Modeling scatter through sides of island blocks used for intensity-modulated bolus electron conformal therapy.

PURPOSE: Passive Radiotherapy Intensity Modulators for Electrons (PRIME) devices are comprised of cylindrical tungsten island blocks imbedded in a machinable foam slab within the patient's cutout. Intensity-modulated bolus electron conformal therapy (IM-BECT) uses PRIME devices to reduce dose heterogeneity caused by the irregular bolus surface. Heretofore, IM-BECT dose calculations used the pencil beam redefinition algorithm (PBRA) assuming perfect collimation. This study investigates modeling electron scatter into and out the sides of island blocks. METHODS: Dose distributions were measured in a water phantom at 7, 13, and 20 MeV for devices having nominal intensity reduction factors of 1.000 (foam only), 0.937, 0.812, and 0.688, corresponding to nominal island block diameters (dnom ) of 0.158, 0.273, and 0.352 cm, respectively. Pencil beam theory derived an effective diameter (dIS ) to account for in-scattered electrons as a function of dnom and beam energy (Ep,0 ). However, for out-scattered electrons, an effective diameter (dmod ) was estimated by best fitting measured data. RESULTS: In the modulated region (under island blocks, depth < R90 ), modified PBRA-calculated dose distributions showed 2%/2 mm passing rates for dnom  = 0.158, 0.273, and 0.352 cm of (100%, 100%, 100%) at 7 MeV, (100%, 100%, 93.5%) at 13 MeV, and (99.8%, 85.4%, and 71.5%) at 20 MeV. The largest dose differences (≤ 6%) occurred at the highest energy (20 MeV), largest dnom , shallowest depths (≤ 2 cm), and on central axis. CONCLUSIONS: An equation for modeling island block scatter, dmod (dnom , Ep,0 ), has been developed for use in the PBRA, insignificantly impacting calculation time. Although inaccuracy sometimes exceeded our 2%/2 mm criteria, it could be clinically acceptable, as superficial dose differences often fall inside the bolus. Also, patient PRIME devices are expected to have fewer large diameter island blocks than did test devices. Inaccuracies are attributed to out-scattered electrons having energy spectra different than the primary beams.

Planning and delivery of intensity modulated bolus electron conformal therapy.

PURPOSE: Bolus electron conformal therapy (BECT) is a clinically useful, well-documented, and available technology. The addition of intensity modulation (IM) to BECT reduces volumes of high dose and dose spread in the planning target volume (PTV). This paper demonstrates new techniques for a process that should be suitable for planning and delivering IM-BECT using passive radiotherapy intensity modulation for electrons (PRIME) devices. METHODS: The IM-BECT planning and delivery process is an addition to the BECT process that includes intensity modulator design, fabrication, and quality assurance. The intensity modulator (PRIME device) is a hexagonal matrix of small island blocks (tungsten pins of varying diameter) placed inside the patient beam-defining collimator (cutout). Its design process determines a desirable intensity-modulated electron beam during the planning process, then determines the island block configuration to deliver that intensity distribution (segmentation). The intensity modulator is fabricated and quality assurance performed at the factory (.decimal, LLC, Sanford, FL). Clinical quality assurance consists of measuring a fluence distribution in a plane perpendicular to the beam in a water or water-equivalent phantom. This IM-BECT process is described and demonstrated for two sites, postmastectomy chest wall and temple. Dose plans, intensity distributions, fabricated intensity modulators, and quality assurance results are presented. RESULTS: IM-BECT plans showed improved D90-10 over BECT plans, 6.4% versus 7.3% and 8.4% versus 11.0% for the postmastectomy chest wall and temple, respectively. Their intensity modulators utilized 61 (single diameter) and 246 (five diameters) tungsten pins, respectively. Dose comparisons for clinical quality assurance showed that for doses greater than 10%, measured agreed with calculated dose within 3% or 0.3 cm distance-to-agreement (DTA) for 99.9% and 100% of points, respectively. CONCLUSION: These results demonstrated the feasibility of translating IM-BECT to the clinic using the techniques presented for treatment planning, intensity modulator design and fabrication, and quality assurance processes.

Useful island block geometries of a passive intensity modulator used for intensity-modulated bolus electron conformal therapy.

PURPOSE: This project determined the range of island block geometric configurations useful for the clinical utilization of intensity-modulated bolus electron conformal therapy (IM-BECT). METHODS: Multiple half-beam island block geometries were studied for seven electron energies 7-20 MeV at 100 and 103 cm source-to-surface distance (SSD). We studied relative fluence distributions at 0.5 cm and 2.0 cm depths in water, resulting in 28 unique beam conditions. For each beam condition, we studied intensity reduction factor (IRF) values of 0.70, 0.75, 0.80, 0.85, 0.90, and 0.95, and hexagonal packing separations for the island blocks of 0.50, 0.75, 1.00, 1.25, and 1.50 cm, that is, 30 unique IM configurations and 840 unique beam-IM combinations. A combination was deemed acceptable if the average intensity downstream of the intensity modulator agreed within 2% of that intended and the variation in fluence was less than ±2%. RESULTS: For 100 cm SSD, and for 0.5 cm depth, results showed that beam energies above 13 MeV did not exhibit sufficient scatter to produce clinically acceptable fluence (intensity) distributions for all IRF values (0.70-0.95). In particular, 20 MeV fluence distributions were unacceptable for any values, and acceptable 16 MeV fluence distributions were limited to a minimum IRF of 0.85. For the 2.0 cm depth, beam energies up to and including 20 MeV had acceptable fluence distributions. For 103 cm SSD and for 0.5 cm and 2.0 cm depths, results showed that all beam energies (7-20 MeV) had clinically acceptable fluence distributions for all IRF values (0.70-0.95). In general, the more clinically likely 103 cm SSD had acceptable fluence distributions with larger separations (r), which allow larger block diameters. CONCLUSION: The geometric operating range of island block separations and IRF values (block diameters) producing clinically appropriate IM electron beams has been determined.

Evaluation of prototype of improved electron collimation system for Elekta linear accelerators.

PURPOSE: This study evaluated a new electron collimation system design for Elekta 6-20 MeV beams, which should reduce applicator weights by 25%-30%. Such reductions, as great as 3.9 kg for the largest applicator, should result in considerably easier handling by members of the radiotherapy team. METHODS: Prototype 10 × 10 and 20 × 20-cm2 applicators, used to measure weight, in-field flatness, and out-of-field leakage dose, were constructed according to the previously published design with two minor modifications: (a) rather than tungsten, lead was used for trimmer material; and (b) continuous trimmer outer-edge bevel was approximated by three steps. Because of lead plate softness, a 0.32-cm aluminum plate replaced the equivalent lead thickness on the trimmer's downstream surface for structural support. Models of all applicators (6 × 6-25 × 25 cm2 ) with these modifications were inserted into a Monte Carlo (MC) model for dose calculations using 7, 13, and 20 MeV beams. Planar dose distributions were measured and calculated at 1- and 2-cm water depths to evaluate in-field beam flatness and out-of-field leakage dose. RESULTS: Prototype 10 × 10 and 20 × 20-cm2 applicator measurements agreed with calculated weights, in-field flatness, and out-of-field leakage doses for 7, 13, and 20 MeV beams. Also, MC dose calculations showed that all applicators (6 × 6-25 × 25 cm2 ) and 7, 13, and 20 MeV beams met our stringent in-field flatness specifications (±3% major axes; ±4% diagonals) and IEC out-of-field leakage dose specifications. CONCLUSIONS: Our results validated the new electron collimating system design for Elekta 6-20 MeV electron beams, which could serve as basis for a new clinical electron collimating system with significantly reduced applicator weights.

Impact of database quality in knowledge-based treatment planning for prostate cancer.

