Robert A. Boyd

Dosimetry of a prototype retractable eMLC for fixed-beam electron therapy

An electron multileaf collimator (eMLC) has been designed that is unique in that it retracts to 37 cm from the isocenter [63-cm source-to-collimator distance (SCD)] and can be deployed to distances of 20 and 10 cm from the isocenter (80 and 90 cm SCD, respectively). It is expected to be capable of arc therapy at 63 cm SCD; isocentric, fixed-beam therapy at 80 cm SCD; and source-to-surface distance (SSD), fixed-beam therapy at 90 cm SCD. In all positions, its leaves could be used for unmodulated or intensity-modulated therapy. Our goal in the present work is to describe the general characteristics of the eMLC and to demonstrate that its leakage characteristics and dosimetry are adequate for SSD, fixed-beam therapy as an alternative to Cerrobend cutouts with applicators once the prototypes leaves are motorized. Our eMLC data showed interleaf electron leakage at 15 MeV to be less than 0.1% based on a 0.0025 cm manufacturing tolerance, and lateral electron leakage at 5 and 15 MeV to be less than 2%. X-ray leakage through the leaves was 1.6% at 15 MeV. Our data showed that beam penumbra was independent of direction and leaf position. The dosimetric properties of square fields formed by the eMLC were very consistent with those formed by Cerrobend inserts in the 20 x 20 cm2 applicator. Output factors exhibited similar field-size dependence. Airgap factors exhibited almost identical field-size dependence at two SSDs (105 and 110 cm), consistent with the common assumption that airgap factors are applicator independent. Percent depth-dose curves were similar, but showed variations up to 3% in the buildup region. The pencil-beam algorithm (PBA) fit measured data from the eMLC and applicator-cutout systems equally well, and the resulting two-dimensional (2-D) dose distributions, as predicted by the PBA, agreed well at common airgap distance. Simulating patient setups for breast and head and neck treatments showed that almost all fields could be treated using similar SSDs as when using applicators, although head and neck treatments require placing the patients head on a head-holder treatment table extension. The results of this work confirmed our design goals and support the potential use of the eMLC design in the clinical setting. The eMLC should allow the same treatments as are typically delivered with the electron applicator-cutout system currently used for fixed-beam therapy.

Electron conformal radiotherapy using bolus and intensity modulation

PURPOSE Conformal electron beam therapy can be delivered using shaped bolus, which varies the penetration of the electrons across the incident beam so that the 90% isodose surface conforms to the distal surface of the planning target volume (PTV). Previous use of this modality has shown that the irregular proximal surface of the bolus causes the dose heterogeneity in the PTV to increase from 10%, the typical dose spread of a flat-water surface to approximately 20%. The present work evaluates the ability to restore dose homogeneity by varying the incident electron intensity. METHODS AND MATERIALS Three patients, one each with chest wall, thorax, and head-and-neck cancer, were planned using electron conformal therapy with bolus, with and without intensity modulation. Resulting dose distributions and dose-volume histograms were compared with non-intensity-modulated bolus plans. RESULTS In all cases, the DeltaD(90%-10%) for the PTV was reduced; for example, for the head-and-neck case, the DeltaD(90%-10%) for the PTV was reduced from 14.9% to 9.2%. This reduction in dose spread is a direct result of intensity modulation. CONCLUSIONS The results showed that intensity-modulated electron beams could significantly improve the dose homogeneity in the PTV for patients treated with electron conformal therapy using shaped bolus.

Electron pencil-beam redefinition algorithm dose calculations in the presence of heterogeneities.

