Pencil-beam Redefinition Algorithm Research Articles

Dosimetric validation of intensity-modulated bolus electron conformal therapy planning and delivery using an anthropomorphic cylindrical head phantom.

This work investigated the dosimetric accuracy of the intensity-modulated bolus electron conformal therapy (IM-BECT) planning and delivery process using the decimal ElectronRT (eRT) treatment planning system. An IM-BECT treatment plan was designed using eRT for a cylindrical, anthropomorphic retromolar trigone phantom. Treatment planning involved specification of beam parameters and design of a variable thickness wax bolus and Passive Radiotherapy Intensity Modulator for Electrons (PRIME) device, which was comprised of 33 tungsten island blocks of discrete diameters from 0.158 to 0.223cm (Intensity Reduction Factors from 0.937 to 0.875, respectively) inside a 10.1×6.7 cm2 copper cutout. For comparison of calculation accuracy, a BECT plan was generated by copying the IM-BECT plan and removing the intensity modulation. For both plans, a 16 MeV electron beam was used with 104.7cm source-to-surface distance to bolus. In-phantom TLD-100 measurements (N=47) were compared with both eRT planned dose distributions, which used the pencil beam redefinition algorithm with modifications for passive electron intensity modulation (IM-PBRA). Dose difference and distance to agreement (DTA) metrics were computed for each measurement point. Comparison of measured dose distributions with planned dose distributions yielded dose differences (calculated minus measured) characterized by a mean and standard deviation of -0.36%±1.64% for the IM-BECT plan, which was similar to -0.36%±1.90% for the BECT plan. All dose measurements were within 5% of the planned dose distribution, with both the BECT and IM-BECT measurement sets having 46/47 (97.8%) points within 3% or within 3mm of the respective treatment plans. It was found that the IM-BECT treatment plan generated using eRT was sufficiently accurate for clinical use when compared to TLD measurements in a cylindrical, anthropomorphic phantom, and was similarly accurate to the BECT treatment plan in the same phantom.

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

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. 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 0.352cm, 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. In the modulated region (under island blocks, depth<R90 ), modified PBRA-calculated dose distributions showed 2%/2mm passing rates for dnom =0.158, 0.273, and 0.352cm 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 (≤2cm), and on central axis. 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%/2mm 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.

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.

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 commercial 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 smoothing 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.PACS number(s): 87.55.kd

SU‐E‐T‐182: Clinical Implementation of TG71‐Based Electron MU Calculation and Comparison with a Commercial Secondary Calculation

Purpose:The TG‐71 report was published in 2014 to present standardized methodologies for MU calculations and determination of dosimetric quantities. This work explores the clinical implementation of a TG71‐based electron MU calculation algorithm and compares it with a recently released commercial secondary calculation program–Mobius3D (Mobius Medical System, LP).Methods:TG‐71 electron dosimetry data were acquired, and MU calculations were performed based on the recently published TG‐71 report. The formalism in the report for extended SSD using air‐gap corrections was used. The dosimetric quantities, such PDD, output factor, and f‐air factors were incorporated into an organized databook that facilitates data access and subsequent computation. The Mobius3D program utilizes a pencil beam redefinition algorithm. To verify the accuracy of calculations, five customized rectangular cutouts of different sizes–6×12, 4×12, 6×8, 4×8, 3×6 cm2–were made. Calculations were compared to each other and to point dose measurements for electron beams of energy 6, 9, 12, 16, 20 MeV. Each calculation / measurement point was at the depth of maximum dose for each cutout in a 10×10 cm2 or 15×15cm2 applicator with SSDs 100cm and 110cm. Validation measurements were made with a CC04 ion chamber in a solid water phantom for electron beams of energy 9 and 16 MeV.Results:Differences between the TG‐71 and the commercial system relative to measurements were within 3% for most combinations of electron energy, cutout size, and SSD. A 5.6% difference between the two calculation methods was found only for the 6MeV electron beam with 3×6 cm2cutout in the 10×102cm applicator at 110cm SSD. Both the TG‐71 and the commercial calculations show good consistency with chamber measurements: for 5 cutouts, &lt;1% difference for 100cm SSD, and 0.5–2.7% for 110cm SSD.Conclusions:Based on comparisons with measurements, a TG71‐based computation method and a Mobius3D program produce reasonably accurate MU calculations for electron‐beam therapy.

