Abstract
Purpose:A computational toolkit (spektr 3.0) has been developed to calculate x-ray spectra based on the tungsten anode spectral model using interpolating cubic splines (TASMICS) algorithm, updating previous work based on the tungsten anode spectral model using interpolating polynomials (TASMIP) spectral model. The toolkit includes a matlab (The Mathworks, Natick, MA) function library and improved user interface (UI) along with an optimization algorithm to match calculated beam quality with measurements.Methods:The spektr code generates x-ray spectra (photons/mm2/mAs at 100 cm from the source) using TASMICS as default (with TASMIP as an option) in 1 keV energy bins over beam energies 20–150 kV, extensible to 640 kV using the TASMICS spectra. An optimization tool was implemented to compute the added filtration (Al and W) that provides a best match between calculated and measured x-ray tube output (mGy/mAs or mR/mAs) for individual x-ray tubes that may differ from that assumed in TASMICS or TASMIP and to account for factors such as anode angle.Results:The median percent difference in photon counts for a TASMICS and TASMIP spectrum was 4.15% for tube potentials in the range 30–140 kV with the largest percentage difference arising in the low and high energy bins due to measurement errors in the empirically based TASMIP model and inaccurate polynomial fitting. The optimization tool reported a close agreement between measured and calculated spectra with a Pearson coefficient of 0.98.Conclusions:The computational toolkit, spektr, has been updated to version 3.0, validated against measurements and existing models, and made available as open source code. Video tutorials for the spektr function library, UI, and optimization tool are available.
Highlights
At its heart, 2.0 is a (The Mathworks, Natick, MA) function library and user interface (UI) implementation of the tungsten anode spectral model using interpolating polynomials (TASMIP),54 which interpolates the measurements of Fewell et al.55 (2 keV bins) and uses polynomial fitting to approximate the photon fluence per mAs in 1 keV bins from 10 to 140 keV at x-ray tube potentials ranging from 30 to 140 kV as described in the work of Boone
Recent work extends TASMIP to a new spectral model developed by Hernandez and Boone56 dubbed the tungsten anode spectral model using interpolating cubic splines (TASMICS), which uses piecewise third-order polynomial spline approximations analogous to the original TASMIP to compute the number of photons in each energy bin as a function of tube potential
A function call without optional arguments generates a 70 kV spectrum using the TASMICS model, with 1.6 mm Al inherent filtration, 0% kV ripple, and normalization of mGy/mAs to match that of the TASMIP/Fewell spectrum
Summary
The toolkit for calculation and analysis of x-ray spectra in the diagnostic energy range has been employed in a variety of imaging applications, such as modeling of imaging performance, analysis of spectral/dual-energy imaging, phase contrast imaging, development of novel x-ray detectors, modeling of x-ray scatter and beam-hardening corrections, development of 3D image reconstruction algorithms, development of new contrast agents, and modeling (and reduction) of radiation dose. At its heart, 2.0 is a (The Mathworks, Natick, MA) function library and user interface (UI) implementation of the tungsten anode spectral model using interpolating polynomials (TASMIP), which interpolates the measurements of Fewell et al. (2 keV bins) and uses polynomial fitting to approximate the photon fluence per mAs in 1 keV bins from 10 to 140 keV at x-ray tube potentials ranging from 30 to 140 kV as described in the work of Boone. (1b) generates a 70 kV spectrum using the TASMICS model, with 1.6 mm Al inherent filtration, 0% kV ripple, and normalization of mGy/mAs to match that of the TASMIP/Fewell spectrum. (1d) computes a 70 kV TASMICS spectrum with no added filtration, 0% kV ripple, and no normalization of tube output. An optimization tool called spektrTuner() was developed to assist in matching spectral calculations to measurements for a particular x-ray tube in terms of the output (mGy/mAs or mR/mAs). There are several means by which calculations could be tuned to match the output of a particular x-ray tube, e.g., adjusting added filtration to match the HVL and/or mGy/mAs measured at various kV. (b) Illustration of the 2D search space over Al and W thickness (with a normalized 60 kV TASMICS spectrum) to match measured tube output (mR/mAs). The UI allows users to generate x-ray spectra, modify filtration, and calculate beam-quality characteristics. (A) Plotting. (B) X-ray tube settings. (C) Added filtration. (D) Spectrum characteristics. (E) File operations. (F) Reset all
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