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Functional magnetic resonance imaging 

Functional magnetic resonance imaging
Functional magnetic resonance imaging

E. T. Bullmore

and J. Suckling

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Functional magnetic resonance imaging (fMRI) is a relatively new technique for measuring changes in cerebral blood flow. The first fMRI studies, showing functional activation of the occipital cortex by visual stimulation and activation of the motor cortex by finger movement, were published in the early 1990s.(1–3) In the years since then, fMRI has been used to investigate the physiological response to a wide variety of experimental procedures in both normal human subjects and diverse patient groups. In the next 10 years, fMRI will probably establish a role for itself in radiological and psychiatric practice; currently the clinical role of fMRI is limited to specialized applications such as assessment of hemispheric dominance prior to neurosurgery.(4)

The outstanding advantage of fMRI over alternative methods of imaging cerebral blood flow, such as positron emission tomo-graphy (PET) and single-photon emission computed tomography (SPECT), is that it does not involve exposure to radioactivity. This means that a single subject can safely be examined by fMRI on many occasions, and that the ethical problems of examining patients are minimized. Functional MRI also has superior spatial resolution (in the order of millimetres) and temporal resolution (in the order of seconds) compared with PET and SPECT.

In this chapter, we provide an introduction to technical issues relevant to fMRI data acquisition, study design, and analysis. An introduction to the basic physical principles of magnetization and nuclear magnetic resonance, and the technology, is given in Chapter 2.3.7.

Many excellent specialist texts covering all aspects of functional magnetic resonance imaging are available for the reader seeking more detailed treatment of the issues.(5–7)

Cerebral activation and blood-flow changes

Try closing your eyes and then opening them again. At the moment that you open your eyes, neurones in the occipital cortex that are specialized for the perception of visual stimuli will show a sudden and dramatic increase in their rate of discharge. There is a short delay (approximately 100 ms) between the stimulus and neural response owing to the propagation of electrical activity from the retina via the optic nerves and tracts to the visual cortex. Later, some 3 to 8 s after stimulus onset, there will be an accompanying change in the local blood supply to the stimulated area of cortex. Blood flow increases without a commensurate increase in oxygen uptake by the visual cortex, leading to a local increase in the ratio of oxygenated to deoxygenated forms of haemoglobin.

The linkage between neural activity and regional cerebral blood flow, sometimes called neurovascular coupling, has been known since Roy and Sherrington first reported ‘changes in blood supply in accordance with local variations of functional activity’ in 1894. However, the biophysical and biochemical mechanisms for neuro-vascular coupling are complex and not yet completely defined in detail.(7)

Endogenous contrast agents

The fact that neural activity is linked to local blood flow provides the opportunity for functional MRI. The most common, and non-invasive, approach exploits the paramagnetic properties of iron in deoxygenated haemoglobin as an endogenous contrast agent. Neural activity causes a local reduction in the ratio of deoxygenated to oxygenated haemoglobin, so that the paramagnetic effects of deoxyhaemoglobin are ‘diluted’. Since apparent spin–spin relaxation or dephasing is accelerated by microscopic inhomogeneities in the magnetic field due to the presence of paramagnetic contrast agents, the net effect of diluting deoxyhaemoglobin will be to prolong T*2 times in areas of the brain that receive an increased blood flow as a consequence of neural activity. The haemodynamic effect on spin–spin relaxation can be measured by a T*2-weighted signal change (of 3 per cent or less) which is blood oxygen level dependent (BOLD).

Imaging sequences for fMRI

Several different pulse sequences can be used to collect MRI data that are sensitive to functionally determined changes in signal strength. Here we will concentrate on gradient echo sequences which, combined with special techniques for very rapid data acquisition, are most widely used to date for fMRI. However, spin echo sequences can also be used for functional MRI data acquisition, and gradient echo sequences can be used for structural MRI.