Implementation of a triple Gaussian beam model with subdivision and redefinition against density heterogeneities in treatment planning for scanned carbon-ion radiotherapy

Challenging issues in treatment planning for scanned carbon-ion (C-ion) therapy are (i) accurate calculation of dose distribution, including the contribution of large angle-scattered fragments, (ii) reduction in the memory space required to store the dose kernel of individual pencil beams and (iii) shortening of computation time for dose optimization and calculation. To calculate the dose contribution from fragments, we modeled the transverse dose profile of the scanned C-ion beam with the superposition of three Gaussian distributions. The development of pencil beams belonging to the first Gaussian component was calculated analytically based on the Fermi–Eyges theory, while those belonging to the second and third components were transported empirically using the measured beam widths in a water phantom. To reduce the memory space for the kernels, we stored doses only in the regions of interest considered in the dose optimization. For the final dose calculation within the patient’s whole body, we applied a pencil beam redefinition algorithm. With these techniques, the triple Gaussian beam model can be applied not only to final dose calculation but also to dose optimization in treatment planning for scanned C-ion therapy. To verify the model, we made treatment plans for a homogeneous water phantom and a heterogeneous head phantom. The planned doses agreed with the measurements within ±2% of the target dose in both phantoms, except for the doses at the periphery of the target with a high dose gradient. To estimate the memory space and computation time reduction with these techniques, we made a treatment plan for a bone sarcoma case with a target volume of 1.94 l. The memory space for the kernel and the computation time for final dose calculation were reduced to 1/22 and 1/100 of those without the techniques, respectively. Computation with the triple Gaussian beam model using the proposed techniques is rapid, accurate and applicable to dose optimization and calculation in treatment planning for scanned C-ion therapy.

SU-E-T-356: Accuracy of Eclipse Electron Macro Monte Carlo Dose Algorithm for Use in Bolus Electron Conformal Therapy

Purpose: To evaluate the accuracy of electron dose distribution calculated by the Varian Eclipse electron Monte Carlo (eMC) algorithm for use with recent commercially available bolus electron conformal therapy (ECT). Methods: eMC-calculated electron dose distributions for bolus ECT have been compared to those previously measured for cylindrical phantoms (retromolar trigone and nose), whose axial cross sections were based on the mid-PTV CT anatomy for each site. The phantoms consisted of SR4 muscle substitute, SR4 bone substitute, and air. The bolus ECT treatment plans were imported into the Eclipse treatment planning system and calculated using the maximum allowable histories (2×10^9), resulting in a statistical error of <0.2%. Smoothing was not used for these calculations. Differences between eMC-calculated and measured dose distributions were evaluated in terms of absolute dose difference as well as distance to agreement (DTA). Results: Results from the eMC for the retromolar trigone phantom showed 89% (41/46) of dose points within 3% dose difference or 3 mm DTA. There was an average dose difference of −0.12% with a standard deviation of 2.56%. Results for the nose phantom showed 95% (54/57) of dose points within 3% dose difference or 3 mm DTA. There was an average dose difference of 1.12% with a standard deviation of 3.03%. Dose calculation times for the retromolar trigone and nose treatment plans were 15 min and 22 min, respectively, using 16 processors (Intel Xeon E5-2690, 2.9 GHz) on a Varian Eclipse framework agent server (FAS). Results of this study were consistent with those previously reported for accuracy of the eMC electron dose algorithm and for the .decimal, Inc. pencil beam redefinition algorithm used to plan the bolus. Conclusion: These results show that the accuracy of the Eclipse eMC algorithm is suitable for clinical implementation of bolus ECT.

