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The true activity in the left central region was 25% lower than the left frontal region. The left central region mask was dilated into the left frontal region, this parcellation error resulted in an over-correction (RC > 1) in the central region and under-correction in the frontal region when performing RBV with the erroneous mask. The RC for both regions is reported in table 5.4. The left frontal region RC significantly increases (p < 0.05) from 0.988 to 0.993 with SMPVC. The over-correction in the central region significantly decreases (p < 0.05) from 1.010 to 0.998 when SMPVC is applied.

Significant reductions in CoV_r were observed in both regions after SMPVC compared to RBV (table 5.5). The frontal region exhibited an average 32% reduction in CoV_r (p< 0.05) when SMPVC was performed. A 22% average reduction (p< 0.05) in observed in the central region when using SMPVC compared to RBV. Despite the reduction for the central region, the CoV_r remained 10% higher with SMPVC than the ground truth. A magnified section of a PV-corrected slice on the border between the left frontal and central regions can be seen in figure 5.8. The boundary between the two regions is more clearly defined after SMPVC compared to RBV. Over-correction in the neighbouring WM can also be observed when RBV was performed with the parcellation errors. The WM over-correction is due to under-

5.3. Phantom experiments 139 correction for the frontal region. Therefore, the WM is more accurately corrected in this area with SMPVC, although WM was not analysed in this study.

The DC is reported for both regions in table 5.6. The frontal and central region DC in- creases when SMPVC is applied. These increases were significant (p< 0.05) for both regions. This suggests that the SMPVC improves the accuracy of the segmentation in both regions. A lower DC value was observed in the central region compared to the frontal. This is probably due to the magnitude of the parcellation relative to the size of the region. The parcellation error increase the size of the central region by 18%, whereas the frontal region decreased by 7%.

RBV (error) True SMPVC

Left frontal 0.988 (± 2.63e-03) 0.996 (± 2.82e-03) 0.993 (± 2.76e-03) Left central 1.010 (± 4.81e-03) 0.997 (± 5.36e-03) 0.998 (± 6.60e-03) Table 5.4: The RC (±SD) for PV-correction of the anthropomorphic brain phantom.

RBV (error) True SMPVC

Left frontal 0.025 (± 4.60e-04) 0.018 (± 2.65e-04) 0.019 (± 2.95e-04) Left central 0.028 (± 6.10e-04) 0.021 (± 5.33e-04) 0.023 (± 5.32e-04) Table 5.5: The CoV_r (±SD) for PV-correction of the anthropomorphic brain phantom.

RBV (error) True SMPVC Left frontal 0.965 1.00 0.985 (± 8.41e-04) Left central 0.920 1.00 0.965 (± 1.94e-03)

5.3. Phantom experiments 140

RBV (error) True SMPVC

0

4

Figure 5.8: A magnified section of a transaxial slice after PV-correction of the anthropomor- phic brain phantom. The top row depicts the region mask. The frontal region is shown in green and the central in purple. The bottom row displays the PV-corrected PET data. All PET images are normalised to the cerebellar GM and image intensities are scaled between 0 and 4.

5.3.3 Discussion

SMPVC was evaluated using digital phantom simulations. Two phantoms were created; a geometric phantom and an anthropomorphic brain phantom. The geometric phantom was used during the initial stages of the SMPVC algorithm development to evaluate how the sur- faces evolved over iterations and to assess whether the approach was sensitive to noise. The brain phantom data provided a more realistic test in terms of activity distribution, the size of the surfaces to operate on and anatomical complexity. A typical[11C]PIB uptake for an AD subject was modeled during these experiments.

Parcellation errors were induced in the masks used to perform PVC. A comparison between SMPVC and RBV was carried out, evaluating the performance of both techniques, given the parcellation errors. RBV correction with the true region mask was considered to be the ground truth. RBV correction and SMPVC were performed with the erroneous mask and compared to the ground truth in terms of RC, CoV_r and DC. These phantom studies have shown that the SMPVC algorithm is able to modify and reduce the effects of parcellation errors. Correcting the parcellation with SMPVC resulted in a more accurate PVC compared to RBV when parcellation errors were not accounted for. This improved the quantitative accuracy for both the geometric and anthropomorphic phantom.

In terms of RC for the geometric phantom, there is little difference between the RBV with the mask errors, SMPVC and the ground truth. This suggests that the regional trimmed mean value is fairly insensitive to border errors. However, large parcellation errors relative

5.3. Phantom experiments 141 to the size of the regions were induced, and the errors are reflected in the CoV_r, particularly in region 2. Errors in the RC were observed in the anthropomorphic brain phantom with RBV. The effect of the parcellation error was larger in the central region than the frontal. The inclusion of the ‘hotter’ frontal voxels in the central region created the observed over- correction in the central region as these voxels caused a positive bias in the estimation of the regional mean value. Under-correction is also observed in the frontal region when RBV is performed with the erroneous mask. Both the over- and under-correction of the brain regions are reduced after SMPVC.

Large significant reductions in the CoV_r for both phantoms were observed after SMPVC. In the geometric phantom the most notable reduction in CoV_r was in region 2, as it was subjected to parcellation errors from both regions 1 and 3. Region 2 was also colder than its neighbours, causing a larger error than in the other regions. SMPVC accurately cor- rected the geometric phantom over ten realisations, at two noise levels; 1.0e7counts and with five times fewer counts at 2.0e6_{. The CoV}

r also significantly reduced when SMPVC was ap-

plied to the brain phantom. After SMPVC correction, the average CoV_r values for both brain regions reduced and were comparable to the ground truth. The SD of the CoV_r values with SMPVC is also similar to the ground truth. This suggests SMPVC is reproducible, at least for these phantom datasets. The SMPVC CoV_r values are higher than the ground truth and this is likely to be due to remaining errors in the parcellation.

In addition to the PET-related measures of RC and CoV_r, the DC was also reported for the phantom datasets to evaluate the accuracy of the parcellation. After SMPVC, the DC sig- nificantly increased for all regions in both phantoms. This suggests that the parcellation was more similar to the ground truth than the erroneous parcellation. Given the improvements in RC and CoV_r, this is unsurprising as these would not have occurred had the parcellation been poorer. However, there are still errors in the parcellation, albeit relatively small. SMPVC ap- pears to find the correct boundary, but can define a ragged edge along it. The behaviour can be observed in figure 5.7. This is likely due to noise, although noise did not affect the overall movement of the boundaries in the phantom data.