The results shown in this section were obtained using the 3D phantoms described above and 3D reconstruction in all cases. However, in what follows we will only be presenting a central axial reconstructed slice of the 3D data set since the off-centered slices will also display artifacts due to truncation of projections in the longitudinal direction in addition to the insufficient sampling of cone beam projections. As is well known, these artifacts could be reduced by moving either the animal bed or the gantry in incremental steps in the longitudinal direction to acquire additional data. This will be the subject of a future study.
3.1. Effects of out-of-field objects on the resolution phantom
The resolution phantom shown in was reconstructed by using both techniques with a LFOV of 10 mm diameter. The LFOV is overlaid on the phantom and reconstructed images in in red indicate its position. The results are shown in . In this case we assumed no background signal.
(a) Resolution phantom; (b) reconstructed image using the K-SPECT technique; (c) reconstructed image using the standard ML-EM method that does not use any a priori information; and (d) horizontal intensity profiles through all three images.
In the case of the reconstruction was performed over the entire reconstruction area in contrast to where it was only performed within the LFOV. The intensity profiles shown in indicate that the K-SPECT profile is very close to the actual profile obtained from the phantom whereas the profile obtained using reconstruction without the a priori underestimates the signal intensities considerably within the LFOV (between two black solid lines).
3.2. Reduction of artifacts from outside the LFOV
The image reconstruction of an ROI positioned inside of the LFOV was performed using the adaptive system matrix (equation (5a)
), which was generated by reducing the dimensions of the original system matrix using the a priori
information. The RMSE criterion (equation (8)
) was used to evaluate the artifacts within the ROI using the K-SPECT reconstruction and compare it with the ML-EM method (equation (5a)
) that did not use any a priori
information (to be called the ‘standard method’ henceforward).
shows the reduction of artifacts from outside the LFOV. The object was a sphere 8 mm diameter embedded within a prism of dimensions 29 mm × 29 mm × 58 mm using a uniform background with a T/B activity ratio of 5:1, . In this case the LFOV diameter was 10 mm whereas the ROI diameter was 8 mm. The reconstructed image with the ML-EM with no a priori is shown in . Due to the background noise the artifact inside the ROI is high (RMSE = 0.32). The reconstructed image using the K-SPECT method is shown in and the error (RMSE = 0.08) is improved by 74.5% within the ROI. The global RMSE for the area of the LFOV is 0.24 for (c) and 0.41 for (d), which is improved by 40.4% by using the K-SPECT method. The image shown in shows larger artifacts along the diagonal directions. This is due to the prism shape of the entire object resulting in larger background signals along the diagonal directions compared to the vertical and horizontal directions. It is seen that the K-SPECT method eliminates these artifacts considerably.
Figure 6 (a) Spherical phantom (8 mm in diameter) with 5:1 contrast; (b) illustrative description of (a) the ROI (8 mm in diameter) within the LFOV (10 mm in diameter); (c) reconstructed image of (a) with the K-SPECT method, and (d) reconstructed image of (a) (more ...)
An additional example of the image artifacts recovered by using the adaptive system matrix is shown in . The image in is the input phantom of two 10 mm diameter spheres, one is at the center of the LFOV that would be taken as the ROI and the other one is outside of the LFOV representing a high intensity object outside the field of interest. The area of the LFOV is the same as the sphere at the center of . Therefore, the sphere at the center of covers the whole area of the LFOV. shows the reconstructed image of the ROI with the K-SPECT method. shows the reconstructed image of the ROI using the ‘standard’ ML-EM method that does not take into account any a priori information. The RMSE of the area for the LFOV for (RMSE = 0.17) is improved by 60.1% compared to (RMSE = 0.43). show horizontal and diagonal profiles through . It is seen that in all cases the intensity profiles obtained by the K-SPECT method are much closer to the actual ones when compared to the ML-EM reconstruction without a priori data. Thus both the overall artifact reduction as quantified by the RMSE and plotted image profiles demonstrate significant improvements due to the use of a priori data during the reconstruction process.
Figure 7 (a) Two spherical digital phantoms with 10 mm diameter: one at the center of image space and another off-centered; (b) reconstructed image of the phantom within the LFOV with the K-SPECT method; (c) reconstructed image of the same phantom with the ML-EM (more ...)