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

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. 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. 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. 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.

Application of the pencil-beam redefinition algorithm in heterogeneous media for proton beam therapy

In proton beam therapy, changes in the proton range due to lateral heterogeneity may cause serious errors in the dose distribution. In the present study, the pencil-beam redefinition algorithm (PBRA) was applied to proton beam therapy to address the problem of lateral density heterogeneity. In the calculation, the phase-space parameters were characterized for multiple range (i.e. proton energy) bins for given pencil beams. The particles that were included in each pencil beam were transported and redefined periodically until they had stopped. The redefined beams formed a detouring path that was different from that of the non-redefined pencil beams, and the path of each redefined beam was straight. The results calculated by the PBRA were compared with measured proton dose distributions in a heterogeneous slab phantom and an anthropomorphic phantom. Through the beam redefinition process, the PBRA was able to predict the measured proton-detouring effects. Therefore, the PBRA may allow improved calculation accuracy when dealing with lateral heterogeneities in proton therapy applications.

Delivery confirmation of bolus electron conformal therapy combined with intensity modulated x-ray therapy

The purpose of this study was to demonstrate that a bolus electron conformal therapy (ECT) dose plan and a mixed beam plan, composed of an intensity modulated x-ray therapy (IMXT) dose plan optimized on top of the bolus ECT plan, can be accurately delivered. Calculated dose distributions were compared with measured dose distributions for parotid and chest wall (CW) bolus ECT and mixed beam plans, each simulated in a cylindrical polystyrene phantom that allowed film dose measurements. Bolus ECT plans were created for both parotid and CW PTVs (planning target volumes) using 20 and 16 MeV beams, respectively, whose 90% dose surface conformed to the PTV. Mixed beam plans consisted of an IMXT dose plan optimized on top of the bolus ECT dose plan. The bolus ECT, IMXT, and mixed beam dose distributions were measured using radiographic films in five transverse and one sagittal planes for a total of 36 measurement conditions. Corrections for film dose response, effects of edge-on photon irradiation, and effects of irregular phantom optical properties on the Cerenkov component of the film signal resulted in high precision measurements. Data set consistency was verified by agreement of depth dose at the intersections of the sagittal plane with the five measured transverse planes. For these same depth doses, results for the mixed beam plan agreed with the sum of the individual depth doses for the bolus ECT and IMXT plans. The six mean measured planar dose distributions were compared with those calculated by the treatment planning system for all modalities. Dose agreement was assessed using the 4% dose difference and 0.2 cm distance to agreement. For the combined high-dose region and low-dose region, pass rates for the parotid and CW plans were 98.7% and 96.2%, respectively, for the bolus ECT plans and 97.9% and 97.4%, respectively, for the mixed beam plans. For the high-dose gradient region, pass rates for the parotid and CW plans were 93.1% and 94.62%, respectively, for the bolus ECT plans and 89.2% and 95.1%, respectively, for the mixed beam plans. For all regions, pass rates for the parotid and CW plans were 98.8% and 97.3%, respectively, for the bolus ECT plans and 97.5% and 95.9%, respectively, for the mixed beam plans. For the IMXT component of the mixed beam plans, pass rates for the parotid and CW plans were 93.7% and 95.8%. Bolus ECT and mixed beam therapy dose delivery to the phantom were more accurate than IMXT delivery, adding confidence to the use of planning, fabrication, and delivery for bolus ECT tools either alone or as part of mixed beam therapy. The methodology reported in this work could serve as a basis for future standardization of the commissioning of bolus ECT or mixed beam therapy. When applying this technology to patients, it is recommended that an electron dose algorithm more accurate than the pencil beam algorithm, e.g., a Monte Carlo algorithm or analytical transport such as the pencil beam redefinition algorithm, be used for planning to ensure the desired accuracy.

