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Functional Magnetic Resonance Imaging

Abstract and Keywords

Functional magnetic resonance imaging (fMRI) is the most frequently used functional neuroimaging method and the one that accounts for most of the neuroimaging literature. It measures the blood oxygen level-dependent (BOLD) signal in different parts of the brain during rest and during task-induced activation of functional networks mediating basic and higher functions. A basic understanding of the various instruments and techniques of recording the hemodynamic responses of different brain regions and the manner in which we establish activation and connectivity patterns out of these responses is necessary for an appreciation of the contemporary functional neuroimaging literature. To facilitate such an understanding is the purpose of this chapter.

Keywords: MRI, fMRI, BOLD, preprocessing, experimental design, connectivity

Physiological Processes Underlying the fMRI Signal

There are three indicators of brain activation: neuronal signaling, metabolism and enhanced blood flow supplying oxygen and glucose to the activated regions. The rate of metabolism varies from one tissue type to another as does the rate of signaling. It also varies within a given tissue sample, depending on workload. Since the main type of work neurons perform is signaling, we may infer that the rate of signaling is closely related with the rate of metabolism. Although there is little doubt that such a relationship exists (e.g., Logothetis, 2008), its precise nature is not completely understood.

The functional magnetic resonance imaging (fMRI) signal depends on the fact that activated neurons—that is, neurons that are signaling and metabolizing oxygen at enhanced rates—are supplied with more oxygenated blood and that increased activity leads to increased local demands for delivery of oxygen. Consequently, the amount of oxygenated blood, abundant with oxyhemoglobin, delivered to a brain region increases with its increased metabolic demand. The nature of the relationship between oxygen supply and oxygen consumption is complex, most likely not linear, and it only holds within a certain range. In fact, it has been shown that, under certain conditions, blood flow rates and metabolic rates are dissociated, a phenomenon called neurovascular decoupling. Despite this decoupling, it has been suggested that oxygen consumption is predominantly neuronal (Pellerin & Magistrettti, 1994). Recent evidence suggests that the complexity of activity-induced blood flow increases may be largely modulated by neurotransmitters such as glutamate, rather than simply by the amount of energy consumed (Attwell et al., 2010).

It is nevertheless generally believed that the fMRI signals, whether increasing or decreasing in (p. 44) intensity, reflect regional neural activity (Shmuel, Augath, Oeltermann, & Logothetis, 2006). However, there are indications that the fMRI signal may not always reflect function-specific activation, and it may not always differentiate between excitatory and inhibitory activity (Logothetis, 2008).

The order of events that leads to the emergence of the fMRI signal is as follows. As soon as a particular tissue sample (set of neurons) engages in increased signaling, its metabolic rate will increase, resulting in increased oxygen consumption. This is associated with regional alterations of the oxyhemoglobin to deoxyhemoglobin ratio, resulting in relatively lower amounts of oxyhemoglobin as compared to deoxyhemoglobin in the activated area. The vascular system responds to local oxygen demands 1–2 seconds following neuronal activation, resulting in an oversupply of oxygenated blood to that group of firing neurons that peaks 4–6 seconds later, providing relative excessive amounts of oxyhemoglobin in the tissue sample compared to deoxyhemoglobin. Continuous neuronal signaling causes a sustained plateau in the local supply of oxygenated blood and, when signaling stops, the supply usually falls below the original baseline. It is worth noting that the specificity of this vascular response (i.e., whether it is directed to the neuronal sample activated or extends over a larger area to encompass neighboring tissue samples that are not activated), is not known.

The fMRI signal value is relative and not absolute, which may create problems in the interpretation of fMRI images (see especially Chapter 9). However, progress is continuously made toward the attainment of quantitative fMRI measures; until these become available, estimates of regional cerebral activation must rely on the subtraction procedure (discussed later).

Two further points should be mentioned in this connection: first, unlike the magnetoencephalography (MEG) signal that reflects neuronal activity at the time it happens, the fMRI signal reveals activation patterns with a 4- to 6-second delay. This is taken into account during the analysis stage of the data. Second, the typical temporal resolution of fMR images is in the order of 1–2 seconds; therefore fMRI is not well suited for imaging rapidly changing patterns of activity. However, the popularity of the method stems from the fact that it offers excellent spatial resolution and, unlike MEG, permits identification of several simultaneously activated cortical and subcortical regions.

MRI Principles and Instrumentation

Water, which dominates the composition of biological tissues, consists of hydrogen and oxygen with two hydrogen atoms bonded to a single oxygen atom in every molecule. Consequently, hydrogen is the most readily available element in biological tissues.

