Advances in magnetic resonance imaging have made it possible to image with high resolution not only the structure of the human brain in vivo (including details of the white matter connecting various brain areas by means of diffusion-weighted MRI) but also functional changes. For a long time it was believed that local glucose consumption, local oxygen consumption, and rCBF were routinely coupled. The reasoning was that increased neural activity requires more glucose, more glucose requires more oxygen to be utilized, and more glucose and oxygen are delivered by more blood flow. These parameters are indeed strongly correlated at rest. However, rCBF and local glucose uptake increase much more than local oxygen consumption during physiological increases in neural activity, suggesting true uncoupling. At first glance this uncoupling between local oxygen consumption and rCBF might seem like a potential problem, but in fact it is another factor that can be used as an index of neural activity. Such uncoupling results in an increase in the concentration of oxygenated hemoglobin (HbO or oxy-Hb) and an apparent decrease in deoxygenated hemoglobin (Hb or deoxy-Hb) in neurally active areas relative to inactive areas. The most popular types of fMRI and optical imaging exploit the magnetic and optical properties of Hb and HbO.

1. Physical Foundations of MRI

Because fMRI is the neuroimaging technique most widely used today, we will describe some of its physical foundations in slightly more detail. According to quantum theory, electrons, protons, and neutrons possess a fundamental property referred to as "spin." We will consider a small group of protons, H + . The spins of these protons can be thought of as magnetic moment vectors, which cause the protons to behave like tiny magnets with a north (n) and a south (s) pole.

When the protons are placed in an external magnetic field with a north (N) and a south (S) pole, their spin vectors align themselves with the external field, just as a magnet would. For each proton there is a low-energy state in which the poles are aligned N-s-n-S and a high-energy state N-n-s-S (opposites attract and like signs repel; thus, more energy is required to keep the s-S and n-N poles aligned than when opposite poles are aligned). At room temperature, the number of spins in the lower energy level, N+, slightly outnumbers the number in the upper energy level, N—, depending on the molecular makeup of the substance. The difference between N+ and N— is referred to as the "net magnetization'' of the substance. The net magnetization vector is typically decomposed into two components: the longitudinal magnetization, in the direction of the external field, and the transverse magnetization, orthogonal to it. At equilibrium, the net magnetization vector lies along the axis of the imposed magnetic field and there is no transverse magnetization.

A crucial idea for magnetic resonance imaging is that the net magnetization vector can be moved by exposing the spin system to energy of a frequency equal to the energy difference between the spin states (e.g., by a radio frequency pulse). If enough energy is delivered to the system, it is possible to make the net magnetization vector orthogonal to that of the external magnetic field. Upon removal of the external energy source, the longitudinal magnetization returns to its equilibrium state, with a time constant labeled T\. T depends on the particular substance; for example, the T of brain white matter is about 500 mse. The difference in T between different types of tissues (such as gray versus white matter in the brain) is one of the main parameters used to construct structural MRI; these MRI images picture the physical structure of the brain, not its functioning.

While returning to equilibrium, the net magnetization vector will start to rotate about the axis of the external field. This is often depicted as a slow "wobble" or, more technically, precession. The precession of the net magnetization vector generates an electromagnetic signal that can be detected by an appropriate receiving coil. The precession occurs at a rate (the Larmor frequency) that depends on the properties of the material and is directly proportional to the strength of the applied field. Thus, if the strength of the applied magnetic field has a linear gradient of strength, then the precession rates at different spatial locations along the gradient will be different in predictable ways: the frequency of the electromagnetic signal received encodes the spatial location of its source.

To summarize so far: the key idea is that the net magnetization vector can be moved from the equilibrium position along the axis of the external field by applying a radio frequency pulse at the proper frequency, thus giving rise to a transverse magnetization component rotating around the axis of the external magnetic field. Such a component is the result of all of the spins precessing synchronously, thanks to the radio frequency pulse.

