# Measuring Identification and Quantification Errors in Spectral CT Material Decomposition
## 3 Results
Top (**a–c**): spectral CT image with one of the energy bins (27–33 keV), image with only HA density, and image with only gadolinium density. Bottom (**d,e**): image with lipid density and image with only water density. The window levels are normalized from 0 to 1 for display. For post material decomposition evaluation, images corresponding to a thickness of \(\sim\)2 mm were analyzed slice by slice by using Equation (5) for sensitivity, Equation (8) for the specificity of the target material with high-Z materials and Equation (9) for the specificity of the target material with water. Results were then averaged and plotted in the MD misidentification charts as shown in Figures 10 and 11. Once the material separation was quantified, the relationship between the known and measured concentrations of gadolinium and hydroxyapatite was determined from material images. Results indicate that despite good spectral and linear correlation of gadolinium in energy images with protocol-2 (Figures 6c and 7c), the measured concentration of gadolinium is underestimated for protocol-2 (Figure 12a) whereas, protocol-1 indicates a good correlation between the known and measured concentrations over the full range of gadolinium (\(R^{2}\geq 0.99\)). Hydroxyapatite concentrations were observed to be linear with both protocols. Material misidentification and mis-quantification results from Figures 10-12 are summarized in Table 2. These results demonstrate that the methodology can be used to compare how different scanning protocols using one material differentiation method affect the measurement of the concentration of materials. Figure 11: MD identification chart for protocol-2 shows quantitative misidentification of voxels between gadolinium, hydroxyapatite, lipid and water. For given gadolinium solutions, sensitivity decreased from \(\sim\)94% for 8 mg Gd/mL to 42% for 1 mg Gd/mL solution insert. For HA, no misidentification was observed in any of the given calibration rods. A corresponding table in the right is shown to look up individual value in the chart. Figure 10: MD identification chart for protocol-1 shows quantitative misidentification of voxels between gadolinium, hydroxyapatite, lipid, and water. For the 8 mg Gd/mL solution insert, not a single voxel was misidentified (100% sensitivity) as a different material. For 4 mg Gd/mL, \(\sim\)98% voxels were correctly identified as gadolinium and 2% were misidentified as HA. Similarly, for 1 mg Gd/mL solution insert, \(\sim\)62% voxels were identified as gadolinium, \(\sim\)18% were misidentified as HA, \(\sim\)10% misidentified as lipid and water. For HA calibration rods, no misidentification is observed for 808 mg HA/mL and 212 mg HA/mL but \(\sim\)4% voxels from 54 mg HA/mL was misidentified as Gd. A corresponding table in the right is shown to look up individual value in the chart. Spectral CT and material component images of ex-vivo bovine cartilage-bone plugs are shown in Figure 13. The bone in the bovine plugs is represented in the HA component images (see Figure 13b,f). The layer of articular cartilage of the incubated knee specimen is represented by the gadolinium density images (see Figure 13c,g) whereas no gadolinium signal from control specimen was detected with either protocol. However, misidentification of gadolinium as water is observed with protocol-2. Figure 14a,b shows fused images of gadolinium and hydroxyapatite densities with protocol-1 and protocol-2 respectively. Quantitative variations in the gadolinium concentration are plotted (Figure 14c) along the depth of the cartilage. Contrast quantification is crucial in a biological specimen especially when radiologists determine disease burden and contrast delivery by using high-Z contrast materials. Figure 14c shows that despite good qualitative gadolinium decomposition, measured gadolinium concentration with protocol-2 is over 50% lower than with protocol-1. Which measurement of these two concentrations is more reliable?