Determination of Accuracy and Precision of Lesion Uptake Measurements in Human Subjects with Time-of-Flight PET

TOF Scanner

Data were acquired with the University of Pennsylvania prototype TOF PET scanner, based on LaBr₃ scintillators (15,23). This fully 3-dimensional scanner comprises 24 modules of 1,620 crystals (4 × 4 × 30 mm) in a 93-cm-diameter ring. The transverse field of view is 57.6 cm; the axial field of view is 19.2 cm. The intrinsic timing resolution of the scanner, measured with a point source in air, is 375 ps. The energy resolution of 6.5% after energy calibration allows the lower energy threshold to be raised to 470 keV. Data are acquired in list mode with 25-ps timing bins to preserve timing and spatial resolutions. The spatial resolution of the scanner is 5.8 mm (full width at half maximum) at a 1-cm radius.

Data Reconstruction and Corrections

The image reconstruction algorithm was the 3-dimensional list-mode iterative ordered-subsets expectation maximization (OSEM) algorithm (26,27) with a TOF kernel applied in both the forward projection and the backprojection operations (28). The TOF response function was modeled as a 1-dimensional gaussian function along the line of response. All physical effects were incorporated into the system model of the reconstruction. Resolution modeling to compensate for detector blurring was not explicitly included in the reconstruction; instead of voxels, however, modified Kaiser–Bessel (“blob”) basis functions (29,30) were used to constrain the image to be a continuous function during reconstruction. Blob basis functions control image noise without the need for postfiltering while maintaining spatial resolution (30), albeit in a spatially invariant manner. The blobs used for this study had a 7.5-mm radius placed on a 6-mm body center cubic grid (shape parameter, 8.63). The final image was interpolated to 2 × 2 × 2 mm voxels. All TOF OSEM reconstructions had 25 chronologically ordered subsets. Although clinical TOF reconstructions are typically stopped after 4 or 5 iterations, in this study the data were reconstructed for up to 20 iterations to determine the convergence with clinical data.

A rotating line source was used to correct the measured timing differences between crystals (23). Attenuation correction was performed by use of transmission imaging with a rotating ¹³⁷Cs point source (31). The model-based single scatter simulation was extended to estimate the 4-dimensional scatter distribution in the radial and TOF domains (32,33). The scatter estimate used in non-TOF reconstructions was derived from the 4-dimensional single-scatter simulation–TOF scatter sinogram by compression of the sinogram along the time domain. Random coincidences were estimated by use of the delayed coincidence window technique with the smoothing technique of Casey and Hoffman (34).

Healthy Volunteer Studies

The institutional review board of the University of Pennsylvania approved this study, and all subjects signed written informed consent forms before the study. Six healthy volunteers (5 men and 1 woman; body mass index, 25–38) were injected with 555 MBq (15 mCi) of ¹⁸F-FDG and scanned after an average 105-min uptake period. Four frames were acquired to cover the region from the neck to the pelvis. The patient bed was moved between frames to allow for nearly 50% overlap of bed positions to ensure uniform axial noise behavior. The scan duration for each subject was chosen to provide counts comparable, on average, to the events measured in a 2-min–per–frame clinical ¹⁸F-FDG study on a Philips Gemini TF TOF PET scanner with our standard 60-min postinjection protocol. Totals of 115–270 megacounts (prompts) and 45–100 million counts (true events) were acquired in the 4-frame studies, in which the ranges in counts were the ranges seen across the 6 subjects.

Sphere Insertion Methodology

To assess the impact of TOF information on the accuracy and precision of sphere uptake measurements in clinically realistic conditions, we inserted spheres with known uptake into the measured healthy volunteer data. El Fakhri et al. (16) and Surti et al. (17) developed a technique for merging list-mode data from spheric lesions measured in air with data from patients for their studies on lesion detectability. In those studies, spheres were embedded at an activity ratio calculated with respect to the local activity in the organ. For this work, their technique was modified to insert spheres having known activity with respect to the average whole-body uptake, similar to a fixed standardized uptake value.

Spheres (10-mm diameter; 1-mm wall thickness) were scanned in air at 77 locations throughout the scanner field of view (radius, 0–12 cm; z-axis, 0 ± 4 cm from the center of the scanner), and the data were stored in list-mode format. Spheres were selected for insertion into the liver and lung regions of the healthy volunteer data such that no 2 spheres were closer than 3.5 cm from center to center. A total of 6 spheres were chosen for each organ.

The desired ratio (a_o) of sphere uptake to the average whole-body activity concentration was 10:1. The average whole-body uptake per volume (B_WB) was determined by averaging all voxels inside the body in the image after 20 iterations of list-mode TOF OSEM. The transmission image was used to define the interior of the body for this calculation. Voxels in slices within 28 mm of the ends of the whole-body image were excluded from the calculations because those slices were noisy as a result of low slice sensitivity near the ends of the axial field of view.

The procedure for calculating the number of sphere events to insert is illustrated in Figure 1. The desired total sphere activity (A) at the location of each sphere isEq. 1where V_sph is the volume of the sphere; a_o was 10 for this study. However, the whole-body image before sphere insertion had some background activity in the region of the sphere (A_b,i); therefore, the total activity to be inserted into the healthy volunteer data for sphere i (A_i) is given byEq. 2The number of list-mode events to be inserted for sphere i () was calculated by scaling A_i by the ratio of the number of events in the sphere dataset () to the total activity (A_tot,i) in the sphere-in-air image as follows:Eq. 3

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FIGURE 1.