As soon as the pulse is turned off, the various spins begin to fall out of phase and the MRI signal begins to decay. This decay occurs for two reasons: intrinsic and extrinsic. The intrinsic factor is that the random configuration of the spins itself creates small inhomo-geneities in the local magnetic field. The magnetic field is slightly stronger in regions where many spins line up with the field and slightly weaker in regions where many spins are in the opposite direction. These slight changes in the local magnetic field result in slight variations in the precession frequency, causing de-phasing. The time constant that describes the return to equilibrium of the transverse magnetization is called T2. T2 depends on the molecular environment of the spins (it is about 70 msec for brain white matter). The extrinsic factor for dephasing is the slight inhomo-geneities in the external magnetic field. Substances that possess paramagnetic properties (such as Hb) will distort the field, causing faster dephasing (the time constant in this case is referred to as T2).

2. MRI Scanners

MRI scanners exploit the principles just described to create images of the human brain. In practice, an MRI scanner is composed of a magnet, usually a horizontal tube (referred to as the "bore") in which a person is placed, a radio transmitter, and a radio receiver. The radiofrequency pulses described earlier are transmitted by electrical coils located inside the magnet. Often, the same coils also receive the radiofrequency signals generated after the excitation radiofrequency pulse is turned off. The signals generated during this phase induce voltage changes in the receiver coil, which are then sent to suitable amplifiers. The image is reconstructed on the basis of these signals. The intensity of the MRI signal increases with field strength, which explains the trend toward building scanners with higher and higher field strengths: although most existing scanners have a field strength of 1.5 T, the number of 3- and 4-T scanners is rapidly increasing, with a handful of sites in the process of building 7-T scanners.

3. Blood Oxygenation Level-Dependent Contrast (BOLD)

The most popular type of fMRI, blood oxygenation level-dependent (BOLD) contrast, is based on the fact that Hb is paramagnetic whereas HbO is not. As described earlier, rCBF increases brought about by increased synaptic activity are not matched by corresponding increases in oxygen extraction. This causes an apparent decrease in Hb, which results in less rapid dephasing of protons (longer T2). The final outcome is that a local increase in synaptic activity will result in an increased MRI signal. This phenomenon was first demonstrated in humans in 1992.

Although BOLD contrast is the predominant technique for functional mapping, other techniques have been developed. Among them, techniques to measure rCBF noninvasively by using arterial spin labeling (ASL) hold much promise. In essence, ASL techniques "label" arterial blood by changing the magnetic state of arterial water protons as they are carried up through the brain and then following the effect of labeled blood on the amplitude of the MRI signal. The advantages of ASL over BOLD are that, in theory, it should provide better localization of functional activation because of reduced sensitivity to intravenous signals, and that ASL signals are quantitatively related to CBF, which in turn is generally assumed to be tightly coupled with local neural activity. The main disadvantages of ASL relative to BOLD are that the ASL signal is 2-4 times smaller than the BOLD signal, and that ASL is limited in its maximum rate of image acquisition relative to BOLD imaging because of the time required for the tagged blood to flow into the portion of the brain being imaged.

The relationship between the BOLD signal, and the underlying activity is more complex than the well-established one between rCBF and neural activity. Thus, the issue of the extent to which the BOLD signal actually reflects neural events arises. Studies comparing the BOLD signal with rCBF (measured with PET H215O) have found a linear relationship between PET and fMRI across sets of distributed regions. Animal studies have also provided evidence that BOLD, rCBF, and evoked potentials in response to visual stimuli at various frequencies are highly correlated, which is consistent with the hypothesis that the BOLD signal reflects neural events in a quantitative manner. However, exceptions to this relationship have also been found: in some cases, fMRI seemed more sensitive to activation in a number of cortical areas, whereas PET seemed more sensitive to activation in deep nuclei.

Even without considering the spatial limitations of the imaging devices, the locus of the metabolic and especially of the vascular responses may not coincide with that of brain cell activity. The theoretical spatial resolution of the BOLD signal is limited by the size of the smallest vascular unit that can be modulated independently in response to neural activity. If synap-tic activity only produced changes in the BOLD signal in large blood vessels, then the spatial resolution of BOLD would be very low. In theory, the smallest of such vascular units is the capillary. Based on the fact that capillary walls possess some contractile elements and that there are precapillary sphincters, the capillary recruitment hypothesis states that a major mechanism of blood flow regulation in the brain relies on the complete opening and closing of capillaries. This hypothesis is problematic, however, because under resting conditions all cerebral capillaries seem to be continuously perfused with plasma and most of them also contain moving red blood cells. From these considerations, we can infer that the spatial resolution of the hemodynamic response is at least 1 mm3, the approximate size of arterioles feeding capillaries. Empirical work, noted shortly, suggests that in fact the spatial resolution of fMRI using BOLD may be a bit better than this.

