# Measuring Identification and Quantification Errors in Spectral CT Material Decomposition
## 3 Results  
To calibrate biological data against the phantom containing known concentrations of known materials, calibration phantom images were evaluated in the energy domain (spectroscopic images) as well as the material domain (material segmentation and quantification) before they could be used for calibration purposes. The overall image quality produced by the MARS scanner was adequate for the analysis task, i.e., no major artefacts (beam hardening, partial volume effect, photon starvation or undersampling) were observed in the images. A few ring artefacts were observed towards the center of the reconstructed images. Figure 5 shows the spectral response of the transverse slices of the Gd/HA phantom with 4 energy bins for two imaging protocols. Figure 6 shows the relationship between CT number and energy bins. The CT number of the gadolinium and hydroxyapatite decreases with energy due to the decreasing influence of the photoelectric effect and increasing Compton scattering, however, for both protocols, a higher value for CT numbers is noticeable due to the influence of k-edge at gadolinium's k-edge energy range. Moreover, the CT number of the lipid (effective \(Z\approx 6.5\)) increases uniformly with energy. The spectral separation between different materials is the key information required for the segmentation task of the material decomposition. The linear fitted lines in Figure 7 indicate the system's linearity response over a range of concentration and energy bins (\(R^{2}\geq 0.99\)). Linearity determines the ability of a system to detect the presence or absence of any material. This information is important for material quantification and is therefore used to correlate between the known (contrast material) and unknowns (suspected regions). It can be affected by random noise, beam hardening, and photon starvation [58]. The non-zero CT number at zero concentration can be related to possible imperfections of the photon counting detectors or contributions of random (quantum) noise and systematic effects of the system. Figures 8 and 9 show identification of hydroxyapatite, gadolinium, lipid and water in Gd/HA phantom with protocol-1 and protocol-2 respectively. Some misidentification in material voxels (crosstalk) is observed between different materials, especially at the lower concentrations of gadolinium  
Figure 5: Transverse CT slices of Gd/HA with protocol-1 (top row images) and protocol-2 (bottom images) with 4 energy bins acquired at 118 kVp tube voltage. The grayscale map represents spectroscopic HU ranging from \(-1000\) to \(1500\). and hydroxyapatite decomposed images. It is important to highlight that despite clear material separation in attenuation profiles of gadolinium and hydroxyapatite in energy images (see Figures 6 and 7), the misidentification of material type and its concentration is difficult to assess visually in the images in Figures 8 and 9. It is also observed that the phantom body (PMMA) was significantly misidentified as gadolinium with protocol-2 (see Figure 9c), hence the need for a voxel by voxel assessment method for quantifying the degree of misidentification. Figure 6: Spectroscopic HU of gadolinium, lipid and hydroxyapatite across different energy bins with protocol-1 (**a,b**) and protocol-2 (**c,d**). Figure 7: HU as a function of the concentration of gadolinium and hydroxyapatite with protocol-1 (**a,b**) and protocol-2 (**c,d**). The linear fitted lines for both materials indicate average correlation coefficient of \(\geq\)0.99 for all four energy bins. Figure 8: Identification of a spectral CT image into individual elements using protocol-1. Top (**a-c**): spectral CT image with one of the energy bins (30–45 keV), an image with only HA density, and an image with only gadolinium density. Bottom (**d,e**): image with lipid density and an image with only water density. The window levels are normalized from 0 to 1 for display. Figure 9: Identification of spectral CT image into individual elements using protocol-2.