Functional magnetic resonance imaging or functional MRI (fMRI) measures brain activity by detecting changes associated with blood flow. This technique relies on the fact that cerebral blood flow and neuronal activation are coupled: When an area of the brain is in use, blood flow to that region increases. The primary form of fMRI uses the blood-oxygen-level dependent (BOLD) contrast, discovered by Seiji Ogawa and his colleagues in 1990. This is a type of specialized brain and body scan used to map neural activity in the brain or spinal cord of humans or other animals by imaging the change in blood flow (hemodynamic response) related to energy use by nerve cells. Since the early 1990s, fMRI has come to dominate brain mapping research because it is noninvasive, typically requiring no injections, surgery, or the ingestion of substances such as radioactive tracers as in positron emission tomography. Data acquired using fMRI, however, is frequently corrupted by noise from various sources; hence, statistical procedures are used to extract the underlying signal. The resulting brain activation can be graphically represented by color-coding the strength of activation across the brain or the specific region studied. The technique can localize activity to within millimeters but, using standard techniques, no better than within a window of a few seconds. Other methods of obtaining contrast are arterial spin labeling and diffusion MRI. Diffusion MRI is similar to BOLD fMRI but provides contrast based on the magnitude of diffusion of water molecules in the brain. In addition to detecting BOLD responses from activity due to tasks or stimuli, fMRI can measure resting state, or negative-task state, which shows the subjects' baseline BOLD variance. Since about 1998 studies have shown the existence and properties of the default mode network, a functionally connected neural network of apparent resting brain states. fMRI is used in research, and to a lesser extent, in clinical work. It can complement other measures of brain physiology such as electroencephalography (EEG), and near-infrared spectroscopy (NIRS). Newer methods which improve both spatial and time resolution are being researched, and these largely use biomarkers other than the BOLD signal. Some companies have developed commercial products such as lie detectors based on fMRI techniques, but the research is not believed to be developed enough for widespread commercial use.
Overview
The fMRI concept builds on the earlier MRI scanning technology and the discovery of properties of oxygen-rich blood. MRI brain scans use a strong, uniform, static magnetic field to align the spins of nuclei in the brain region being studied. Another magnetic field, with a gradient strength rather than a uniform one, is then applied to spatially distinguish different nuclei. Finally, a radiofrequency (RF) pulse is applied to flip the nuclear spins, with the effect depending on where they are located, due to the gradient field. After the RF pulse, the nuclei return to their original (equilibrium) spin populations, and the energy they emit is measured with a coil. The use of the gradient field allows the positions of the nuclei to be determined. MRI thus provides a static structural view of brain matter. The central thrust behind fMRI was to extend MRI to capture functional changes in the brain caused by neuronal activity. Differences in magnetic properties between arterial (oxygen-rich) and venous (oxygen-poor) blood provided this link.
Since the 1890s, it has been known that changes in blood flow and blood oxygenation in the brain (collectively known as brain hemodynamics) are closely linked to neural activity. When neurons become active, local blood flow to those brain regions increases, and oxygen-rich (oxygenated) blood displaces oxygen-depleted (deoxygenated) blood around 2 seconds later. This rises to a peak over 4–6 seconds, before falling back to the original level (and typically undershooting slightly). Oxygen is carried by the hemoglobin molecule in red blood cells. Deoxygenated hemoglobin (dHb) is more magnetic (paramagnetic) than oxygenated hemoglobin (Hb), which is virtually resistant to magnetism (diamagnetic). This difference leads to an improved MR signal since the diamagnetic blood interferes with the magnetic MR signal less. This improvement can be mapped to show which neurons are active at a time.