Gradient echo sequence

The basic principle is similar to spin echo imaging. An initial excitation pulse of radiofrequency energy is supplied at the Larmor frequency to the brain in the presence of a powerful static magnetic field. Protons are excited to a state characterized by increased transverse magnetization and a coherent phase of precession around the axis of the external field. Immediately the radiofrequency pulse has ceased, protons begin to relax back to their equilibrium state of maximum longitudinal magnetization and random phase of precession, emitting a radiofrequency signal by free induction decay.

In gradient echo imaging, the process of spin–spin relaxation (dephasing) is first accelerated by briefly applying a gradient to the magnetic field shortly after the excitation pulse. Then, at some time (TE/2) after the excitation pulse, a second gradient is applied to reverse the process of dephasing, causing rephasing and a signal maximum or echo some time (TE) after excitation. The sequence is repetitively applied with a constant time interval between consecutive excitations (TR).

The objective is to manipulate spin–spin relaxation by brief perturbations of the external magnetic field rather than by supplying additional pulses of radiofrequency energy as in spin echo imaging. Frequency- and phase-encoding gradients are applied to locate the sources of signal in three-dimensional space (see Chapter 2.3.7).

One advantage of gradient echo imaging is that TE and TR can both be shorter than in spin echo imaging, allowing an overall reduction in scanning time. However, if TR is short, spoiler gradients or radiofrequency pulses may be needed to ensure that the protons have returned to equilibrium before the next excitation pulse is supplied. The flip angle a induced by radiofrequency excitation can be adjusted to generate images weighted by different sources of tissue contrast. T1-weighted images are generated by radiofrequency pulses causing flip angles of the order of 10 ° to 20 °. For functionally sensitive T2-weighted images, more radiofrequency energy must be supplied in the excitation pulse to give a flip angle approaching 90 °.

Echoplanar imaging

The gradient echo sequence equivalent to a fast spin echo sequence is obtained by rapidly applying, or blipping, a series of rephasing gradients following the excitation pulse and dephasing gradient. Gradient blipping is done extremely rapidly (<1 ms), and up to 128 echoes can be generated from a single excitation. Clearly, the advantage of such echoplanar imaging is the speed of acquisition. Multislice images of the entire cortex, with slice thickness of only a few millimetres, can be acquired in 2 s or less. Such high-speed imaging is highly desirable for functional MRI, where we wish to detect physiologically determined changes in magnetic resonance signal with the best possible temporal resolution. However, the hardware required for rapid gradient blipping has only become widely available in the last few years.


The main sources of artefact in functional MRI are the same as for structural MRI (see Chapter 2.3.7).


Movement of the subject's head during fMRI data acquisition is inevitable, and attempts to eliminate it by fixing the head in the scanner may paradoxically exacerbate the problem. The best approach of minimizing movement is to ensure that the subjects are not unduly anxious about the scanning procedure, that they understand clearly what they are being asked to do, and that they are comfortable in the scanner before data acquisition begins. Experiments should be designed so that they do not require the subject to move extensively; small finger movements required for button pressing do not generally cause severe head movement. However, even very small movements of the head (less than 1 mm) can cause significant artefacts in fMRI data.

Involuntary or physiological movements are mostly due to the cardiorespiratory cycle causing pulsation of the cerebrospinal fluid and vascular spaces. Therefore, these movements often occur at a higher frequency than the frequency of image volume acquisition, and are aliased into the signal as a low frequency confound.


The susceptibility artefact is exaggerated by gradient echoplanar imaging, typically causing signal loss in inferior temporal and orbitofrontal brain regions close to bone or sinuses. The problem is further compounded if subjects are asked to speak during scanning, since slight deformations of the sinuses associated with overt articulation can cause changes in susceptibility artefact, which can mimic signal changes due to speech-related neural activity. If overt articulation is necessary to monitor the subject's performance on the experimental task, then it is advisable to design the sequence so that images are not acquired while the subject is speaking.


The hardware requirements for functional MRI include a superconducting magnet, a radiofrequency coil, computers, and a purpose-built room, as described in Chapter 2.3.7.