PURPOSE: This article investigates dose-volume prediction improvements in a common knowledge-based planning (KBP) method using a Pareto plan database compared with using a conventional, clinical plan database. METHODS AND MATERIALS: Two plan databases were created using retrospective, anonymized data of 124 volumetric modulated arc therapy (VMAT) prostate cancer patients. The clinical plan database (CPD) contained planning data from each patient's clinically treated VMAT plan, which were manually optimized by various planners. The multicriteria optimization database (MCOD) contained Pareto-optimal plan data from VMAT plans created using a standardized multicriteria optimization protocol. Overlap volume histograms, incorporating fractional organ at risk volumes only within the treatment fields, were computed for each patient and used to match new patient anatomy to similar database patients. For each database patient, CPD and MCOD KBP predictions were generated for D10, D30, D50, D65, and D80 of the bladder and rectum in a leave-one-out manner. Prediction achievability was evaluated through a replanning study on a subset of 31 randomly selected database patients using the best KBP predictions, regardless of plan database origin, as planning goals. RESULTS: MCOD predictions were significantly lower than CPD predictions for all 5 bladder dose-volumes and rectum D50 (P = .004) and D65 (P < .001), whereas CPD predictions for rectum D10 (P = .005) and D30 (P < .001) were significantly less than MCOD predictions. KBP predictions were statistically achievable in the replans for all predicted dose-volumes, excluding D10 of bladder (P = .03) and rectum (P = .04). Compared with clinical plans, replans showed significant average reductions in Dmean for bladder (7.8 Gy; P < .001) and rectum (9.4 Gy; P < .001), while maintaining statistically similar planning target volume, femoral head, and penile bulb dose. CONCLUSION: KBP dose-volume predictions derived from Pareto plans were more optimal overall than those resulting from manually optimized clinical plans, which significantly improved KBP-assisted plan quality. SUMMARY: This work investigates how the plan quality of knowledge databases affects the performance and achievability of dose-volume predictions from a common knowledge-based planning approach for prostate cancer. Bladder and rectum dose-volume predictions derived from a database of standardized Pareto-optimal plans were compared with those derived from clinical plans manually designed by various planners. Dose-volume predictions from the Pareto plan database were significantly lower overall than those from the clinical plan database, without compromising achievability.

An improved distance-to-dose correlation for predicting bladder and rectum dose-volumes in knowledge-based VMAT planning for prostate cancer.

The overlap volume histogram (OVH) is an anatomical metric commonly used to quantify the geometric relationship between an organ at risk (OAR) and target volume when predicting expected dose-volumes in knowledge-based planning (KBP). This work investigated the influence of additional variables contributing to variations in the assumed linear DVH-OVH correlation for the bladder and rectum in VMAT plans of prostate patients, with the goal of increasing prediction accuracy and achievability of knowledge-based planning methods. VMAT plans were retrospectively generated for 124 prostate patients using multi-criteria optimization. DVHs quantified patient dosimetric data while OVHs quantified patient anatomical information. The DVH-OVH correlations were calculated for fractional bladder and rectum volumes of 30, 50, 65, and 80%. Correlations between potential influencing factors and dose were quantified using the Pearson product-moment correlation coefficient (R). Factors analyzed included the derivative of the OVH, prescribed dose, PTV volume, bladder volume, rectum volume, and in-field OAR volume. Out of the selected factors, only the in-field bladder volume (mean R = 0.86) showed a strong correlation with bladder doses. Similarly, only the in-field rectal volume (mean R = 0.76) showed a strong correlation with rectal doses. Therefore, an OVH formalism accounting for in-field OAR volumes was developed to determine the extent to which it improved the DVH-OVH correlation. Including the in-field factor improved the DVH-OVH correlation, with the mean R values over the fractional volumes studied improving from -0.79 to -0.85 and -0.82 to -0.86 for the bladder and rectum, respectively. A re-planning study was performed on 31 randomly selected database patients to verify the increased accuracy of KBP dose predictions by accounting for bladder and rectum volume within treatment fields. The in-field OVH led to significantly more precise and fewer unachievable KBP predictions, especially for lower bladder and rectum dose-volumes.