History
During the late 19th century, Angelo Mosso invented the 'human circulation balance', which could non-invasively measure the redistribution of blood during emotional and intellectual activity. However, although briefly mentioned by William James in 1890, the details and precise workings of this balance and the experiments Mosso performed with it remained largely unknown until the recent discovery of the original instrument as well as Mosso's reports by Stefano Sandrone and colleagues. Angelo Mosso investigated several critical variables that are still relevant in modern neuroimaging such as the 'signal-to-noise ratio', the appropriate choice of the experimental paradigm and the need for the simultaneous recording of differing physiological parameters. Mosso's manuscripts do not provide direct evidence that the balance was really able to measure changes in cerebral blood flow due to cognition, however a modern replication performed by David T Field has now demonstrated—using modern signal processing techniques unavailable to Mosso—that a balance apparatus of this type is able to detect changes in cerebral blood volume related to cognition. In 1890, Charles Roy and Charles Sherrington first experimentally linked brain function to its blood flow, at Cambridge University. The next step to resolving how to measure blood flow to the brain was Linus Pauling's and Charles Coryell's discovery in 1936 that oxygen-rich blood with Hb was weakly repelled by magnetic fields, while oxygen-depleted blood with dHb was attracted to a magnetic field, though less so than ferromagnetic elements such as iron. Seiji Ogawa at AT&T Bell labs recognized that this could be used to augment MRI, which could study just the static structure of the brain, since the differing magnetic properties of dHb and Hb caused by blood flow to activated brain regions would cause measurable changes in the MRI signal. BOLD is the MRI contrast of dHb, discovered in 1990 by Ogawa. In a seminal 1990 study based on earlier work by Thulborn et al., Ogawa and colleagues scanned rodents in a strong magnetic field (7.0 T) MRI. To manipulate blood oxygen level, they changed the proportion of oxygen the animals breathed. As this proportion fell, a map of blood flow in the brain was seen in the MRI. They verified this by placing test tubes with oxygenated or deoxygenated blood and creating separate images. They also showed that gradient-echo images, which depend on a form of loss of magnetization called T2* decay, produced the best images. To show these blood flow changes were related to functional brain activity, they changed the composition of the air breathed by rats, and scanned them while monitoring brain activity with EEG. The first attempt to detect the regional brain activity using MRI was performed by Belliveau and colleagues at Harvard University using the contrast agent Magnevist, a paramagnetic substance remaining in the bloodstream after intravenous injection. However, this method is not popular in human fMRI, because of the inconvenience of the contrast agent injection, and because the agent stays in the blood only for a short time. Three studies in 1992 were the first to explore using the BOLD contrast in humans. Kenneth Kwong and colleagues, using both gradient-echo and inversion recovery echo-planar imaging (EPI) sequence at a magnetic field strength of 1.5 T published studies showing clear activation of the human visual cortex. The Harvard team thereby showed that both blood flow and blood volume increased locally in activity neural tissue. Ogawa and Ugurbil conducted a similar study using a higher magnetic field (4.0 T) in Ugurbil's laboratory at the University of Minnesota, generating higher resolution images that showed activity largely following the gray matter of the brain, as would be expected; in addition, they showed that fMRI signal depended on a decrease in T2*, consistent with the BOLD mechanism. T2* decay is caused by magnetized nuclei in a volume of space losing magnetic coherence (transverse magnetization) from both bumping into one another and from experiencing differences in the magnetic field strength across locations (field inhomogeneity from a spatial gradient). Bandettini and colleagues used EPI at 1.5 T to show activation in the primary motor cortex, a brain area at the last stage of the circuitry controlling voluntary movements. The magnetic fields, pulse sequences and procedures and techniques used by these early studies are still used in current-day fMRI studies. But today researchers typically collect data from more slices (using stronger magnetic gradients), and preprocess and analyze data using statistical techniques.