Experimental evaluation of a spatial resampling technique to improve the accuracy of pencil-beam dose calculation in proton therapy

In proton therapy, pencil-beam algorithms (PBAs) are the most widely used dose calculation methods. However, the PB calculations that employ one-dimensional density scaling neglect the effects of lateral density heterogeneity on the dose distributions, whereas some particles included in such pencil beams could overextend beyond the interface of the density heterogeneity. We have simplified a pencil-beam redefinition algorithm (PBRA), which was proposed for electron therapy, by a spatial resampling technique toward an application for proton therapy. The purpose of this study is to evaluate the calculation results of the spatial resampling technique in terms of lateral density heterogeneity by comparison with the dose distributions that were measured in heterogeneous slab phantoms. The pencil beams are characterized for multiple residual-range (i.e., proton energy) bins. To simplify the PBRA, the given pencil beams are resampled on one or two transport planes, in which smaller sub-beams that are parallel to each other are generated. We addressed the problem of lateral density heterogeneity comparing the calculation results to the dose distributions measured at different depths in heterogeneous slab phantoms using a two-dimensional detector. Two heterogeneity slab phantoms, namely, phantoms A and B, were designed for the measurements and calculations. In phantom A, the heterogeneity slab was placed close to the surface. On the other hand, in phantom B, it was placed close to the Bragg peak in the mono-energetic proton beam. In measurements, lateral dose profiles showed a dose reduction and increment in the vicinity of x = 0 mm in both phantoms at depths z = 142 and 161 mm due to lateral particle disequilibrium. In phantom B, these dose reduction∕increment effects were higher∕lower, respectively, than those in phantom A. This is because a longer distance from the surface to the heterogeneous slab increases the strength of proton scattering. Sub-beams, which were generated from the resampling plane, formed a detouring∕overextending path that was different from that of elemental pencil beams. Therefore, when the spatial resampling was implemented at the surface and immediately upstream of the lateral heterogeneity, the calculation could predict these dose reduction∕increment effects. Without the resampling procedure, these dose reduction∕increment effects could not be predicted in both phantoms owing to the blurring of the pencil beam. We found that the PBA with the spatial resampling technique predicted the dose reduction∕increment at the dose profiles in both phantoms when the sampling plane was defined immediately upstream of the heterogeneous slab. We have demonstrated the implementation of a spatial resampling technique for pencil-beam calculation to address the problem of lateral density heterogeneity. While further validation is required for clinical use, this study suggests that the spatial resampling technique can make a significant contribution to proton therapy.

SU-E-T-750: Interfacing the Pencil Beam Redefinition Algorithm with a Commercial Treatment Planning System

Purpose: The purpose of this work was to interface the pencil beam redefinition algorithm (PBRA) dose engine with the Pinnacle treatment planning system (TPS) for use in bolus electron conformal therapy (ECT) dose planning. Currently Pinnacle TPS uses the Hogstrom pencil beam algorithm (PBA). Methods: A C program that calculates electron dose using the PBRA has been developed. This program inputs the Pinnacle files for the CT data, the user‐generated plan data, and the PBA beam data. The 3D calculated dose outputs a binary file that is uploaded into Pinnacle. This method allows the Pinnacle TPS to be used for plan analysis, e.g. dose display and dose volume histograms of the planning target volume and normal tissues Results: To date our program has been validated by demonstrating, for each beam energy, that agreements of PBRA calculated with measured dose distributions in a water phantom, as a function of field size and SSD, are consistent with previously published results. Also, the accuracy of the PBRA in heterogeneous phantoms agrees with previously published geometric phantom measurements and with patient based phantoms measurements (subject of companion paper). The PBRA is advantageous because it requires no additional beam commissioning data and its accuracy in patients is comparable to Monte Carlo. Calculation times in water for 4×4cm and 20×20cm fields for the 9 MeV beam are 5sec and 120sec respectively on a 2.93Ghz processor using a non‐optimized code. Using the 20 MeV beam these times are 14sec and 290sec, respectively. Conclusion: Our stand alone C program demonstrates a reasonable way to perform patient dose calculations using the PBRA with the Pinnacle TPS. Use of the PBRA might be beneficial for some sites when planning bolus ECT. This work was supported in part by a research agreement with .decimal Inc.