Introduction to passive electron intensity modulation.

This work introduces a new technology for electron intensity modulation, which uses small area island blocks within the collimating aperture and small area island apertures in the collimating insert. Due to multiple Coulomb scattering, electrons contribute dose under island blocks and lateral to island apertures. By selecting appropriate lateral positions and diameters of a set of island blocks and island apertures, for example, a hexagonal grid with variable diameter circular island blocks, intensity modulated beams can be produced for appropriate air gaps between the intensity modulator (position of collimating insert) and the patient. Such a passive radiotherapy intensity modulator for electrons (PRIME) is analogous to using physical attenuators (metal compensators) for intensity modulated x-ray therapy (IMXT). For hexagonal spacing, the relationship between block (aperture) separation (r) and diameter (d) and the local intensity reduction factor (IRF) is discussed. The PRIME principle is illustrated using pencil beam calculations for select beam geometries in water with half beams modulated by 70%-95% and for one head and neck field of a patient treated with bolus electron conformal therapy. Proof of principle is further illustrated by showing agreement between measurement and calculation for a prototype PRIME. Potential utilization of PRIME for bolus electron conformal therapy, segmented-field electron conformal therapy, modulated electron radiation therapy, and variable surface geometries is discussed. Further research and development of technology for the various applications is discussed. In summary, this paper introduces a practical, new technology for electron intensity modulation in the clinic, demonstrates proof of principle, discusses potential clinical applications, and suggests areas of further research and development.

Improved electron collimation system design for Elekta linear accelerators.

Prototype 10 × 10 and 20 × 20-cm2 electron collimators were designed for the Elekta Infinity accelerator (MLCi2 treatment head), with the goal of reducing the trimmer weight of excessively heavy current applicators while maintaining acceptable beam flatness (±3% major axes, ±4% diagonals) and IEC leakage dose. Prototype applicators were designed initially using tungsten trimmers of constant thickness (1% electron transmission) and cross-sections with inner and outer edges positioned at 95% and 2% off-axis ratios (OARs), respectively, cast by the upstream collimating component. Despite redefining applicator size at isocenter (not 5 cm upstream) and reducing the energy range from 4-22 to 6-20 MeV, the designed 10 × 10 and 20 × 20-cm2 applicator trimmers weighed 6.87 and 10.49 kg, respectively, exceeding that of the current applicators (5.52 and 8.36 kg, respectively). Subsequently, five design modifications using analytical and/or Monte Carlo (MC) calculations were applied, reducing trimmer weight while maintaining acceptable in-field flatness and mean leakage dose. Design Modification 1 beveled the outer trimmer edges, taking advantage of only low-energy beams scattering primary electrons sufficiently to reach the outer trimmer edge. Design Modification 2 optimized the upper and middle trimmer distances from isocenter for minimal trimmer weights. Design Modification 3 moved inner trimmer edges inward, reducing trimmer weight. Design Modification 4 determined optimal X-ray jaw positions for each energy. Design Modification 5 adjusted middle and lower trimmer shapes and reduced upper trimmer thickness by 50%. Design Modifications 1→5 reduced trimmer weights from 6.87→5.86→5.52→5.87→5.43→3.73 kg for the 10 × 10-cm2 applicator and 10.49→9.04→8.62→7.73→7.35→5.09 kg for the 20 × 20-cm2 applicator. MC simulations confirmed these final designs produced acceptable in-field flatness and met IEC-specified leakage dose at 7, 13, and 20 MeV. These results allowed collimation system design for 6 × 6-25 × 25-cm2 applicators. Reducing trimmer weights by as much as 4 kg (25 × 25-cm2 applicator) should result in easier applicator handling by the radiotherapy team.

Radiation leakage dose from Elekta electron collimation system.

