4.1 Introduction: Overview and Purpose of fMRI

The 2003 Nobel Prize in Medicine went to Paul Lauterbur and Sir Peter Mansfield for the invention of magnetic resonance imaging (MRI) in the 1970s. Since its invention MRI has rapidly changed the world of medicine; there are currently more than $20{,}000$ MRI scanners in the world and many millions of images are generated by them each year. In the early 1990s, [40], [1] and [28] showed that MRI could be used for the detection of brain function. Because the technique is non-invasive and does not require the injection of dyes or radioactive tracers, functional MRI (fMRI), has opened up opportunities that were never before possible for studying the living human brain in its working state.

One of the primary uses for fMRI is the mapping of brain function onto brain structure. This is done by engaging a subject in a specific motor, sensory, or cognitive task while collecting MR images of the brain. The regions of increased activity are presumed to be those which perform the task. A particular example is given in Fig. 4.1.

Figure 4.1: Brain activity while performing a short term memory task, in a high school athlete with mild traumatic brain injury. This single slice shows only a portion of the activity in the entire brain. Because it was derived by thresholding a test statistic there may be both false positive and false negative pixels. The physical contiguity of the regions of activity suggests that there are not any false positives

Although mapping of function to structure is an important use of fMRI, the possibilities of its application for investigating the dynamics of brain function are many. Researchers have recently begun using fMRI to study brain development in both normal and pathological situations ([15]). The method can also be used to examine the aging brain ([42]), as well as to study the brain under situations of learning ([41]) and injury ([35]).

Scientific fields other than psychology and neuroscience are also developing an interest in fMRI research. For example, pharmaceutical applications may use fMRI to investigate the brain before and after the administration of a drug, and geneticists may be interested in how the expression of similar or different genotypes may alter brain functioning in one individual versus another.

As the field of fMRI grows, the problems that it presents for statisticians and other quantitative scientists are also growing. There are several reviews of fMRI work in the statistical literature; see, e.g., [9], [29] and [31]. While collecting the data from subjects has become easier, the data sets are usually very large ( $100\,$MB or more) and are especially variable, containing both systematic and random noise. Storage, processing, and analysis of fMRI data are complicated, and the computational problems are legion. In this chapter a brief background of fMRI is first given from a physics and psychology point of view. A full description of the fMRI data as well as the challenges that it presents from a computational statistics viewpoint are then discussed in detail.