Physiology The brain does not store a lot of glucose, its primary source of energy. When neurons become active, getting them back to their original state of polarization requires actively pumping ions across the neuronal cell membranes, in both directions. The energy for those ion pumps is mainly produced from glucose. More blood flows in to transport more glucose, also bringing in more oxygen in the form of oxygenated hemoglobin molecules in red blood cells. This is from both a higher rate of blood flow and an expansion of blood vessels. The blood-flow change is localized to within 2 or 3 mm of where the neural activity is. Usually the brought-in oxygen is more than the oxygen consumed in burning glucose (it is not yet settled whether most glucose consumption is oxidative), and this causes a net decrease in deoxygenated hemoglobin (dHb) in that brain area's blood vessels. This changes the magnetic property of the blood, making it interfere less with the magnetization and its eventual decay induced by the MRI process. The cerebral blood flow (CBF) corresponds to the consumed glucose differently in different brain regions. Initial results show there is more inflow than consumption of glucose in regions such as the amygdala, basal ganglia, thalamus and cingulate cortex, all of which are recruited for fast responses. In regions that are more deliberative, such as the lateral frontal and lateral parietal lobes, it seems that incoming flow is less than consumption. This affects BOLD sensitivity. Hemoglobin differs in how it responds to magnetic fields, depending on whether it has a bound oxygen molecule. The dHb molecule is more attracted to magnetic fields. Hence, it distorts the surrounding magnetic field induced by an MRI scanner, causing the nuclei there to lose magnetization faster via the T2* decay. Thus MR pulse sequences sensitive to T2* show more MR signal where blood is highly oxygenated and less where it is not. This effect increases with the square of the strength of the magnetic field. The fMRI signal hence needs both a strong magnetic field (1.5 T or higher) and a pulse sequence such as EPI, which is sensitive to T2* contrast. The physiological blood-flow response largely decides the temporal sensitivity, that is how accurately we can measure when neurons are active, in BOLD fMRI. The basic time resolution parameter (sampling time) is designated TR; the TR dictates how often a particular brain slice is excited and allowed to lose its magnetization. TRs could vary from the very short (500 ms) to the very long (3 s). For fMRI specifically, the hemodynamic response lasts over 10 seconds, rising multiplicatively (that is, as a proportion of current value), peaking at 4 to 6 seconds, and then falling multiplicatively. Changes in the blood-flow system, the vascular system, integrate responses to neuronal activity over time. Because this response is a smooth continuous function, sampling with ever-faster TRs does not help; it just gives more points on the response curve obtainable by simple linear interpolation anyway. Experimental paradigms such as staggering when a stimulus is presented at various trials can improve temporal resolution, but reduces the number of effective data points obtained.
BOLD hemodynamic response
The change in the MR signal from neuronal activity is called the hemodynamic response (HR). It lags the neuronal events triggering it by a couple of seconds, since it takes a while for the vascular system to respond to the brain's need for glucose. From this point it typically rises to a peak at about 5 seconds after the stimulus. If the neurons keep firing, say from a continuous stimulus, the peak spreads to a flat plateau while the neurons stay active. After activity stops, the BOLD signal falls below the original level, the baseline, a phenomenon called the undershoot. Over time the signal recovers to the baseline. There is some evidence that continuous metabolic requirements in a brain region contribute to the undershoot. The mechanism by which the neural system provides feedback to the vascular system of its need for more glucose is partly the release of glutamate as part of neuron firing. This glutamate affects nearby supporting cells, astrocytes, causing a change in calcium ion concentration. This, in turn, releases nitric oxide at the contact point of astrocytes and intermediate-sized blood vessels, the arterioles. Nitric oxide is a vasodilator causing arterioles to expand and draw in more blood. A single voxel's response signal over time is called its timecourse. Typically, the unwanted signal, called the noise, from the scanner, random brain activity and similar elements is as big as the signal itself. To eliminate these, fMRI studies repeat a stimulus presentation multiple times.