This study provided baseline data required for a greater project, whose objective was to design a new Elekta electron collimation system having significantly lighter electron applicators with equally low out-of field leakage dose. Specifically, off-axis dose profiles for the electron collimation system of our uniquely configured Elekta Infinity accelerator with the MLCi2 treatment head were measured and calculated for two primary purposes: 1) to evaluate and document the out-of-field leakage dose in the patient plane and 2) to validate the dose distributions calculated using a BEAMnrc Monte Carlo (MC) model for out-of-field dose profiles. Off-axis dose profiles were measured in a water phantom at 100 cm SSD for 1 and 2 cm depths along the in-plane, cross-plane, and both diagonal axes using a cylindrical ionization chamber with the 10 × 10 and 20 × 20 cm2 applicators and 7, 13, and 20 MeV beams. Dose distributions were calculated using a previously developed BEAMnrc MC model of the Elekta Infinity accelerator for the same beam energies and applicator sizes and compared with measurements. Measured results showed that the in-field beam flatness met our acceptance criteria (± 3% on major and ±4% on diagonal axes) and that out-of-field mean and maximum percent leakage doses in the patient plane met acceptance criteria as specified by the International Electrotechnical Commission (IEC). Cross-plane out-of-field dose profiles showed greater leakage dose than in-plane profiles, attributed to the curved edges of the upper X-ray jaws and multileaf collimator. Mean leakage doses increased with beam energy, being 0.93% and 0.85% of maximum central axis dose for the 10 × 10 and 20 × 20 cm2 applicators, respectively, at 20 MeV. MC calculations predicted the measured dose to within 0.1% in most profiles outside the radiation field; however, excluding model-ing of nontrimmer applicator components led to calculations exceeding measured data by as much as 0.2% for some regions along the in-plane axis. Using EGSnrc LATCH bit filtering to separately calculate out-of-field leakage dose components (photon dose, primary electron dose, and electron dose arising from interactions in various collimating components), MC calculations revealed that the primary electron dose in the out-of-field leakage region was small and decreased as beam energy increased. Also, both the photon dose component and electron dose com-ponent resulting from collimator scatter dominated the leakage dose, increasing with increasing beam energy. We concluded that our custom Elekta Infinity with the MLCi2 treatment head met IEC leakage dose criteria in the patient plane. Also, accuracy of our MC model should be sufficient for our use in the design of a new, improved electron collimation system.

A dosimetric comparison of copper and Cerrobend electron inserts.

The purpose of this work was to evaluate differences in dose resulting from the use of copper aperture inserts compared to lead-alloy (Cerrobend) aperture inserts for electron beam therapy. Specifically, this study examines if copper aperture inserts can be used clinically with the same commissioning data measured using lead-alloy aperture inserts. The copper inserts were acquired from .decimal, LLC and matching lead-alloy, Cerrobend inserts were constructed in-house for 32 com-binations of nine square insert field sizes (2 × 2 to 20 × 20 cm2) and five applicator sizes (6 × 6 to 25 × 25 cm2). Percent depth-dose and off-axis relative dose profiles were measured using an electron diode in water for select copper and Cerrobend inserts for a subset of applicators (6 × 6, 10 × 10, 25 × 25 cm2) and energies (6, 12, 20 MeV) at 100 and 110 cm source-to-surface distances (SSD) on a Varian Clinac 21EX accelerator. Dose outputs were measured for all field size-insert combina-tions and five available energies (6-20 MeV) at 100 cm SSD and for a smaller subset at 110 cm SSD. Using these data, 2D planar absolute dose distributions were generated and compared. Criteria for agreement were ± 2% of maximum dose or 1 mm distance-to-agreement for 99% of points. A gamma analysis of the beam dosimetry showed 94 of 96 combinations of insert size, applicator, energy, and SSD were within the 2%/1 mm criteria for > 99% of points. Outside the field, copper inserts showed less bremsstrahlung dose under the insert compared to Cerrobend (greatest difference was 2.5% at 20 MeV and 100 cm SSD). This effect was most prominent at the highest energies for combinations of large applicators with small field sizes, causing some gamma analysis failures. Inside the field, more electrons scattered from the collimator edge of copper compared to Cerrobend, resulting in an increased dose at the field edge for copper at shallow depths (greatest increase was 1% at 20 MeV and 100 cm SSD). Dose differences decreased as the SSD increased, with no gamma failures at 110 cm SSD. Inserts for field sizes ≥ 6 × 6 cm2 at any energy, or for small fields (≤ 4 × 4 cm2) at energies < 20 MeV, showed dosimetric differences less than 2%/1 mm for more than 99% of points. All areas of comparison criteria failures were from lower out-of-field dose under copper inserts due to a reduction in bremsstrahlung production, which is clinically beneficial in reducing dose to healthy tissue outside of the planned treatment volume. All field size-applicator size-energy combinations passed 3%/1 mm criteria for 100% of points. Therefore, it should be clinically acceptable to utilize copper insets with dose distributions measured with Cerrobend inserts for treatment planning dose calculations and monitor unit calculations.

