Statistics and Brain Mapping

The scientiic aim of brain mapping is to investigate which regions of the brain are used when a subject is involved in a particular task, such as cognitive tasks, sensory stimuli, or memory challenges, or how brain function diiers between diierent groups of subjects, such as normals and schizophrenics. A second aim is the study of how brain anatomy diiers between diierent groups of subjects. There are three diierent types of images for measuring brain function: cerebral blood ow (CBF) measured by positron emission tomography (PET) (Raichle, 1994), blood oxygenation level dependent (BOLD) response, measured by functional magnetic resonance imaging (fMRI) (Lange & Zeger, 1997), and neurotransmitter kinetics measured by dynamic PET (Dagher et al., 1998). There are three diierent types of images for measuring changes in shape of brain structures, such as the cortex: binary structure masks (1=inside, 0=outside) from segmented MRI scans; normal displacements of the structure surface; and vector deformations required to warp the structure to an atlas (standard structure). On the surface, this looks like a standard statistical problem of relating dependent variables Y(t) (function, anatomy) to explanatory variables X (tasks, groups). The novelty is that the dependent variables are 3D images with a value at each voxel t 2 S < 3. Usually S is the entire brain or part of it, or, in the case of surface normal displacements, the 2D manifold of the surface of the structure. The most widely used tool is the linear model which is applied separately to each voxel t: Y(t) = X(t) + (t) (Friston et al., 1995). The errors (t) may be correlated for images taken on the same subject, either because of random eeects, or because of temporal correlation, particularly for PET kinetics and fMRI data, where images are aquired every few seconds. This methodology has been found to be suuciently exible to treat image data from all the above six sources; the only slight generalisation required is a multivariate linear model for the three components of the vector deformations data (Cao & Worsley, 1999), logistic regression for binary structure masks (Taylor et al., 1998), and nonlinear models for PET kinetics (Dagher et al., 1998). Lange & Zeger (1997) have developed a more sophisticated model for fMRI data that incorporates spatial as well as temporal information. In most laboratories worldwide, this is done using the SPM (Statistical Parametric Mapping) software package (see Friston et al., 1995). …