Spatial resolution Spatial resolution of an fMRI study refers to how well it discriminates between nearby locations. It is measured by the size of voxels, as in MRI. A voxel is a three-dimensional rectangular cuboid, whose dimensions are set by the slice thickness, the area of a slice, and the grid imposed on the slice by the scanning process. Full-brain studies use larger voxels, while those that focus on specific regions of interest typically use smaller sizes. Sizes range from 4 to 5 mm, or with laminar resolution fMRI (lfMRI), to submillimeter. Smaller voxels contain fewer neurons on average, incorporate less blood flow, and hence have less signal than larger voxels. Smaller voxels imply longer scanning times, since scanning time directly rises with the number of voxels per slice and the number of slices. This can lead both to discomfort for the subject inside the scanner and to loss of the magnetization signal. A voxel typically contains a few million neurons and tens of billions of synapses, with the actual number depending on voxel size and the area of the brain being imaged. The vascular arterial system supplying fresh blood branches into smaller and smaller vessels as it enters the brain surface and within-brain regions, culminating in a connected capillary bed within the brain. The drainage system, similarly, merges into larger and larger veins as it carries away oxygen-depleted blood. The dHb contribution to the fMRI signal is from both the capillaries near the area of activity and larger draining veins that may be farther away. For good spatial resolution, the signal from the large veins needs to be suppressed, since it does not correspond to the area where the neural activity is. This can be achieved either by using strong static magnetic fields or by using spin-echo pulse sequences. With these, fMRI can examine a spatial range from millimeters to centimeters, and can hence identify Brodmann areas (centimeters), subcortical nuclei such as the caudate, putamen and thalamus, and hippocampal subfields such as the combined dentate gyrus/CA3, CA1, and subiculum.
Temporal resolution Temporal resolution is the smallest time period of neural activity reliably separated out by fMRI. One element deciding this is the sampling time, the TR. Below a TR of 1 or 2 seconds, however, scanning just generates sharper hemodynamic response (HR) curves, without adding much additional information (e.g. beyond what is alternatively achieved by mathematically interpolating the curve gaps at a lower TR). Temporal resolution can be improved by staggering stimulus presentation across trials. If one-third of data trials are sampled normally, one-third at 1 s, 4 s, 7 s and so on, and the last third at 2 s, 5 s and 8 s, the combined data provide a resolution of 1 s, though with only one-third as many total events. The time resolution needed depends on brain processing time for various events. An example of the broad range here is given by the visual processing system. What the eye sees is registered on the photoreceptors of the retina within a millisecond or so. These signals get to the primary visual cortex via the thalamus in tens of milliseconds. Neuronal activity related to the act of seeing lasts for more than 100 ms. A fast reaction, such as swerving to avoid a car crash, takes around 200 ms. By about half a second, awareness and reflection of the incident sets in. Remembering a similar event may take a few seconds, and emotional or physiological changes such as fear arousal may last minutes or hours. Learned changes, such as recognizing faces or scenes, may last days, months, or years. Most fMRI experiments study brain processes lasting a few seconds, with the study conducted over some tens of minutes. Subjects may move their heads during that time, and this head motion needs to be corrected for. So does drift in the baseline signal over time. Boredom and learning may modify both subject behavior and cognitive processes.
Linear addition from multiple activation When a person performs two tasks simultaneously or in overlapping fashion, the BOLD response is expected to add linearly. This is a fundamental assumption of many fMRI studies that is based on the principle that continuously differentiable systems can be expected to behave linearly when perturbations are small; they are linear to first order. Linear addition means the only operation allowed on the individual responses before they are combined (added together) is a separate scaling of each. Since scaling is just multiplication by a constant number, this means an event that evokes, say, twice the neural response as another, can be modeled as the first event presented twice simultaneously. The HR for the doubled-event is then just double that of the single event. To the extent that the behavior is linear, the time course of the BOLD response to an arbitrary stimulus can be modeled by convolution of that stimulus with the impulse BOLD response. Accurate time course modeling is important in estimating the BOLD response magnitude. This strong assumption was first studied in 1996 by Boynton and colleagues, who checked the effects on the primary visual cortex of patterns flickering 8 times a second and presented for 3 to 24 seconds. Their result showed that when visual contrast of the image was increased, the HR shape stayed the same but its amplitude increased proportionally. With some exceptions, responses to longer stimuli could also be inferred by adding together the responses for multiple shorter stimuli summing to the same longer duration. In 1997, Dale and Buckner tested whether individual events, rather than blocks of some duration, also summed the same way, and found they did. But they also found deviations from the linear model at time intervals less than 2 seconds. A source of nonlinearity in the fMRI response is from the refractory period, where brain activity from a presented stimulus suppresses further activity on a subsequent, similar, stimulus. As stimuli become shorter, the refractory period becomes more noticeable. The refractory period does not change with age, nor do the amplitudes of HRs. The period differs across brain regions. In both the primary motor cortex and the visual cortex, the HR amplitude scales linearly with duration of a stimulus or response. In the corresponding secondary regions, the supplementary motor cortex, which is involved in planning motor behavior, and the motion-sensitive V5 region, a strong refractory period is seen and the HR amplitude stays steady across a range of stimulus or response durations. The refractory effect can be used in a way similar to habituation to see what features of a stimulus a person discriminates as new. Further limits to linearity exist because of saturation: with large stimulation levels a maximum BOLD response is reached.
Matching neural activity to the BOLD signal Researchers have checked the BOLD signal against both signals from implanted electrodes (mostly in monkeys) and signals of field potentials (that is the electric or magnetic field from the brain's activity, measured outside the skull) from EEG and MEG. The local field potential, which includes both post-neuron-synaptic activity and internal neuron processing, better predicts the BOLD signal. So the BOLD contrast reflects mainly the inputs to a neuron and the neuron's integrative processing within its body, and less the output firing of neurons. In humans, electrodes can be implanted only in patients who need surgery as treatment, but evidence suggests a similar relationship at least for the auditory cortex and the primary visual cortex. Activation locations detected by BOLD fMRI in cortical areas (brain surface regions) are known to tally with CBF-based functional maps from PET scans. Some regions just a few millimeters in size, such as the lateral geniculate nucleus (LGN) of the thalamus, which relays visual inputs from the retina to the visual cortex, have been shown to generate the BOLD signal correctly when presented with visual input. Nearby regions such as the pulvinar nucleus were not stimulated for this task, indicating millimeter resolution for the spatial extent of the BOLD response, at least in thalamic nuclei. In the rat brain, single-whisker touch has been shown to elicit BOLD signals from the somatosensory cortex. However, the BOLD signal cannot separate feedback and feedforward active networks in a region; the slowness of the vascular response means the final signal is the summed version of the whole region's network; blood flow is not discontinuous as the processing proceeds. Also, both inhibitory and excitatory input to a neuron from other neurons sum and contribute to the BOLD signal. Within a neuron these two inputs might cancel out. The BOLD response can also be affected by a variety of factors, including disease, sedation, anxiety, medications that dilate blood vessels, and attention (neuromodulation). The amplitude of the BOLD signal does not necessarily affect its shape. A higher-amplitude signal may be seen for stronger neural activity, but peaking at the same place as a weaker signal. Also, the amplitude does not necessarily reflect behavioral performance. A complex cognitive task may initially trigger high-amplitude signals associated with good performance, but as the subject gets better at it, the amplitude may decrease with performance staying the same. This is expected to be due to increased efficiency in performing the task. The BOLD response across brain regions cannot be compared directly even for the same task, since the density of neurons and the blood-supply characteristics are not constant across the brain. However, the BOLD response can often be compared across subjects for the same brain region and the same task. More recent characterization of the BOLD signal has used optogenetic techniques in rodents to precisely control neuronal firing while simultaneously monitoring the BOLD response using high field magnets (a technique sometimes referred to as "optofMRI"). These techniques suggest that neuronal firing is well correlated with the measured BOLD signal including approximately linear summation of the BOLD signal over closely spaced bursts of neuronal firing. Linear summation is an assumption of commonly used event-related fMRI designs.
