurance procedure. Our methods could be implemented on other kinds of machines with minor modifications.

Dual scattering foil design for poly-energetic electron beams**Presented at the Current Topics in Monte Carlo Treatment Planning, Advanced Workshop, McGill University, Montréal, Québec, Canada, 3–5 May 2004.

The laser wakefield acceleration (LWFA) mechanism can accelerate electrons to energies within the 6–20 MeV range desired for therapy application. However, the energy spectrum of LWFA-generated electrons is broad, on the order of tens of MeV. Using existing laser technology, the therapeutic beam might require a significant energy spread to achieve clinically acceptable dose rates. The purpose of this work was to test the assumption that a scattering foil system designed for a mono-energetic beam would be suitable for a poly-energetic beam with a significant energy spread. Dual scattering foil systems were designed for mono-energetic beams using an existing analytical formalism based on Gaussian multiple-Coulomb scattering theory. The design criterion was to create a flat beam that would be suitable for fields up to 25 × 25 cm2 at 100 cm from the primary scattering foil. Radial planar fluence profiles for poly-energetic beams with energy spreads ranging from 0.5 MeV to 6.5 MeV were calculated using two methods: (a) analytically by summing beam profiles for a range of mono-energetic beams through the scattering foil system, and (b) by Monte Carlo using the EGS/BEAM code. The analytic calculations facilitated fine adjustments to the foil design, and the Monte Carlo calculations enabled us to verify the results of the analytic calculation and to determine the phase-space characteristics of the broadened beam. Results showed that the flatness of the scattered beam is fairly insensitive to the width of the input energy spectrum. Also, results showed that dose calculated by the analytical and Monte Carlo methods agreed very well in the central portion of the beam. Outside the useable field area, the differences between the analytical and Monte Carlo results were small but significant, possibly due to the small angle approximation. However, these did not affect the conclusion that a scattering foil system designed for a mono-energetic beam will be suitable for a poly-energetic beam with the same central energy. Further studies of the dosimetric properties of LWFA-generated electron beams will be done using Monte Carlo methods.

233 poster Gaussian source convolution with non planar fluence matrix for photon output factor in air calculations

233 poster Gaussian source convolution with non planar fluence matrix for photon output factor in air calculations

Photon beam characterization and modelling for Monte Carlo treatment planning

Photon beams of 4, 6 and 15 MV from Varian Clinac 2100C and 2300C/D accelerators were simulated using the EGS4/BEAM code system. The accelerators were modelled as a combination of component modules (CMs) consisting of a target, primary collimator, exit window, flattening filter, monitor chamber, secondary collimator, ring collimator, photon jaws and protection window. A full phase space file was scored directly above the upper photon jaws and analysed using beam data processing software, BEAMDP, to derive the beam characteristics, such as planar fluence, angular distribution, energy spectrum and the fractional contributions of each individual CM. A multiple-source model has been further developed to reconstruct the original phase space. Separate sources were created with accurate source intensity, energy, fluence and angular distributions for the target, primary collimator and flattening filter. Good agreement (within 2%) between the Monte Carlo calculations with the source model and those with the original phase space was achieved in the dose distributions for field sizes of 4 cm × 4 cm to 40 cm × 40 cm at source surface distances (SSDs) of 80-120 cm. The dose distributions in lung and bone heterogeneous phantoms have also been found to be in good agreement (within 2%) for 4, 6 and 15 MV photon beams for various field sizes between the Monte Carlo calculations with the source model and those with the original phase space.

