Figure 1.
Principle of line-of-response (LOR) rebinning.
A LOR represents the detected path of a pair of coincident gamma photons. The left side of the figure shows an LOR detected on the line joining detectors A and B when the object (ellipse) was in a certain (moved) pose. The right side shows the original object pose, and indicates how the LOR ought to be reoriented so as to correctly coincide with this pose i.e. it now lies on A′B′. Notice that in both cases the path through the object is the same. Although shown here in 2D, the transformations are 3D in general.
Figure 2.
The MicronTracker stereo tracking system is shown here in the foreground attached to the scanner bed unit via a custom-made mount. In the background is the microPET scanner bore. A 4-part marker affixed to the scanner bore is used to define a reference coordinate system and enables changes in the relative pose of the tracker and scanner to be accounted for.
Figure 3.
The small 3-point marker (left) suitable for rat head tracking, and the larger 8-point marker (right) used as a performance reference. A minimum of three X-points (intersections of black and white regions) are required for six degree-of-freedom pose tracking. The 8-point marker therefore has considerable redundancy for pose estimation.
Figure 4.
Hardware setup for synchronisation of tracker and list mode PET data.
Acquisition of time-stamped stereo image frames is initiated and controlled by a signal generator triggering the tracker's external input at the desired frequency. With each frame the tracker triggers the gating input of the microPET, initiating the insertion of a data ‘tag’ in the list mode event stream.
Figure 5.
Timing for the synchronisation procedure.
The diagram shows the relative timing for key events in the data acquisition and synchronisation processes. Here f is the frequency at which the tracker is triggered, TE is the exposure time for images collected by the cameras, and TS is the duration of pulses strobed by the tracker when each frame commences. Synchronisation is achieved by matching list mode data segments between consecutive synchronisation tags (eg. shaded rectangle shown between Tagn and Tagn+1) with a pose. For the list mode segment between Tagn and Tagn+1, Posen+1 was the best temporal match.
Figure 6.
Setup for the robot-controlled motion.
Diagram showing the six degree-of-freedom robot with the hot rod phantom attached to the end-effector. The apparent location of the end-effector was shifted along the axis of the phantom by 45 mm, corresponding to the middle third of the cylinder. This more closely resembled the proximity of the marker to the brain in the original motion data. The 8-point and 3-point markers used for tracking were stuck to the marker substrate (on the opposite side to that visible here).
Figure 7.
Manually applied motion (‘slow-moderate’).
Motion data recorded for each degree-of-freedom during the 20-min phantom study involving slow-moderate manually applied motion. Continuous, arbitrary motion was applied for 2–3 min intervals, interspersed by approximately 1 min intervals when the phantom was kept stationary. Data are shown in the scanner coordinate system and represent the cumulative motion since the start of the scan. The pose sampling rate during tracking was 30 Hz.
Figure 8.
Manually applied motion (‘fast’).
Motion data recorded in each degree-of-freedom during the 5-min phantom study involving fast manually applied motion. Continuous, arbitrary motion was applied for approximately 4.5 minutes out of the total scan time. Data are shown in the scanner coordinate system and represent the cumulative motion since the start of the scan. The pose sampling rate during tracking was 30 Hz.
Figure 9.
Measurement jitter for motion tracking markers.
Comparison of the measurement jitter in typical segments (15–20 s duration) of motion data obtained from the 3-point marker (black line) and 8-point marker (grey line) during the first 5 minutes of the 20 min manually applied motion study (slow-moderate motion). (a, b) Measured rotation about the x and y axes, respectively, when the phantom was stationary; (c, d) measured rotation about the x and y axes, respectively, when the phantom was moving. Rotations about x and y are shown because they exhibited the greatest measurement jitter. Note that these data are in scanner coordinates and that sample numbers are relative to the start of the selected segments. The pose sampling rate during tracking was 30 Hz.
Table 1.