One method researchers have used to assess empirically the spatial resolution of fMRI, and particularly that of the BOLD signal, has been to map anatomical structures with known functional properties. Activation in the lateral geniculate nucleus of the thalamus (LGN) during photic stimulation has been demonstrated by using BOLD contrast in a 4-T magnet. The LGN is a very small structure and is located near other structures (e.g., the hippocampus) that did not exhibit activation during this task. Although the BOLD signal in the LGN was smaller than that in the primary visual cortex (area V1), it had a similar time course. Furthermore, task-related activation in the pulvinar nucleus of the thalamus was also detected, and its activated location could be discriminated from that of the LGN. More recent work has also shown visual topography in the LGN. Furthermore, a study used high spatial resolution fMRI to map the activation in the ocular dominance columns (less than 1 mm thick) of area V1 during alternate visual stimulation of the left and right eyes. (Note that the success of this study indicates that the spatial resolution is better than 1 mm.)

Animal studies have also provided evidence regarding the spatial resolution of BOLD contrast. For example, stimulation of a rat's whiskers elicits BOLD signals with a spatial distribution that overlaps that of electrical activity in the rat whisker ''barrel cortex.'' These results show empirically that the site of the BOLD activation is spatially very close to the sites of expected neural activity. Despite this convergent evidence, some findings also suggest that caution is warranted in the interpretation of the spatial location of fMRI foci based on BOLD contrast. Other work has compared BOLD signals with rCBF measured by PET during a visually cued sequential finger movement task. The results showed a general similarity in the pattern of activation, but in some cases they also showed a discrepancy between the precise location of foci detected with PET and fMRI (almost 1 cm average), perhaps due to the higher sensitivity of the BOLD contrast to signals coming from draining veins.

We have focused so far on the spatial resolution of fMRI, but the technique is also useful for its temporal resolution—especially in comparison with PET (which requires about 40 sec to obtain an image). The temporal resolution of fMRI depends not only on the sampling rates possible with current MRI hardware but also on the temporal characteristics intrinsic to the hemodynamic response (relative to that of the neural events that generate it). MRI sampling rates depend on the pulse sequences used. In practice, a whole-brain image can be obtained on the order of 1-2 sec with the commonly used gradient echo echoplanar imaging (EPI). Note that the MRI signal becomes smaller and smaller for sampling rates faster than about 3 sec because the magnetic spins do not have enough time to return to equilibrium. A clever method to get around this problem is to vary the onset of the trials relative to the sampling times. For example, if a voxel is sampled every 3 sec, half of the trials can be initiated in synchrony with the excitation pulses whereas the other half can be initiated 1.5 sec later. By combining the two trial types, one can achieve a temporal resolution that is twice the actual sampling rate. The temporal characteristics of the BOLD response have been well-characterized. The onset of detectable differences in the BOLD response, relative to the putative onset of neural activity, is about 2 sec; the BOLD response peaks between 6 and 9 sec and returns to baseline slightly more slowly after the cessation of neural activation. An initial undershoot, reaching a maximum around 1 sec after stimulus onset, has been observed in some studies, although the reliability and nature of this phenomenon are still under investigation. A more reliable post-undershoot in the BOLD

signal, peaking a few seconds after stimulus offset and lasting for about 20 sec, has also been observed.

The effective temporal resolution is affected by the variability of the parameters of the hemodynamic response (such as rise time) rather than by the absolute value of such parameters. For example, if the onset time is very large (e.g., several seconds) but the variance is very small (e.g., 100 msec), one can still determine relative latency shifts between conditions with accuracy. A few studies have addressed the issue of latency estimation variability within a region of interest. These studies measured the variability of a number of parameters such as the onset time and the time to peak of the hemodynamic response within specific regions of interest elicited by a brief sensory stimulus. Typically, the stability of the onset time and the time to peak in a given region are very high, especially within the same subject.

