The goal of statistical inference is to make decisions based on our data, while accounting for uncertainty due to noise in the data. From a broad perspective, statistical inference on fMRI data is no different from traditional data analysis on, say, a response time dataset. Inference for fMRI is challenging, however, because of the massive nature of the datasets and their spatial form. Thus, we need to define precisely what are the features of the images that we want to make inference on, and we have to account for the multiplicity in searching over the brain for an effect.

We begin with a brief review of traditional univariate statistical inference and then discuss the different features in images we can make inference on and finally cover the very important issue of multiple testing.

Basics of statistical inference

We will first briefly review the concepts of classical hypothesis testing, which is the main approach used for statistical inference in fMRI analysis. A null hypothesis H0 is an assertion about a parameter, some feature of the population from which we're sampling. H0 is the default case, typically that of “no effect,” and the alternative hypothesis H1 corresponds to the scientific hypothesis of interest. A test statistic T is a function of the data that summarizes the evidence against the null hypothesis. We write T for the yet-to-be-observed (random valued) test statistic, and t for a particular observed value of T.

Many of the operations that are performed on fMRI data involve transforming images. In this chapter, we provide an overview of the basic image processing operations that are important for many different aspects of fMRI data analysis.

What is an image?

At its most basic, a digital image is a matrix of numbers that correspond to spatial locations. When we view an image, we do so by representing the numbers in the image in terms of gray values (as is common for anatomical MRI images such as in Figure 2.1) or color values (as is common for statistical parametric maps). We generally refer to each element in the image as a “voxel,” which is the three-dimensional analog to a pixel. When we “process” an image, we are generally performing some kind of mathematical operation on the matrix. For example, an operation that makes the image brighter (i.e., whiter) corresponds to increasing the values in the matrix.

In a computer, images are represented as binary data, which means that the representation takes the form of ones and zeros, rather than being represented in a more familiar form such as numbers in plain text or in a spreadsheet. Larger numbers are represented by combining these ones and zeros; a more detailed description of this process is presented in Box 2.1.

Numeric formats. The most important implication of numeric representation is that information can be lost if the representation is not appropriate.

Functional magnetic resonance imaging (fMRI) has, in less than two decades, become the most commonly used method for the study of human brain function. FMRI is a technique that uses magnetic resonance imaging to measure brain activity by measuring changes in the local oxygenation of blood, which in turn reflects the amount of local brain activity. The analysis of fMRI data is exceedingly complex, requiring the use of sophisticated techniques from signal and image processing and statistics in order to go from the raw data to the finished product, which is generally a statistical map showing which brain regions responded to some particular manipulation of mental or perceptual functions. There are now several software packages available for the processing and analysis of fMRI data, several of which are freely available.

The purpose of this book is to provide researchers with a sophisticated understanding of all of the techniques necessary for processing and analysis of fMRI data. The content is organized roughly in line with the standard flow of data processing operations, or processing stream, used in fMRI data analysis. After starting with a general introduction to fMRI, the chapters walk through all the steps that one takes in analyzing an fMRI dataset. We begin with an overview of basic image processing methods, providing an introduction to the kinds of data that are used in fMRI and how they can be transformed and filtered.

Introduction

Just as music recorded in a studio requires mixing and editing before being played on the radio, MRI data from the scanner require a number of preprocessing operations in order to prepare the data for analysis. Some of these operations are meant to detect and repair potential artifacts in the data that may be caused either by the MRI scanner itself or by the person being scanned. Others are meant to prepare the data for later processing stages; for example, we may wish to spatially blur the data to help ensure that the assumptions of later statistical operations are not violated. This chapter provides an overview of the preprocessing operations that are applied to fMRI data prior to the analyses discussed in later chapters. The preprocessing of anatomical data will be discussed in Chapter 4.

In many places, the discussion in this chapter assumes basic knowledge of the mechanics of MRI data acquisition. Readers without a background in MRI physics should consult a textbook on MRI imaging techniques, such as Buxton (2002).

An overview of fMRI preprocessing

Preprocessing of fMRI data varies substantially between different software packages and different laboratories, but there is a standard set of methods to choose from. Figure 3.1 provides an overview of the various operations and the usual order in which they are performed. However, note that none of these preprocessing steps is absolutely necessary in all cases, although we believe that quality control measures are mandatory.

Introduction to pattern classification

The statistical methods discussed in the book so far have had the common feature of trying to best characterize the dataset at hand. For example, when we apply the general linear model to a dataset, we use methods that determine the model parameters that best describe that dataset (where “best” means “with the lowest mean squared difference between the observed and fitted data points”). The field known variously as machine learning, statistical learning, or pattern recognition takes a different approach to modeling data. Instead of finding the model parameters that best characterize the observed data, machine learning methods attempt to find the model parameters that allow the most accurate prediction for new observations. The fact that these are not always the same is one of the most fundamental intuitions that underlies this approach.

The field of machine learning is enormous and continually growing, and we can only skim the surface of these methods in this chapter. At points we will assume that the reader has some familiarity with the basic concepts of machine learning. For readers who want to learn more, there are several good textbooks on machine learning methods, including Alpaydin (2004), Bishop (2006), Duda et al. (2001), and Hastie et al. (2001).

The general linear model is an important tool in many fMRI data analyses. As the Name “general” suggests, this model can be used for many different types of analyses, including correlations, one-sample t-tests, two-sample t-tests, analysis of variance (ANOVA), and analysis of covariance (ANCOVA). This appendix is a review of the GLM and covers parameter estimation, hypothesis testing, and model setup for these various types of analyses.

Some knowledge of matrix algebra is assumed in this section, and for a more detailed explanation of the GLM, it is recommended to read Neter et al. (1996).

Estimating GLM parameters

The GLM relates a single continuous dependent, or response, variable to one or more continuous or categorical independent variables, or predictors. The simplest model is a simple linear regression, which contains a single independent variable. For example, finding the relationship between the dependent variable of mental processing speed and the independent variable, age (Figure A.1). The goal is to create a model that fits the data well and since this appears to be a simple linear relationship between age and processing speed, the model is Y = β0+β1X1, where Y is a vector of length T containing the processing speeds for T subjects, β0 describes where the line crosses the y axis, β1 is the slope of the line and X1 is the vector of length T containing the ages of the subjects.

In the early days of fMRI, image formats were truly a Tower of Babel. Because most data were collected using research pulse sequences, the data were largely reconstructed offline and saved to file formats that varied from center to center. Because most analysis software was also written in-house, this was not a particular problem, so long as one didn't need to share data between centers. As the field developed, several standard file formats came into use, and the use of different formats between centers or laboratories was largely driven by the requirements of different analysis software packages, but until recently there still remained a substantial variety of file formats. Fortunately, the situation has gotten much better in the last decade, with the development and near-universal implementation of a common file format, known as NiFTI. In this appendix, we briefly describe some general issues regarding the storage of fMRI data along with some of the most important file formats.

Data storage

As discussed in Chapter 2, MRI data are usually stored in a binary data file as either 8-or 16-bit integers. The size of the data file on disk will thus be the product of the data size and the dimensions of the image. For example, storing a 16-bit integer image with dimensions of 128 × 128 × 96 will take up 25,165,824 bits (or 3 megabytes).

Whereas the previous chapter focused on analyzing the data from a single run for a single subject, this chapter focuses on how we combine the single subject results to obtain group results and test group hypotheses. The most important consideration of the group fMRI model is that it accounts for the so-called repeated measures aspect of the data, which means that subjects are randomly sampled from a larger population, and multiple fMRI measurements are obtained for each subject. If the proper model is not used, inferences will only apply to the particular subjects in the study, as opposed to the population from which they were sampled. In general, it is important that subjects are treated as random effects in the model, which is known as a mixed effects model. The difference between treating subjects as random versus fixed quantities is discussed in the following section.

The mixed effects model

Motivation

To motivate the need for a mixed effects analysis, we use a simple example from outside of the imaging domain. Instead of measuring brain activity for a subject, imagine that we measure hair length. The goal is to see if there is a difference in the length of hair between men and women and since we clearly cannot measure hair length on all people we randomly sample from the population. Once we know the distributions of hair length for men and women, they can be compared statistically to see if there is a difference.

Summary

Narcolepsy is characterized by excessive daytime sleepiness (EDS), cataplexy, and/or other dissociated manifestations of rapid eye movement (REM) sleep (hypnagogic hallucinations and sleep paralysis).

The major pathophysiology of human narcolepsy has been recently elucidated based on the discovery of narcolepsy genes in animals. Using forward (i.e., positional cloning in canine narcolepsy) and reverse (i.e., mouse gene knock-out) genetics, the genes involved in the pathogenesis of narcolepsy (hypocretin/orexin ligand and its receptor) in animals have been identified. Hypocretins/orexins are novel hypothalamic neuropeptides also involved in various hypothalamic functions such as energy homeostasis and neuroendocrine functions. Mutations in hypocretin-related genes are rare in humans, but hypocretin-ligand deficiency is found in many narcolepsy–cataplexy cases.

After the discovery of sleep-onset REM periods (SOREMs) in narcolepsy, narcolepsy has often been referred as an “REM-sleep disorder.” REM sleep can intrude in active wake or at sleep onset, resulting in cataplexy, sleep paralysis, and hypnagogic hallucinations; these three symptoms are often categorized as “dissociated manifestations of REM sleep.” Although cataplexy and REM-sleep abnormalities are the hallmarks of narcolepsy and these symptoms differentiated narcolepsy from other types of hypersomnia, it is now conceived that impairments of hypocretin neurotransmission cause both the EDS (possibly due to the sleep–wake fragmentation) and REM-sleep abnormalities in narcolepsy; it is impossible to discuss these mechanisms independently.

While sleep paralysis and hypnagogic hallucinations exist in other sleep disorders (such as obstructive sleep apnea) and even in normal subjects, since cataplexy is tightly associated with hypocretin impairments, cataplexy is likely to be pathophysiologically distinct from other dissociated manifestations of REM sleep.

In this review, the clinical and pathophysiological aspects of sleep abnormalities in narcolepsy, with a special focus on those of REM sleep-related symptoms, are discussed.

Summary

The amount, timing, and structure of REM sleep are regulated. Three major determinants in REM sleep regulation have been identified: (1) the circadian pacemaker in the suprachiasmatic nucleus (SCN) of the hypothalamus, which through its outputs generates daily cycles in REM sleep propensity; (2) a homeostatic (i.e., need-based) drive for REM sleep that increases in the absence of REM sleep and decreases during its presence; (3) the inhibition of REM sleep by non-REM (NREM) sleep. In humans, the circadian modulation of REM sleep shows a maximum shortly after the nadir of the circadian rhythm of core body temperature. A sleep-dependent disinhibition of REM sleep (i.e., a gradual increase of REM sleep in the course of a sleep episode that is distinct from a circadian influence) is also evident and attributed primarily to the decrease in NREM sleep intensity. The circadian rhythm and the sleep-dependent disinhibition of REM sleep are the dominant factors influencing the distribution of REM sleep within a sleep episode. In humans that are normally entrained to the 24-hour day, the interaction of these two factors results in maximal REM sleep propensity in the morning, coinciding with habitual wake time. The homeostatic regulation counteracts deviations from a reference level of REM sleep need such that loss of REM sleep results in increased REM sleep propensity. However, rebounds in REM sleep following selective deprivation often remain partial suggesting that the homeostatic drive is relatively weak. On the other hand, recent studies have emphasized that REM sleep can undergo changes in its quality that may compensate for its loss in duration. In the present chapter, the evidence for circadian and homeostatic regulation of REM sleep will be reviewed, the physiological markers that are indicative of such regulation will be presented, and the interdependence of REM sleep and NREM sleep regulation will be examined.

Summary

In the decade immediately following the discovery of REM sleep (Aserinsky and Kleitman, 1953), scientists in the United States and in Europe made a second, striking observation (Jouvet-Mounier et al., 1970; Roffwarg et al., 1966; Valatx et al., 1964). In several mammalian species, including humans, REM sleep amounts were two to three times higher in infancy than in adulthood, and then declined dramatically across development. This basic ontogenetic pattern has now been observed in a wide variety of mammals (Davis et al., 1999; Thurber et al., 2008; Walker and Berger, 1980) and suggests that REM sleep may play a crucial role in brain development. In this chapter, I review the evidence in support of this general hypothesis. I begin with an overview of several landmark events in the ontogenesis of sleep and sleep regulation to provide context to the more function-based discussions that follow. I then discuss the results of several studies that provide indirect or suggestive evidence of a role for REM sleep in general brain maturation. This is followed by a review of findings in the developing visual system that more specifically address a possible role for REM sleep in brain development and plasticity.

