Spatial Resolution and Sensitivity of the Inveon Small-Animal PET Scanner

Spatial Resolution

The results for transaxial tangential and radial resolutions using FORE and FBP are shown in Figure 1A for an MRD of 79. These transaxial resolutions were found to be almost independent of MRD; therefore, the results for the other MRDs have been left out for clarity. The axial resolutions, on the contrary, were highly dependent on the MRD and increased as a function of radial distance from the CFOV, as shown in Figure 1B.

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FIGURE 1. 

(A) Transaxial spatial resolutions (FWHM and FWTM) obtained with FORE and FBP, using MRD of 79 as function of radial distance from CFOV. Other settings for MRD yielded highly similar results, which have been left out for clarity. (B) Axial spatial resolutions (FWHM and FWTM) obtained with FORE and FBP as function of radial distance from CFOV for different MRD settings.

According to NEMA-NU2-2007 (9), which was designed for the characterization of clinical PET scanners, spatial resolution should be reported for source positions at radial offsets of 1 and 10 cm to obtain numbers that can be considered representative for the CFOV and the edge of the FOV (EFOV), respectively. For small-animal scanners, NEMA prescriptions do not exist. We chose to average the resolution values for radial offsets between 2 and 5 mm, yielding representative numbers for the CFOV (averaged over 8 point source positions), and between 36 and 46 mm, representing the radial EFOV (averaged over 6 point source positions). The resulting FWHMs have been summarized in Table 2.

Spatial resolutions in all 3 directions were found to be independent of the MRD using AFORE and FBP. A comparison of the AFORE and FORE results for the transaxial resolutions is shown in Figure 2A. Only the results for an MRD of 79 have been plotted, because both algorithms yielded negligible differences on variation of MRD. A comparison of the axial resolutions is shown in Figure 2B. For AFORE, only the results for an MRD of 79 have been plotted because differences upon variation of MRD were negligible. However, the FORE results depended strongly on the MRD, as already shown in Figure 1A. Therefore, as a typical example for smaller MRDs, the graph for FORE with an MRD of 13 is included in Figure 2B. The averaged FWHMs for CFOV and EFOV obtained with AFORE are presented in Table 2.

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FIGURE 2. 

(A) Comparison of transaxial spatial resolutions using FORE and AFORE, with FBP as function of radial distance from CFOV. Only results for MRD of 79 have been plotted, because both algorithms yielded negligible differences upon variation of MRD. (B) Comparison of axial spatial resolutions using FORE and AFORE as function of radial distance from CFOV. For AFORE, only results for MRD of 79 have been plotted, because differences upon variation of MRD were negligible. FORE results depended strongly on MRD. As example for small MRDs, FORE results with MRD of 13 are shown.

The radial profiles of FWHM and FWTM in all directions for OSEM3D/MAP for both MAP smoothing parameters (β = 0.5 and 1.5) are shown in Figures 3A and 3B. The numeric values of FWHM for CFOV and EFOV are given in Table 2.

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FIGURE 3. 

Spatial resolution (FWHM and FWTM) in all directions as function of radial distance from CFOV for OSEM3D/MAP with β of 1.5 (A) and β of 0.5 (B).

Sensitivity

Figures 4A and 4B show axial and radial profiles, respectively, of sensitivity using default ΔE and Δt for different MRDs. The axial profiles are for the radial center of the scanner; the radial profiles are for a middle plane. Point source positions were as indicated in the “Materials and Methods” section of this article.

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FIGURE 4. 

(A) Axial sensitivity profiles at radial center for different MRDs. Dashed red line indicates sensitivity as would be obtained for MRD of 79, with linear decrease down to axial edge of FOV of scanner. (B) Radial sensitivity profiles for middle plane for different MRDs. (C) Sensitivity for complete FOV for MRD of 79. All sensitivities correspond to default ΔE and Δt and are based on histogrammed (Hist) trues rates, except for ♦, which were calculated using total trues rate.

Figure 4C shows the sensitivity obtained for the whole FOV for an MRD of 79 using the additional radial profiles separated by 10 mm in the axial direction. On the basis of cylinder symmetry, the original data were mirrored 2-fold to cover the complete FOV.