Medical use
Physicians use fMRI to assess how risky brain surgery or similar invasive treatment is for a patient and to learn how a normal, diseased or injured brain is functioning. They map the brain with fMRI to identify regions linked to critical functions such as speaking, moving, sensing, or planning. This is useful to plan for surgery and radiation therapy of the brain.
Clinical use of fMRI still lags behind research use. Patients with brain pathologies are more difficult to scan with fMRI than are young healthy volunteers, the typical research-subject population. Tumors and lesions can change the blood flow in ways not related to neural activity, masking the neural HR. Drugs such as antihistamines and even caffeine can affect HR. Some patients may have disorders such as compulsive lying, which makes certain studies impossible. It is harder for those with clinical problems to stay still for long. Using head restraints or bite bars may injure epileptics who have a seizure inside the scanner; bite bars may also discomfort those with dental prostheses. Despite these difficulties, fMRI has been used clinically to map functional areas, check left-right hemispherical asymmetry in language and memory regions, check the neural correlates of a seizure, study how the brain recovers partially from a stroke, and test how well a drug or behavioral therapy works. Mapping of functional areas and understanding lateralization of language and memory help surgeons avoid removing critical brain regions when they have to operate and remove brain tissue. This is of particular importance in removing tumors and in patients who have intractable temporal lobe epilepsy. Lesioning tumors requires pre-surgical planning to ensure no functionally useful tissue is removed needlessly. Recovered depressed patients have shown altered fMRI activity in the cerebellum, and this may indicate a tendency to relapse. Pharmacological fMRI, assaying brain activity after drugs are administered, can be used to check how much a drug penetrates the blood–brain barrier and dose vs effect information of the medication.
Animal research Research is primarily performed in non-human primates such as the rhesus macaque. These studies can be used both to check or predict human results and to validate the fMRI technique itself. But the studies are difficult because it is hard to motivate an animal to stay still and typical inducements such as juice trigger head movement while the animal swallows it. It is also expensive to maintain a colony of larger animals such as the macaque.
Analyzing the data The goal of fMRI data analysis is to detect correlations between brain activation and a task the subject performs during the scan. It also aims to discover correlations with the specific cognitive states, such as memory and recognition, induced in the subject. The BOLD signature of activation is relatively weak, however, so other sources of noise in the acquired data must be carefully controlled. This means that a series of processing steps must be performed on the acquired images before the actual statistical search for task-related activation can begin. Nevertheless, it is possible to predict, for example, the emotions a person is experiencing solely from their fMRI, with a high degree of accuracy.
Sources of noise Noise is unwanted changes to the MR signal from elements not of interest to the study. The five main sources of noise in fMRI are thermal noise, system noise, physiological noise, random neural activity and differences in both mental strategies and behavior across people and across tasks within a person. Thermal noise multiplies in line with the static field strength, but physiological noise multiplies as the square of the field strength. Since the signal also multiplies as the square of the field strength, and since physiological noise is a large proportion of total noise, higher field strengths above 3 T do not always produce proportionately better images. Heat causes electrons to move around and distort the current in the fMRI detector, producing thermal noise. Thermal noise rises with the temperature. It also depends on the range of frequencies detected by the receiver coil and its electrical resistance. It affects all voxels similarly, independent of anatomy. System noise is from the imaging hardware. One form is scanner drift, caused by the superconducting magnet's field drifting over time. Another form is changes in the current or voltage distribution of the brain itself inducing changes in the receiver coil and reducing its sensitivity. A procedure called impedance matching is used to bypass this inductance effect. There could also be noise from the magnetic field not being uniform. This is often adjusted for by using shimming coils, small magnets physically inserted, say into the subject's mouth, to patch the magnetic field. The nonuniformities are often near brain sinuses such as the ear and plugging the cavity for long periods can be discomfiting. The scanning process acquires the MR signal in k-space, in which overlapping spatial frequencies (that is repeated edges in the sample's volume) are each represented with lines. Transforming this into voxels introduces some