Atoms consist of a nucleus, which is surrounded by negatively charged electrons. Nuclei contain a mix of positively charged protons and neutrons. The hydrogen nucleus is the simplest stable nucleus in that it contains a single proton and no neutrons. Protons naturally spin around their axis, which has a random orientation relative to other protons (Figure 3.1). Spins are important for the MRI signal, as will be explained later. When biological tissue, such as brain tissue, is placed in a strong magnetic field like that produced by an MRI scanner, the relative orientation of the proton spin changes (see Figure 3.2). Protons in a magnetic field can adopt two possible energy states, parallel to the magnetic field B0 (ground state or spin-up) or antiparallel to B0 (high energy or spin-down). Ground state is associated with lower energy requirements, and therefore slightly more protons align with B0 in a parallel manner and fewer in an antiparallel manner (see Figure 3.2).

Moving charges such as protons create magnetic fields at right angles to the direction of their motion. Protons therefore behave like tiny magnets, and their axes of spin indicate their magnetic “north” and “south” poles. While in a static magnetic field, such as that produced by the scanner B0, protons are unable to completely align with the magnetic field and so they precess about their axis at a characteristic frequency known as the Larmor frequency (Figure 3.3).

The Larmor frequency of precession of all protons is expressed by the equation ω0=γΒ0,

with ω0 being the frequency in revolutions per second, B0 the strength of the static magnetic field, and γ a constant (the gyromagnetic ratio) specific to each element. Hydrogen protons have a gyromagnetic ratio of 42.6 MHz per Tesla. In an MRI scanner with strength of 1.5 Tesla (15,000 Gauss), protons revolve 639,000,000 times per second or have a precession frequency of 63.9 MHz. At 3 Tesla, this doubles to 127.7 MHz.

Protons do not typically precess in phase (i.e. they are not all at the same point of the precessing cycle at any given moment in time). The magnetization (p. 45) vector of each proton—that is, its magnetic strength in a particular direction—comprises two components: a longitudinal component parallel to the static field B0, and a transverse component, at right angles to the longitudinal (Figure 3.4).

Functional Magnetic Resonance Imaging

Figure 3.1 Hydrogen protons anywhere in the brain spin around axes with different orientation.

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Figure 3.2 In a magnetic field B0, like the one produced by the magnetic resonance imaging (MRI) scanner, the axes of spin of protons tend to align with the magnetic field, with most of them pointing in approximately the same direction (parallel) and some in the opposite direction (antiparallel).

The net magnetization of all protons in a given tissue sample is important for the MRI signal and can be expressed as the sum of all their transverse and longitudinal components. Out-of-phase protons have a net transverse magnetization of zero because the randomly directed signals cancel each other out. However, there are more parallel (ground state) than antiparallel (high energy) components, so the sum of the longitudinal components is not zero and adds up to a net longitudinal magnetization of a specific strength. Any sample of protons anywhere in the brain, placed in an MRI scanner with a static magnetic field B0, will have a net magnetization only along the direction of the static magnetic field. The strength of the net magnetization is determined by the number of parallel minus the number of antiparallel protons, as shown in Figure 3.5. (p. 46)

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Figure 3.3 Protons align with a magnetic field but move around the field axis in a motion called precession.

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Figure 3.4 The magnetic field of protons, whether parallel (left) or antiparallel (right), consists of a transverse and a longitudinal component.

To create a recordable MR signal, we utilize transmitter coils at 90 degrees to B0, which deliver an electromagnetic pulse resulting in an additional magnetic field B1 (figure 3.6). The additional field B1 is not static (like B0) but pulsates at a high frequency (radio frequency [RF]). For reasons that will become apparent later, this additional field B1 pulsates at the Larmor frequency, which for hydrogen protons in a 1.5 Tesla MR scanner is 63.9 MHz.

The RF pulse affects the spinning and precessing protons by adding energy to them such that parallel (ground state) protons jump to the antiparallel (high energy) state and begin to spin and precess in the antiparallel direction, with resulting overall reduction in longitudinal magnetization. Additionally, since the RF pulse is delivered at the same frequency as that of the precessing protons, it tends to force them to precess in phase, as shown in Figure 3.7.

This ultimately results in equal numbers of protons at each energy state, which in turn results in changes in net magnetization. Net longitudinal magnetization becomes zero (since there is an equal proportion of parallel and antiparallel spinning protons), and transverse magnetization acquires strength proportional to the number of protons precessing in phase. When the RF stops, this temporary organization ceases, and the protons return to their previous state. Essentially, longitudinal magnetization is dependent on the difference between the number of protons in parallel and antiparallel states, and transverse magnetization is dependent on the number of protons getting to precess in phase. (p. 47)

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Figure 3.5 The sum of the transverse magnetization component is zero, and the sum of the longitudinal components is some positive value.

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Figure 3.6 The relation of the radio frequency (RF) pulse to the constant field B0.