SU-E-T-732: Accuracy of Electron Dose from Pencil-Beam Redefinition Algorithm in Patient-Like 2D Phantoms

Purpose: To evaluate the accuracy of electron dose calculated using the pencil‐beam redefinition algorithm (PBRA) in patient‐like 2D phantoms. With the recent availability of bolus electron conformal therapy (ECT), conforming of the 90% dose surface to the planning target volume (PTV) might require a more accurate dose calculation than the Hogstrom pencil beam algorithm (PBA). Methods: PBRA‐calculated dose distributions have been compared to those previously measured in three cylindrical phantoms (retromolar trigone, maxillary sinus, and nose), whose axial cross sections were based on the mid‐PTV CTanatomy for each site. The phantoms consisted of SR4 muscle substitute, SR4 bone substitute, and air. TLD measured doses were reported for a matrix of locations in the SR4 muscle only. Current CT scan data was used for planning with CT to stopping and scattering power tables created based on the chemical compositions and current densities of the materials. Differences between PBRA‐calculated and measured dose were expressed as distance‐to‐dose agreement in regions of high dose gradient (90%–10%) and as a percent of given dose elsewhere. Results: Results from the PBRA for the retromolar trigone phantom showed 100% (27/27) TLD dose points within 5% and 95% (19/20) within 4mm. Similar results for the maxillary sinus phantom showed 79% (26/33) and 100% (19/19), respectively, and results forthe nose showed 96%(23/24) and 100% (38/38), respectively. For each phantom, results were better than previously reported PBA results, e.g. results for the nose showed 81% (26/32) and 60% (18/30), respectively. Dose calculation times for the three sites (single 2.93GHz) were 1min, 45sec, and 1min. Conclusions: Results of this study were consistent with those previously reported, namely that the PBRA is more accurate than the PBA and that it should be suitable for clinical situations where dose accuracy is more important, e.g. bolus ECT. This work was supported in part by a research agreement with .decimal Inc.

Calculating percent depth dose with the electron pencil‐beam redefinition algorithm

In the present work, we investigated the accuracy of the electron pencil‐beam redefinition algorithm (PBRA) in calculating central‐axis percent depth dose in water for rectangular fields. The PBRA energy correction factor C(E) was determined so that PBRA‐calculated percent depth dose best matched the percent depth dose measured in water. The hypothesis tested was that a method can be implemented into the PBRA that will enable the algorithm to calculate central‐axis percent depth dose in water at a 100‐cm source‐to‐surface distance (SSD) with an accuracy of 2% or 1‐mm distance to agreement for rectangular field sizes ≥2×2 cm. Preliminary investigations showed that C(E), determined using a single percent depth dose for a large field (that is, having side‐scatter equilibrium), was insufficient for the PBRA to accurately calculate percent depth dose for all square fields ≥2×2 cm. Therefore, two alternative methods for determining C(E) were investigated. In Method 1, C(E), modeled as a polynomial in energy, was determined by fitting the PBRA calculations to individual rectangular‐field percent depth doses. In Method 2, C(E) for square fields, described by a polynomial in both energy and side of square W [that is, C=C(E,W)], was determined by fitting the PBRA calculations to measured percent depth dose for a small number of square fields. Using the function C(E, W), C(E) for other square fields was determined, and C(E) for rectangular field sizes was determined using the geometric mean of C(E) for the two measured square fields of the dimension of the rectangle (square root method). Using both methods, PBRA calculations were evaluated by comparison with measured square‐field and derived rectangular‐field percent depth doses at 100‐cm SSD for the Siemens Primus radiotherapy accelerator equipped with a 25×25‐cm applicator at 10 MeV and 15 MeV. To improve the fit of C(E) and C(E, W) to the electron component of percent depth dose, it was necessary to modify the PBRA's photon depth dose model to include dose buildup. Results showed that, using both methods, the PBRA was able to predict percent depth dose within criteria for all square and rectangular fields. Results showed that second‐ or third‐order polynomials in energy (Methods 1 and 2) and in field size (Method 2) were typically required. Although the time for dose calculation using Method 1 is approximately twice that using Method 2, we recommend that Method 1 be used for clinical implementation of the PBRA because it is more accurate (most measured depth doses predicted within approximately 1%) and simpler to implement.PACS number: 87.53.Fs