The effect of different ΔE and Δt settings on the sensitivity in the CFOV is shown in Table 3. This table also shows the sensitivity as calculated from a total trues rate instead of from a histogrammed trues rate (numbers in parentheses). The corresponding spatial resolutions were found to be essentially independent of ΔE and Δt.

The images of the homogeneous ⁶⁸Ge cylinder that were used to compare the noise levels associated with FORE and AFORE are shown in Figure 5. As an indication for image noise, we used the relative SD (SD_rel = SD divided by mean pixel value) in a central circular region of interest of 15-mm diameter, as shown in the figure. The resulting values for SD_rel were 0.10 and 0.22 for FORE and AFORE, respectively, indicating that FORE resulted in lower noise levels.

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FIGURE 5. 

Comparison of reconstructed images of uniform ⁶⁸Ge cylinder with 6-cm diameter using FORE (A) and AFORE (B) for central transaxial plane. Reconstruction algorithm for both images was FBP with matrix size of 128 × 128. Color was scaled to maximum pixel value in both images. SD_rel was calculated for circular regions of interest. ROI = region of interest.

Spatial Resolution

To compare spatial resolutions of different PET scanners, an agreement on rebinning and reconstruction algorithms has to be made. According to NEMA-NU2-2007 (9), the reconstruction method should be FBP. Although no prescription exists for the rebinning method, in most cases FORE is used, as was done in the present study.

In Figure 1A, the deterioration of the transaxial radial resolution at the EFOV is clearly noticed. The transaxial tangential resolution, on the contrary, is more or less constant over the complete radial range of point source positions. We observed only a negligible dependency of both transaxial resolutions on MRD. These observations are in line with results for other (clinical and preclinical) PET scanners, for which the deterioration of the radial resolution has been attributed to the transaxial parallax or DOI effect (7).

As can be seen in Figure 1B and Table 2, axial resolution is markedly deteriorated for large MRDs. Both the axial parallax or DOI effect and the breakdown of FORE contribute to this deterioration. These effects are caused by large LOR acceptance angles, but whereas the breakdown of FORE is a mathematic phenomenon, the axial parallax or DOI effect is related to the way in which coincidence photons are being detected in the crystal elements. In general, these effects cannot be disentangled. However, for the radial CFOV, FORE is exact, and the larger FWHM should be attributed entirely to the axial parallax or DOI effect. In the CFOV for an MRD of 79, axial FWHM is 1.98 mm, and by comparison with an MRD of 1, for which axial FWHM is 1.14 mm, it can be concluded that approximately 0.8 mm of increase of axial FWHM is caused by the parallax or DOI effect. For example, for the crystal size of 1.5 × 1.5 × 10 mm and a pitch of 1.59 mm, the absorption length will be distributed axially over 5 neighboring crystals when using a 10-mm crystal length as the typical length over which detected photons are absorbed, for photons with the maximum LOR acceptance angle of 38.3°. At the EFOV, also the breakdown of FORE adds to the deterioration of axial resolution, as shown by an axial FWHM of 2.75 mm for an MRD of 79.

For the smallest MRDs, the axial resolution is significantly better than the transaxial ones, both for the radial CFOV and for the EFOV. For an MRD of 1 (corresponding to a 2D mode operation of the scanner), we even found a submillimeter axial FWHM of 0.97 mm (Fig. 1B, value at exact CFOV). This FWHM value could be explained as follows. For LORs passing through the center of the FOV striking both detector elements perpendicularly, the theoretic FWHM—determined on the basis of only geometric arguments—equals d/2 (d = crystal size) if the point source is located midway between both detectors and approaches d when the source is close to 1 of the detectors (7). However, because the crystal elements are arranged in blocks with flat faces, they are not located on an exact circle. LORs passing through the CFOV strike the outermost crystals of a detector block under an angle of approximately 5° with the normal in the transaxial direction. Therefore, a certain parallax or DOI effect will be present in transaxial directions, even if the point source is located at the exact CFOV. The axial resolution, on the contrary, is not influenced, because cylinder symmetry implies that axially, the photons strike all crystal elements perpendicularly provided MRD is small. Finally, the fact that we do not observe an axial FWHM of exactly d/2 = 0.75 mm may be attributed to a combination of many confounding effects: noncolinearity of the photon pairs, finite source dimension, finite positron range, geometric imperfections in the detector block array, or intracrystal scattering.