3.3. Simulation with the MOBY phantom
The image reconstructions were performed with the digital mouse phantom (MOBY) provided by Dr Segars' group at Duke University (Chen et al 2007
). The phantoms were generated either with high activity in the heart chamber (blood pool imaging) or in the myocardium (myocardial uptake imaging) separately to show different uptake patterns. The evaluation of the reconstructed images with respect to the input digital phantom was done using the RMSE criteria as described earlier using equation (8)
3.3.1. Heart chamber imaging
The image in is the input phantom of digital mouse with activity inside the heart chamber. The image in was reconstructed by using the system matrix generated with the K-SPECT method, and that the image in (c) was reconstructed by using the ‘standard’ ML-EM method. Images shown are the axial center slice of a 3D image data set. By using the adaptive system matrix (K-SPECT technique), the output image of the ROI is improved. The RMSE of the area for the LFOV (K-SPECT) for (b) (RMSE = 0.19) is improved by 48.5% compared to (c) (RMSE = 0.38). The improved image due to inclusion of a priori data can be observed in .
(a) MOBY phantom-cardiac chamber, (b) reconstructed image with the K-SPECT method, (c) reconstructed image with the ML-EM reconstruction without a priori and (d) corresponding intensity profiles along the lines shown in (a)–(c).
3.3.2. Myocardium imaging
The digital mouse phantom was generated with a high uptake in the myocardium muscle wall as shown in . The images in were reconstructed by using the new adaptive system matrix (K-SPECT method) and the ‘standard’ ML-EM method without any a priori information, respectively. The same axial slices reconstructed by both methods are shown in . It is seen that the image reconstructed by using the adaptive system matrix is improved over the other. The RMSE for the LFOV reconstruction with K-SPECT for (RMSE = 0.25) is improved by 52.6% compared to that for (RMSE = 0.53) without a priori information during reconstruction. We note that in one cannot even distinguish the walls of the two heart chambers without a priori information provided by MRI.
(a) MOBY phantom-myocardium, (b) reconstructed image with the K-SPECT method, (c) reconstructed image with the ML-EM reconstruction without a priori and (d) corresponding intensity profiles along the lines shown in (a)–(c).
3.4. Importance of alignment of the ROI within the LFOV
For the K-SPECT reconstruction, it is important to position the ROI within the area of the LFOV. When they are misaligned, which represents partial correlation between MRI and SPECT, the high radioactive area can be left outside the LFOV; therefore, the activity from the area is treated as noise in the K-SPECT. As an example, the image in shows the reconstructed image of the spherical phantom, , when the LFOV fully covers the ROI. If the LFOV and the ROI are misaligned as shown in , the resultant reconstructed image is shown in . We see that in addition to truncation of the target area the signal intensity in the image is non-uniform.
Figure 10 (a) Spherical phantom (10 mm diameter); (b) reconstructed image of (a) when the ROI is aligned with the center of the LFOV using the K-SPECT reconstruction method, (c) example of misaligned ROI with the LFOV (1.5 mm off in both x-and y-axis directions (more ...)
3.5. Effect of the T/B ratio on K-SPECT reconstruction
To study the effect of the T/B ratio on the K-SPECT image reconstruction method three phantoms with different T/B ratios were generated as shown in . The phantom was a 29 mm × 29 mm × 58 mm prism with a 5.4 mm sphere positioned at the center. Thus the ROI covering the tar object (the sphere) was 5.4 mm in diameter and the LFOV was 10 mm in diameter as previously. We assumed three different T/B ratios, namely 2:1, 5:1 and 10:1 (see ).
The input phantoms with T/B ratios of (a) 2:1, (b) 5:1 and (c) 10:1 used in the simulation.
Figure 12 The effect of T/B on the K-SPECT method. In all cases the first column is the phantom, the second column is a reconstructed image without any a priori, the third column is a reconstructed image with the K-SPECT method and the fourth column is a horizontal (more ...)
The simulation result showed that the normalized RMSE by the intensity within the ROI was 0.34%, 0.25% and 0.15% for the T/B ratios of 2:1, 5:1 and 10:1, respectively. Therefore, as expected the K-SPECT image reconstruction method reduces the error better for the objects with higher T/B ratios.