Vertical capillary tubes of Tc-99m were imaged at various distances from the apertures. Horizontal count profiles were obtained through the mid-level of the capillary tubes. Gaussian curves were fitted to each peak of the count profile by the method of least-squares. The parameters of the fitted curve were used to determine the full-width at half-maximum numerically from the parameters of the fitted curve. This method is much more objective than simply counting pixels beneath peaks. All values were corrected for magnification.
For planar measurements, the effective pixel size varies with source distance and must be corrected for magnification / minification effects. This is done by calculating a “magnification-corrected” pixel size for that distance.
If D is distance from source to aperture and x is the “magnification-corrected” or effective projected pixel size and given that the hardware pixel size is 2.5 mm and the detector to aperture distance in CardiArc is 150 mm, by similar triangles:
Due to parallax effects on effective aperture width, the measured resolution is dependent on the off-axis angle of the source-to-detector ray at each projection:
In SPECT imaging, the net resolution at which a given source is seen is a weighted average of the resolution at all projections. Since the impact each projection has on a reconstructed image is (mostly) dependent on the relative efficiency of that projection for that source. With the pseudo-knife edge slots in CardiArc®, efficiency of detection (A0) of a source at off-axis angle theta is:
Since each source is viewed, in a SPECT acquisition, by 5 apertures simultaneously, it is difficult to predict the net weighted average planar resolution seen over the acquisition. For these planar measurements, an average of measurements obtained with the source directly in front of a slot and a small distance (symmetrically) to either side. Although this procedure underestimates the net resolution seen during a SPECT acquisition (overestimates FWHM), it has the advantage of being more readily measured and more easily understood.
Reconstructed (SPECT) Resolution Measurements
Measurement of reconstructed resolution was made using 2.5 mm thick, ramp-filtered transaxial sections of the same datasets as above. As above, the data represents 256 arc positions over 180°. Since there are 5 projection sets obtained at each arc position (one from each slot), this may be considered to actually represent 5*256 = 1,280 unique angular projection sets. Note that this gives an extraordinary average angular sampling of 180°/1280 = 0.14°.
Both horizontal and vertical (x and y), single-pixel thickness count profiles were drawn through the hottest pixel of two levels for each study. FWHM was determined using the same semi-automated, least-squares curve fitting method described earlier. The x and y-axis values were averaged for each distance.