Application of the electron pencil beam redefinition algorithm to electron arc therapy

This project investigated the potential of summing fixed-beam dose distributions calculated using the pencil-beam redefinition algorithm (PBRA) at small angular steps (1 degree) to model an electron arc therapy beam. The PRBA, previously modified to model skin collimation, was modified further by incorporating two correction factors. One correction factor that is energy, SSD (source-to-surface distance), and field-width dependent constrained the calculated dose output to be the same as the measured dose output for fixed-beam geometries within the range of field widths and SSDs encountered in arc therapy. Another correction factor (single field-width correction factor for each energy) compensated for large-angle scattering not being modeled, allowing a more accurate calculation of dose output at mid arc. The PBRA was commissioned to accurately calculate dose in a water phantom for fixed-beam geometries typical of electron arc therapy. Calculated central-axis depth doses agreed with measured doses to within 2% in the low-dose gradient regions and within 1-mm in the high-dose gradient regions. Off-axis doses agreed to within 2 mm in the high-dose gradient regions and within 3% in the low-dose gradient regions. Arced-beam calculations of dose output and depth dose at mid arc were evaluated by comparing to data measured using two cylindrical water phantoms with radii of 12 and 15 cm at 10 and 15 MeV. Dose output was measured for all combinations of phantom radii of curvature, collimator widths (4, 5, and 6 cm), and arc angles (0 degrees, 20 degrees, 40 degrees, 60 degrees, 80 degrees, and 90 degrees) for both beam energies. Results showed the calculated mid-arc dose output to agree within 2% of measurement for all combinations. For a 90 degree arc angle and 5 x 20 cm2 field size, the calculated mid-arc depth dose in the low-dose gradient region agreed to within 2% of measurement for all depths at 10 MeV and for depths greater than depth of dose maximum R100 at 15 MeV. For depths in the buildup region at 15 MeV the calculations overestimated the measured dose by as much as 3.4%. Mid-arc depth dose in the high-dose gradient region agreed to within 2.2 mm of measured dose. Calculated two-dimensional relative dose distributions in the plane of rotation were compared to dose measurements using film in a cylindrical polystyrene phantom for a 90 degree arc angle and field widths of 4, 5, and 6 cm at 10 and 15 MeV. Results showed that off-axis dose at the ends of arc (without skin collimation) agreed to within 2% in the low-dose gradient region and to within 1.2 mm in the high-dose gradient region. This work showed that the accuracy of the PBRA arced-beam dose model met the criteria specified by Van Dyk et al. [Int. J. Radiat. Oncol. Biol. Phys. 26, 261-273 (1993)] with the exception of the buildup region of the 15 MeV beam. Based on the present results, results of a previous study showing acceptable accuracy in the presence of skin collimation, and results of a previous study showing acceptable accuracy in the presence of internal heterogeneities, it is concluded that the PBRA arced-beam dose model should be adequate for planning electron arc therapy.