loss and distortions. Physiological noise is from head and brain movement in the scanner from breathing, heart beats, or the subject fidgeting, tensing, or making physical responses such as button presses. Head movements cause the voxel-to-neurons mapping to change while scanning is in progress. Noise due to head movement is a particular issue when working with children, although there are measures that can be taken to reduce head motion when scanning children, such as changes in experimental design and training prior to the scanning session. Since fMRI is acquired in slices, after movement, a voxel continues to refer to the same absolute location in space while the neurons underneath it would have changed. Another source of physiological noise is the change in the rate of blood flow, blood volume, and use of oxygen over time. This last component contributes to two-thirds of physiological noise, which, in turn, is the main contributor to total noise. Even with the best experimental design, it is not possible to control and constrain all other background stimuli impinging on a subject—scanner noise, random thoughts, physical sensations, and the like. These produce neural activity independent of the experimental manipulation. These are not amenable to mathematical modeling and have to be controlled by the study design. A person's strategies to respond or react to a stimulus, and to solve problems, often change over time and over tasks. This generates variations in neural activity from trial to trial within a subject. Across people too neural activity differs for similar reasons. Researchers often conduct pilot studies to see how participants typically perform for the task under consideration. They also often train subjects how to respond or react in a trial training session prior to the scanning one.
Preprocessing The scanner platform generates a 3 D volume of the subject's head every TR. This consists of an array of voxel intensity values, one value per voxel in the scan. The voxels are arranged one after the other, unfolding the three-dimensional structure into a single line. Several such volumes from a session are joined to form a 4 D volume corresponding to a run, for the time period the subject stayed in the scanner without adjusting head position. This 4 D volume is the starting point for analysis. The first part of that analysis is preprocessing. The first step in preprocessing is conventionally slice timing correction. The MR scanner acquires different slices within a single brain volume at different times, and hence the slices represent brain activity at different timepoints. Since this complicates later analysis, a timing correction is applied to bring all slices to the same timepoint reference. This is done by assuming the timecourse of a voxel is smooth when plotted as a dotted line. Hence the voxel's intensity value at other times not in the sampled frames can be calculated by filling in the dots to create a continuous curve. Head motion correction is another common preprocessing step. When the head moves, the neurons under a voxel move and hence its timecourse now represents largely that of some other voxel in the past. Hence the timecourse curve is effectively cut and pasted from one voxel to another. Motion correction tries different ways of undoing this to see which undoing of the cut-and-paste produces the smoothest timecourse for all voxels. The undoing is by applying a rigid-body transform to the volume, by shifting and rotating the whole volume data to account for motion. The transformed volume is compared statistically to the volume at the first timepoint to see how well they match, using a cost function such as correlation or mutual information. The transformation that gives the minimal cost function is chosen as the model for head motion. Since the head can move in a vastly varied number of ways, it is not possible to search for all possible candidates; nor is there right now an algorithm that provides a globally optimal solution independent of the first transformations we try in a chain. Distortion corrections account for field nonuniformities of the scanner. One method, as described before, is to use shimming coils. Another is to recreate a field map of the main field by acquiring two images with differing echo times. If the field were uniform, the differences between the two images also would be uniform. Note these are not true preprocessing techniques since they are independent of the study itself. Bias field estimation is a real preprocessing technique using mathematical models of the noise from distortion, such as Markov random fields and expectation maximization algorithms, to correct for distortion. In general, fMRI studies acquire both many functional images with fMRI and a structural image with MRI. The structural image is usually of a higher resolution and depends on a different signal, the T1 magnetic field decay after excitation. To demarcate regions of interest in the functional image, one needs to align it with the structural one. Even when whole-brain analysis is done, to interpret the final results, that is to figure out which regions the active voxels fall in, one has to align the functional image