Gradient coils

The essential extra prerequisite is gradient coils capable of very rapidly blipping the external magnetic field for echoplanar imaging. The gradients required are small compared with the external field (1 to 10 mT/m) but may need to be applied for less than 1 ms. The speed with which the gradient is switched on, the slew rate, is necessarily fast (up to 200 mT/m/s). Such rapidly changing gradients can cause eddy currents in the gradient coils, adversely affecting the homogeneity of the field. This problem is minimized by actively shielding the coils, which requires yet another set of coils.

Audiovisual equipment

It must be possible to present visual and auditory stimuli to subjects while they are lying with their heads in the bore of the magnet. Headphones are required to clearly present auditory stimuli in the presence of the loud background noise of gradient switching. Visual stimuli can be projected on to a screen, viewed through a periscope. The subject should have access to an alert button. In addition, it is generally useful for subjects to use a button-press device to indicate their response to cognitively demanding experimental tasks. These behavioural data will need to be monitored during scanning.

Experimental design

The basic principle of experimental design in fMRI is to manipulate the subject's experience or behaviour in some way that is likely to produce a functionally specific neurovascular response. It is usually important that the experiment should be designed to allow some other measure of response, for instance a button press, to be monitored simultaneously. We shall illustrate these and other principles by considering how one might design an experiment to identify the regions of the brain that are important in making a (semantic) decision about the meaning of words. As will become clear, no single design is ideal; each has its strengths and weaknesses, and the choice between them should also be considered carefully in the light of the particular hypothesis one is using fMRI to test.

Blocked periodic design

This experimental design, in its simplest form, involves alternately presenting the subject with two conditions: an activation (A) condition and a baseline (B) condition. Each condition is presented for an identical epoch of time. During each epoch, several stimuli are sequentially presented with an interstimulus interval (ISI) that is less than the epoch length. The cycle of alternation between A and B conditions is repeated a number of times over the course of each experiment.

For example, during each 30-s epoch of the A condition, we could visually present subjects with a series of 12 common concrete nouns (ISI = 2.5 s) and ask them to decide for each word whether it refers to an animate object (e.g. ‘goat’) or an inanimate object (e.g. ‘bucket’). The subjects could be asked to indicate their decision by pressing one of two buttons: left for living objects and right for non-living objects. During each 30-s epoch of the B condition, we could present words at the same rate, but ask subjects to decide whether they are written in upper- or lowercase letters. This decision could be monitored by button press as in the A condition. The two epochs could be presented alternately, beginning with the B condition, in five cycles for a total experimental time of 5 min. Functional MRI data would be acquired continuously throughout the experiment (Fig.

Fig. Design, response, and modelled response for a blocked periodic experiment. The experimental design or input function is represented by a square wave (solid line), which alternates periodically between a baseline (B) and an activation (A) condition. The B condition is presented first, and the BA cycle is repeated five times in the course of the experiment. Images are acquired every 3 s during the experiment, and the T*2-weighted signal observed at an activated voxel is shown by points joined by a solid line. There is clearly a signal increase during the A condition. The modelled response is shown by the broken line.

Design, response, and modelled response for a blocked periodic experiment. The experimental design or input function is represented by a square wave (solid line), which alternates periodically between a baseline (B) and an activation (A) condition. The B condition is presented first, and the BA cycle is repeated five times in the course of the experiment. Images are acquired every 3 s during the experiment, and the T*2-weighted signal observed at an activated voxel is shown by points joined by a solid line. There is clearly a signal increase during the A condition. The modelled response is shown by the broken line.

The rationale for this design is that the two conditions are matched in all respects apart from semantic analysis; words are visually presented at an identical rate, and subjects are asked to signal their decision by an identical device. But while condition A demands semantic analysis of the words (what do they mean?), condition B demands only orthographic analysis (what do they look like?). We assume that only those regions of the brain that are specifically responsible for semantic analysis will show an increased magnetic resonance signal during condition A; those regions responsible for visual perception and motor output will be activated identically under both conditions, and so will not demonstrate a periodic signal change at the frequency of AB alternation. This set of assumptions is sometimes referred to as cognitive subtraction.