Schematic of sphere insertion process for list-mode data. Sphere activity to insert (A_i) depends on desired activity ratio (a_o) with respect to average whole-body (WB) uptake per unit volume (B_WB), reduced by activity already present in patient image at location of sphere (A_b,i). Sphere-in-air data were acquired at known locations on grid (photograph). Sphere data were reconstructed, and ratio of sphere-in-air list-mode events to total sphere image activity () was used to scale A_i to determine number of list-mode events () that would generate that activity. These list-mode events were reduced by sampling of probability of attenuation by body for line of response of given event and then were merged with subject’s list-mode data (⊕). This procedure was adapted from that used in earlier lesion detectability studies (16,17).

This scaling undoes any geometric efficiency corrections performed during reconstruction (e.g., solid-angle correction).

To compensate for attenuation effects seen in the whole-body study but not present in the sphere-in-air data, the selected sphere events were reduced by rejecting events through random sampling of the probability of attenuation by the body for the line of response of each sphere event. The “attenuated” sphere events were then merged with the healthy volunteer data by random insertion into the subject’s list-mode data stream. The net result was an increase in the total number of events of less than 1%. This technique implicitly includes partial-volume blurring of the sphere but does not include wall effects. Unlike physical spheres in phantom measurements, the sphere wall does not displace activity around the sphere because counts are present in the subject’s data in the region of the sphere wall; this scenario results in the insertion of effectively wall-less lesions into the clinical data. The merged list-mode data were then reconstructed with TOF information and without TOF information as described earlier.

The sphere insertion process was validated by scanning a 35-cm cylinder that had 5 physical spheres (10-mm diameter; 6:1 activity ratio) located at radial positions from 0 to 11 cm. Fifteen additional 10-mm-diameter spheres were inserted into the phantom data in accordance with the procedure described earlier, with an a_o of 6. The data were reconstructed with list-mode TOF OSEM for 20 iterations. Volumes of interest (VOIs; 10-mm diameter) were drawn on the spheres, and the background activity was determined by averaging all voxels inside the phantom image without inserted spheres, analogous to B_WB. The average uptake in the physical spheres divided by the background activity was 2.37 ± 0.13 (mean ± SD; range, 2.19–2.48); the average uptake in the inserted spheres was 2.51 ± 0.14 (range, 2.29–2.69). The slightly higher (<10%) uptake measured in the inserted spheres than in the physical spheres can be explained by and is consistent with the findings for wall-less spheres compared with spheres having glass walls (35).

Bootstrapped Replicates

To determine the statistical variability of the measured sphere uptake for TOF and non-TOF reconstructions, we generated 60 replicates of the list-mode data with and without inserted spheres by using bootstrapping as proposed by Haynor and Woods (36) and as demonstrated and validated by Dahlbom (37) and Buvat (38). Bootstrapping permits an assessment of the statistical variability in TOF and non-TOF images at clinically realistic noise levels.

Analysis

Sphere uptake was calculated for VOIs with a 10-mm diameter. The VOI centers were determined from the sphere-in-air reconstructions, and the same VOIs were used on the images reconstructed from the merged sphere and subject data. The sphere VOIs (VOI_sph) were normalized by the average whole-body uptake (B_WB) after 20 iterations to define a normalized uptake ratio (NUV):Eq. 4B_WB was calculated separately for TOF images and non-TOF images to compensate for differences in calibration for TOF and non-TOF reconstructions. Without partial-volume effects, the NUV for each sphere should be 10 (i.e., equal to a_o). Because no resolution modeling was included in the reconstruction, the measured NUV was less than 10.

From the 60 replicates of the 6 patient studies with 6 inserted spheres in the lung and liver, we calculated 4 measures.

1. The average NUV for 1 replicate across all subjects and spheres for each organ j (NUVj) was calculated asEq. 5where is the uptake in organ j of sphere s in subject p for 1 replicate. This quantity was not averaged across all replicates because each bootstrapped replicate was derived from the same dataset (37).

2. The statistical variability of sphere uptake across the 60 bootstrapped replicates, expressed as the percentage coefficient of variation and averaged across all subjects and spheres for each organ j (), was calculated asEq. 6where NUV_j(r,s,p) is the uptake in organ j of sphere s in subject p for replicate r.

3. The variability of sphere uptake across sphere locations for the 6 spheres in each organ j of a subject, averaged across all subjects (), was calculated asEq. 7where is the average uptake in organ j of all spheres in subject p for 1 replicate.

4. The variability of sphere uptake across subjects and spheres in each organ j (COV_subj,j) was calculated asEq. 8where is as defined in Equation 5. The same 6 spheres could not be inserted in all subjects because the relative locations of the subjects within the scanner with respect to the sphere positions varied; therefore, the variability across subjects included the variability across location within a subject.

Image noise was calculated as the average statistical noise (across the 60 replicates) for a group of voxels in a large region of interest drawn in the liver. A cylindric region of interest with a diameter of 50–80 mm and an axial length of 7 slices (14 mm) was drawn in the liver for this average.