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Calculating percent depth dose with the electron pencil-beam redefinition algorithm.

ABSTRACT: 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.

SUBMITTER: Price MJ

PROVIDER: S-EPMC5722410 | biostudies-literature | 2007 Apr

REPOSITORIES: biostudies-literature

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Calculating percent depth dose with the electron pencil-beam redefinition algorithm.

Price Michael J MJ Hogstrom Kenneth R KR Antolak John A JA White R Allen RA Bloch Charles D CD Boyd Robert A RA

Journal of applied clinical medical physics 20070419 2

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 ...[more]

PMID: 17592466

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Project description: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.

Project description:IntroductionThis study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (Sc) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check.Methods and materialsThe PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of [Formula: see text] with the main parameter of d (depth in water) and n, while the tail function was in the form of e-μd and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = [Formula: see text]. The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ.ResultsThe main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc = nE(S)0.63μE to get the collimator to scatter factor Sc for 6 and 10 MV photon beam, while nE, μE, S denotes n, μ at photon energy E of field size S, respectively. The calculated Sc were compared with the measured data and showed agreement at different field sizes to within ±1.5%.ConclusionsWe proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the Sc factors for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment.

Project description:BackgroundPencil beam scanning (PBS) proton therapy can provide highly conformal target dose distributions and healthy tissue sparing. However, proton therapy of hepatocellular carcinoma (HCC) is prone to dosimetrical uncertainties induced by respiratory motion. This study aims to develop intra-treatment tumor motion monitoring during respiratory gated proton therapy and combine it with motion-including dose reconstruction to estimate the delivered tumor doses for individual HCC treatment fractions.MethodsThree HCC-patients were planned to receive 58 GyRBE (n=2) or 67.5 GyRBE (n=1) of exhale respiratory gated PBS proton therapy in 15 fractions. The treatment planning was based on the exhale phase of a 4-dimensional CT scan. Daily setup was based on cone-beam CT (CBCT) imaging of three implanted fiducial markers. An external marker block (RPM) on the patient's abdomen was used for exhale gating in free breathing. This study was based on 5 fractions (patient 1), 1 fraction (patient 2) and 6 fractions (patient 3) where a post-treatment control CBCT was available. After treatment, segmented 2D marker positions in the post-treatment CBCT projections provided the estimated 3D motion trajectory during the CBCT by a probability-based method. An external-internal correlation model (ECM) that estimated the tumor motion from the RPM motion was built from the synchronized RPM signal and marker motion in the CBCT. The ECM was then used to estimate intra-treatment tumor motion. Finally, the motion-including CTV dose was estimated using a dose reconstruction method that emulates tumor motion in beam's eye view as lateral spot shifts and in-depth motion as changes in the proton beam energy. The CTV homogeneity index (HI) The CTV homogeneity index (HI) was calculated as D2% - D98%D50% ×100% .ResultsThe tumor position during spot delivery had a root-mean-square error of 1.3 mm in left-right, 2.8 mm in cranio-caudal and 1.7 mm in anterior-posterior directions compared to the planned position. On average, the CTV HI was larger than planned by 3.7%-points (range: 1.0-6.6%-points) for individual fractions and by 0.7%-points (range: 0.3-1.1%-points) for the average dose of 5 or 6 fractions.ConclusionsA method to estimate internal tumor motion and reconstruct the motion-including fraction dose for PBS proton therapy of HCC was developed and demonstrated successfully clinically.

Project description:Planar integral spot dose (PISD) of proton pencil beam spots (PPBSs) is a required input parameter for beam modeling in some treatment planning systems used in proton therapy clinics. The measurement of PISD by using commercially available large area ionization chambers, like the PTW Bragg peak chamber (BPC), can have large uncertainties due to the size limitation of these chambers. This paper reports the results of our study of a novel method to determine PISD values from the measured lateral dose profiles and peak dose of the PPBS.The PISDs of 72.5, 89.6, 146.9, 181.1, and 221.8 MeV energy PPBSs were determined by area integration of their planar dose distributions at different depths in water. The lateral relative dose profiles of the PPBSs at selected depths were measured by using small volume ion chambers and were investigated for their angular anisotropies using Kodak XV films. The peak spot dose along the beam's central axis (D(0)) was determined by placing a small volume ion chamber at the center of a broad field created by the superposition of spots at different locations. This method allows eliminating positioning uncertainties and the detector size effect that could occur when measuring it in single PPBS. The PISD was then calculated by integrating the measured lateral relative dose profiles for two different upper limits of integration and then multiplying it with corresponding D(0). The first limit of integration was set to radius of the BPC, namely 4.08 cm, giving PISD(RBPC). The second limit was set to a value of the radial distance where the profile dose falls below 0.1% of the peak giving the PISD(full). The calculated values of PISD(RBPC) obtained from area integration method were compared with the BPC measured values. Long tail dose correction factors (LTDCFs) were determined from the ratio of PISD(full)∕PISD(RBPC) at different depths for PPBSs of different energies.The spot profiles were found to have angular anisotropy. This anisotropy in PPBS dose distribution could be accounted in a reasonable approximate manner by taking the average of PISD values obtained using the in-line and cross-line profiles. The PISD(RBPC) values fall within 3.5% of those measured by BPC. Due to inherent dosimetry challenges associated with PPBS dosimetry, which can lead to large experimental uncertainties, such an agreement is considered to be satisfactory for validation purposes. The PISD(full) values show differences ranging from 1 to 11% from BPC measured values, which are mainly due to the size limitation of the BPC to account for the dose in the long tail regions of the spots extending beyond its 4.08 cm radius. The dose in long tail regions occur both for high energy beams such as 221.8 MeV PPBS due to the contributions of nuclear interactions products in the medium, and for low energy PPBS because of their larger spot sizes. The calculated LTDCF values agree within 1% with those determined by the Monte Carlo (MC) simulations.The area integration method to compute the PISD from PPBS lateral dose profiles is found to be useful both to determine the correction factors for the values measured by the BPC and to validate the results from MC simulations.

