Dimensional Gamma Research Articles

Exactly solvable one-dimensional quantum models with gamma matrices.

In this paper we write exactly solvable generalizations of one-dimensional quantum XY and Ising-like models by using 2^{d}-dimensional gamma matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner-like transformations. We illustrate the techniques using a specific case of four-dimensional gamma matrices and explore the quantum phase transitions present in the model.

Application of the Approximate Bayesian Computation Algorithm to Gamma-Ray Spectroscopy

Radioisotope identification (RIID) algorithms for gamma-ray spectroscopy aim to infer what isotopes are present and in what amounts in test items. RIID algorithms either use all energy channels in the analysis region or only energy channels in and near identified peaks. Because many RIID algorithms rely on locating peaks and estimating each peak’s net area, peak location and peak area estimation algorithms continue to be developed for gamma-ray spectroscopy. This paper shows that approximate Bayesian computation (ABC) can be effective for peak location and area estimation. Algorithms to locate peaks can be applied to raw or smoothed data, and among several smoothing options, the iterative bias reduction algorithm (IBR) is recommended; the use of IBR with ABC is shown to potentially reduce uncertainty in peak location estimation. Extracted peak locations and areas can then be used as summary statistics in a new ABC-based RIID. ABC allows for easy experimentation with candidate summary statistics such as goodness-of-fit scores and peak areas that are extracted from relatively high dimensional gamma spectra with photopeaks (1024 or more energy channels) consisting of count rates versus energy for a large number of gamma energies.

Dosimetric and Radiobiological Evaluation of Delivered Dose Distribution with Intra-Fractional Motion in Prostate Stereotactic Radiation Therapy Treatments Using VMAT and Helical Tomotherapy

The implementation of motion-management techniques during intensity modulated radiation therapy (IMRT) is still under challenging issue. Moreover, the dose-per-fraction regime and beam-delivery methods affect the dose distribution owing to the interplay effect. Hypofractionation may be a uniquely appropriate treatment for prostate cancer because of a lower α/β ratio. Several prospective studies support the safety of moderate hypofractionation; however, extreme fractionation may lead to greater toxicity. It has been reported that respiratory motion during IMRT delivery of stereotactic body radiation therapy (SBRT) can lead to dosimetric errors in the target of up to ±20%. Therefore, intra-fractional prostate motion may occur unpredictably during IMRT and lead to under-treatment of the target. In this study, we evaluated the dosimetric and radiobiological effects of the SBRT dose distributions with patient-specific intra-fractional motion in prostate cancer for volumetric modulated arc therapy (VMAT) and helical tomotherapy (HT) using a commercially available six-dimensional (6D) motion system. Dose distributions with patient-specific prostate intra-fractional motion were evaluated using the 6D-motion simulator system, which was coupled to a biplanar diode array detector phantom. These bidirectional prostate motions were acquired from magnetic resonance (MR)-cine images. Then, these motions were continuously generated for approximately 4 min, and dose measurements were repeated 5 times to measure the uncertainty of prostate motion during irradiation. We tested two typical motion patterns: large (over 2.0 mm) and small (under 1.0 mm). The SBRT plan was created in VMAT and HT with a prescription of 36.25 Gy/5 fractions to D95% of the PTV. We compared dose distributions with static irradiations using the 3 dimensional gamma (3D-γ) analysis. Moreover, the equivalent uniform dose (EUD)-based tumor control probability (TCP) and normal tissue complication probability (NTCP) of the rectum were compared with 76 Gy/38 fractions, which is the standard prostate fractionation plan. In the results of the dosimetric evaluation, the pass rate of the γ-analysis (criterion of 2 mm, 3%) was degraded by 9.5% and 22.7% in VMAT and HT plans in the large motion patterns and 3.0% and 8.7% in the small motion patterns, respectively. However, degradation of the D99 for CTV was only 0.7% and 1.8% in VMAT and HT plans, respectively, even in the large motion patterns. Moreover, these errors were negligible in small motion patterns. For the radiobiological evaluation, no significant differences in TCP and NTCP degradations were found in VMAT and HT SBRT plans compared with the standard fractionation plan. SBRT dose distributions with intra-fractional motion over 2.0 mm in prostate cancer were more degraded in HT than those observed in VMAT; however, these dosimetric errors might not be clinically significant degradation for TCP and/or NTCP.