The electron pencil-beam redefinition algorithm (PBRA) is currently being refined and evaluated for clinical use. The purpose of this work was to evaluate the accuracy of PBRA-calculated dose in the presence of heterogeneities and to benchmark PBRA dose accuracy for future improvements to the algorithm. The PBRA was evaluated using a measured electron beam dose algorithm verification data set developed at The University of Texas M. D. Anderson Cancer Center. The data set consists of measurements made using 9 and 20 MeV beams in a water phantom with air gaps, internal air and bone heterogeneities, and irregular surfaces. Refinements to the PBRA have enhanced the speed of the dose calculations by a factor of approximately 7 compared to speeds previously reported in published data; a 20 MeV, 15 x 15 cm2 field electron-beam dose distribution took approximately 10 minutes to calculate. The PBRA showed better than 4% accuracy in most experiments. However, experiments involving the low-energy (9 MeV) electron beam and irregular surfaces showed dose differences as great as 22%, in albeit a small fractional region. The geometries used in this study, particularly those in the irregular surface experiments, were extreme in the sense that they are not seen clinically. A more appropriate clinical evaluation in the future will involve comparisons to Monte Carlo generated patient dose distributions using actual computed tomography scan data. The present data also serve as a benchmark against which future enhancements to the PBRA can be evaluated.

Effect of using an initial polyenergetic spectrum with the pencil-beam redefinition algorithm for electron-dose calculations in water

This work compares the accuracy of dose distributions computed using an incident polyenergetic (PE) spectrum and a monoenergetic (ME) spectrum in the electron pencil-beam redefinition algorithm (PBRA). It also compares the times required to compute PE and ME dose distributions. This has been accomplished by comparing PBRA calculated dose distributions with measured dose distributions in water from the National Cancer Institute electron collaborative working group (ECWG) data set. Comparisons are made at 9 and 20 MeV for the 15 x 15 cm2 and 6 x 6 cm2 fields at 100- and 110-cm SSD. The incident PE spectrum is determined by a process that best matches the weighted sum of monoenergetic PBRA calculated central-axis depth doses, each calculated with the energy correction factor, C(E), equal to unity, to the ECWG measured depth dose for the 15 x 15 cm2 field at 100-cm SSD. C(E) is determined by a least square fit to central-axis depth dose for the PE PBRA. Results show that both the PE and ME PBRA accurately calculate central-axis depth dose at 100-cm SSD for the 6 x 6 cm2 and 15 x 15 cm2 field sizes and also at 110-cm SSD for the 15 x 15 cm2 field size. In the penumbral region, the PE PBRA calculation is significantly more accurate than the ME PBRA for all measurement conditions. Both the PE and ME PBRA exhibit significant dose errors (> 4%) outside the penumbra at shallow depths for the 6 x 6 cm2 and 15 x 15 cm2 fields at 100-cm SSD and inside the penumbra at shallow depths for the 6 x 6 cm2 field size at 110-cm SSD. These errors are attributed to the fact that the PBRA does not model collimator scatter in the incident beam. Calculation times for the PE PBRA are approximately 70%-140% greater than those for the ME PBRA. We conclude that the PE PBRA is significantly more accurate than the ME PBRA, and we believe that the increase in time for the PE PBRA will not significantly impact the clinical utility of the PBRA.

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.

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.

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 PBRAs 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

The use of an extra-focal electron source to model collimator-scattered electrons using the pencil-beam redefinition algorithm.

