List of Figures

• These registered images which display the three cardinal planes (transverse-top row, sagittal-middle row, coronal-bottom row) from MR (left column) and SPECT (middle column) show the correspondence of HMPAO uptake and rCBF in the preferrential uptake of gray to white matter. The right column shows the SPECT images transparently overlayed on the registered MR images to more clearly show the underlying neuroanatomy of the corresponding SPECT. This patient had a mild right hippocampal atrophy with seizure onset in the left hippocampus. Co-registered MR and interictal SPECT shows hypopefusion in the left hippocampus. The patient had a left selective amygdalo-hippocampectomy.
• A typical pair of unregistered SPECT (top) and MR (bottom) coronal cuts from the same patient. Left is on the viewer's left etc. from the neurological viewing convention (see appendix).
• A cascaded linear system depicting some of the components which degrade the imaging system. The input is a -function or exact point location. The output is a Gaussian spread of possible locations of homologous points.
• An isometric plot of an actual tomographic Gaussian PSRF reconstructed with a ramp filter only.
• Diagram of two point sources on and off the axis of rotation. The net effect of reduced scatter as the off axis source approaches the collimator is a narrower PSRF in the tangential component.
• Lassen's 3-compartment model for Tc-hexamethylpropyleneamine oxime (HMPAO) uptake in the brain. represents the rate of transfer of the lipophillic tracer across the blood-brain-barrier (BBB). represents the rate of change of the lipophillic form into a hydrophillic form. is the reversion of the hydrophillic form to the lipophillic form which is usualy taken to be zero. represents the rate of back diffusion of the tracer into the arterial blood pool.
• A cascaded linear system which accounts human interaction. The input is a -function or exact point location. The output is a Gaussian spread of possible locations of homologous points. Note that a PSRF which includes the interaction of a human operator may also be measured. It is simply the distribution of positions which results when a person is asked to locate the mean in an image of the Gaussian distribution of a point source.
• is the anatomical correspondence error in angular orientation. trueA &trueB denote the direction of the correct angular orientations of the rigid bodies defined by points x &o, respectively. Although the Procrustes statistic from this registration will be zero if the configurations were exactly homologous, a registration error of angle still exists because of the anatomical correspondence error.
• The 6 fiducials were fastened symmetrically on the phantom's cylindrical exterior so that their centroid corresponds to the centroid of the cylinder and at approximately the centroid of the distribution of points from the real scans (at the body of the corpus callosum).
• A transaxial (top), sagittal (middle), and coronal (bottom) cut of the MR (left column) and SPECT (right column) of the Hoffman brain phantom. Note that these are unregistered images. The MR image bears similarities to a segmented MR image of a real brain. It may easily be imagined that the SPECT images shown are simply the corresponding MR images convolved with a 3-dimensional Gaussian blurring kernel. Simulated PET images were produced in this way in the study by Neelin et al .
• The general form of the external fiducials used on the exterior of the brain phantom. The fiducials may be fastened solidly to the phantom with cut-out tape around the flared bases.
• 's variation with r for spheres: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points.
• 's variation with r for spheres: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points.
• 's variation with for shells: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points.
• 's variation with for shells: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points.
• The top plot shows the standard deviation (in degrees) of the rotation error difference between the Simplex fits and the simulation data for different FWHM for spheres (*) and shells (o). The constants k (in degrees/mm) are also given in the bottom plot for different FWHM for spheres (*) and shells (o).
• 's variation with r for spheres: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points. The curve shows a simplex fit to the data for points where .
• 's variation with r for spheres: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points. The curve shows a simplex fit to the data for points where .
• 's variation with for shells: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points. The curve shows a simplex fit to the data for points where .
• 's variation with for shells: 0 = 5 points, + = 15 points, * = 25 points, x = 35 points. The curve shows a simplex fit to the data for points where .
• For the same homology error at and where , from simple geometrical considerations.
• A histogram plot of the frequency distribution of the translation error through x for , 11 bins. These values for were selected to give , the normalized expected distribution of with (see the appendix), so that singularity of the function at the tails of distribution are avoided. The curve is the corresponding Gaussian distribution which has been normalized for the interval size, N, and the calculated .
• The neurological display and viewing orientation convention.