Modeling skin collimation using the electron pencil beam redefinition algorithm

Skin collimation is an important tool for electron beam therapy that is used to minimize the penumbra when treating near critical structures, at extended treatment distances, with bolus, or using arc therapy. It is usually made of lead or lead alloy material that conforms to and is placed on patient surface. Presently, commercially available treatment-planning systems lack the ability to model skin collimation and to accurately calculate dose in its presence. The purpose of the present work was to evaluate the use of the pencil beam redefinition algorithm (PBRA) in calculating dose in the presence of skin collimation. Skin collimation was incorporated into the PBRA by terminating the transport of electrons once they enter the skin collimator. Both fixed- and arced-beam dose calculations for arced-beam geometries were evaluated by comparing them with measured dose distributions for 10- and 15-MeV beams. Fixed-beam dose distributions were measured in water at 88-cm source-to-surface distance with an air gap of 32 cm. The 6 x 20-cm2 field (dimensions projected to isocenter) had a 10-mm thick lead collimator placed on the surface of the water with its edge 5 cm inside the field's edge located at +10 cm. Arced-beam dose distributions were measured in a 13.5-cm radius polystyrene circular phantom. The beam was arced 90 degrees (-45 degrees to +45 degrees), and 10-mm thick lead collimation was placed at +/- 30 degrees. For the fixed beam at 10 MeV, the PBRA- calculated dose agreed with measured dose to within 2.0-mm distance to agreement (DTA) in the regions of high-dose gradient and 2.0% in regions of low dose gradient. At 15 MeV, the PBRA agreed to within a 2.0-mm DTA in the regions of high-dose gradient; however, the PBRA underestimated the dose by as much as 5.3% over small regions at depths less than 2 cm because it did not model electrons scattered from the edge of the skin collimation. For arced beams at 10 MeV, the agreement was 1-mm DTA in the high-dose gradient regions, and 2% in the low-dose gradient regions. For arced beams at 15 MeV, the agreement was 1 mm in the high-dose gradient regions, and in the low-dose gradient region at depth less than 2 cm, as much as 5% dose difference was observed. This study demonstrated the ease with which skin collimation can be incorporated into the PBRA. The good agreement of PBRA calculated with measured dose shows that the PBRA is likely sufficiently accurate for clinical use in the presence of skin collimation for electron arc therapy. To further improve the accuracy of the PBRA in regions having significant electrons scattered from the edge of the skin collimation would require transporting the electrons through the lead skin collimation near its edges.

SU-FF-T-326: Application of the Pencil-Beam Redefinition Algorithm to Electron Arc Therapy

Purpose: A dose algorithm suitable for electron arc therapy is not available on existing commercial treatment planning systems. This project investigated the potential for simulating an electron arc therapy beam by summing (1° angular steps) fixed-beam dose distributions calculated using the pencil-beam redefinition algorithm (PBRA). Method and Materials: Similar to the Hogstrom pencil-beam algorithm (PBA), the PBRA was commissioned for fixed beam geometries typical of electron arc therapy. The PBRA was constrained to calculate dose output for fixed beams as a function of field width and SSD. For arced beams, a small width correction was incorporated to conserve integral dose. Resulting arced beam calculations of dose output and mid-arc depth dose were evaluated by comparing to data measured using cylindrical water phantoms (ρ=12, 15 cm). Calculated 2D relative dose distributions in the plane of rotation were evaluated using film dosimetry in a polystyrene cylindrical phantom (ρ=13.5 cm). A wide range of treatment parameter combinations was investigated — three field sizes, three radii of curvature, and multiple arc angles at 10 and 15 MeV. Results: For arced beams, the maximum difference between PBRA-calculated and measured dose output at mid-arc was 2%. Along mid arc, the maximum dose difference in low dose-gradient regions was 3.4%, and the maximum distance to agreement (DTA) of dose values in high dose-gradient regions was 2.2 mm. Away from mid-arc, the maximum dose difference was 2%, and the maximum DTA was 1.2 mm. Conclusion: Results showed that the PBRA summation method can calculate dose in homogeneous phantoms within 3.4%. Since PBRA calculations in patients have been shown to be within 4% by Boyd et al., this method should be suitably accurate for use with electron arc therapy patients. User experience with the PBA and ease of PBRA beam commissioning make the PBRA attractive for this application.

