Computing Brain Change over Time

Glossary Diffeomorphism A smooth (technically differentiable) mapping, such as a spatial transformation, that has a smooth inverse. Jacobian (tensor/matrix and determinant) The matrix of all first-order partial derivatives of a mapping, or the determinant thereof, at a given point. The Jacobian determinant encodes the factor by which the mapping expands or shrinks space. Considering every point in space, the Jacobians form a tensor field. Probabilistic segmentation An image in which each voxel's value indicates the probability that it belongs to a particular region or tissue type. SPM Depending on context, either a statistical parametric map or the Statistical Parametric Mapping software – http:// Statistical parametric map An image in which each voxel is the result of a statistical test on a set of spatially aligned images. Tensor-based morphometry (TBM) Typically refers to SPM-like analysis of Jacobian tensor fields, for example, the Jacobian determinants following spatial normalization, such that the value of each voxel in the reference space equals the equivalent volume of the corresponding voxel in the original (unnormalized) images. Voxel-based morphometry (VBM) Can be seen as a form of tissue-specific TBM. Using serial imaging to compute changes in the brain over time has important applications whenever an inherently longitudinal process is of interest. Such processes encompass growth and development during childhood (Giedd et al. or other disease-related change. Examples of neurological applications include Alzheimer's disease Longitudinal imaging is particularly powerful for the evaluation of response to treatment (Douaud et al., 2013; Fox et al., 2005; Jack et al., 2008); for example, Ridha et al. (2008) reported a fivefold reduction in the number of subjects required to power an AD treatment trial using a measure of brain volume change (the boundary shift integral, discussed in the succeeding text) compared to the change in minimental state examination. Serial MRI has proven capable of measuring preclinical brain change in AD and other dementias and has the potential to power a secondary prevention trial (Andrews et al., 2013). Serial data have major advantages for measuring changes over time compared to multiple cross-sectional samples at different stages, related to both increasing statistical power and reducing confounds (Cook & Ware, 1983). Longitudinal brain imaging data can dramatically improve sensitivity because the interindividual variability is typically much greater than the change over time. To give an example, based on Leung, Barnes, et al. (2010), the coefficient of variation (i.e., the standard deviation as a percentage of …