To fully exploit the high sensitivity of the Inveon, it is clear from Figure 4A that an MRD of 79 should be used. However, it was demonstrated that for 2D reconstruction and FORE, a serious deterioration of axial resolution occurs. The AFORE algorithm overcomes this problem of deterioration to a certain extent. As can be seen in Figure 2B, the axial resolution is indeed considerably improved for an MRD of 79 when using AFORE instead of FORE. However, for small MRDs there is no improvement, and in the EFOV axial resolution is even seriously deteriorated using AFORE, as can be seen in Figure 2B in the comparison with FORE at an MRD of 13. Furthermore, although we expected that AFORE would not influence transaxial resolutions, Figure 2A demonstrates that already for radial offsets greater than 15 mm, the tangential FWHM is larger for AFORE than it is for FORE. This effect is even stronger for FWTM, which is associated with highly nongaussian tangential profiles with extending tails for AFORE. Because no information is available on the mathematics used in AFORE, we presently cannot explain these phenomena. Finally, because AFORE results in lower effective sensitivity, as demonstrated by Figure 5 and the corresponding SD_rel values, we believe that AFORE is not the reconstruction method of choice for the Inveon.

For users who are not prohibited by the long reconstruction times of OSEM3D/MAP (4 h for 256 × 256 and 1 h for 128 × 128 image planes on the personal computer configuration, as mentioned in “Materials and Methods”), this reconstruction method is preferable in terms of uniform, high resolution and high sensitivity. As can be seen in Figures 3A and 3B, the spatial resolution is uniform across the FOV of the scanner and almost direction-independent, especially for FWMH. This result is explained by noting that OSEM3D/MAP is a fully 3D reconstruction technique without rebinning errors and that parallax or DOI effects in both the transaxial and the axial directions are suppressed because they have already been modeled in the P-matrices and blur kernels that are used in each iteration step of this reconstruction algorithm. Further, all LORs belonging to an MRD of 79 are being used, so maximum sensitivity is maintained. However, OSEM3D/MAP parameters still require optimization in terms of overall image quality (uniformity, recovery coefficients for small lesions, quantitative imaging, etc.). This optimization was outside the scope of the present study.

The spatial resolution of the Inveon based on FORE and FBP can be compared with that of the commercial crystal-based small-animal scanners given in Table 1. For the F120, Figures 1A and 1B of Kim et al. (12) demonstrate transaxial spatial resolutions similar to those for the Inveon. The same holds for the axial resolutions of an MRD of 46 (which is closest to the maximum MRD of 47 of the F120). The Mosaic (Philips) (13) is characterized by FWHMs ranging between 2.7 (radial, CFOV) and 5.8 mm (axial, EFOV; 46 mm from radial center), which are larger than the corresponding values for the Inveon. The Vista (GE Healthcare) has an FWHM of 1.4 mm for all directions in the CFOV. The tangential resolution is more or less independent of the radial offset, whereas both the axial and the radial FWHMs increase to approximately 2.4 mm for the radial EFOV at 29 mm (data estimated from Figure 1A in Wang et al. (14)). The radial and tangential resolutions of the Vista are approximately equal to those of the Inveon. Axial resolution is better for the Vista than for the Inveon at an MRD of 79; however, for an MRD of 46 (which gives a better comparison with the smaller maximum LOR acceptance angle of 22.1° of the Vista), axial FWHMs are similar. For the ClearPET (Raytest) in the small–crystal ring configuration (diameter, 135 mm), FWHMs in all directions were reported as less than or equal to 1.3 mm in the CFOV and less than or equal to 2.0 at a radial offset of 30 mm from the center (15). These values are clearly better than those of the Inveon. However, unlike for the other scanners, the values have not been obtained using the NEMA prescriptions (9). Instead of using rebinning and FBP, an iterative 3D reconstruction method (OSMAPOSL) was used, and resolutions were determined in gaussian fits of the profiles instead of by using the NEMA interpolation method. On the other hand, when comparing the ClearPET OSMAPOSL results with the Inveon OSEM3D/MAP results, we found the ClearPET performance to be still better. It is not clear yet, though, to what extent this should be attributed to differences in the MAP-based reconstruction algorithms or to real differences in intrinsic spatial resolution between the scanners.