SU-FF-T-330: Modeling Skin Collimation Using Electron Pencil-Beam Redefinition Algorithm

Purpose: To modify the pencil‐beam redefinition algorithm (PBRA) to model skin collimation and to verify that the modified PBRA can accurately calculate dose in the presence of skin collimation for both electron fixed and arced beams. Method and Materials: The PBRA continuously redefines pencil beams at equally spaced depth. For pencil beam pixels fully (partially) shielded by skin collimation further propagation of all (a portion) of the pencil beam is terminated. The accuracy of the modified PBRA for skin collimation (10‐mm thick lead) was verified at 10 and 15 MeV. Fixed beam measurements were performed using a scanning diode detector in water: air gap is 32 cm, field size is 20×6 cm2, and skin collimation is at ±5.0 cm. Arced beam measurements were performed in a cylindrical, plastic phantom (ρ=13.5 cm) using film dosimetry: arc angle is ± 45°, skin collimation edge is at ± 30°, and field size is 5×20 cm2. Results: Fixed beam: For 10 MeV, the calculations and measurements agreed within 2% in the low dose‐gradient region (Dose>90% and Dose <10%) and within 2 mm distance to agreement (DTA) in the high dose‐gradient region (10%<Dose<90%). For 15 MeV, calculations and measurements agreed within 5% in the low dose‐gradient region and within 2 mm DTA in the high dose‐gradient region. Differences from 3–5%, limited to a small volume distal to and just inside the skin collimation edge, were due to the modified PBRA not modeling scatter from the skin collimation.Arced beam: For both energies, the calculations and measurements agreed within 2% in the low dose‐gradient region and within 1 mm DTA in the high dose‐gradient region. Conclusion: Results showed that the PBRA is easily modified to include skin collimation and that it can calculate dose in a water or plastic phantom sufficiently accurately for clinical use.

Custom electron bolus treatment planning with skin collimation using the pencil-beam redefinition algorithm

Purpose/Objective: The aims are to demonstrate (1) the improvement in the patient dose distribution from using skin collimation when treating with bolus electron conformal therapy (ECT) and (2) the utility of the pencil beam redefinition algorithm (PBRA) for calculating dose in the presence of bolus and skin collimation.

Modelling pencil-beam divergence with the electron pencil-beam redefinition algorithm

The electron pencil-beam redefinition algorithm (PBRA), which is used to calculate electron beam dose distributions, assumes that the virtual source of each pencil beam is identical to that of the broad beam incident on the patient. In the present work, a virtual source specific for each pencil beam is modelled by including the source distance as a pencil-beam parameter to be redefined with depth. To incorporate a variable pencil-beam source distance parameter, the transport equation was reformulated to explicitly model divergence resulting in the algorithm divPBRA. Allowing the virtual source position to vary with individual pencil beams is expected to better model the effects of heterogeneities on local electron fluence divergence (or convergence). Selected experiments from a measured data set developed at The University of Texas M D Anderson Cancer Center were used to evaluate the accuracy of the dose calculated using divPBRA. Results of the calculation showed that the theory accurately predicted the virtual source position in regions of side-scatter equilibrium and predicted reasonable virtual source positions in regions lacking side-scatter equilibrium (i.e. penumbra and in the vicinity and shadow of internal heterogeneities). Results of the evaluation showed the dose accuracy of divPBRA to be marginally better to that of PBRA, except in regions of extremely sharp dose perturbations, where the divPBRA calculations were significantly greater than the measured data. Dose calculations using divPBRA took 45% longer than those using PBRA. Therefore, we concluded that divPBRA offers no significant advantage over PBRA for the purposes of clinical treatment planning. However, the results were promising and divPBRA might prove useful if further modelling were to include large-angle scattering, low-energy delta rays and brehmsstrahlung.