Some protons lose the additional energy they acquired from the RF pulse and, with more of them becoming parallel than antiparallel, they recover the overall longitudinal magnetization. Protons also fall out of phase, with resulting loss of their transverse magnetization component. These two processes (loss of energy and dephasing) are independent of each other in that they are affected differently by different environmental factors. Thus, the rate of recovery of the longitudinal magnetization and the rate of loss of the transverse magnetization are different. Most relevant for fMR imaging is the fate of the transverse component because it is recorded as an electromagnetic signal. A receiver coil is used to record the signal from the transverse field (Figure 3.8), and, in some instances, the same coil may act both as receiver and as the transmitter of the RF pulse.

The strength of the magnetic field B0 created by the scanner differs by small amounts from one point in space to another. This is known as inhomogeneity of the Β0 field. Because precession frequency ω0 depends on the strength of the magnetic field Β0, these differences in the magnetic field will cause differential proton dephasing. The decay of the transverse component and the consequent reduction of the strength of the signal is called free induction decay (see Figure 3.9), and it is described by the T2 time constant. Although T2 decay is a time constant, the actual decay of the signal is typically faster than that due to phase incoherence influenced by factors such as heterogeneity of the local magnetic field (p. 48) due to artifacts and adjacent structures, in particular the presence of ferromagnetic, diamagnetic, and paramagnetic substances. The measured T2 decay constant is called T2*, which describes the signal decay due to spin interactions, field inhomogeneities, and susceptibility effects. The relationship of T2 to T2* is 1/T2*=1/T2+1/T2inhomogeneity, where T2 is the intrinsic T2 decay constant of the substance and T2inhomogeneity is the decay constant as influenced by field heterogeneities.

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Figure 3.7 The radio frequency (RF) pulse brings all protons in phase and results in maximum transverse magnetization.

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Figure 3.8 The transverse magnetization component (right) results in a “resonant” magnetic signal (left).

The loss of transverse magnetization due to free induction decay can be reversed, and the lost signal can be in part recovered with a new delivery of the RF pulse. However, tissue-specific factors also contribute to signal loss, and their effect is not entirely reversible and cannot be corrected by the reapplication (echo) of the RF. Furthermore, the magnitude of this effect varies from one tissue sample to the next, with some tissues producing bigger and some producing smaller differences between the original and the echo signal intensities. It is on this basis that the tissues can be imaged. This is why some tissues will appear brighter and some darker in an MR image.

This effect is called transverse relaxation, and the rate at which transverse relaxation occurs is called T2 and is measured by the amount of time (in milliseconds) required for the transverse magnetization to be reduced to 37% of its original intensity (the intensity after the first RF pulse application; see Figure 3.10). This reduction depends on the local magnetic field, which is influenced by tissue type (p. 49) and can vary from 50 to 500 ms in different tissues. If the RF pulses are applied at a sufficiently long time interval (also called echo time or TE; see Figure 3.10), the intensity of the signal recorded will vary in different tissue types.

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Figure 3.9 Free induction decay of the resonant signal and its recovery following repeated activation of the radio frequency (RF) pulse.

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Figure 3.10 Reapplication of the radio frequency (RF) pulse leads to partial recovery of the resonant signal or of the phenomenon of transverse relaxation.

As mentioned earlier, the rate at which the transverse magnetization decays (T2*) is dependent on several factors, including the magnetic susceptibility of surrounding tissues. An example of this phenomenon, and one which is the basis of the fMRI signal, is associated with changes in blood oxygenation during neural activity and, more specifically, alterations in the relative concentration of deoxygenated and oxygenated blood. The oversupply of oxygenated blood that replenishes active neurons after neurophysiological activity has transpired is transported in the form of oxyhemoglobin. In contrast to deoxyhemoglobin, which is paramagnetic and thus locally strengthens the magnetic field, oxyhemoglobin is diamagnetic and therefore locally weakens the magnetic field. This increase in the ratio of oxyhemoglobin to deoxyhemoglobin results in a net decrease in the magnetic susceptibility of the region, which in turn results in an enhanced MR signal.

At sufficiently long TE intervals, the intensity of the recorded signal will differ depending on how much oxyhemoglobin (as compared to deoxyhemoglobin) is present in the same tissue sample from one moment to next. Using a specific TE interval, a stronger signal will be produced when a particular tissue sample contains more oxygen and a weaker one when it contains (p. 50) less. Signal intensities can be transformed into visual representations (e.g., shades of gray or different hues), and in this manner, we obtain fMRI images that are based on the blood oxygen level dependent (BOLD) signal.

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Figure 3.11 When the static magnetic field B0 is graded along all the three dimensions (x,y,z), it has a slightly different value in each part of the space inside the magnet (voxel), represented here by cubes of different shades of gray. Consequently, resonant signals originating in the different voxels will have different characteristic frequencies.

The final issue to address involves MR signal localization; in other words, how we can tell where in the brain the MR signal is coming from. We already explained that the strength of the magnetic field B0 is not uniform throughout (inhomogeneous) but that it has different values at each point in space (Figure 3.11). Any two resonant signals arriving at the receiver coils simultaneously from two unknown spots within the inhomogeneous magnetic field B0, will have different frequency, whether they are of equal or different intensity, because the strength of the magnetic field B0 differs from one point in space to another (i.e., the field is graded), and frequency depends on the local values of B0. Because we know in advance the precise value of field B0 at each point of space in the scanner, and we know precisely the position of the head with respect to that space, the exact frequency of the resonant signal we record provides the localization information we need.