Range and rate of motion for the slow-moderate manually applied motion.
Table 2.
Range and rate of motion for the fast manually applied motion.
Figure 10.
Motion correction of slow-moderate manual motion.
Motion correction of the 20-min hot rod study with slow-moderate manually applied motion (see figure 7). Left to right are orthogonal views of the centre of the phantom. Row 1: no motion correction; row 2: motion free; row 3: correction based on the 8-point marker; row 4: correction based on the 3-point marker. The pose sampling rate during tracking was 30 Hz. Note that the white bars marked on the motion-free image represent the location of profiles shown in figure 12.
Figure 11.
Motion correction of fast manual motion.
Motion correction of the 5-min hot rod study with fast manually applied motion (see figure 8). Left to right are orthogonal views through the centre of the phantom. Row 1: no motion correction; row 2: motion free; row 3: correction based on the 8-point marker; row 4: correction based on the 3-point marker. The pose sampling rate during tracking was 30 Hz. Note that the white bars marked on the motion-free image represent the location of profiles shown in figure 12.
Figure 12.
Quantitative assessment of motion correction.
Comparison of the reconstructed hot rod phantom images with and without motion correction. The top panel shows profiles for the 20-min study with slow-moderate manually applied motion, and the bottom panel shows profiles for the 5 min study with fast manually applied motion. Profiles were drawn through the transverse reconstructed images at the level indicated in figures 10 and 11. The pose sampling rate during tracking was 30 Hz.
Figure 13.
Effect of motion rate on motion correction.
Motion correction of the hot rod study with slow-moderate manually applied motion. A 72 s segment of the data has been corrected so that it is comparable (in terms of counting statistics) with the fast motion study. Left to right shows orthogonal views of the centre of the phantom. Correction was based on the 8-point marker measurements. These images can be compared with those in figure 11 (row 3) in order to see the effect that the rate of motion had on motion correction accuracy.
Figure 14.
Comparison of commanded and measured robot motion.
Commanded robot motion (black) overlaid with measured motion (red). Data are shown for the x-axis rotation. Note that there were 20,000 poses spanning 11 min. All measurements are in robot coordinates and represent the cumulative motion since the start of the scan.
Table 3.
Range and rate of motion for the robot-generated motion.
Figure 15.
Motion correction of simulated rat motion (hot rod phantom).
Motion correction of the hot rod study corrupted by the robot-generated rat motion. Left to right are orthogonal views of the centre of the phantom. Row 1: no motion correction; row 2: motion free; row 3: correction based on the 8-point marker; row 4: correction based on the 3-point marker. The pose sampling rate during tracking was 30 Hz.
Figure 16.
Motion correction of simulated rat motion (2-compartment phantom).
Central transverse slice of the compartment phantom shown for the uncorrected (left), motion-corrected (middle) and motion-free (right) reconstructions. Correction was based on the 8-point marker data. The hot (1.3 MBq.ml−1), cold (0 MBq.ml−1) and background (0.43 MBq.ml−1) compartments of the phantom were clearly visible in the corrected and motion-free reconstructions. The pose sampling rate during tracking was 30 Hz.
Figure 17.
Effect of synchronisation error and pose sampling rate on motion correction.
Examples of motion-corrected hot rod phantom reconstructions obtained with varying degrees of tracker-scanner synchronisation error (top row) and various pose sampling rates (bottom row). Results are shown for a central transverse slice.
Figure 18.
Quantitative performance of PET as a function of synchronisation error and pose sampling rate.
Bias (%) in concentration for the hot cylinder of the 2-compartment phantom as a function of pose sampling rate (top) and synchronisation error (bottom). The simulated pose sampling rates ranged from 0.25 to 48 Hz and the simulated synchronisation error ranged from −2 to 2 s.
Figure 19.
Motion correction applied to an awake rat study.
Orthogonal reconstructed slices for the corrected (top row) and uncorrected (bottom row) study.