Sensitivity

The peak sensitivity as specified by the manufacturer (>0.1) is confirmed by our value of 0.111. This value holds for the CFOV, large ΔE and Δt, and total trues rate instead of histogrammed trues rate. Sensitivity values for default ΔE are lower, as shown in Table 3. The measured sensitivities are almost independent of Δt, indicating that the timing resolution is good for the counting rates observed with the present point source activity (prompt rates, 86.0 and 56.5 kcps for ΔE = 250–750 and 350–650 keV, respectively).

Because sensitivities were calculated using the rate at which photon pairs are emitted from the ²²Na point source, their accuracy is determined by the accuracy of the source activity (the influence of count statistics on the observed trues rate is negligible in view of the large number of coincidence counts in each measurement). This accuracy is ±4%, which leads to ±4% accuracy of all sensitivity values presented in this article. Our dose calibrators are regularly checked by the manufacturer using sources (provided by North American Scientific Inc.) that have been calibrated against the standards at The Netherlands Metrology Institute (Nederlands Meetinstituut) and the German Federal Metrology Institute (Physikalisch-Technische Bundesanstalt). However, the activity, as specified on the ²²Na point source calibration data sheet of the IPL, is 7% smaller than the value measured by us. Accordingly, when using this value, we would have increased all sensitivity data by 7%. However, we preferred to use the value measured by us because the accuracy specified by IPL is as large as ±15%.

The axial sensitivity profiles in Figure 4A are in accordance with straightforward geometric considerations based on the total number of LORs contained in the FOV of the scanner when the point source is stepped in the axial direction. This explains the central plateaus for an MRD of less than 79 and the more or less linear drop to zero when moving the point source toward the axial EFOVs. It is not immediately clear why the observed drop in sensitivity is less than predicted by mere geometry, but the following could be speculated. For a point source in the CFOV, the maximum angle at which coincidences are detected is 38.3°, whereas for positions closer to the axial edges, this angle decreases. Oblique photons may be less effectively detected by crystals at the edge of detector blocks because of the gaps between blocks, which could explain the observed less-than-linear drop of sensitivity. Coincidences are detected even when the point source is located beyond the EFOVs. This effect should be attributed mostly to scatter effects in the detector crystals or in the lead ring that shields the detectors at the axial EFOVs and to a lesser extent to the natural radioactivity of LSO crystals because of the presence of ¹⁷⁶Lu. The background contribution just outside the FOV at 71 mm from the center was 6%.

Sensitivity across the whole FOV as shown in Figure 4C may be illustrative for researchers who wish to optimize their experiments by scanning more than 1 animal at the same time. On the basis of only sensitivity, it would be preferable to place 2 animals (e.g., mice) on top of or next to each other instead of behind each other. However, it should be verified whether attenuation and scatter correction is still effective, because more attenuating and scattering mass will then be present in the transaxial FOV.

It is interesting to compare the sensitivity of the Inveon with its predecessor, the F120, which has the same crystal size and similar geometry but fewer crystal rings. A sensitivity of 0.040 was found for an ΔE of 350–650 keV (Table 2 in Kim et al. (12)) for the maximum MRD of 47. The closest attainable MRD in the Inveon is 46, for which we found a sensitivity of 0.0451 (average plateau value in Fig. 4A). It is therefore concluded that the higher sensitivity of the Inveon is due not only to its larger axial FOV but also, for approximately 13%, to its better detection efficiency for each crystal ring separately. In fact, the difference is still somewhat larger, because the data of Kim et al. (12) were based on total trues rate (written communication with J.S. Lee, second author of reference 12, 2008), whereas we used histogrammed trues rate in our study.

The Inveon showed higher sensitivity than did the other commercial small-animal scanners presented in Table 1. The values reported in the literature for these scanners cannot directly be compared with those of the Inveon, mainly because of the use of different energy windows, but they are summarized here. The peak sensitivity of the Mosaic for an ΔE of 410–665 keV is 0.0114 (13). The Vista is characterized by peak sensitivities of 0.065, 0.040, and 0.021 for energy windows of 100–700, 250–700, and 400–700 keV, respectively (14). Finally, the reported peak sensitivity for the ClearPET is 0.045 (15) for the small-diameter, full-ring configuration with an ΔE of 250–750 keV.