Blocked periodic designs can generate robust signal changes in fMRI, as long as the two conditions are not too closely matched. The drawbacks are that it is impossible to assess the response to a single stimulus and the critical assumption of cognitive subtraction may not always be valid. Sometimes two experimental tasks that appear to differ only in terms of one component process may actually invoke entirely different cognitive strategies and so cause activation of entirely different neurocognitive networks.

Parametric design

Parametric designs are so called because the same task is presented throughout the experiment but some continuously variable parameter of the task is experimentally manipulated. For example, we could ask subjects to perform the semantic analysis task for 5 min, but continuously vary the interval between consecutive stimuli (words) from 10 s at the start of the experiment to 1 s at the end. Here we are assuming that as the task becomes more difficult, i.e. the interstimulus interval becomes shorter, blood flow to the regions specialized for semantic analysis will increase. The main advantage of this design is that it avoids the assumption of cognitive subtraction; the main disadvantage is that it may lack specificity. Motor and visual cortex, as well as brain regions specialized for semantic analysis, will probably show an increased blood flow as the rate of stimulus presentation is increased.

Event-related design

Event-related designs are composed of a series of individual stimuli. They may be coupled with sequences for very rapid image acquisition so that the temporal pattern of response to a single event can be resolved in detail. An event-related design would be advantageous for our semantic analysis experiment if we were particularly interested in correlating some aspect of the behavioural response to each stimulus, for instance accuracy of decision or reaction time, with the neurovascular response measured using fMRI. A disadvantage of such designs is that signal changes induced by a single trial are generally weak compared with the 2 to 5 per cent signal changes that are typical in blocked periodic experiments.

Beyond a single experiment

Generally, the hypothesis in question demands the investigation of more than a few subjects and/or more than one experimental condition. When designing the studies it is important that randomization should be used appropriately to eliminate confounding effects of the order in which experiments are conducted, and of the order in which different subjects are scanned. Practice on a task may substantially alter the neurovascular response, and so all subjects should receive preliminary training on the task according to a standard protocol. If there is considerable variability between subjects in their ability to perform a task, consider adjusting the difficulty of the task presented in the scanner so that each subject is performing at the same level in terms of accuracy or reaction time. The use of functional MRI to study longitudinal changes by repeated examination of the same subject(s), for instance before and after the administration of a drug, will generally improve the statistical power to detect the effect of interest by controlling for idiosyncratic variability of functional response between subjects.

Data analysis

General principles of data analysis are reviewed here; for more detailed coverage of the issues and the methods implemented in a variety of software packages, see.(5–7)

Movement estimation and correction

The first step in fMRI data analysis is to estimate the extent of head motion during data acquisition and to correct it. Due to the multislice acquisition protocols generally used for fMRI, the magnetic field to which the brain is exposed will change dramatically within the space of a few micrometres at the superior and inferior edges of a selectively irradiated slice. This means that minute head movements (<1 mm) can have disproportionately large effect on magnetic resonance signal.

Head movement occurring at the same time as time as experimental stimuli are present, namely stimulus correlated motion, can artefactually exaggerate the neurovascular response. Head movement occurring randomly with respect to the experimental design is more likely to cause the opposite problem of artefactually attenuating the measured response. Therefore it is essential to use a computerized method for movement estimation and correction.