Overview of the Derivation of Activation Patterns

The signals arriving at the receiver coil, as described earlier, can be assembled in a three-dimensional (3D) matrix of intensity values representing the relative content of tissue oxygen and, by inference, the relative activation in the brain at a given time. The signal intensity value in a voxel (a 3D volume element) is influenced by the interaction of the resonant signal and the characteristics of the recording apparatus. A voxel represents a specific part of the brain or surrounding tissue, with typical voxels representing around 3 × 3 × 4 mm3 samples of tissue, although this varies considerably from scanner to scanner.

Processing of fMRI images to detect activated regions on the basis of such distributions of signal intensities is a more certain operation than that based on MEG signals. In the case of fMRI, we do not have to deal with the “inverse problem.” That is, we do not have to estimate the probable position of any particular activated sample of brain tissue. Because of the superior spatial resolution inherent to fMRI, we know precisely where the sample is located and therefore where the signal is coming from. Each voxel position is uniquely coded by the (p. 51) precise value of the frequency of the signals that originate in it. It is worth noting that, despite the superior spatial resolution offered by fMRI over other methods, a voxel still represents activity over many thousands of neurons.

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Figure 3.12 A schematic representation of the process of co-registration of relatively low-resolution functional images to high-resolution structural images.

Statistical analyses of fMRI images to establish activated areas are usually preceded by a series of preprocessing steps that are designed to deal with artifacts inherent to the process. One such artifact is created by movement. fMRI experiments can last from a few minutes up to an hour (longer experiments include intervals of rest), so even the most compliant volunteers will move their head by a small amount while scanning is taking place. Another challenge involves separating signals due to activation of tissue from those coming from blood vessels that appear as activated tissue. Still another is to decide on how to determine episodes of activation as opposed to local background fluctuations in oxygenated blood supply. Typically, an fMRI whole-brain volume takes 2 seconds to scan, so fMRI signals are integrated over a time period of 2 seconds. Brief surges of activation, unless they are exceedingly intense, may not be distinguishable from the background activation level because the resonant signals associated with them are integrated with those of baseline activation. Thus, brief events of interest, which could be recorded by techniques that offer higher temporal resolution, such as MEG, may not be detected by fMRI. All these challenges that affect the fidelity of the fMR images must be overcome if an accurate activation pattern is to be detected.

There are various computer algorithms designed to aid the removal of artifacts from fMRI datasets. Once these artifacts have been removed, the fMRI images are subjected to statistical analyses, which most frequently utilize the generalized linear model to perform regressions, and the results are then statistically thresholded. These analyses are performed on the level of voxels, which is why they are usually referred to as voxel-based analyses. fMRI image analysis results in a set of pictures of relative concentration of oxyhemoglobin of the different brain regions and, by inference, the relative degree of activation (i.e., neuronal signaling) within those regions.

fMRI images do not provide a clear indication as to which anatomical structures are activated, so in order to obtain this information, it is necessary to either (a) superimpose them onto the corresponding structural images of the brain (Figure 3.12), as in the case of MEG, or (b) transform these images into a standard space (such as the one defined by Talairach & Tournoux, 1988) and then refer to a corresponding stereotactic anatomical atlas to identify the various activated structures. Further discussion on the image analysis processes that must be applied to fMR images after acquisition to obtain a reliable activation pattern follows in the later analysis section.

Designing an fMRI Experiment

The planning of an fMRI study is of crucial importance because our understanding of any observed changes in brain activity depends to a great extent on how well the design helps narrow down the possible interpretations. There are two main issues to consider when planning an fMRI experiment: (1) experimental design and stimulus presentation and (2) image analysis procedures (see Amaro & Barker, 2006, for a review). A basic requirement in planning a functional imaging study is subtraction of images representing the level of regional brain activity during a control condition from images of activation during an experimental (p. 52) task condition, or two activation images representing activation during any two experimental tasks. This is necessary because, as previously mentioned, on the basis of the BOLD signal, it is impossible to estimate the absolute amount of activation of each brain area. Moreover, in view of the fact that a number of brain areas are activated during any two scanning conditions, the activation pattern representing the difference between any two tasks can be discerned in the image of the residual activation following subtraction. The rationale and the utility of the subtraction procedure is illustrated by an example presented in Figure 3.13, where the purpose of the experiment is to isolate the activation pattern specific to semantic processing of words. Both conditions involve presentation of verbal material. The first involves presentation of words that automatically trigger acoustic, phonological, and semantic processing. The second involves presentation of pseudowords that can only trigger acoustic and phonological processing. Therefore the set of brain regions that are activated in both conditions is eliminated in the subtraction, revealing only those activated regions that mediate semantic processing.