Several studies have shown large differences in the onset latency of the hemodynamic response in different brain regions. Variations in the delay of the BOLD response between 4 and 8 sec in visual and motor cortical areas are common. Such variations are too large to be accounted for by variations in neuronal activity latencies. Even longer delays, between 8 and 14 sec, can be observed in large vessels. Given the large spread of hemodynamic response latencies over space (several seconds), in general it is not possible to infer the temporal order of activation of two arbitrary regions (less than 1 sec for most cognitive tasks) from the absolute hemodynamic onset latencies. It is, however, possible to determine the relative timing of neural activation stages within a region of interest in response to two or more experimental manipulations. Although more problematic, it is also possible to determine the relative timing of neural activation stages between two regions of interest if these have comparable hemodynamic properties (e.g., striate cortex representation of the left and right hemifields). A few studies have shown that, within these limits, subsecond temporal resolution can be achieved.

4. Analyses of fMRI Data

A wide spectrum of methods for the analysis of fMRI data is currently in use. Not surprisingly, the range of techniques has expanded over the last few years. It is interesting to note that the analysis methods used most widely depend, to a large extent, on the availability of software packages. Often the software package that is the least difficult to use and the least expensive becomes the one used most widely, to a large extent independent of the soundness of the implemented algorithms. Although some preprocessing and artifact removal issues are specific to fMRI, the general statistical problems are similar to those encountered in the analysis of EEG, MEG, and PET data but are more difficult to solve because of the size of the data sets. A typical fMRI session produces tens of thousands of time series, one for each voxel. Typically 64 x 64 x 64 = 262,144 voxels are monitored. Thus, the same kinds of type I error issues described for the previous techniques arise with fMRI. Many analysis techniques take advantage of the fact that the probability of obtaining clusters of active voxels decreases with cluster size (the actual probability depends on the detailed assumptions made).

The first fMRI paradigms were based on the same activation paradigms employed with PET, often referred to as blocked paradigms. These paradigms consist of administering the various conditions for several tens of seconds in a blocked manner. Analyses typically involve generating statistical maps of contrasts between images collected during the various conditions. Developments in the analysis of fMRI data have expanded the range of the paradigms available with fMRI. Such paradigms originated from researchers familiar with the ERP methodology and are thus referred to as event-related paradigms. Event-related paradigms essentially allow the presentation of trials in the various conditions in a mixed manner, thus eliminating several confounds inherent in the blocked paradigms, such as the effect of expectancy. The analytical methods used to analyze event-related paradigms usually rely on the assumption that the hemodynamic response is linear and time-invariant. That is, the methods assume that the response to stimuli A and B presented in close temporal succession can be estimated by summing the responses to stimuli A and B presented independently of each other. Results from several studies are consistent with the assumption that activation-induced hemodynamic responses behave in a roughly linear manner. For example, the hemodynamic response in the visual cortex is approximately linear, although the response to brief stimuli is greater than that predicted by a linear, time-invariant system. Despite such documented deviations from linearity, several studies have shown that useful results can be obtained by using the linearity assumption. For example, responses to visual stimuli delivered as rapidly as 1 per second can be resolved. Furthermore, reliable activation maps can be obtained with stimuli presented at an average rate of 2 per second, provided that the interval between stimuli varies randomly. The possibility of using rapid presentation paradigms with fMRI is important in part because it has allowed the use of exactly the same paradigms typically employed with electromagnetic techniques, which has promoted the direct comparison of fMRI results with those obtained from EEG and MEG.

5. Summary of Advantages and Disadvantages of fMRI

To summarize, fMRI is the most common form of functional neuroimaging today for good reasons: in addition to its relatively good spatial and temporal resolution, it is also widely available (most hospitals have an MRI machine) and is relatively inexpensive, especially compared to PET. However, the technique is not ideal. First, it is very noisy; the shifting magnetic fields cause physical movements ofthe magnets, which, like a conventional loudspeaker, displace air and thus produce sound. Second, the hole in the bore is relatively narrow but very deep, which some people find uncomfortable. Third, the technique is very sensitive to motion. Although statistical methods have been designed to correct for the distortions produced by motion, this is still a major problem. Fourth, gradient echo EPI, the method most widely used for fast imaging, does not work well for areas adjacent to tissue-air interfaces.

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