Statistical models for the neurovascular response

The next step in analysis is to estimate the strength of the experimentally determined signal change in the time series of magnetic resonance signal measurements at each voxel in the image. This requires some sort of model for the response. The simplest model, for a blocked periodic design, is a square wave at the same frequency as the experimental input function. This model assumes that a brain region activated specifically by condition A will show an immediate increase in signal intensity, which is sustained throughout the epoch until the onset of condition B. The problem with this model is that the increase in magnetic resonance signal during condition A is due to changes in blood flow and oxygenation, which are dispersed and delayed by several seconds relative to the onset of condition A. Furthermore, this haemodynamic delay between stimulus onset and measurable response will be variable from one voxel to another. Therefore it is important that the experimental effect should be modelled as an increase in signal intensity that is arbitrarily delayed relative to the onset of the activating stimulus. The most general way of achieving this is to convolve the experimental input function (the vector coding changes in experimental conditions) with a model of the haemodynamic response. The haemodynamically convolved input function can then be regressed on the fMRI time series at each voxel to estimate the neurovascular response to changing experimental conditions.

In fitting linear regression models to fMRI time series, one important technical issue is that the residuals of the regression will generally not be white noise or serially independent. Rather the residuals will typically have long-range dependency or long memory in time and this will need to be addressed for proper estimation of linear model parameters.(8) There are probably several possible artefactual sources of autocorrelation in fMRI time series residuals—including imperfectly modelled experimental activation, uncorrected head movement, and aliased cardiorespiratory pulsation. However, recently attention has focused on the role of low frequency, spatially coherent, endogenous oscillations of large neuronal ensembles as a source of long memory in fMRI time series.(9) This hypothesis has encouraged studies of the univariate and multivariate properties of fMRI data recorded at rest, i.e. in the absence of experimentally controlled task processing.(10,11)

Activation mapping

The next step in analysis is often to decide which of the several thousand voxels in the image have demonstrated such a strong response to the experiment that it is unlikely to be due to chance. In other words, we want to identify the significantly activated voxels. Let us assume that we have estimated the neurovascular response by the magnitude of a linear model coefficient at each and every voxel, and refer to this as our test statistic. The problem is then to assign a probability to each test statistic under the null hypothesis that the experiment had no effect on the brain. To do this we need to know the probability distribution of our test statistic under the null hypothesis. There are broadly two ways we can know this distribution: we can work it out from mathematical theory, or we can sample it by randomly permuting the data. Theoretical distributions are quicker to evaluate than permutation distributions, but permutation entails many fewer assumptions and is the gold standard against which the validity of theoretical approximations should be checked.

Once we have a probability distribution for the test statistic, we still have to decide what p-value we wish to adopt as our threshold for activation. If we choose a small (conservative) p-value (e.g. <0.00001), only those voxels that demonstrate a very powerful response will be identified as activated. There will be few false-positive or type 1 errors, i.e. almost all the voxels we identify as activated will truly be activated. But there will probably be a large number of false-negative or type 2 errors, i.e. many voxels that are truly activated will not be identified as such. Conversely, if we choose a large (lenient) p-value (e.g. <0.01), there will be a larger number of false-positive errors but a smaller number of false-negative errors. The choice of p-value should be informed by the search volume, or the number of voxels tested for significance. The larger the search volume, the smaller the p-value will need to be for an acceptable degree of type 1 error control. A rule of thumb is that the p-value should be approximately the reciprocal of the search volume. More elaborate methods have been advocated for correcting p-values for large numbers of tests on imaging data.

An alternative approach to testing tens of thousands of voxels against a suitably small probability threshold, with an associated risk of major type 2 error, is to combine information about the experimental response over several voxels. For example, we can initially apply a lenient threshold (p = 0.05) to the test statistics estimated at each voxel, and set to zero any voxel that does not have a test statistic greater than the corresponding critical value. The result will be a map of several spatially contiguous clusters, ranging in size from a single voxel to several hundred voxels (Plate 10). We can ascertain the probability distribution for cluster size under the null hypothesis either by theory or permutation. Then we can proceed to identify significantly activated clusters instead of voxels. The advantage of hypothesis testing at cluster level is a greater power to detect significant foci of activation, partly because there will be many fewer clusters than voxels to test, so the p-value can be legitimately increased. The disadvantage is the loss of spatial resolution of activation.