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Figure 3.13 The logic behind cognitive subtraction: both words and pseudowords involve acoustic and phonological processing. When we subtract the activation maps produced by pseudowords from those produced by words, then we are left with activation maps for areas responsible for lexical/semantic processing. (The activation images do not represent actual data.).

One of the main shortcomings of the subtraction method is known as pure insertion or pure deletion (Friston et al., 1996). In the example illustrated in Figure 3.13, the word and pseudoword processing conditions have two functions in common, but word recognition also requires the lexical/semantic processing function. The pure insertion assumption is that this extra function does not influence the operation of the other two functions common to both conditions. Yet this assumption is not always valid because it is possible that the extra function may interact and alter the other two (phonological and acoustic) that are common to both tasks (Jenings, McIntosh, Kapur, Tulving, & Houle, 1997). This potential interaction among functions reduces the interpretability of the images resulting from the subtraction procedure.

A number of alternative procedures that try to circumvent the problem of pure insertion have been proposed. Cognitive conjunction, put forward by Friston (1997), is one such procedure. It requires the identification of two or more conditions that share the cognitive function of interest. Then, unlike the subtraction procedure that is meant to reveal the difference between conditions, it identifies areas of activation that are common to the condition compared.

In designing an fMRI study, one has to decide the order in which the stimuli will be presented. As shown in Figure 3.14, one possibility is to present stimuli belonging to condition A one after the other in succession (e.g., words), alternating with other blocks where stimuli of a different condition B are presented (e.g., pseudowords). This is known as a block design, and it dominated the first years of fMRI experimentation. The second option is to use an event-related design, in which different stimuli belonging to different conditions are intermingled. The analysis can then recover the response to each stimulus (Figure 3.14). (p. 53)

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Figure 3.14 In a block design, similar stimuli are grouped together. In an event-related design, different stimuli are intermingled and are separated out in the analysis.

The main advantage of the block design lies in its increased statistical power (Friston, Zarahn, Josephs, Henson, & Dale, 1999), which in practical terms means that, with a block design, small differences may be more readily detected. Yet, event-related designs are better suited for detecting brief changes in the hemodynamic response, thus improving temporal resolution (Josephs, Turner, & Friston, 1997). Moreover, in their context, it is possible to retrieve responses to individual trials, thus permitting correlations between individual behavioral responses and neuronal activation.

The choice of a design is largely determined by the type of question one is intending to answer. Event-related designs are the only choice for some questions; for example, for events that do not occur on demand, such as the tip-of-the-tongue phenomenon (Maril, Wagner, & Schacter, 2001; Shafto, Stamatakis, Tam, & Tyler, 2010), hallucinations, or unexpected and infrequent events such as those in an oddball paradigm (e.g., Kirino, Belger, Goldman-Rakic, & McCarthy, 2000).

Analysis of fMR Images

Thus far, a general overview of the processing of fMR images has been presented. In this section, we provide a more detailed description of the processing steps and statistical modeling required to produce activation maps like those seen in Figure 3.12. There are various software packages (e.g., SPM, AFNI, Brain Voyager, FSL) that will do this processing, but they involve slightly different versions of the required processes. However, they all attempt to address the same issues: first, volunteers move during scanning, and too much movement can render the fMR images collected unusable. Second, group statistics and group comparisons of fMR data require images from all volunteers to be in the same reference space. Third, fMR images are noisy; therefore, some kind of spatial smoothing is required before analysis to improve the signal-to-noise ratio. There is great variability in what the fMRI community considers appropriate preprocessing of fMR images, so the steps described here represent one approach to preprocessing. To preprocess fMR images, one may adopt many different yet equally valid approaches.

fMRI scanning sessions may last from a few minutes to over an hour (although the latter is rare) and involve the collection of multiple fMR images (usually one every 2 seconds). During this time, it is unlikely that volunteers will stay completely still, and in order to carry out statistical comparisons on the images collected, corresponding voxels from image to image should represent the same brain tissue sample; otherwise, one part of the brain may be compared to a different part of the brain, in which case activation findings would be incorrect. To correct for movement that occurred during fMRI data acquisition, we carry out within-subject realignment (p. 54) or movement correction (see Figure 3.15). Many scanners can do this online, but processing the images independently after acquisition usually offers better results. Movement correction involves realigning all scans to the first scan acquired (or to the mean of all scans acquired) using linear transformations (translations and rotations, in x, y, and z directions; see, for example, Friston et al., 1996). Successful realignment results in a series of images that are in the same subject-specific space, such that a voxel with coordinates x,y,z represents the same tissue sample in all the images.

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Figure 3.15 Typical movement parameters (as calculated by the movement correction algorithm) from a 5-minute functional magnetic resonance imaging (fMRI) scan. X axis shows scan number.

Within-subject realignment may be followed by spatial normalization. fMRI experiments normally involve scanning more than one volunteers using the same set of stimuli and producing a group result for the experimental question asked, utilizing intersubject averaging. To facilitate intersubject averaging, all volunteers’ scans need to be in the same space, and the process that does exactly that is called spatial normalization. The reference space is an approximation of the space described in the atlas of Talairach and Tournoux (1988). Spatial normalization involves warping images that have already been corrected for movement into the space defined by a template image, and it generally works by minimizing the sum of squares of differences between the image that is to be normalized and the template image. Although here the usual approach to solving the spatial normalization problem is described, various other approaches exist (Ashburner & Friston, 1997; 1999; Ashburner, Andersson, & Friston, 2000). Successful spatial normalization is important if the aim of a study is to extrapolate findings to the population as a whole. There are instances (e.g., patient scans) where the presence of gross focal lesions on the fMR images has a detrimental effect on the process of spatial normalization. If indeed fMR images cannot be correctly spatially normalized, it is best if further processing (i.e., statistical modeling) is done in the individual’s native space (i.e., the space in which the image was acquired). Even in cases where spatial normalization is not possible, correction for movement still needs to be carried out before statistical analysis.

Spatial smoothing is the last preprocessing step and is used to render fMRI data more normally distributed but also to increase the signal-to-noise ratio and to account for variability in anatomy that is not fully compensated for by spatial normalization. Smoothing involves the use of a stationary Gaussian filter, the size of which is determined by the size of the brain region in which we expect to find activation (Worsley, Marrett, Neelin, & Evans, 1996).

Once the images have been preprocessed, the data for each subject are frequently modeled using a voxel-wise general linear model Y=Xβ+εY=Xβ+ε (Friston et al., 1995). In this equation, Y represents the observed fMRI time course from a single voxel and X is the predictor variable. It codes the conditions of interest and is referred to as the design matrix. β is the parameter estimate and quantifies how much each predictor contributes to the observed data. Finally, ε is the error term that represents variance not explained by the model. Effectively, ε represents the mismatch between the observed data and the described model.

The general linear model equation given here contains only one predictor, X, but real-life models will contain as many predictors as stimulus types used in the experiment. These are frequently generated by convolving stimulus onset times with a (p. 55) canonical hemodynamic response function that describes the signal changes in time (Friston, Jezzard, & Turner, 1994). The convolution with canonical hemodynamic response function is used to model the nature of the response signal recorded with fMRI. As postulated earlier, the hemodynamic response rises to a peak over 4–6 seconds after neuronal activity, before falling back to baseline, and it may undershoot slightly (see Figure 3.16). The statistical model constructed may also include regressors modeling the amount of movement calculated during the movement correction stage, to reduce the probability of false positives occurring because of residual movement-related artifacts. Finally, because the MRI scanner produces low-frequency noise, fMRI data is almost always high-pass filtered during or just before statistical models are built.

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Figure 3.16 The canonical hemodynamic response function.

Statistical comparisons between regressors make up contrasts (see subtraction procedure described earlier) showing areas that are activated by one type of experimental stimulus over and above those activated by another stimulus type. To assess group significance, one-sample t-tests are frequently used to bring together contrasts from all participants. Because the brain is represented by a multitude of voxels in an fMR image, and the statistical analysis we described here is carried out on a voxel-by-voxel basis, the results are normally corrected for multiple comparisons, and the activation maps (such as those shown in Figure 3.14) are normally reported at a significance level of p < 0.05.

Functional Connectivity

Conventional subtractive analyses of fMRI data as just described show brain regions that activate over and above the rest of the brain during the performance of a specific task. Although this is an excellent approach for localizing and identifying regions that activate in response to specific stimuli and tasks, it does not tells us how these regions interact to execute the task. Since goal-directed behavior and cognition are facilitated by cascades of neural events, subtractive fMRI analysis alone does not seem adequate to describe brain function. As well as knowing which regions are involved in a task, it is also important to know the manner in which these regions interact in order to establish a more complete understanding of how the brain works. It can be argued that an analysis restricted to regional effects alone is impoverished and insensitive compared to the analysis of distributed brain networks (Rowe, 2010).

Functional connectivity analyses are attempts to provide some insight into these interactions by exploring time-dependent changes in the coupling or decoupling of remote brain areas to study integration in the brain in the context of changing task conditions in a dynamic manner (see Friston et al., 1997). With this type of analysis, we ask whether activity in one area, in the context of a specific task, can predict activity in other areas (see Figure 3.17), and we thus investigate interactions between different cortical regions with respect to a specific cognitive function. (p. 56)

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Figure 3.17 Functional connectivity analysis: A time series is extracted from an area such as the left inferior frontal gyrus (LIFG), and the question we ask is whether other brain areas become coupled with it during the execution of a task.

This kind of analysis is open-ended and allows the experimenter to examine the interaction between a region and the rest of the brain. However, this type of analysis does not provide any information on causality or directionality of the interaction between regions. More sophisticated methods, such as dynamic causal modeling (DCM), may address such issues more efficiently. In its simplest form, DCM requires the experimenter to determine a priori a set of regions that constitute a functional network and to determine a set of connections between these regions that can then be tested for goodness of fit to the model (Friston, 2009). Competing hypotheses can be tested in this manner, and the best fitting model can be established.

Kumar et al. (2007) used DCM to test alternative models in an effort to establish the exact nature of auditory object processing and concluded that the most likely architecture is that represented by a serial model. Having tested various alternatives, their analyses provided support for a processing model implemented in a serial fashion with connections from Heschl’s gyrus to planum temporale and then to superior temporal sulcus. The danger with this type of analysis is that if the models under consideration are not well-characterized and comprehensive (i.e., they include misspecified regional activity), then one is less likely to infer that a true connection is present (Lee, Friston, & Horwitz, 2006). For additional discussion of the merits and limitations of all analysis methods based on the hemodynamic response variation over time, see Chapter 9 of this volume.

Beyond Linear Methods in fMRI

The fMRI analysis techniques discussed so far are mostly univariate (DCM can be multivariate) in that the statistical modeling is carried out for single voxels. This, it can be argued, is not an accurate representation of how the brain works. In the neuroimaging community, multivariate methods have increased in popularity in the recent years. These techniques take into account distributed patterns of activity and thus provide a more accurate reflection of actual brain processing. These include model-free and model-centric approaches.

One such popular approach is multivoxel pattern analysis (MVPA), which utilizes complex pattern classification algorithms to classify patterns observed in groups of voxels as members of one of usually two categories. An implementation of MVPA was reported by Rissman et al. (2010) who investigated individual memory states and past experiences. The authors reported that the MVPA classifier correctly distinguished whether a given face stimulus was subjectively experienced as old or new, as well as the degree of recollection or familiarity with which faces were experienced.

The most prominent model-free approach to multivariate analysis of fMRI data is independent component analysis (ICA), which is frequently used when a priori models of brain activity are not available. ICA is used to separate fMRI data into spatially independent patterns of activity and has been shown to be a suitable method for exploratory fMRI analyses. ICA has found an application into the analysis of resting state fMRI data (e.g., Beckmann et al., 2005), as explained in the following section.

Activation Versus Deactivation

Most of our knowledge about brain function comes from studies like the ones sketched thus far, in which volunteers are required to execute a task (or tasks) while their brain activity is recorded. Typically, the increased signaling during the experimental condition of interest, referred to as “activation,” is estimated in comparison to a baseline condition, which, on some occasions, may be resting (presumably doing nothing). Recently, there has been enormous growth in the number studies exploring the flip side of this phenomenon. That is, an exploration of areas that deactivate during fMRI activation paradigms or, conversely, are more active during “no task” baseline conditions.

The set of areas that increase their activity during the absence of external stimuli have become collectively known as the default mode network (DMN). (p. 57) Although Ingvar observed increases in activity during rest as early as 1974, his ideas (Ingvar, 1974) did not enjoy much attention until the turn of the century, when Raichle et al. (2001), among others, used quantitative positron emission tomography (PET) to demonstrate the existence of such a baseline state of human brain function that is remarkably uniform in the awake resting state. They used the term baseline default mode of brain function to describe activity in the regions involved.

fMRI studies using a wide range of tasks have consistently reported task-related decreases in activity in several brain areas, including the posterior cingulate cortex (PCC), ventral anterior cingulate cortex (vACC), and bilateral inferior parietal cortex, among others (Mazoyer et al., 2001). Although DMN data are accumulating, a number of key questions around its actual existence and function remain. Mapping and understanding the exact role of such a network in cognitive brain function will inform our current interpretations of “activation” and “deactivation” in functional imaging studies using cognitive activation paradigms (Gusnard & Raichle, 2001). Typically, current study of the DMN involves fMR images acquired while volunteers are resting in the MRI scanner for time periods of 4 minutes up to an hour.

Another noteworthy finding in the field of resting fMRI is the existence of multiple resting state networks. These encompass distinct collections of cortical and subcortical regions that have been attributed specific functional roles during task-specific activation imaging. As early as 1995, Biswal et al. demonstrated that fluctuations in activity during rest were coherent within the motor cortex. More recently, Beckmann et al. (2005) expanded on this idea, using independent component analysis to demonstrate that distinct cortical/subcortical regions shown to coactivate during task-specific functional imaging also comodulate in activity at rest. The principle has been demonstrated many times over for the motor system (De Luca, Smith, De Stefano, Federico, & Matthews, 2005), and also for visual (Cordes et al., 2001; Lowe, Mock, & Sorenson, 1998), auditory (Cordes et al., 2001), and memory (Rombouts, Stam, Kuijer, Scheltens, & Barkhof, 2003, Vincent et al., 2006) systems. This is not surprising given that spontaneous activity appears to be present at all levels of the nervous system from neurons (Tsodyks, Kenet, Grinvald, & Arieli, 1999) to systems (Beckmann et al., 2005). The emerging inference may be that distinct neuroanatomical systems that coactivate in response to stimuli also display levels of distinct functional and/or structural organization at rest. The functionality of most of these resting systems can be easily inferred because they track the functional anatomy of systems demonstrated many times over with activation paradigms and lesion studies from neuropsychology. However, the role of the resting networks, which has no obvious cognate activity that can be used as a reference, is still under discussion (see Chapter 9, this volume).

