Statistical Analysis of Functional Magnetic Resonance Imaging Data

Introduction

Human beings have long been interested in how we ourselves work and function. Of particular fascination has been the working of the human brain. Through the ages we have had opportunity to learn about how our brain functions, mostly haphazardly as the result of illness or accident: a Roman gladiator who suffered amnesia after a blow to the skull; an elderly person who had a stroke, lost the use of one side of the body, but gradually recovered much of the original functionality; savants who were unable to speak but were musical or mathematical prodigies. From all of these isolated incidents, together with postmortem dissections of the brains of healthy individuals, scientists were able to build models of how the brain functions, how information is processed, and what specific regions in the brain are responsible for different types of tasks.

It is only relatively recently, however, that technological advances have allowed us to study the function of the human brain – healthy or diseased – in something closer to real time. Neuroimaging techniques such as positron emission tomography (PET), electroencephalography (EEG), magnetoencephalography (MEG), and functional magnetic resonance imaging (fMRI) have brought a wealth of new knowledge and new understanding to cognitive neuroscientists. Statisticians have been an important part of this exciting endeavor.

Consider fMRI as an example. With this imaging modality, the subject is put into a magnetic resonance machine – a large powerful magnet – and is asked to perform some task, for example to tap his or her fingers in a particular pattern, or to do a simple math problem. While the subject is carrying out the task, a complex array of machinery takes images of the brain in action; actually, the neuronal activity itself is not measured, but rather an indirect measure called the blood-oxygenation level dependent, or BOLD, signal, which is related to the oxygen requirements of the brain when it processes information. In general terms, parts of the brain that are responding to a stimulus or performing a cognitive task require more oxygen than those that are not. Hence, the blood that is delivered to different areas of the brain will differ in the ratio of oxygenated to deoxygenated hemoglobin. Oxygenated and deoxygenated hemoglobin, in turn, have different magnetic properties. Functional MRI takes advantage of that difference through the measured BOLD signal.

This is obviously a complicated process, and the data that result in the end are also complicated, in ways that make them interesting and challenging for statistical analysis. Some of the crucial features of fMRI data are: