3.1

Baseline Experiments

We use module A of the ACR CT accreditation phantom (model 464, Gammex-RMI, USA). Module A is a cylinder of water-equivalent material with a diameter of 20 cm and a length of 4 cm. It contains five cylindrical inserts representing the X-ray attenuation behaviour of bone, polyethylene, acrylic, air, and water. The chemical composition characteristics of each material were provided by the phantom’s manufacturer. In addition, the module shows horizontal ramps for slice thickness evaluation and four 1 mm diameter steel beads to center the module in the z-direction. In 2018, the phantom was scanned using a state-of-the-art CT system (SOMATOM Definition AS+, Siemens Healthineers). All scans consisted of 2304 projections at a fixed bed position using an in-plane flying focal spot. The detector coverage was defined by 736 channels and 60 rows with a row width of 0.6 mm. The dual energy scans were acquired sequentially, i.e., the high and low energy scans were performed consecutively, with the X-ray tube set to 120 kV and 300 mAs, and to 80 kV and 500 mAs, respectively. The phantom was placed so that the center of module A closely matches the center of the scan field of view (FOV). The scans were repeated ten times and then averaged to reduce noise in the data for easier image analysis.

The collected data was processed with both image-based and data-based material decomposition methods explained in Section 2. The decomposition used the water-equivalent and bone-equivalent materials that are used to create the water and bone inserts in the ACR phantom. An offline filtered backprojection implementation of the vendor’s own reconstruction software was used for image reconstruction. A semi-smooth kernel (D40s) that is recommended for quantitative applications was systematically applied.

3.2

Experiments on Reproducibility

New scans were taken three years later, in 2021, using the exact same phantom with a different scanner (SOMATOM Definition Flash, Siemens Healthineers). The scan geometry was the same except for the bowtie filter material and the beam collimation, which was changed to 32 rows with a 1.2 mm row width, so that the energy response model used in the data-based decomposition needed to be adjusted. The phantom was scanned using three different positionings. The first one was the same as that used for the baseline scan, i.e., the phantom is centered in the scan FOV. The second one included a vertical shift of 4.8 cm up. The last one included a counterclockwise rotation of 45° together with a vertical shift of 4.8 cm.

All projection data was processed as described previously to create mono-energetic images with the image- and the data-based approaches. For non-centered positionings of the phantom, a shifted grid of pixels was used.

4.1

Baseline Results

Fig. 1 shows the reconstructions of the high and low energy scans used as baseline. Fig. 2 presents the mono-energetic images at 70 keV, as obtained with the image- and data-based decompositions. This energy was selected because it results in the lowest amount of noise in the images. The image-based decomposition leads to streak artifacts originating from the metal beads and to a bright artifact between the bone and the air insert, which is not present in the data-based result. To convey the quality of the implemented material decomposition approaches, Table 1 compares the mean attenuation value within the inserts in the mono-energetic images of Fig. 2 against the corresponding ideal attenuation values.

Figure 1.

Reconstructed images of the baseline (a) low and (b) high energy scans.

Figure 2.

Mono-energetic images at 70 keV as computed from the baseline data, using (a) image-based and (b) data-based material decomposition.

Table 1.

Mean linear attenuation values within the phantom’s inserts in cm−1, as obtained at 70 keV using the baseline scan. Reference values given by NIST.3

4.2

Results on Reproducibility

Reconstructions of the new high and low energy scans in the centered, off-centered, and off-centered and rotated positionings are displayed in Fig. 3 as an initial guide to interpret the mono-energetic reproducibility results, which are presented in Fig. 4. For the centered phantom, the images in Fig. 4 have an appearance similar to those from the baseline scans. When the phantom is moved out of the centered position, strong image artifacts around the bone insert can be observed in the image-based approach. These artifacts appear either absent or strongly reduced for the data-based approach.

Figure 3.

Reconstructed images for the new, high and low energy scans for the centered, off-centered, and off-centered and rotated positionings of the phantom.

Figure 4.

Mono-energetic images at 70 keV from the new scans: (left) image-based and (right) data-based material decomposition. Top to bottom: centered, off-centered, and off-centered and rotated positionings of the phantom.

For quantitative evaluation of the images in Fig. 4, Fig. 5 to Fig. 7 provide profile plots for differences with the baseline results. The mono-energetic images were registered to geometrically match the baseline results; the registration used cubic interpolation. Fig. 5 shows a circular profile around the bone insert, which was created by using 360 small ROIs around the bone insert, each with a radius of 5 pixels and placed at the same distance from the center of the bone insert. The differences in mean values for these ROIs are plotted starting at the 12 o’clock position going clockwise. The plots reveal more important deviations for the image-based approach than the data-based approach. For example, the image-based approach yields differences of −20 to 13 HU for the off-centered positioning of the phantom that only are of −6 to 5 HU when the decomposition is performed in the data domain. A second circular plot was created around the air insert in a similar manner as around the bone. Fig 6 shows that errors around the air insert are always in an acceptable range of −5 to 5 HU. It also shows that the results for the image-based approach are slightly better than for the data-based approach: for the off-centered positioning of the phantom, the curve for the data-based approach has a standard deviation of 2.03 HU while that for the image-based approach is 1.21 HU. A third profile plot is presented in Fig. 7, showing a thick horizontal profile, located below the bone insert within the main body of the phantom. Again, higher deviations from the baseline result can be observed when the image-based decomposition is used. We have also compared the mean values within the five inserts. The results (not shown here) convey that both image- and the data-based decomposition yields similar accuracy, with all absolute differences less than 5.0 HU.

Figure 5.

Quantitative analysis using a circular profile plot around the bone insert. The plots show the difference in mean ROI values relative to the baseline result. The position of the ROIs is highlighted in red in the left image. The angular location of the ROIs starts at the 12 o’clock location and moves clockwise.

Figure 6.

Quantitative analysis using a circular profile plot around the air insert. The plots show the difference in mean ROI values relative to the baseline result. The position of the ROIs is highlighted in red in the left image. The angular location of the ROIs starts at the 12 o’clock location and moves clockwise.

Figure 7.

Quantitative analysis using a thick profile that averages values over 31 neighboring horizontal lines within the phantom. In the left image, the central line of the profile is marked with a solid line and the vertical range with dashed lines. The plots show the difference relative to the baseline results.