The default and other resting networks can be obtained using multiple approaches, with the most popular being seed-based voxel correlations (see, for example, Fox et al., 2005; Stamatakis, Adapa, Absalom, & Menon, 2011). The general principle behind seed-based correlation approaches is very similar to the functional connectivity approach we described earlier, in which a predictor time series is obtained from an ROI, and its correlations with the rest of the brain are calculated on a voxel by voxel basis. The difference is that our earlier description of functional connectivity was in the context of task-based fMRI, whereas here the application is in the context of task-free fMRI.

The seed-based approach to calculate the DMN can be realized with many variations, but, in its most common form, it involves extracting a time-series using a spherical region of interest (ROI) centered in the PCC or the precuneus (PC). Published literature includes a variety of candidate coordinates defining the center of this sphere (e.g., Fox et al., 2005 use −5, −49, 40). For completeness we must mention that Fox et al., also used spherical ROIs from medial prefrontal cortex −1, 47, −4 and lateral parietal cortex −45, −67, 36 to calculate the DMN. Whole-brain voxel-based correlations with the extracted time-series are then estimated, having excluded sources of noise such as global mean, white matter, and cerebrospinal fluid (CSF) signals in order to remove any non–tissue specific confounding effects. In practical terms, white matter and CSF signals are extracted using whole-brain white matter and CSF ROIs. Movement parameters (calculated during the realignment stage of preprocessing) may also be included in the model as nuisance variables to account for excessive residual movement (Stamatakis et al., 2010). An ongoing debate in this literature is on the influence of the global signal of fMRI data on resting state functional connectivity results. There have been suggestions that the inclusion of the global signal in the model as a nuisance variable introduces artifactual anticorrelated networks (Murphy, Birn, Handwerker, Jones, & Bandettini, 2009), although (p. 58) recent research suggests that resting state global fluctuations and network-specific fluctuations are uncorrelated (Carbonell, Bellec, & Shmuel, 2011).

This spherical ROI approach may produce variable results depending on the center of the spherical ROI selected. A different implementation of the seed-based approach for calculating the default network has been described. Horovitz et al. (2009), among others, utilized a time-series estimate using a mean value for the entire PCC. The PCC ROI can be spatially defined from standard anatomical atlases such as the AAL (Tzourio-Mazoyer et al., 2002). At this point, it is worth highlighting the fact that the seed-based approach can be used to calculate other resting networks and is not only used for estimating the default network. For example, a time series obtained from a seed in the primary motor cortex should correlate with the resting motor network.

Another popular approach for analyzing resting state fMRI for calculating the DMN, as well as other resting networks, is ICA (Calhoun, Adali, Pearlson, & Pekar, 2001), mentioned earlier. The ICA approach depends on maximizing statistical independence between components detected, and this independence can be calculated either over spatial maps or between time courses. Different authors argue for the advantage of one or the other (e.g., Friston 1998), while Beckmann et al. (2005) demonstrated that (a) through ICA, one is able to estimate even largely overlapping spatial processes and (b) that ICA can be used to decompose an fMRI time series into a set of components that describe the temporal as well as the spatial characteristics of underlying hidden signals.

One advantage of the ICA approach is that it requires few a priori assumptions, but the user usually needs to select the components of interest manually among those emerging from the analysis. This is because unconstrained ICA can result in a great set of components that may include components not readily attributable to known sensory, cognitive, or behavioral systems but may be noise components. For this reason, popular implementations of the ICA technique almost always allow the users to define the number of components they want to extract from the data. Some of these components can be attributed to noise, while others are visually similar to sensory-motor, visual, auditory, executive control, and default mode (among other) networks (Beckmann et al., 2005). Another approach to identifying useful components from a large set involves comparing each component to already established networks. For example, if one wanted to find the default network component among a set of 40 unidentified components, this approach would involve computing a similarity measure between each of the 40 components with a preexisting map of the default network obtained from an earlier analysis.

Both seed-based and ICA approaches have advantages and disadvantages, with the seed-based approaches being more popular for theoretically and/or anatomically driven experimental questions, while the ICA method is more popular for data-driven analyses. Despite the fundamental differences in the two approaches, there are studies suggesting that findings from the two are significantly similar (Rosazza et al., 2012).

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