Evaluation of the Eclipse eMC algorithm for bolus electron conformal therapy using a standard verification dataset.

The purpose of this study was to evaluate the accuracy and calculation speed of electron dose distributions calculated by the Eclipse electron Monte Carlo (eMC) algorithm for use with bolus electron conformal therapy (ECT). The recent com-mercial availability of bolus ECT technology requires further validation of the eMC dose calculation algorithm. eMC-calculated electron dose distributions for bolus ECT have been compared to previously measured TLD-dose points throughout patient-based cylindrical phantoms (retromolar trigone and nose), whose axial cross sections were based on the mid-PTV (planning treatment volume) CT anatomy. The phantoms consisted of SR4 muscle substitute, SR4 bone substitute, and air. The treatment plans were imported into the Eclipse treatment planning system, and electron dose distributions calculated using 1% and < 0.2% statistical uncertainties. The accuracy of the dose calculations using moderate smoothing and no smooth-ing were evaluated. Dose differences (eMC-calculated less measured dose) were evaluated in terms of absolute dose difference, where 100% equals the given dose, as well as distance to agreement (DTA). Dose calculations were also evaluated for calculation speed. Results from the eMC for the retromolar trigone phantom using 1% statistical uncertainty without smoothing showed calculated dose at 89% (41/46) of the measured TLD-dose points was within 3% dose difference or 3 mm DTA of the measured value. The average dose difference was -0.21%, and the net standard deviation was 2.32%. Differences as large as 3.7% occurred immediately distal to the mandible bone. Results for the nose phantom, using 1% statistical uncertainty without smoothing, showed calculated dose at 93% (53/57) of the measured TLD-dose points within 3% dose difference or 3 mm DTA. The average dose difference was 1.08%, and the net standard deviation was 3.17%. Differences as large as 10% occurred lateral to the nasal air cavities. Including smoothing had insignificant effects on the accuracy of the retromolar trigone phantom calculations, but reduced the accuracy of the nose phantom calculations in the high-gradient dose areas. Dose calculation times with 1% statistical uncertainty for the retromolar trigone and nose treatment plans were 30 s and 24 s, respectively, using 16 processors (Intel Xeon E5-2690, 2.9 GHz) on a framework agent server (FAS). In comparison, the eMC was significantly more accurate than the pencil beam algorithm (PBA). The eMC has comparable accuracy to the pencil beam redefinition algorithm (PBRA) used for bolus ECT planning and has acceptably low dose calculation times. The eMC accuracy decreased when smoothing was used in high-gradient dose regions. The eMC accuracy was consistent with that previously reported for accuracy of the eMC electron dose algorithm and shows that the algorithm is suitable for clinical implementation of bolus ECT.

Permanent-magnet energy spectrometer for electron beams from radiotherapy accelerators.