The impact of mass density variations on an electron Monte Carlo algorithm for radiotherapy dose calculations.

Background and PurposeA key step in electron Monte Carlo dose calculation requires converting Computed Tomography (CT) numbers from a tomographic acquisition to a mass density. This study investigates the dosimetric consequences of perturbations applied to a calibration table between CT number and mass density.Materials and MethodsA literature search was performed to define lower and upper bounds for physically reasonable perturbations to a reference CT number to mass density calibration table. Electron beam dose was calculated for ten patients using these variations and the results were compared to clinical plans originally derived with a reference calibration table. Dose differences both globally and in the Planning Target Volume (PTV) were assessed using dose- and volume-based metrics and 3- dimensional gamma analysis for each patient.ResultsSmall but statistically significant differences were observed between perturbations and reference data for certain metrics including volume of the 50% prescription isodose. Upper and lower variations in CT number to mass density calibration yielded mean values of V50% that were 4.4% larger and 2.1% smaller than reference values respectively. Gamma analysis using 3%/3mm criteria indicated >99% passing rate for the PTV for all patients. Global gamma analysis for some patients showed larger discrepancies possibly due to large electron path lengths through inhomogeneities.ConclusionsIn most patients, physically reasonable perturbations in CT number to mass density curves will not induce clinically significant impact on calculated target dose distributions. Strong dependence of electron transport on voxel material may produce dose speckle throughout the volume. Care should be taken in evaluating critical structures at depths beyond the target volume in highly heterogeneous regions.

Gamma index based criterion for the characterization of dosimetrically matched beams

Dosimetry commissioning, beam modelling in a treatment planning system and patient quality assurance are the basic dosimetric steps in modern radiotherapy. As technology has evolved, beams with equal nominal energy from linear accelerators of the same make and model are very likely interchangeable in terms of beam features. This work presents a novel approach to the characterization of matched beams, which can be based on commissioning data as it is being acquired and before any beam modelling tasks are started. Gamma analysis has become a gold standard for patient quality assurance assessment, which is evaluated statistically as the conformance of measurement points in an array to the planned data. Beam matching implies plans optimized for one of the beams would pass a stringent patient QA. One way to ensure this is to apply gamma index to the input data for beam modelling, comparing homologous profiles and percentage depth dose curves on both machines. This method has been applied to a set of beams of the same nominal energy. Results have proven that a stringent gamma index test is met by beams matched according to the usual criteria, but it also rejects as non equivalent beams from different models and slightly different quality indices. The use of one dimensional gamma analysis, which is the one actually developed in the original article by Low et al, is, apart from a powerful tool to assess patient quality assurance results, an analysis tool for the definition of pools of matched beams from different machines.

A Monte Carlo simulation method for reconstruction of accelerator based on verified 6 MV X-ray phase-space and energy spectrum information

Objective To establish a novel Monte Carlo simulation method for reconstruction of medical accelerator model and X-ray energy spectrum based on IAEA Varian 6 MV X-ray phase-space file and photon energy spectrum of the target accelerator. Methods The verified 6 MV X-ray phase-space files were preprocessed to elevate the energy of each particle. Particles were saved in different Phase-Space-Let (PSL) files according to their position and energy, yielding an initial photon energy spectrum for Monte Carlo simulation of accelerator under an initial target energy. The initial photon energy spectrum was fit to a photon energy spectrum of an accelerator (Elekta Precise 10 MV X-ray accelerator) under an unknown target energy to yield a fitting coefficient, which was the weight of each PSL. Finally, an accelerator model under an unknown target energy was reconstructed using the initial PSL files and the weight information. The percentage depth dose (PDD) distribution was calculated in different square open fields. The effectiveness of this method was verified using one dimensional gamma passing rate. Results The peak position and overall distribution of the reconstructed 10 MV photon energy spectrum were in accordance with those of the verified 10 MV photon energy spectrum. The PDD calculated from the reconstructed 10 MV accelerator model agreed well with the measured PDD. The one-dimensional gamma passing rate was above 96%(1%/1 mm, threshold=0%). Conclusion The Monte Carlo reconstruction method proposed in this study is reliable, accurate, and effective. Key words: X-ray energy spectrum; Linac head beamreconstruction; Phase-Space-Let files; Monte Carlo simulation

