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A generalized 2D pencil beam scaling algorithm for proton dose calculation in heterogeneous slab geometries.

ABSTRACT: Pencil beam algorithms are commonly used for proton therapy dose calculations. Szymanowski and Oelfke ["Two-dimensional pencil beam scaling: An improved proton dose algorithm for heterogeneous media," Phys. Med. Biol. 47, 3313-3330 (2002)] developed a two-dimensional (2D) scaling algorithm which accurately models the radial pencil beam width as a function of depth in heterogeneous slab geometries using a scaled expression for the radial kernel width in water as a function of depth and kinetic energy. However, an assumption made in the derivation of the technique limits its range of validity to cases where the input expression for the radial kernel width in water is derived from a local scattering power model. The goal of this work is to derive a generalized form of 2D pencil beam scaling that is independent of the scattering power model and appropriate for use with any expression for the radial kernel width in water as a function of depth.Using Fermi-Eyges transport theory, the authors derive an expression for the radial pencil beam width in heterogeneous slab geometries which is independent of the proton scattering power and related quantities. The authors then perform test calculations in homogeneous and heterogeneous slab phantoms using both the original 2D scaling model and the new model with expressions for the radial kernel width in water computed from both local and nonlocal scattering power models, as well as a nonlocal parameterization of Molière scattering theory. In addition to kernel width calculations, dose calculations are also performed for a narrow Gaussian proton beam.Pencil beam width calculations indicate that both 2D scaling formalisms perform well when the radial kernel width in water is derived from a local scattering power model. Computing the radial kernel width from a nonlocal scattering model results in the local 2D scaling formula under-predicting the pencil beam width by as much as 1.4 mm (21%) at the depth of the Bragg peak for a 220 MeV proton beam in homogeneous water. This translates into a 32% dose discrepancy for a 5 mm Gaussian proton beam. Similar trends were observed for calculations made in heterogeneous slab phantoms where it was also noted that errors tend to increase with greater beam penetration. The generalized 2D scaling model performs well in all situations, with a maximum dose error of 0.3% at the Bragg peak in a heterogeneous phantom containing 3 cm of hard bone.The authors have derived a generalized form of 2D pencil beam scaling which is independent of the proton scattering power model and robust to the functional form of the radial kernel width in water used for the calculations. Sample calculations made with this model show excellent agreement with expected values in both homogeneous water and heterogeneous phantoms.

SUBMITTER: Westerly DC

PROVIDER: S-EPMC3676383 | biostudies-other | 2013 Jun

REPOSITORIES: biostudies-other

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Project description: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 > or = 2 x 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 > or = 2 x 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 x 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.

Project description:Stereotactic body radiation therapy (SBRT) has been increasingly used as an efficacious treatment modality for early-stage non-small cell lung cancer. The accuracy of dose calculations is compromised due to the presence of inhomogeneity. For the purpose of a consistent prescription, radiation doses were calculated without heterogeneity correction in several RTOG trials. For patients participating in these trials, recalculations of the planned doses with more accurate dose methods could provide better correlations between the treatment outcomes and the planned doses. Using a Monte Carlo (MC) dose calculation algorithm as a gold standard, we compared the recalculated doses with the MC algorithm to the original pencil beam (PB) calculations for our institutional clinical lung SBRT plans. The focus of this comparison is to investigate the volume and location dependence on the differences between the two dose calculations. Thirty-one clinical plans that followed RTOG and other protocol guidelines were retrospectively investigated in this study. Dosimetric parameters, such as D1, D95, and D99 for the PTV and D1 for organs at risk, were compared between two calculations. Correlations of mean lung dose and V20 of lungs between two calculations were investigated. Significant dependence on tumor size and location was observed from the comparisons between the two dose calculation methods. When comparing the PB calculations without heterogeneity correction to the MC calculations with heterogeneity correction, we found that in terms of D95 of PTV: (1) the two calculations resulted in similar D95 for edge tumors with volumes greater than 25.1 cc; (2) an average overestimation of 5% in PB calculations for edge tumors with volumes less than 25.1 cc; and (3) an average overestimation of 9% or underestimation of 3% in PB calculations for island tumors with volumes smaller or greater than 22.6 cc, respectively. With heterogeneity correction, the PB calculations resulted in an average reduction of 23.8% and 15.3% in the D95 for the PTV for island and edge lesions, respectively, when compared to the MC calculations. For organs at risks, very small differences were found among all the comparisons. Excellent correlations for mean dose and V20 of lungs were observed between the two calculations. This study demonstrated that using a single scaling factor may be overly simplified when accounting for the effects of heterogeneity correction. Accurate dose calculations, such as the Monte Carlo algorithms, are highly recommended to understand dose responses in lung SBRT.

