. "Spatially independent activity patterns in functional MRI data during the Stroop color-naming task." (NAS Colloquium) Neuroimaging of Human Brain Function. Washington, DC: The National Academies Press, 1998.
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Colloquium on Neuroimaging of Human Brain Function
termined amount (e.g., >95%) of the variance in the data. However, because performance-related fMRI changes are only a small part of total signal variance, projecting the data onto orthogonal eigenimages capturing the greatest variance in the data may prove ill-suited for detecting task-related activations. In addition, if these involve activations of numerous voxels simultaneously, analysis methods based solely on voxel-pair relationships may not accurately detect the full spatiotemporal extent of the activations.
A decomposition method suitable for detecting task-related activations should be consistent with fundamental neurophysiological principles regarding the spatial extent of neural activity during the performance of psychomotor tasks. The principle of localization (7) implies that each psychomotor function is performed in a small set of brain areas, different for each function. This is based on a large body of empirical knowledge correlating psychomotor deficits with regions of cerebral damage, for example, the characteristic language deficits seen after damage to Wernicke’s and Broca’s areas.
We assume that an appropriate goal for the decomposition of fMRI data into cognitively and physiologically meaningful components is the determination of separate groups of multifocal anatomical brain areas that are coactivated during the acquisition of the fMRI slices throughout the experimental trial. Artifacts secondary to subtle movements (8), machine noise (9), and cardiac and respiratory pulsations (10), which may make up the bulk of variability in the measured fMRI signals, should have spatial patterns of activity separate from the localization of brain areas involved in task-related activation. Specifically, with such a model, each fMRI scan can be considered the sum of a mean activity level at each time point plus activations (or suppressions) belonging to one or more spatially independent components. Each individual component may be described by a graded spatial distribution or map and an associated time course of activation.
Here we use a recently developed statistical technique, independent component analysis (ICA) (11, 12), to determine the three-dimensional brain topographies and time courses of activations associated with spatially independent components that together sum to the measured fMRI signals recorded during the performance of a Stroop color-naming task. Our results suggest that ICA can be used effectively to isolate the spatiotemporal extent of both consistently and transiently task-related activations from artifacts and other sources of variability that comprise the fMRI signals.
Independent Component Analysis
Separating fMRI data into independent spatial components involves determining three-dimensional brain maps and their associated time courses of activation that together sum to the observed fMRI data. The primary assumption is that the component maps, specified by fixed spatial distributions of values (one for each brain voxel), are spatially independent. This means that, if pk(Ck) specifies the probability distribution of the voxel values Ck in the kth component map, then the joint probability distribution of all N components factorizes:
This is equivalent to saying that voxel values in any one map do not convey any information about the voxel values in any of the other maps. This is a much stronger criterion than merely assuming that map values of voxel pairs from different components are uncorrelated, i.e.,
for all components i≠j,
where M is the number of voxels and Cij is the jth value in the ith component map. This is because Eq. 1 implies that higher order correlations, or polynomial sums of map voxel values, are also zero. For example, for two maps,
for all natural numbers p and q.
With these assumptions, fMRI signals recorded from one or more sessions can be separated by the ICA algorithm of Bell and Sejnowski (11, 12) into a number of independent component maps with unique, associated time courses of activation. Assuming that the data are mixtures of spatially independent components, the algorithm determines an unmixing matrix, W, from which the component maps and time courses of activation can be computed (see Appendix). The matrix of component map values, C, can then be computed by multiplying the observed data by W,
where X is the (row mean-zero) N by M fMRI signal data matrix (N, the number of time points in the trial, and M, the number of brain voxels) obtained by removing the mean signal level from each time point. In matrix notation, this simplifies to:
Noise in the data is not explicitly modeled, but instead is included in one or more of the components. The number of components determined by the algorithm is equal to the number of input time points in the data. Note that although a nonlinear function is used in the determination of W (described in the Appendix). W still provides a linear decomposition of the data.
To determine whether a given component map is influenced by its requirement to be spatially independent of other maps, the data may be reconstructed with one or more of the components removed and the resultant data matrix may be separated again by using the ICA algorithm (see Appendix).
A subject volunteer participated in two 6-min trials of a Stroop color-naming task. Each trial consisted of five 40-sec control blocks alternating with four 40-sec experimental task blocks. A 1.5 T General Electric Signa MRI system was used to monitor brain activity by using blood oxygen level-dependent (BOLD) contrast. Ten 64×64 echo planar, gradient-recalled (TR=2,500 msec, TE=40 msec) axial images (5-mm thick, 1-mm interslice gap) with a 24-cm field of view were collected at 2.5-sec sampling intervals, corresponding to 146 images for each slice.
Stimuli spanning a visual angle of 2° by 3° were presented one at a time by overhead projector onto a screen placed at the base of the magnet. In control blocks, the subject was simply required to covertly name the color of a displayed rectangle (red, blue, or green). During experimental Stroop-task blocks, the subject was required to covertly name the discordant color of the script used to print a color name. For example, if the word “green” was presented in blue script, the subject was to covertly “say” the word “blue” without vocalizing or activating the muscles of articulation.
Voxels corresponding to active brain regions were determined by examining their mean signal values. These were found to have a bimodal probability distribution. The local minimum between the two peaks of a third-order polynomial