SU‐E‐T‐313: The Accuracy of the Acuros XB Advanced Dose Calculation Algorithm for IMRT Dose Distributions in Head and Neck

Purpose:To investigate the accuracy of the Acuros XB version 11 (AXB11) advanced dose calculation algorithm by comparing with Monte Caro (MC) calculations. The comparisons were performed with dose distributions for a virtual inhomogeneity phantom and intensity‐modulated radiotherapy (IMRT) in head and neck.Methods:Recently, AXB based on Linear Boltzmann Transport Equation has been installed in the Eclipse treatment planning system (Varian Medical Oncology System, USA). The dose calculation accuracy of AXB11 was tested by the EGSnrc‐MC calculations. In additions, AXB version 10 (AXB10) and Analytical Anisotropic Algorithm (AAA) were also used. First the accuracy of an inhomogeneity correction for AXB and AAA algorithms was evaluated by comparing with MC‐calculated dose distributions for a virtual inhomogeneity phantom that includes water, bone, air, adipose, muscle, and aluminum. Next the IMRT dose distributions for head and neck were compared with the AXB and AAA algorithms and MC by means of dose volume histograms and three dimensional gamma analysis for each structure (CTV, OAR, etc.).Results:For dose distributions with the virtual inhomogeneity phantom, AXB was in good agreement with those of MC, except the dose in air region. The dose in air region decreased in order of MC<AXB11<AXB10. This may be caused by the difference of the electron cut‐off energy for algorithms, ie: 0.700 MeV for MC, 0.711 MeV for AXB11, and 1.011 MeV for AXB 10. Since the AAA algorithm is based on the dose kernel of water, the doses in regions for air, bone, and aluminum considerably became higher than those of AXB and MC. The pass rates of the gamma analysis for IMRT dose distributions in head and neck were similar to those of MC in order of AXB11<AXB10<AAA.Conclusion:The dose calculation accuracy of AXB11 was almost equivalent to the MC dose calculation.

TH‐E‐BRE‐03: A Novel Method to Account for Ion Chamber Volume Averaging Effect in a Commercial Treatment Planning System Through Convolution

Purpose:Fourier‐based deconvolution approaches used to eliminate ion chamber volume averaging effect (VAE) suffer from measurement noise. This work aims to investigate a novel method to account for ion chamber VAE through convolution in a commercial treatment planning system (TPS).Methods:Beam profiles of various field sizes and depths of an Elekta Synergy were collected with a finite size ion chamber (CC13) to derive a clinically acceptable beam model for a commercial TPS (Pinnacle3), following the vendor‐recommended modeling process. The TPS‐calculated profiles were then externally convolved with a Gaussian function representing the chamber (σ = chamber radius). The agreement between the convolved profiles and measured profiles was evaluated with a one dimensional Gamma analysis (1%/1mm) as an objective function for optimization. TPS beam model parameters for focal and extra‐focal sources were optimized and loaded back into the TPS for new calculation. This process was repeated until the objective function converged using a Simplex optimization method. Planar dose of 30 IMRT beams were calculated with both the clinical and the re‐optimized beam models and compared with MapCHEC™ measurements to evaluate the new beam model.Results:After re‐optimization, the two orthogonal source sizes for the focal source reduced from 0.20/0.16 cm to 0.01/0.01 cm, which were the minimal allowed values in Pinnacle. No significant change in the parameters for the extra‐focal source was observed. With the re‐optimized beam model, average Gamma passing rate for the 30 IMRT beams increased from 92.1% to 99.5% with a 3%/3mm criterion and from 82.6% to 97.2% with a 2%/2mm criterion.Conclusion:We proposed a novel method to account for ion chamber VAE in a commercial TPS through convolution. The reoptimized beam model, with VAE accounted for through a reliable and easy‐to‐implement convolution and optimization approach, outperforms the original beam model in standard IMRT QA verification.