PURPOSE: The purpose of this work was to adapt a lightweight, permanent magnet electron energy spectrometer for the measurement of energy spectra of therapeutic electron beams. METHODS: An irradiation geometry and measurement technique were developed for an approximately 0.54-T, permanent dipole magnet spectrometer to produce suitable latent images on computed radiography (CR) phosphor strips. Dual-pinhole electron collimators created a 0.318-cm diameter, approximately parallel beam incident on the spectrometer and an appropriate dose rate at the image plane (CR strip location). X-ray background in the latent image, reduced by a 7.62-cm thick lead block between the pinhole collimators, was removed using a fitting technique. Theoretical energy-dependent detector response functions (DRFs) were used in an iterative technique to transform CR strip net mean dose profiles into energy spectra on central axis at the entrance to the spectrometer. These spectra were transformed to spectra at 95-cm source to collimator distance (SCD) by correcting for the energy dependence of electron scatter. The spectrometer was calibrated by comparing peak mean positions in the net mean dose profiles, initially to peak mean energies determined from the practical range of central-axis percent depth-dose (%DD) curves, and then to peak mean energies that accounted for how the collimation modified the energy spectra (recalibration). The utility of the spectrometer was demonstrated by measuring the energy spectra for the seven electron beams (7-20 MeV) of an Elekta Infinity radiotherapy accelerator. RESULTS: Plots of DRF illustrated their dependence on energy and position in the imaging plane. Approximately 15 iterations solved for the energy spectra at the spectrometer entrance from the measured net mean dose profiles. Transforming those spectra into ones at 95-cm SCD increased the low energy tail of the spectra, while correspondingly decreasing the peaks and shifting them to slightly lower energies. Energy calibration plots of peak mean energy versus peak mean position of the net mean dose profiles for each of the seven electron beams followed the shape predicted by the Lorentz force law for a uniform z-component of the magnetic field, validating its being modeled as uniform (0.542 ± 0.027 T). Measured Elekta energy spectra and their peak mean energies correlated with the 0.5-cm (7-13 MeV) and the 1.0-cm (13-20 MeV) R90 spacings of the %DD curves. The full-width-half-maximum of the energy spectra decreased with decreasing peak mean energy with the exception of the 9-MeV beam, which was anomalously wide. Similarly, R80-20 decreased linearly with peak mean energy with the exception of the 9 MeV beam. Both were attributed to suboptimal tuning of the high power phase shifter for the recycled radiofrequency power reentering the traveling wave accelerator. CONCLUSIONS: The apparatus and analysis techniques of the authors demonstrated that an inexpensive, lightweight, permanent magnet electron energy spectrometer can be used for measuring the electron energy distributions of therapeutic electron beams (6-20 MeV). The primary goal of future work is to develop a real-time spectrometer by incorporating a real-time imager, which has potential applications such as beam matching, ongoing beam tune maintenance, and measuring spectra for input into Monte Carlo beam calculations.

Real-time simulator for designing electron dual scattering foil systems.

The purpose of this work was to develop a user friendly, accurate, real-time com- puter simulator to facilitate the design of dual foil scattering systems for electron beams on radiotherapy accelerators. The simulator allows for a relatively quick, initial design that can be refined and verified with subsequent Monte Carlo (MC) calculations and measurements. The simulator also is a powerful educational tool. The simulator consists of an analytical algorithm for calculating electron fluence and X-ray dose and a graphical user interface (GUI) C++ program. The algorithm predicts electron fluence using Fermi-Eyges multiple Coulomb scattering theory with the reduced Gaussian formalism for scattering powers. The simulator also estimates central-axis and off-axis X-ray dose arising from the dual foil system. Once the geometry of the accelerator is specified, the simulator allows the user to continuously vary primary scattering foil material and thickness, secondary scat- tering foil material and Gaussian shape (thickness and sigma), and beam energy. The off-axis electron relative fluence or total dose profile and central-axis X-ray dose contamination are computed and displayed in real time. The simulator was validated by comparison of off-axis electron relative fluence and X-ray percent dose profiles with those calculated using EGSnrc MC. Over the energy range 7-20 MeV, using present foils on an Elekta radiotherapy accelerator, the simulator was able to reproduce MC profiles to within 2% out to 20 cm from the central axis. The central-axis X-ray percent dose predictions matched measured data to within 0.5%. The calculation time was approximately 100 ms using a single Intel 2.93 GHz processor, which allows for real-time variation of foil geometrical parameters using slider bars. This work demonstrates how the user-friendly GUI and real-time nature of the simulator make it an effective educational tool for gaining a better understanding of the effects that various system parameters have on a relative dose profile. This work also demonstrates a method for using the simulator as a design tool for creating custom dual scattering foil systems in the clinical range of beam energies (6-20 MeV). 