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Project description:The novel deterministic radiation transport algorithm, Acuros XB (AXB), has shown great potential for accurate heterogeneous dose calculation. However, the clinical impact between AXB and other currently used algorithms still needs to be elucidated for translation between these algorithms. The purpose of this study was to investigate the impact of AXB for heterogeneous dose calculation in lung cancer for intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT).The thorax phantom from the Radiological Physics Center (RPC) was used for this study. IMRT and VMAT plans were created for the phantom in the Eclipse 11.0 treatment planning system. Each plan was delivered to the phantom three times using a Varian Clinac iX linear accelerator to ensure reproducibility. Thermoluminescent dosimeters (TLDs) and Gafchromic EBT2 film were placed inside the phantom to measure delivered doses. The measurements were compared with dose calculations from AXB 11.0.21 and the anisotropic analytical algorithm (AAA) 11.0.21. Two dose reporting modes of AXB, dose-to-medium in medium (Dm,m) and dose-to-water in medium (Dw,m), were studied. Point doses, dose profiles, and gamma analysis were used to quantify the agreement between measurements and calculations from both AXB and AAA. The computation times for AAA and AXB were also evaluated.For the RPC lung phantom, AAA and AXB dose predictions were found in good agreement to TLD and film measurements for both IMRT and VMAT plans. TLD dose predictions were within 0.4%-4.4% to AXB doses (both Dm,m and Dw,m); and within 2.5%-6.4% to AAA doses, respectively. For the film comparisons, the gamma indexes (± 3%∕3 mm criteria) were 94%, 97%, and 98% for AAA, AXB_Dm,m, and AXB_Dw,m, respectively. The differences between AXB and AAA in dose-volume histogram mean doses were within 2% in the planning target volume, lung, heart, and within 5% in the spinal cord. However, differences up to 8% between AXB and AAA were found at lung∕soft tissue interface regions for individual IMRT fields. AAA was found to be 5-6 times faster than AXB for IMRT, while AXB was 4-5 times faster than AAA for VMAT plan.AXB is satisfactorily accurate for the dose calculation in lung cancer for both IMRT and VMAT plans. The differences between AXB and AAA are generally small except in heterogeneous interface regions. AXB Dw,m and Dm,m calculations are similar inside the soft tissue and lung regions. AXB can benefit lung VMAT plans by both improving accuracy and reducing computation time.

Project description:PurposePatients with bilateral breast cancer (BBC), who require postmastectomy radiation therapy or radiation as part of breast conservation treatment, present a unique technical challenge. Even with modern techniques, such as intensity modulated radiation therapy or volumetric modulated arc therapy (VMAT), adequate target coverage is rarely achieved without the expense of increased integral dose to important organs at risk (OARs), such as the heart and lungs. Therefore, we present several BBC techniques and a treatment algorithm using intensity-modulated proton therapy (IMPT) for patients treated at our center.Materials and methodsWe describe 3 different BBC treatment techniques using IMPT on patients treated at our center, with comparison VMAT plans to demonstrate the dosimetric benefit of proton therapy in these patients. Following RADCOMP (Radiation Therapy Oncology Group, Philadelphia, Pennsylvania) guidelines, a single physician approved all target volumes and OARs. Plans were designed so that ≥ 95% of the prescribed dose covered ≥ 95% of all targets. Parameters for dosimetric volume histograms for the clinical targets and OARs are reported for the 2 radiation methods.ResultsAll methods demonstrated acceptable target coverage with 95% of the prescription planning target volume reaching a mean (± SD) of 98.0% (± 0.87%) and 97.5% (± 2.39%), for VMAT and IMPT plans, respectively. Conformity and homogeneity were also similar between the 2 techniques. Proton therapy provided observed improvements in mean heart dose (average heart mean [SD], 9.98 Gy [± 0.87 Gy] versus 2.12 Gy [± 0.96 Gy]) and total lung 5% prescription dose (V5; mean [SD] total lung V5, 97.9% [± 2.84%]), compared with 39.8% [± 9.39%]). All IMPT methods spared critical OARs; however, the single, 0° anterior-posterior plan allowed for the shortest treatment time.ConclusionBoth VMAT and all 3 IMPT techniques provided excellent target coverage in patients with BBC; however, proton therapy was superior in decreasing the dose to OARs. A single-field optimization approach should be the IMPT method of choice when feasible.

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A generalized 2D pencil beam scaling algorithm for proton dose calculation in heterogeneous slab geometries.

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