Project description:Monte Carlo (MC) methods are considered the gold-standard approach to dose estimation for normal tissues outside the treatment field (out-of-field) in proton therapy. However, the physics of secondary particle production from high-energy protons are uncertain, particularly for secondary neutrons, due to challenges in performing accurate measurements. Instead, various physics models have been developed over the years to reenact these high-energy interactions based on theory. It should thus be acknowledged that MC users must currently accept some unknown uncertainties in out-of-field dose estimates. In the present study, we compared three MC codes (MCNP6, PHITS, and TOPAS) and their available physics models to investigate the variation in out-of-field normal tissue dosimetry for pencil beam scanning proton therapy patients. Total yield and double-differential (energy and angle) production of two major secondary particles, neutrons and gammas, were determined through irradiation of a water phantom at six proton energies (80, 90, 100, 110, 150, and 200 MeV). Out-of-field normal tissue doses were estimated for intracranial irradiations of 1-, 5-, and 15-year-old patients using whole-body computational phantoms. Notably, the total dose estimates for each out-of-field organ varied by approximately 25% across the three codes, independent of its distance from the treatment volume. Dose discrepancies amongst the codes were linked to the utilized physics model, which impacts the characteristics of the secondary radiation field. Using developer-recommended physics, TOPAS produced both the highest neutron and gamma doses to all out-of-field organs from all examined conditions; this was linked to its highest yields of secondary particles and second hardest energy spectra. Subsequent results when using other physics models found reduced yields and energies, resulting in lower dose estimates. Neutron dose estimates were the most impacted by physics model choice, and thus the variation in out-of-field dose estimates may be even larger than 25% when considering biological effectiveness.

Project description:Radiographic film dosimetry suffers from its energy dependence in proton dosimetry. This study sought to develop a method of measuring proton beams by the film and to evaluate film response to proton beams for the constancy check of depth dose (DD). It also evaluated the film for profile measurements. To achieve this goal, from DDs measured by film and ion chamber (IC), calibration factors (ratios of dose measured by IC to film responses) as a function of depth in a phantom were obtained. These factors imply variable slopes (with proton energy and depth) of linear characteristic curves that relate film response to dose. We derived a calibration method that enables utilization of the factors for acquisition of dose from film density measured at later dates by adapting to a potentially altered processor condition. To test this model, the characteristic curve was obtained by using EDR2 film and in-phantom film dosimetry in parallel with a 149.65 MeV proton beam, using the method. An additional validation of the model was performed by concurrent film and IC measurement perpendicular to the beam at various depths. Beam profile measurements by the film were also evaluated at the center of beam modulation. In order to interpret and ascertain the film dosimetry, Monte Carlos simulation of the beam was performed, calculating the proton fluence spectrum along depths and off-axis distances. By multiplying respective stopping powers to the spectrum, doses to film and water were calculated. The ratio of film dose to water dose was evaluated. Results are as follows. The characteristic curve proved the assumed linearity. The measured DD approached that of IC, but near the end of the spread-out Bragg peak (SOBP), a spurious peak was observed due to the mismatch of distal edge between the calibration and measurement films. The width of SOBP and the proximal edge were both reproducible within a maximum of 5mm; the distal edge was reproducible within 1 mm. At 5 cm depth, the dose was reproducible within 10%. These large discrepancies were identified to have been contributed by film processor uncertainty across a layer of film and the misalignment of film edge to the frontal phantom surface. The deviations could drop from 5 to 2 mm in SOBP and from 10% to 4.5% at 5 cm depth in a well-controlled processor condition(i.e., warm up). In addition to the validation of the calibration method done by the DD measurements, the concurrent film and IC measurement independently validated the model by showing the constancy of depth-dependent calibration factors. For profile measurement, the film showed good agreement with ion chamber measurement. In agreement with the experimental findings, computationally obtained ratio of film dose to water dose assisted understanding of the trend of the film response by revealing relatively large and small variances of the response for DD and beam profile measurements, respectively. Conclusions are as follows. For proton beams, radiographic film proved to offer accurate beam profile measurements. The adaptive calibration method proposed in this study was validated. Using the method, film dosimetry could offer reasonably accurate DD constancy checks, when provided with a well-controlled processor condition. Although the processor warming up can promote a uniform processing across a single layer of the film, the processing remains as a challenge.

Dataset Information

Calculating percent depth dose with the electron pencil-beam redefinition algorithm.

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Calculating percent depth dose with the electron pencil-beam redefinition algorithm.

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