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      A fast algorithm for gamma evaluation in 3D.

      Medical physics

      Tomography, X-Ray Computed, Computer Simulation, Gamma Rays, therapeutic use, Humans, Lung Neoplasms, Algorithms, radiography, radiotherapy, Radiotherapy Dosage, Radiotherapy Planning, Computer-Assisted, methods

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          Abstract

          The gamma-evaluation method is a tool by which dose distributions can be compared in a quantitative manner combining dose-difference and distance-to-agreement criteria. Since its introduction, the gamma evaluation has been used in many studies and is on the verge of becoming the preferred dose distribution comparison method, particularly for intensity-modulated radiation therapy (IMRT) verification. One major disadvantage, however, is its long computation time, which especially applies to the comparison of three-dimensional (3D) dose distributions. We present a fast algorithm for a full 3D gamma evaluation at high resolution. Both the reference and evaluated dose distributions are first resampled on the same grid. For each point of the reference dose distribution, the algorithm searches for the best point of agreement according to the gamma method in the evaluated dose distribution, which can be done at a subvoxel resolution. Speed, computer memory efficiency, and high spatial resolution are achieved by searching around each reference point with increasing distance in a sphere, which has a radius of a chosen maximum search distance and is interpolated "on-the-fly" at a chosen sample step size. The smaller the sample step size and the larger the differences between the dose distributions, the longer the gamma evaluation takes. With decreasing sample step size, statistical measures of the 3D gamma distribution converge. Two clinical examples were investigated using 3% of the prescribed dose as dose-difference and 0.3 cm as distance-to-agreement criteria. For 0.2 cm grid spacing, the change in gamma indices was negligible below a sample step size of 0.02 cm. Comparing the full 3D gamma evaluation and slice-by-slice 2D gamma evaluations ("2.5D") for these clinical examples, the gamma indices improved by searching in full 3D space, with the average gamma index decreasing by at least 8%.

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          Most cited references 10

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          A technique for the quantitative evaluation of dose distributions.

          The commissioning of a three-dimensional treatment planning system requires comparisons of measured and calculated dose distributions. Techniques have been developed to facilitate quantitative comparisons, including superimposed isodoses, dose-difference, and distance-to-agreement (DTA) distributions. The criterion for acceptable calculation performance is generally defined as a tolerance of the dose and DTA in regions of low and high dose gradients, respectively. The dose difference and DTA distributions complement each other in their useful regions. A composite distribution has recently been developed that presents the dose difference in regions that fail both dose-difference and DTA comparison criteria. Although the composite distribution identifies locations where the calculation fails the preselected criteria, no numerical quality measure is provided for display or analysis. A technique is developed to unify dose distribution comparisons using the acceptance criteria. The measure of acceptability is the multidimensional distance between the measurement and calculation points in both the dose and the physical distance, scaled as a fraction of the acceptance criteria. In a space composed of dose and spatial coordinates, the acceptance criteria form an ellipsoid surface, the major axis scales of which are determined by individual acceptance criteria and the center of which is located at the measurement point in question. When the calculated dose distribution surface passes through the ellipsoid, the calculation passes the acceptance test for the measurement point. The minimum radial distance between the measurement point and the calculation points (expressed as a surface in the dose-distance space) is termed the gamma index. Regions where gamma > 1 correspond to locations where the calculation does not meet the acceptance criteria. The determination of gamma throughout the measured dose distribution provides a presentation that quantitatively indicates the calculation accuracy. Examples of a 6 MV beam penumbra are used to illustrate the gamma index.
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            Evaluation of the gamma dose distribution comparison method.

            The gamma tool was developed to quantitatively compare dose distributions, either measured or calculated. Before computing gamma, the dose and distance scales of the two distributions, referred to as evaluated and reference, are renormalized by dose and distance criteria, respectively. The renormalization allows the dose distribution comparison to be conducted simultaneously along dose and distance axes. The gamma quantity, calculated independently for each reference point, is the minimum distance in the renormalized multidimensional space between the evaluated distribution and the reference point. The gamma quantity degenerates to the dose-difference and distance-to-agreement tests in shallow and very steep dose gradient regions, respectively. Since being introduced, the gamma quantity has been used by investigators to evaluate dose calculation algorithms, and compare dosimetry measurements. This manuscript examines the gamma distribution behavior in two dimensions and evaluates the gamma distribution in the presence of data noise. Noise in the evaluated distribution causes the gamma distribution to be underestimated relative to the no-noise, condition. Noise in the reference distribution adds noise in the gamma distribution in proportion to the normalized dose noise. In typical clinical use, the fraction of points that exceed 3% and 3 mm can be extensive, so we typically use 5% and 2-3 mm in clinical evaluations. For clinical cases, the calculation time is typically 5 minutes for a 1 x 1 mm2 interpolated resolution on an 800 MHz Pentium 4 for a 14.1 x 15.2 cm2 radiographic film.
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              A quantitative evaluation of IMRT dose distributions: refinement and clinical assessment of the gamma evaluation.

              Although intensity modulated radiotherapy (IMRT) is a step forward in comparison to conventional, static beam delivery, quality assurance is more complex and labour intensive, demanding detailed two-dimensional dosimetric verification. Regardless of the technique used for measuring the dose distribution, what is essential to the implementation of routine verification of IMRT fields is the efficient and accurate comparison of the measured versus desired dose distribution. In order to achieve a fast, yet accurate quantitative measure of the correspondence between measured and calculated dose, the theoretical concept of the gamma evaluation method presented by Low et al. (Med. Phys., 25 (1998) 656) was converted into a calculation algorithm, taking into account practical considerations related to the discrete nature of the data. A filter cascade of multiple levels was designed to obtain fast and accurate comparison of the two dose distributions under evaluation. The actual comparison consists of classification into accepted or rejected datapoints with respect to user-defined acceptance criteria (dose difference and distance to agreement). The presented algorithm was tested on dosimetric images calculated and/or acquired by means of a liquid filled portal imaging device during the course of intensity modulated treatments of prostate cancer, including pre-treatment verification as well as verification during treatment. To assess its ability to intercept possible errors in dose delivery, clinically relevant errors were deliberately introduced into the dose distributions. The developed gamma filter method proves successful in the efficient comparison of calculated versus measured IMRT dose distribution. Secondly, intercomparison of dosimetric images acquired during different treatment sessions illustrate its potential to highlight variations in the dosimetric images. The simulated errors were unmistakably intercepted. The readily obtained gamma evaluation images are an easy tool for quality control of IMRT fields. To reduce the artefacts related to the discrete nature and limited resolution of the data, a fast and accurate filter cascade was developed, offering the possibility to use the gamma method for day to day evaluation of patient dosimetric portal images with or without comparison to a predicted portal dose distribution.
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