Summary

Despite substantial research focusing on the interaction between sleep and cognition, especially memory, the impact of sleep and sleep loss on affective and emotional regulation has comparatively attracted much less attention. This might be surprising considering that nearly all psychiatric and neurological disorders with impaired mood express co-occurring abnormalities of sleep, and that many sleep disorders are accompanied by mood disturbances, thus suggesting an intimate relationship between sleep and emotion. Yet, recent studies evaluating subjective as well as objective measures of mood and affect, combined with insights from clinical observations and neuroimaging research, offer new evidence for the emerging role of sleep in regulating emotional brain function. In this chapter, we review clinical and neuroimaging data that support the existence of such complex interactions between sleep and emotion regulation. We report that (1) sleep disorders are frequently associated with affective symptoms; (2) patients with mood disorders often present with sleep disturbances; (3) sleep deprivation may transitorily alleviate depressive symptoms; (4) dream experiences may be highly emotional; (5) brain regions involved in emotion processing and regulation, such as the limbic (e.g., amygdala, anterior cingulate cortex) and ventromedial prefrontal regions, are strongly activated during REM sleep; (6) subjective mood assessments exhibit a circadian modulation. New data also show that some hypothalamic neuropeptides (hypocretin/orexin) play a dual role in the stabilization of sleep–wake states and on mesolimbic dopamine activity, with significant effects on neural plasticity related to emotional learning, reward processing, and addiction. Together, these seemingly disparate observations converge to indicate a physiological interplay between sleep–wake and emotional brain functions serving the modulation, the preparation, and the optimization of waking behavior.

Summary

Although the basic mechanisms of REM sleep regulation are thought to reside in the brain stem, considerable evidence suggests that the forebrain, including the preoptic area and the adjacent basal forebrain (BF) as well as the hypothalamus, participates in the regulation of REM sleep. In this review we will first discuss findings that support the role of the preoptic area (POA) in REM sleep, with special focus on the ventrolateral preoptic nucleus (VLPO) and the median preoptic nucleus (MnPO). We will then review evidence for a role of the BF in REM sleep regulation and briefly discuss the role of the suprachiasmatic nucleus (SCN) in the circadian pattern of REM sleep. We will conclude with a view that the POA and BF house a continuum of distinct sleep–wake regulatory neurons with descending and ascending projections that interact with neurons in the posterior hypothalamus, brain stem, and cortex to regulate sleep and wakefulness, including REM sleep.

Since early transection studies, basic neural mechanisms responsible for the occurrence of REM sleep have been thought to reside in the pons, wherein the cyclic occurrence of REM sleep has been postulated to be controlled through the interaction between neurons that execute (REM-on) and those that block (REM-off) REM sleep. The ideas about the identity of these neurons have gone through several revisions. The current reciprocal interaction model focuses on cholinergic REM-on and monoaminergic REM-off neurons (Pace-Schott and Hobson, 2002), whereas the flip-flop model (Lu et al., 2006) and a similar model (Sapin et al., 2009) emphasize GABAergic/glutamatergic REM-on neurons in the sublaterodorsal nucleus and GABAergic REM-off neurons in the ventrolateral periaqueductal gray. Despite this focus on the brain stem for executive mechanisms of REM sleep, there is considerable evidence to suggest that the forebrain, in particular the hypothalamus as well as the POA and the adjacent BF, participates in REM sleep regulation. This review will focus on the role of the POA, including the VLPO and MnPO, and the BF in REM sleep regulation. The role of the SCN of the hypothalamus in the circadian pattern of REM sleep is also discussed briefly. According to the common usage, the BF here refers to those ventral forebrain regions that contain magnocellular cholinergic neurons (Semba, 2000).