Currently, the pencil-beam redefinition algorithm (PBRA) utilizes a single electron source to model clinical electron beams. In the single-source model, the electrons appear to originate from a virtual source located near the scattering foils. Although this approach may be acceptable for most treatment machines, previous studies have shown dose differences as high as 8% relative to the given dose for small fields for some machines such as the Varian Clinac 1800. In such machines collimation-scattered electrons originating from the photon jaws and the applicator give rise to extra-focal electron sources. In this study, we examined the impact of modeling an additional electron source to better account for the collimator-scattered electrons. The desired dose calculation accuracy in water throughout the dose distribution is 3% or better relative to the given dose. We present here a methodology for determining the electron-source parameters for the dual-source model using a minimal set of data, that is, two central-axis depth-dose curves and two off-axis profiles. A Varian Clinac 1800 accelerator was modeled for beam energies of 20 and 9 MeV and applicator sizes of 15 x 15 and 6 x 6 cm2. The improvement in the accuracy of PBRA-calculated dose, evaluated using measured two-dimensional dose distributions in water, was characterized using the figure of merit, FA3%, which represents the fractional area containing dose differences greater than 3%. For the 15 x 15 cm2 field the evaluation was restricted to the penumbral region, and for the 6 x 6 cm2 field the central region of the beam was included as it was impacted by the penumbra. The greatest improvement in dose accuracy was for the 6 x 6 cm2 applicator. At 9 MeV, FA3% decreased from 15% to 0% at 100 cm SSD and from 34% to 4% at 110 cm SSD. At 20 MeV, FA3% decreased from 17% to 2% at 100 cm SSD and from 41% to 10% at 110 cm SSD. In the penumbra of the 15 x 15 cm2 applicator, the improvement was less, but still significant. At 9 MeV, FA3% changed from 11% to 1% at 100 cm SSD and from 10% to 12% at 110 cm SSD. At 20 MeV, FA3% decreased from 12% to 8% at 100 cm SSD and from 14% to 5% at 110 cm SSD. Results demonstrate that use of a dual-source beam model can provide significantly improved accuracy in the PBRA-calculated dose distribution that was not achievable with a single-source beam model when modeling the Varian Clinac 1800 electron beams. Time of PBRA dose calculation was approximately doubled; however, dual-source beam modeling of newer accelerators (e.g., the Varian Clinac 2100) may not be necessary because of less impact of collimator-scattered electrons on dosimetry.

Multileaf collimation for electron intensity modulation

Dynamic multileaf collimation (DMLC) could prove useful in electron conformal therapy, arc electron therapy, and electron field abutment. For these applications, it is first necessary to understand the ability of the DMLC to modulate electron fluence and its effect on the resulting dose distribution. The objectives of this work were to demonstrate the ability of the pencil-beam algorithm to fit the electron dose distribution created by the DMLC and to demonstrate for non-normal incidence on a flat phantom that the DMLC can restore dose uniformity. Measurements were performed using 12 and 20 MeV electrons with the 25/spl times/25 cm/sup 2/ applicator. Dose was measured using film placed at a depth of 2 cm in a plastic phantom at 100 cm SSD. First, measurements were made with the MLC set to 10/spl times/10 cm/sup 2/ and 20/spl times/20 cm/sup 2/. Another irradiation simulated modulation by irradiating with square fields followed by the MLC blocking half the field. These results showed that the pencil beam algorithm can accurately predict the off-axis dose profiles. Second, the beam was angled at 30/spl deg/ from the normal incidence creating a gradient in dose uniformity. Then, the beam was modulated to achieve dose uniformity by gradually closing the leaves from the side closest to the phantom to the side furthest away. These results indicated that the DMLC can restore beam uniformity for cases where there is a low dose gradient.

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

ECT is defined as the use of one or more electron beams for the following purpose: (1) containing the planning target volume (PTV) in the 90% (of given dose) dose surface: (2) achieving as homogenous a dose as possible (e.g., 90% to 100%) or a prescribed heterogeneous dose distribution to the PTV; and (3) delivering a minimal dose to underlying critical structures and normal tissue [1]. ECT can be achieved through energy modulation Results cont. . The superior aspect of the patient plan using bolus ECT without skin collimation is illustrated in Figure 5. Due to the width of the beam penumbra and the proximity of the PTV to the eye, the lens and ocular orbit receive considerable dose compared to the plan with skin collimation in Figure 6. DVHs in Figure 7 show insignificant changes in the DVH of the PTV, but significant changes in the DVHs of the critical structures. For the lens, dose to the 10% volume is reduced from 24% (13 Gy) to 5% (3 Gy). For the ocular orbit, dose is reduced from