Multivariate approaches

Many of the ‘higher-order’ cognitive tasks that are likely to be of greatest interest to psychiatric research do not activate a single modular region of the brain. Instead, they typically activate several spatially distinct or distributed regions that together comprise a large-scale neurocognitive network for performance of the task. It may then be of interest to investigate functional integration between different regions or nodes of the network. The simplest way to do this is by estimating the correlation between a pair of fMRI time series observed at different voxels or regions. Large correlations, whether negative or positive, may be described as evidence for functional connectivity. Psychiatric disorders may be characterized by abnormal functional relationships between coactivated regions, or functional dysconnectivity.

More sophisticated techniques for investigating functional relationships between large numbers of voxels or regions include multivariate methods such as principal component analysis, discriminant analysis, and path analysis. These methods are equally applicable to structural MRI data, where they may provide indirect evidence for anatomical connectivity between regions.

Within- and between-group analysis

Once a measure or parameter of experimental response has been estimated in each fMRI time series, the resulting parameter maps can be registered in standard space. There are many possible computational algorithms for spatial registration. The most commonly used at present is an affine transformation, which applies a global and linear rescaling in three dimensions to each individual image. A commonly adopted standard space is that represented in a stereotactic atlas of the brain originally written by Talairach and Tournoux to assist neurosurgeons in locating subcortical structures.(12) In these systems, each voxel is assigned a set of {x, y, z} coordinates which define its position. In Talairach–Tournoux space, the coordinates are defined relative to the cerebral midline and a line is drawn between the anterior and posterior commissures (intercommissural or AC–PC line). After registration, parameter maps are usually smoothed by applying a two- or three-dimensional Gaussian filter to accommodate variability in sulcogyral anatomy between subjects and error in spatial registration.

It is then possible to test a wide variety of hypotheses about the response parameters measured over several subjects at each voxel in standard space. For example, one can test the null hypothesis that there is zero mean or median power of experimental response within a group, or the null hypothesis that there is zero difference in the power of response between two groups. It is also possible to test for correlations between the power of functional response and some behavioural or symptom measure within a group.


The final result of fMRI data analysis will often be visualized as a map in standard space. The background for the map will generally be a grey-scale image of cerebral anatomy, such as a structural MRI dataset with fine spatial resolution and good tissue contrast between grey and white matter. In this case, one should beware of the potential discrepancy in geometric distortion between images of the same brain acquired using different sequences.

The background image will often be combined with, or substituted by, a rectangular grid allowing any feature of interest to be referred directly to the appropriate atlas of standard anatomical space. If the image is displayed as a series of two-dimensional slices, the z coordinate for each slice in standard space should also be displayed and the left and right sides of the right clearly indicated.

Voxels or clusters that demonstrate a significant effect are generally coloured against the grey-scale background image (Plate 11). A range of colours can be used to encode additional information. For example, the haemodynamic delay of response at each generically activated voxel may be colour coded by a continuous spectrum. Other strategies for visualization include use of three-dimensional rendering to show foci of activation in the context of the sulcogyral anatomy of a whole hemisphere, and ‘flat mapping’ whereby the template image is deformed to a smooth sphere and then mapped to a plane before activation foci are superimposed on it.

Further information

Comprehensive background information on fMRI physiology, experimental design, and data analysis:

Jezzard, P., Matthews, P.M., and Smith, S.M. (eds) (2003). Functional magnetic resonance imaging: an introduction to methods. (2nd edn) Oxford University Press, Oxford.Find this resource:

    The physiological origins of the BOLD effect:

    Logothetis, N.K., Pauls, J., Augath, M.A., et al. (2001). Neurophysiological investigation of the basis of the fMRI signal. Nature, 412, 150–7.Find this resource:

    Current perspectives of fMRI applications:

    Matthews, P.M., Honey, G.D., and Bullmore, E.T. (2006). Applications of fMRI in translational medicine and clinical practice. Nature Reviews. Neuroscience, 7, 732–44.Find this resource:

    Community web site for information about Brain Mapping and methods:


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