Tungsten anode spectral model using interpolating cubic splines: unfiltered x-ray spectra from 20 kV to 640 kV

Abstract

Purpose: Monte Carlo methods were used to generate lightly filtered high resolution x-ray spectra spanning from 20 kV to 640 kV.

Methods: X-ray spectra were simulated for a conventional tungsten anode. The Monte Carlo N-Particle eXtended radiation transport code (MCNPX 2.6.0) was used to produce 35 spectra over the tube potential range from 20 kV to 640 kV, and cubic spline interpolation procedures were used to create piecewise polynomials characterizing the photon fluence per energy bin as a function of x-ray tube potential. Using these basis spectra and the cubic spline interpolation, 621 spectra were generated at 1 kV intervals from 20 to 640 kV. The tungsten anode spectral model using interpolating cubic splines (TASMICS) produces minimally filtered (0.8 mm Be) x-ray spectra with 1 keV energy resolution. The TASMICS spectra were compared mathematically with other, previously reported spectra.

Results: Using pairedt-test analyses, no statistically significant difference (i.e., p > 0.05) was observed between compared spectra over energy bins above 1% of peak bremsstrahlung fluence. For all energy bins, the correlation of determination (R(2)) demonstrated good correlation for all spectral comparisons. The mean overall difference (MOD) and mean absolute difference (MAD) were computed over energy bins (above 1% of peak bremsstrahlung fluence) and over all the kV permutations compared. MOD and MAD comparisons with previously reported spectra were 2.7% and 9.7%, respectively (TASMIP), 0.1% and 12.0%, respectively [R. Birch and M. Marshall, "Computation of bremsstrahlung x-ray spectra and comparison with spectra measured with a Ge(Li) detector," Phys. Med. Biol. 24, 505-517 (1979)], 0.4% and 8.1%, respectively (Poludniowski), and 0.4% and 8.1%, respectively (AAPM TG 195). The effective energy of TASMICS spectra with 2.5 mm of added Al filtration ranged from 17 keV (at 20 kV) to 138 keV (at 640 kV); with 0.2 mm of added Cu filtration the effective energy was 9 keV at 20 kV and 169 keV at 640 kV.

Conclusions: Ranging from 20 kV to 640 kV, 621 x-ray spectra were produced and are available at 1 kV tube potential intervals. The spectra are tabulated at 1 keV intervals. TASMICS spectra were shown to be largely equivalent to published spectral models and are available in spreadsheet format for interested users by emailing the corresponding author (JMB).

Figure 1

(a) Two-dimensional representation of geometry used in Monte Carlo simulation for modeling x-ray tube. The diagram includes the tungsten anode, electron, source, anode/source enclosure, beryllium window and x-ray tube field of view. (b) A schematic of the 420 mm × 420 mm simulated imaging grid, with a 10 mm × 10 mm, pixel resolution, showing orientation of anode-cathode axis and gray regions used for heel effect analysis. (c) A schematic of the 180 mm × 180 mm scoring plane used for, generating TASMICS spectra and for comparison with previously reported spectra. Diagrams not drawn to scale.

Figure 2

A screenshot of the excel spreadsheet layout which is available for distribution, to interested users. User input cells are highlighted (yellow in EXCEL file).

Figure 3

Minimally-filtered (0.8 mm Be) MCNPX-generated, 140 kV x-ray spectrum.

Figure 4

Simulated photon fluence values (points) and interpolating cubic splines (lines) as a function of tube potential for several 1 keV energy bins. Each 1 keV energy bin is defined as the upper boundary of that energy bin (e.g., the 58 keV energy bin is centered at 57.5 keV and spans from 57 to 58 keV). (a) 59 and 60 keV energy bins chosen to highlight Kα2 and Kα1 characteristic x-rays, respectively, relative to adjacent bins, containing only bremsstrahlung contributions (i.e., 58 and 61 keV); (b) 68 and 70 keV energy bins corresponding to Kβ1 and Kβ2,respectively, and adjacent bremsstrahlung bins (i.e., 67, 69, and 71 keV); (c) 25, 35, and 40 keV energy bins chosen to highlight the nonmonotonic nature of these low energy photon bins; and (d) 100, 200, 300, and 400 keV energy bins chosen to highlight monotonically increasing fluence values.

Figure 5

Comparison of TASMICS-generated spectra (solid lines) and TASMIP-generated spectra, (dashed lines) at (a) 30 kV, (b) 60 kV, (c) 100 kV, and (d) 140 kV.

Figure 6

Correlation plot of TASMIP fluence values vs TASMICS fluence values demonstrating good correlation between the two spectral models at (a) 30 kV, (b) 60 kV, (c) 100 kV, and (d) 140 kV. The coefficient of determination (R²) is shown along with the slope of the linear fit.

Figure 7

Comparison of x-ray spectra generated using TASMICS (solid lines) and Birch and Marshall's model (dashed lines). (a) 30 kV spectrum, R² = 0.998, slope = 0.999; (b) 60 kV spectrum, R² = 0.999, slope = 0.995; (c) 100 kV spectrum, R² = 0.907, slope = 1.034; (d) 140 kV spectrum, R² = 0.777, slope = 1.104; (e) 300 kV spectrum and inset figure in log scale to better visual spectral comparisons, R² = 0.697, slope = 1.259; and (f) 600 kV and inset figure in log scale, R² = 0.690, slope = 1.267.

Figure 8

Comparison of x-ray spectra generated using TASMICS (solid lines) and Poludniowski's model (dashed lines). (a) 30 kV spectrum, R² = 0.980, slope = 0.974; (b) 60 kV spectrum, R² = 0.996, slope = 0.989; (c) 100 kV spectrum, R² = 0.946, slope = 1.033; (d) 140 kV spectrum, R² = 0.861, slope = 1.171; (e) 200 kV spectrum, R² = 0.823, slope = 1.405; and (f) 300 kV spectrum and inset figure in log scale to better visual spectral comparisons, R² = 0.813, slope = 1.794.

Figure 9

(a) Plot of unfiltered 100 kV tungsten anode x-ray spectra generated using TASMICS (solid line) and an AAPM TG 195 MCNP simulation (dotted line); and (b) Photon fluence correlation plot.

Figure 10

(a) Average energy and (b) effective energy of TASMICS spectra as a function of tube potential with 2.5 mm of added aluminum filtration or with 0.2 mm of added copper filtration.

Figure 11

Relative fluence attenuation profiles of TASMICS spectra for added (a) aluminum, (b) copper, and (c) tissue. All spectra used in figure contain 2.5 mm of aluminum filtration to reflect results from conventional x-ray tubes with permanent filtration. The y-axis in figure is in logarithmic scale.

Figure 12

First half-value layer in aluminum as a function of tube potential for various thickness of (a) aluminum and (b) copper added filtration.

Figure 13

Spectral comparison of the cathode, central ray, and anode directions of x-ray tube field of view [see Fig. 1b] for (a) 60 kV, (b) 100 kV, (c) 140 kV, (d) 200 kV, (e) 400 kV, and (f) 600 kV simulated x-ray spectra. All spectra in this figure contain 2.5 mm of aluminum filtration to reflect results from conventional x-ray tubs with permanent filtration.