Illustration of the errors HYPR-LR can cause. The original image in this case is uniform (a), but a region of high uptake is revealed in the composite image (b). As a result, the weighting image (c) is inappropriately blurred, creating errors in the HYPR-LR result (d).
[11C]-PIB TACs for regions of the brain from a [11C]-PIB positive human study (a), and the ratio of the activities of neighboring regions at each time point (b). The phases of the tracer’s temporal behavior can be used to form more appropriate temporally dependent composite images for HYPR-LR. (PAR = parietal cortex, FRT = frontal cortex, TMP = temporal cortex, OCC = occipital cortex, WM = white matter, and CER = cerebellum).
Parametric images generated from the noise-free simulated data with either the reference region Logan graphical method (a)–(c) or RPM2 (d)–(f). RPM2 tends to overestimate BPND values in some regions, particularly the white matter. The parametric images generated from the data processed with the proposed method of forming composite images, HYPR-LR-MC (b) and (e), differ little from the parametric images generated from the unprocessed data (a) and (d). The parametric images generated from the data processed using HYPR-LR-FC (c) and (f) show greater contrast between the high uptake regions of cortex and the surrounding white matter. The biased BPND values seen with HYPR-LR-FC are due to changes in the TACs, demonstrated here for a small ROI (g). HYPR-LR-MC eliminates the bias in the TACs.
The relationship between bias and variance for the BPND parametric images generated from the noisy simulated data with the reference region Logan graphical method (a) and RPM2 (b). The mean bias and coefficient of variation of voxels in the frontal and parietal cortices are shown for the parametric images generated from the original data, the data smoothed spatially with 3 × 3 × 3 and 6 × 6 × 6 mm3 FWHM Gaussians, and for the data processed with HYPR-LR-MC and HYPR-LR-FC using smoothing kernels with either a 3 mm FWHM (open shapes), a 6 mm FWHM (half-open shapes), or a 9 mm FWHM Gaussian (solid shapes). The mean bias and coefficient of variation following both spatial smoothing with a 3 mm FWHM Gaussian and HYPR-LR-MC and HYPR-LR-FC processing with a 9 mm FWHM Gaussian kernel are also shown.
An illustrative example of the effects of HYPR-LR processing on parametric images generated from a human [11C]-PIB data set. The unprocessed data are predictably noisy and the Logan image (a) appears biased compared to the RPM2 image (f). HYPR-LR processing with a 9 mm FWHM Gaussian kernel improves the variance of both Logan and RPM2 parametric images (b), (c), (g), and (h). HYPR-LR-MC processing results in parametric images that have more variance, (b) and (g), than when all the frames of the study are used to form the composite, (c) and (h), but they are also likely less biased. Spatial smoothing with a 3 × 3 × 3 mm3 Gaussian results in improved variance with a corresponding loss of spatial resolution, (d) and (i). HYPR-LR processing can also be done following smoothing to provide a further improvement in variance without any additional loss of spatial resolution, demonstrated here with HYPR-LR-MC, (e) and (j).
BPND values obtained from ROIs drawn on the parametric Logan (a) and RPM2 (b) images compared with the BPND values obtained from the TACs of the same ROIs with the reference region Logan graphical method. Each point on the graphs represents the BPND from either the frontal or parietal cortex of one of the eight [11C]-PIB positive scans studied. Linear fits to the BPND values obtained using different types of processing are also shown with their corresponding equations ( – · – = original data, - - - = smoothed, ····· = HYPR-LR-MC, — - = HYPR-LR-FC). A deviation of the slope from unity or a y intercept other than zero indicates the presence of a bias.
Voxel BPND values obtained with the Logan graphical method and RPM2 plotted against each other from a representative [11C]-PIB study. The parametric images generated from the original data (a) are compared with those generated from the data smoothed with a 3 × 3 × 3 mm3 FWHM Gaussian (b), HYPR-LR-MC (c), and HYPR-LR-FC (d). The correlation between the two analysis methods, measured here with the Pearson correlation coefficient (r), gives an indication of the variance present in the parametric images.
A summary of HYPR-LR terminology.
The mean and range of Pearson correlation coefficients obtained from a linear fit to the voxel-by-voxel comparisons of the reference region Logan method and RPM2 for each of the eight human [11C]-PIB datasets studied. The mean correlation coefficient was significantly improved with each of the denoising methods over the original data (*p<0.01). There was no difference between the two implementations of HYPR-LR (p>0.05), but they both increased the mean correlation coefficient more than simple smoothing (+ p<0.01).
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