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for studying brain functions. An MR scanner is a multi-million dollar device which, by subjecting its contents to carefully modulated magnetic fields and recording the resulting radio signal, produces the Fourier transform of the magnetic field spin density for a particular atomic isotope. Then computing the inverse Fourier transform of the digitized signal reveals an image of the (magnetic field spin density of the) contents of the scanner.

Without going into the detailed physics and neurobiology that relate the magnetic field to brain activity, suffice it to say that increased neuronal activity induces an increase in blood flow to the region of activity (to deliver glucose to the neurons). This increased flow results in an increase of oxygenated blood in the small veins that drain the active region because the increased activity does not require much extra oxygen. The more oxygen carried by the hemoglobin in the blood the smaller the magnetic field generated by the iron in the hemoglobin (the oxygen acts as a magnetic shield) and consequently the less interference with the local magnetic field generated by, e.g., hydrogen nuclei (protons). By mid-1991 researchers had demonstrated that MRI can detect the changes in blood oxygenation caused by brain function and consequently the technique is known as fMRI. Among the first studies to use MRI to assess functional neural activity in humans are [1, 2, 3]. The latter two introduced the now common Blood Oxygenation Level Dependent (BOLD) technique just described for characterizing activation in the brain.

There are several important features of fMRI compared to other imaging techniques. First, the signal comes directly from functionally induced changes. Second, it provides both functional and anatomical information. Third the spatial resolution is on the order of 1 or 2 millimeters. Fourth, there is little known risk from fMRI. Finally, the change in signal due to brain activity is quite small (on the order of 1%) and, in particular, smaller than the noise (on the order of 2%). This last feature means that, utilizing current technology, it is necessary to average a large number of images in order to detect the regions of activation.

3 A Typical Experiment

The simplest fMRI experiment entails the performance of two cognitive tasks which differ in some specific detail. A number of images are gathered during each task and averaged within task. The difference between the average images for the two tasks provides information about the location in the brain of the cognitive function represented by the difference of the two tasks.

An actual experiment might proceed as follows. A subject lies in the MRI magnet with a head restraint intended to minimize movement. A set of preliminary anatomical images are studied to determine the location within the brain where the repeated functional images will be taken. The subject practices each of the two tasks for about a minute each, responding to the task, for example, by pushing a button with the right thumb. The subject performs one of the tasks repeatedly while images are recorded and then switches to the other task. In some of our smaller experiments we are recording 100 images for each task. In order to eliminate left-right effects the entire experiment is repeated with the subject using the left thumb to respond. Thus there are a total of 400 images in this simple experiment. It takes the scanner less than 20 minutes to acquire this amount of data.

The acquired images are multi-slice images with, typically, seven slices: each slice is

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