SU-E-T-119: Evaluation of New VMAT and IMRT Planning QA Devices: Portal Dosimetry Vs Compass.

Wide spread clinical use of advanced radiation treatment delivery techniques such as volumetric modulated arc therapy (VMAT) and IMRT needs an easy-to-use, well-defined, and effective quality assurance (QA) system to ensure the accuracy of dose delivery. The comprehensive evaluation of two delivery QA systems (DQA) (Portal Dosimetry and Compass) for the advanced radiation delivery techniques is necessary for the clinical setting. Portal Dosimetry QA system with Varian PortalVision (PV) provides a quantitative comparison of measured electronic dose profile to a predicted dose profile with Varian's Eclipse™ treatment planning system (TPS) for the VMAT and IMRT plans. Quantitative comparisons of the two images, including dose difference, gamma analysis, points dose measurements, and line profiles are easily acquired in two dimensions. Meanwhile, Compass system with MatriXX can provide an accurate three-dimensional quantitative analysis of dose delivery. We applied the two planning QA systems to our RapidArc patient- specific QAs. Validation of the Compass and Portal Dosimetry systems were performed with ionization chamber measurements for absolute dosimetry and film measurements for gamma index calculations for phantom and patient treatment plans. Compass system was very sensitive to the MLC leaf gap variations in three dimensional gamma analyses. However, Compass system was not enough to fix the errors in dosimetric leaf gap by itself. DQA process with Portal Dosimetry took approximately 6 minutes for the two Arcs VMAT plan. Compass took about 40 minutes for the same plan in our first clinical trial. For the three typical IMRT and VMAT plans, the two systems showed the same passing rates in 95% pixels passing gamma criteria 3%/3mm. Portal Dosimetry DQA system has the advantages of effectiveness and practicality in the clinical setting. On the other hand, Compass was the next supportive system because of its accuracy and reality with patient's anatomy.

SU-E-T-766: Verification of Volumetric Modulated Arc Therapy Plans with Independent Three Dimensional Dose Computation Algorithm

Purpose: To verify the volumetric modulated arc therapy (Rapidarc) plans using a independent three dimensional dose computation algorithm using COMPASS system. Methods: Rapidarc is a treatment technique which produces conformal dose distribution by delivering the dose in a rotational fashion while simultaneously changing MLC position, dose rate as well as gantry speed. COMPASS dosimetry system uses the Collapsed Cone Convolution(CCC) algorithm as a dose calculation engine which requires machine model information and beam modeling to display the 3D dose distribution on a patient CT data. Treatment plans (10 patients) generated for Rapidarc on Eclipse (version 8.9) Treatment Planning System (TPS) using Analytical Anisotropic Algorithm (AAA) were exported as DICOM file to COMPASS for recalculation using CCC algorithm. Pilot studies were performed for 2DRT, 3DCRT and IMRT plans prior to VMAT plan verification. The doses and dose-volume histograms computed using CCC were compared with TPS calculated plans. Plans were analyzed in terms of Conformity Index (CI) for PTV, maximum and mean doses for OARs and difference in three dimensional gamma. Results: The average 3D mean gamma for 1mm(DTA) and 1%(DD) criteria for 2DRT and 3DCRT was 0.11 ±0.002 . Maximum and minimum deviation of PTV Volume receiving 95% of the prescribed dose(V95%) for IMRT and Rapidarc were found to be 1.01%, 0.79% and 1.24%, 0.86% respectively. Average deviation of maximum and mean doses of OARˈs for IMRT and Rapidarc were 0.91±0.002 %, 0.55±0.008 % and 0.25±0.005 %, 1.05±0.009 % respectively. Conclusions: This study illustrates that the compass three dimensional dosimetry system can be used as an accurate and effective tool to clinically validate the Rapidarc plans independently.