Accuracy of pencil-beam redefinition algorithm dose calculations in patient-like cylindrical phantoms for bolus electron conformal therapy.

PURPOSE: The purpose of this study was to document the improved accuracy of the pencil beam redefinition algorithm (PBRA) compared to the pencil beam algorithm (PBA) for bolus electron conformal therapy using cylindrical patient phantoms based on patient computed tomography (CT) scans of retromolar trigone and nose cancer. METHODS: PBRA and PBA electron dose calculations were compared with measured dose in retromolar trigone and nose phantoms both with and without bolus. For the bolus treatment plans, a radiation oncologist outlined a planning target volume (PTV) on the central axis slice of the CT scan for each phantom. A bolus was designed using the planning.decimal(®) (p.d) software (.decimal, Inc., Sanford, FL) to conform the 90% dose line to the distal surface of the PTV. Dose measurements were taken with thermoluminescent dosimeters placed into predrilled holes. The Pinnacle(3) (Philips Healthcare, Andover, MD) treatment planning system was used to calculate PBA dose distributions. The PBRA dose distributions were calculated with an in-house C++ program. In order to accurately account for the phantom materials a table correlating CT number to relative electron stopping and scattering powers was compiled and used for both PBA and PBRA dose calculations. Accuracy was determined by comparing differences in measured and calculated dose, as well as distance to agreement for each measurement point. RESULTS: The measured doses had an average precision of 0.9%. For the retromolar trigone phantom, the PBRA dose calculations had an average ± 1σ dose difference (calculated - measured) of -0.65% ± 1.62% without the bolus and -0.20% ± 1.54% with the bolus. The PBA dose calculation had an average dose difference of 0.19% ± 3.27% without the bolus and -0.05% ± 3.14% with the bolus. For the nose phantom, the PBRA dose calculations had an average dose difference of 0.50% ± 3.06% without bolus and -0.18% ± 1.22% with the bolus. The PBA dose calculations had an average dose difference of 0.65% ± 6.21% without bolus and 1.75% ± 5.94% with the bolus. From a clinical perspective an agreement of 5% or better between planned (calculated) and delivered (measured) dose is desired. Statistically, this was true for 99% (± 2σ) of the dose points for three of the four cases for the PBRA dose calculations, the exception being the nose without bolus for which this was true for 89% (± 1.6σ) of the dose points. For the retromolar trigone, with and without bolus, the PBA showed agreement of 5% or better for approximately 86% (± 1.5σ) of the dose points. For the nose, with and without bolus, the PBA showed agreement of 5% or better for only approximately 58% (± 0.8σ) of the dose points. CONCLUSIONS: The measured data, whose high precision makes them useful for evaluation of the accuracy of electron dose algorithms, will be made publicly available. Based on the spread in dose differences, the PBRA has at least twice the accuracy of the PBA. From a clinical perspective the PBRA accuracy is acceptable in the retromolar trigone and nose for electron therapy with and without bolus.

A model for nucleation and growth of single wall carbon nanotubes via the HiPcO process: a catalyst concentration study.

Using the High Pressure carbon monoxide (HiPco) reactor we conducted an experiment on the effects of changing the catalyst concentration. With each catalyst concentration tested the resulting raw HiPco material was characterized for average SWNT lengths, SWNT diameters, residual iron particle size, and large fullerene content. We were able to determine trends in each of these characteristics as the catalyst concentration was changed. As the catalyst concentration was decreased SWNT lengths increased, SWNT diameters increased, the residual iron particle size increased, and the large fullerene content decreased. From these trends we have developed a Competitive Growth model for nucleation and growth of SWNTs via the HiPco process.