Monte Carlo modelling of radiotherapy kV x-ray units

To obtain accurate information for absorbed dose calculations in water for kilovoltage x-rays, the photon spectrum, planar fluence and the angular distribution of the photons at the collimator exit of the x-ray unit have to be known. The only way to obtain this information is by Monte Carlo (MC) simulation. Compared with the situation for high-energy photons and electrons, where in recent years numerous papers have been devoted to MC modelling of complete clinical accelerator units, there is a lack of similar work for kV x-ray units. A reliable MC model for a kV x-ray unit would allow the output information to be used in a treatment planning system for regular and irregular treatment fields. Furthermore, with MC simulation, perturbation factors of dose-measuring devices, such as those specified in codes of practice, can be calculated. In this work, the MC code EGS4/BEAM was used to build realistic models of two complete x-ray units. The tungsten target, exit window, collimator, additional filtration and applicator were taken into account. For some aspects of the work, a comparison was made with the simulations from another MC code, MCNP4B. The contribution to the characteristic radiation from electron impact ionization and from the photoelectric effect of reabsorbed bremsstrahlung photons was studied. Calculated and measured photon fluence spectra in air and half-value layers for a Philips MCN410 tube were compared for several anode voltages and additional filtrations. Results from the two codes agreed well, and the agreement with measured spectra was found to be good for energies above 50 keV but rather less good below that energy. For a Siemens Stabilipan 2 Th300 x-ray tube, HVLs and dose distributions in water were compared with measurements for several clinical x-ray qualities. For most of the combinations of radiation qualities and applicators, good agreement was obtained, although there were also some cases where the agreement was not so good. Electron contamination and photon build-up at the water surface were studied using MC simulation. The influence of depth on the photon spectral distribution was investigated. Both EGS4/BEAM and MCNP4B, in their default versions, handle inadequately the production of characteristic x-rays. This was found to have only a minor influence on the calculated dosimetric quantities. Simulations with MCNP4B required the use of several variance reduction techniques in order to obtain results within reasonable calculation times.

Multiple scattering theory for total skin electron beam design.

The purpose of this manuscript is to describe a method for designing a broad beam of electrons suitable for total skin electron irradiation (TSEI). A theoretical model of a TSEI beam from a linear accelerator with a dual scattering system has been developed. The model uses Fermi-Eyges theory to predict the planar fluence of the electron beam after it has passed through various materials between the source and the treatment plane, which includes scattering foils, monitor chamber, air, and a plastic diffusing plate. Unique to this model is its accounting for removal of the tails of the electron beam profile as it passes through the primary x-ray jaws. A method for calculating the planar fluence profile for an obliquely incident beam is also described. Off-axis beam profiles and percentage depth doses are measured with ion chambers, film, and thermoluminescent dosimeters (TLD). The measured data show that the theoretical model can accurately predict beam energy and planar fluence of the electron beam at normal and oblique incidence. The agreement at oblique angles is not quite as good but is sufficiently accurate to be of predictive value when deciding on the optimal angles for the clinical TSEI beams. The advantage of our calculational approach for designing a TSEI beam is that many different beam configurations can be tested without having to perform time-consuming measurements. Suboptimal configurations can be quickly dismissed, and the predicted optimal solution should be very close to satisfying the clinical specifications.

Pencil‐beam redefinition algorithm for electron dose distributions

A pencil-beam redefinition algorithm has been developed for the calculation of electron-beam dose distributions on a three-dimensional grid utilizing 3-D inhomogeneity correction. The concept of redefinition was first used for both fixed and arced electron beams by Hogstrom et al. but was limited to a single redefinition. The success of those works stimulated the development of the pencil-beam redefinition algorithm, the aim of which is to solve the dosimetry problems presented by deep inhomogeneities through development of a model that redefines the pencil beams continuously with depth. This type of algorithm was developed independently by Storchi and Huizenga who termed it the "moments method." Such a pencil beam within the patient is characterized by a complex angular distribution, which is approximated by a Gaussian distribution having the same first three moments as the actual distribution. Three physical quantities required for dose calculation and subsequent radiation transport--namely planar fluence, mean direction, and root-mean-square spread about the mean direction--are obtained from these moments. The primary difference between the moments method and the redefinition algorithm is that the latter subdivides the pencil beams into multiple energy bins. The algorithm then becomes a macroscopic method for transporting the complete phase space of the beam and allows the calculation of physical quantities such as fluence, dose, and energy distribution. Comparison of calculated dose distributions with measured dose distributions for a homogeneous water phantom, and for phantoms with inhomogeneities deep relative to the surface, show agreement superior to that achieved with the pencil-beam algorithm of Hogstrom et al. in the penumbral region and beneath the edges of air and bone inhomogeneities. The accuracy of the redefinition algorithm is within 4% and appears sufficient for clinical use, and the algorithm is structured for further expansion of the physical model if required for site-specific treatment planning problems.