to the structural one. This is done with a coregistration algorithm that works similar to the motion-correction one, except that here the resolutions are different, and the intensity values cannot be directly compared since the generating signal is different. Typical MRI studies scan a few different subjects. To integrate the results across subjects, one possibility is to use a common brain atlas, and adjust all the brains to align to the atlas, and then analyze them as a single group. The atlases commonly used are the Talairach one, a single brain of an elderly woman created by Jean Talairach, and the Montreal Neurological Institute (MNI) one. The second is a probabilistic map created by combining scans from over a hundred individuals. This normalization to a standard template is done by mathematically checking which combination of stretching, squeezing, and warping reduces the differences between the target and the reference. While this is conceptually similar to motion correction, the changes required are more complex than just translation and rotation, and hence optimization even more likely to depend on the first transformations in the chain that is checked. Temporal filtering is the removal of frequencies of no interest from the signal. A voxel's intensity change over time can be represented as the sum of a number of different repeating waves with differing periods and heights. A plot with these periods on the x-axis and the heights on the y-axis is called a power spectrum, and this plot is created with the Fourier transform technique. Temporal filtering amounts to removing the periodic waves not of interest to us from the power spectrum, and then summing the waves back again, using the inverse Fourier transform to create a new timecourse for the voxel. A high-pass filter removes the lower frequencies, and the lowest frequency that can be identified with this technique is the reciprocal of twice the TR. A low-pass filter removes the higher frequencies, while a band-pass filter removes all frequencies except the particular range of interest. Smoothing, or spatial filtering, is the idea of averaging the intensities of nearby voxels to produce a smooth spatial map of intensity change across the brain or region of interest. The averaging is often done by convolution with a Gaussian filter, which, at every spatial point, weights neighboring voxels by their distance, with the weights falling exponentially following the bell curve. If the true spatial extent of activation, that is the spread of the cluster of voxels simultaneously active, matches the width of the filter used, this process improves the signal-to-noise ratio. It also makes the total noise for each voxel follow a bell-curve distribution, since adding together a large number of independent, identical distributions of any kind produces the bell curve as the limit case. But if the presumed spatial extent of activation does not match the filter, signal is reduced.
Statistical analysis One common approach to analysing fMRI data is to consider each voxel separately within the framework of the general linear model. The model assumes, at every time point, that the hemodynamic response (HR) is equal to the scaled and summed version of the events active at that point. A researcher creates a design matrix specifying which events are active at any timepoint. One common way is to create a matrix with one column per overlapping event, and one row per time point, and to mark it if a particular event, say a stimulus, is active at that time point. One then assumes a specific shape for the HR, leaving only its amplitude changeable in active voxels. The design matrix and this shape are used to generate a prediction of the exact HR of the voxel at every timepoint, using the mathematical procedure of convolution. This prediction does not include the scaling required for every event before summing them. The basic model assumes the observed HR is the predicted HR scaled by the weights for each event and then added, with noise mixed in. This generates a set of linear equations with more equations than unknowns. A linear equation has an exact solution, under most conditions, when equations and unknowns match. Hence one could choose any subset of the equations, with the number equal to the number of variables, and solve them. But, when these solutions are plugged into the left-out equations, there will be a mismatch between the right and left sides, the error. The GLM model attempts to find the scaling weights that minimize the sum of the squares of the error. This method is provably optimal if the error were distributed as a bell curve, and if the scaling-and-summing model were accurate. For a more mathematical description of the GLM model, see generalized linear models. The GLM model does not take into account the contribution of relationships between multiple voxels. Whereas GLM analysis methods assess whether a voxel or region's signal amplitude is higher or lower for one condition than another, newer statistical models such as multi-voxel pattern analysis (MVPA), utilize the unique contributions of multiple voxels within a voxel-population. In a typical implementation, a classifier or more basic