## 4 Quantitative Methods for the Detection of AD
### Stereotactic Surface Projection  
Where SPM is a general tool for the quantitative analysis of neuroimaging studies primarily based on GLM approaches, which are agnostic to the data under investigation, three-dimensional stereotactic surface projection (3D-SSP) is a voxel-driven method that was purpose-built as a fully automated method of quantifying AD pathology from FDG-PET images [93]. Relevant to the detection and diagnosis of AD, 3D_SSP is an engineered method of extracting metabolic information from FDG-PET images that uses _a priori_ knowledge of AD. Using data from known populations of AD and HC patients, 3D-SSP generates diagnostic indices based on Z-scores generated by voxel-wise comparisons. It has since been expanded to be applicable to DSDs in general, including mixed forms of dementia [34]; 3D-SSP is also incorporated as a primary component of the software package Neurostat(r) (Department of Internal Medicine, University of Michigan, Michigan, Ann Arbor, MI, USA), which is available for download online [94]. PET images will first undergo a c series of operations at the level of both the group and the subject prior to analysis. The images are rotated to ensure they are in the correct anatomical orientation and then undergo stereotactic anatomic standardization to a known template space. Regional anatomical differences are minimized by linear scaling and nonlinear warping, and the image is resampled [93]. Voxel values at predetermined locations on the outer and medial surfaces of the cerebral cortex are considered up to a depth of 6-voxels (13.5 mm) along a vector normal to the surface-most voxel. The maximal voxel value along this 6-voxel deep vector is returned as the value at the surface voxel. This set of maximum-valued voxels is then normalized to the thalamus because, it is a known region of relatively preserved metabolism in AD patients. \[activity_{norm}=activity_{measured}/thalamic_{activity}. \tag{6}\]  
The mean and standard deviation of each surface voxel are then computed using a collection of FDG-PET images from HC patients. Using the same procedure, the surface voxels from the AD population are then compared to those of the HC database, and a Z-score is computed  
\[Z_{AD(xy,z)}=\frac{HC_{mean(x,y,z)}-AD_{x,y,z}}{HC_{sd(x,y,z)}} \tag{7}\]  
on a voxel-by-voxel basis. \(\mathrm{e}\ (x,y,z)\) are the stereotactic coordinates of a surface voxel, \(Z_{AD(x,y,z)}\) is the Z-score of a surface voxel of the suspected AD patient, \(HC_{mean(x,y,z)}\) and \(HC_{sd(x,y,z)}\) are the mean and standard deviation of the surface voxel from the collection of HC controls, and \(AD_{x,y,z}\) is the thalamic-normalized value of the surface voxel of the suspected AD patient. An index of Z-scores is then computed for the primary cortical areas affected by AD--the frontal, parietal, and temporal cortices. The locations of these cortices are defined using predetermined stereotactic grid coordinates. \(\Delta Z\)-scores are then computed by comparing Z-scores of the frontal + parietal + temporal cortices to those of the primary sensorimotor cortex,  
\[\Delta Z=Z_{FC/PC/TC}-Z_{SMC} \tag{8}\]  
such that a large difference in Z-score indicates more severe hypometabolism in the region relative to the primary sensorimotor cortex. This is performed bilaterally, where the values from each hemisphere are averaged together, and the subject may be classified as symmetric or asymmetric based on the degree of hypometabolic similarity between cortices [93]. Diagnostic indices are then determined with respect to the HC database by establishing cut-off values for metabolic abnormality based on the \(\Delta Z\)-scores [93]. These may then be visualized on a subject's MR image, an MR template, or a glass brain in a manner like SPM. After indices have been determined through the database, an individual's neuroimaging data may be compared to that of the HC database, and a diagnostic label may be applied by a physician's quantitatively informed impression of statistically significant differences in tracer uptake.