SU-GG-T-612: Quantitative Tools to Assess the Fidelity of Treatment Planning System Commissioning for IMRT

Purpose: Develop tools for quantitative evaluation of beam modeling of focal‐ and extra‐focal radiation in a 3D treatment planning system (3DTPS) for IMRT.Method and Materials: Cross‐beam photon beam characteristics in a convolution/superposition‐based 3DTPS (Pinnacle3) are typically verified by comparing measured and calculated cross beam profiles for a series of field sizes defined by MLC leaf end at various depths. We employed one dimensional gamma analysis, with 1%/1mm criteria, to evaluate each beam profile. Percentage of points failing gamma analyses in high gradient region and low gradient region were respectively calculated as High Gradient Failure (HGF) and Low Gradient Failure (LGF). A mean gamma score (MGS) was also calculated. HGF, LGF and MGS were averaged over all measurement depths for each measurement field size to arrive at a single score for the evaluation of “goodness” of beam modeling. This approach was used to compute leaf‐end‐separation weighted average of HGF, LGF and MGS from all sub‐fields sizes used in clinic for 30 Head & Neck, 30 lung and 30 prostate SMLC‐based IMRT cases for four different effective source sizes ranging from 0.01 cm to 0.05, 0.1 and 0.2 cm. Results: HGF, LGF and MGS parameters were used to evaluate the overall performance of beam modeling using different effective source sizes. The results of leaf end separation weighted averages of HGF, LGF and MGS show that the beam modeled with 0.1 cm effective source size gives the best overall performance for clinical IMRT cases planned on Pinnacle3 3DTPS. Conclusion: Quantities such as HGF, LGF and MGS described in this work can prove to be extremely useful tools for clinical physicists commissioning and evaluating photon beam models in 3DTPS.

Degradation of creep properties in a long-term thermally exposed nickel base superalloy

Abstract When exposed for long time at elevated temperatures of 430 and 650 °C the nickel base superalloy EI 698 VD can experience a significant decrease in creep resistance. The cause of the creep degradation of nickel base superalloy is generally attributed to the microstructural instability at prolonged high temperature exposure. In this article, the creep-life data, generated on long thermally exposed nickel base superalloy EI698 VD were related to the local microstructural changes observed using SEM and TEM analysing techniques. While structure analysis provided supporting evidence concerning the changes associated with grain boundary carbide precipitation, no persuasive evidence of a morphological and/or dimensional gamma prime change was showed. For clarifying of the role of gamma prime precipitates on alloy on creep degradation, the SANS (small angle neutron scattering) experiment was crucial in the characterization of the bulk-averaged gamma prime morphology and its size distribution with respect to the period of thermal exposure.

Two and three dimensional gamma ray correlations in rotational nuclei

Several new methods for the study of nuclear structure at low temperature are reviewed. The methods analyze the fluctuations of the intensity of Eγ1 · Eγ2 spectra, and the shape and width Γrot of the correlated patterns with different characteristics of the rotational motion in cold and warm nuclei. New results are given for the rotational damping width, and the number of 2-step-paths below and above U0 ≈ 800 keV, considered to be the energy of the borderline between undamped and damped rotational motion. The rotational damping width Γrot is studied as function of rotational frequency for selected regions of entry states in 163Tm , and found to be rather constant ≈ 80 keV, significantly smaller than current theoretical predictions. The fluctuation analysis supports the damping picture in general, and confirms that a strong branching of the transition strength for each step in the E2 cascades exists at high spin. This can be taken as evidence for damping of the rotational motion in warm nuclei.

A new approach to positron angular correlation studies

A new kind of apparatus is described for carrying out positron angular correlation measurements. The apparatus employs a spark chamber as a two dimensional gamma -ray detector and is able to determine two components of the momentum of photon pairs produced by annihilating electron positron pairs. The results of an experiment on a copper single crystal are described and it is shown that the experimental data show the effect of the necks of the copper Fermi surface. Various possibilities for improvements to the apparatus are discussed. Finally a mathematical method is proposed which it is believed would permit the complete momentum for photon pairs to be derived from a single experiment at a mirror plane orientation. If this method were operated successfully then it would allow a Fermi surface to be derived which was correct for electrons in the region of the positron. This has been shown to be very similar to the true Fermi surface.