# Statistical parametric mapping

Statistical parametric mapping or SPM is a statistical technique created by Karl Friston for examining differences in brain activity recorded during functional neuroimaging experiments using neuroimaging technologies such as fMRI or PET. It may also refer to a specific piece of software created by the Wellcome Department of Imaging Neuroscience (part of University College London) to carry out such analyses.

## The statistical parametric mapping approach

### Unit of measurement

Functional neuroimaging, one type of 'brain scanning', involves the measurement of brain activity. The specific technique used to measure brain activity depends on the imaging technology being used (see fMRI and PET for examples). Regardless of which technology is used, the scanner produces a 'map' of the area being scanned that is represented as voxels. Each voxel typically represents the activity of a particular coordinate in three-dimensional space. The exact size of a voxel will vary depending on the technology used, although fMRI voxels typically represent a volume of 27 mm3 (a cube with 3mm length sides).

### Experimental design

Researchers are often interested in examining brain activity linked to a specific psychological process or processes. An experimental approach to this problem might involve asking the question 'which areas of the brain are significantly more active when a person is doing task A compared to task B?'. Although each task might be designed to be identical, except for the aspect of behaviour under investigation, the brain is still likely to show changes in activity between tasks due to factors other than task differences (as the brain is involved with co-ordinating a whole range of parallel functions unrelated to the experimental task). Furthermore, the signal may contain noise from the imaging process itself.

To accommodate these random effects, and to highlight the areas of activity linked specifically to the process under investigation, statistics are used to look for the most significant difference above and beyond background brain activity. This involves a multi-stage process to prepare the data, and to subsequently analyse it using a statistical method known as the general linear model.

### Image pre-processing

Images from the brain scanner may be pre-processed before any statistical comparison takes place to remove noise or correct for sampling errors.

A study will usually scan a subject several times. To account for the motion of the head between scans, the images will usually be adjusted so each of the voxels in the images corresponds (approximately) to the same site in the brain. This is referred to as realignment or motion correction, see image realignment.

Functional neuroimaging studies usually involve several participants, who will have slightly differently shaped brains. All are likely to have the same gross anatomy, but there will be minor differences in overall brain size, individual variation in topography of the gyri and sulci of the cerebral cortex, and morphological differences in deep structures such as the corpus callosum. To aid comparisons, the 3D image of each brain is transformed so that superficial structures line up, a process known as spatial normalization. Such normalization typically involves not only translation and rotation, but also scaling and nonlinear warping of the brain surface to match a standard template. Standard brain maps such as the Talairach-Tournoux or templates from the Montréal Neurological Institute (MNI) are often used to allow researchers from across the world to compare their results.

Images are often smoothed (similar to the 'blur' effect used in some image-editing software) by which voxels are averaged with their neighbours, typically using a Gaussian filter or by wavelet transformation, to make the data less noisy.

### Statistical comparison

Parametric statistical models are assumed at each voxel, using the general linear model to describe the variability in the data in terms of experimental and confounding effects, and residual variability. Hypotheses expressed in terms of the model parameters are assessed at each voxel with univariate statistics.

Analyses may also be conducted to examine differences over a time series (i.e. correlations between a task variable and brain activity in a certain area) using linear convolution models of how the measured signal is caused by underlying changes in neural activity.

Because many statistical tests are being conducted, adjustments have to be made to control for Type I errors (false positives) potentially caused by the comparison of levels of activity at a large number of voxels. In this case, a Type I error would result in falsely detecting background brain activity as activity related to the task. Adjustments are made, based on the number of resels in the image and the theory of continuous random fields in order to set a new criterion for statistical significance that adjusts for the problem of multiple comparisons.

### Graphical representations

Brain activation from fMRI shown as patch of colour on MRI scan

Differences in measured brain activity can be represented in a number of ways.

Most simply, they can be presented as a table, displaying coordinates that show the most significant differences in activity between tasks. However, differences in brain activity are more often shown as patches of colour on an MRI brain 'slice', with the colours representing the location of voxels that have shown statistically significant differences between conditions. The gradient of color is mapped to statistical values, such as t-values or z-scores. This creates an intuitive and visually appealing means of delineating the relative statistical strength of a given area of activation. Recently, an alternative approach has been suggested, in which the statistical map is combined with the map of the original difference in brain activity (or, more generally speaking, with the original contrast) and colorcodes are attributed to the latter.

Differences in activity may also be represented as a 'glass brain', a representation of three outline views of the brain as if it were transparent. Only the patches of activation are visible as areas of shading. This is useful as a quick means of summarizing the total area of significant change in a given statistical comparison.

## SPM software

SPM is software written by the Wellcome Department of Imaging Neuroscience at University College London to aid in the analysis of functional neuroimaging data. It is written using MATLAB and is distributed as free software.