The magnetoencephalogram (MEG) is a record of magnetic fields, measured outside the head, produced by electrical activity within the brain. Typically MEG sensors are housed in a helmet shaped container (or dewar) in which the subject places their head during the measurement process. The magnetic fields are produced by the same underlying electrical changes that give rise to the electroencephalogram (EEG), that is they are due mainly to post-synaptic currents flowing across pyramidal neurons. Unlike the electroencephalogram however the magnetic fields outside the head are hardly affected by the conductivity of the tissues within the head. Accurate reconstruction of the neuronal activity that produced the external magnetic fields therefore requires simpler models than with EEG. The high spatial and temporal resolution with which brain activity can be measured can be used to reveal how groups of neurons communicate and has important clinical applications.
The magnetic fields outside the head due to electrical activity within the brain are in the hundreds of femto (10-15) Tesla, that is approximately 100 million time smaller than the earth's magnetic field. Although the first Magnetoencephalogram was based on a million turn coil (Cohen et al. 1968), modern systems rely on the superconducting quantum interference device or SQUID (Clarke 1994) for sensitivity. These devices convert the sub-quanta changes in magnetic flux into voltage changes. Typically the SQUIDs are coupled to superconducting coils or flux transformers which are situated as close as possible to the subject's head (within 2cm typically). Magnetic field changes in the flux transformers cause a change in superconducting current in the transformer coils that is passed via an input coil to the SQUID itself. The ability to measure such small fields also makes the devices very sensitive to other magnetic field changes in the environment. For example a car at 2km distance would cause a similar change in magnetic flux to that due to brain activity (Weinstock 1996). The next major problem is to separate the brain signal from the external noise.
Magnetically shielded rooms
Typically MEG systems are housed in magnetically shielded rooms. These rooms are often composed of a number of layers of materials with different magnetic properties. For example aluminium shielding is relatively inexpensive and attenuates high (>1Hz) frequency magnetic interference, whereas mu metal shielding () is used to attenuate very low frequency (0.01Hz) interference. Passive shielding factors of 1630 and 240.000 at 0.1 and 1Hz respectively have been reported (Cohen et al. 2002).
The simplest type of flux transformer is the magnetometer. This is a single superconducting coil (radius typically 1cm) situated as close as possible to the subject's head. Such devices are extremely sensitive but also pick up all environmental changes in magnetic field. Most MEG systems therefore contain gradiometers, or a combination of magnetometers and gradiometers, as flux-transformers. A gradiometer comprises two or more oppositely wound coils separated by a certain distance or baseline (typically 5cm), with the coils separated in the direction perpendical to the coils (radial gradiometer, see Figure), or the coils placed in the plane formed by the coils itself (planar gradiometer). Magnetic interference from distant sources will be relatively uniform across the two coils giving an overall net current flow of zero (as they are oppositely wound). Conversely nearby electrical sources (such as those in the head) will differentially effect the coils leading to a net current flow to the SQUID. In practice it is very difficult (even using thin-film fabrication technology) to create two coils of exactly the same dimensions and orientation to better than 0.1% tolerance or balance (Nurminen et al. 2008), which means that 0.1% of a perfectly homogeneous field is measured instead of the required zero output of the gradiometer in this case. Consequently, this imbalance will lead to a small percentage of external noise arriving at the SQUID.
Software noise cancellation
An array of reference channels can be used to compensate for the effects of imbalance, and to noise signals, by subtracting a weighted sum of the reference sensor signals from each signal sensor. The reference sensors are placed in such way that they are least sensitive to the signals of interest, and so contain mostly a record of external noise sources. These weightings can be determined at the factory and effectively create a higher order gradiometer (Vrba et al 1995). Another elegant method is the decomposition of the measured magnetic field into a spherical harmonic set (Taulu and Kajola 2005). Using the assumption that there are no magnetic sources inbetween the sensors and the outside of the brain, one can then show that this set can be split in two part: certain members of this set must have arisen from within the sphere surrounding the head, whilst other harmonics must have arisen at a distance. The removal of these external harmonics means that a large proportion of interference can be rejected. For both these approaches to work effectively, the dynamic range of the MEG electronics should be sufficient to measure the interferences precisely.
The forward problem
This is the problem of computing what the output of the MEG sensors would be if a certain region of cortex were active. To do this, it is necessary to make some assumptions and simplifications:
Dipolar source models
Most measurable MEG signals arise from intracellular longitudinal currents (due to post-dynaptic potentials) within the dendrites of pyramidal cells that are orientated perpendicular to the cortical surface. The electrical current due to a group of adjacent, aligned pyramidal cells can be modelled as an equivalent current dipole. A current dipole is an abstraction that has the dimensions of current times length, though the length is defined as being infinitesimally small. A patch of active cortex may be considered as a set of current dipoles distributed in a palisade. This forms a current dipole layer, which can be considered as a single current dipole when observed from a distance much larger than the dimensions of the area of active cortex. Modelling brain activity with current dipoles has been quite successful, mainly because at a typical measurement distance (at least 2 cm from the source) many current configurations seem dipolar. For larger areas of active cortex, the higher order terms in a multipolar expansion may need to be included in the model (Jerbi et al. 2002). Action potentials are brief and travel in two directions along an axon, which is best modelled as two opposing current dipoles in close proximity, which in turn causes a rapid decay of the produced magnetic field with distance. Temporal and spatial summation, required for a measurable MEG signal, therefore seems unlikely. However, recent work has shown that action potentials may also contribute to the MEG signal (Murakami and Okada 2006), suggesting that alternative models may be required (e.g. a starting or arriving action potential could be modelled as a single stationary dipole).
Volume Conductor Models
The advantage of MEG over EEG lies in the relative simplicity of the volume conductor model required. For example, approximating the outer skull surface by local spheres seems to perform as well as computationally intensive boundary element methods (Huang et al. 1999). This simplicity is due to the fact that MEG is relatively (but not completely) insensitive to secondary currents that flow through the head volume to balance the current flow at the neuronal source (the primary current flow). The price paid for this simplicity is two-fold. Firstly, a substantial loss in sensitivity with distance (proportional to distance squared between source and sensor). That is, MEG is relatively insensitive to sources deep within the brain. Secondly, relative insensitivity to radial sources which theoretically give rise to no external magnetic field (Sarvas 1987) in a perfect spherically symmetric volume conductor (but do produce volume currents, the effect of which are measurable with EEG). Simulation studies have shown that, even if one takes the head to be perfectly spherical, the regions of cortex that are most radial (the crests of the gyri) are also closest to the sensors and surrounded by off-radial cortex to which the MEG system is extremely sensitive. Given that the MEG signal is due to the spatial summation of neuronal currents over at least a few square millimeters, at least part of such gyral sources remain highly visible (Hillebrand and Barnes 2002). The main empirical barrier to MEG is therefore its depth resolution. That said, recent studies have shown that the thalamus (Timmerman et al. 2003), amygdala (Cornwell et al., 2008), and hippocampus (Riggs et al. 2009), can all be reconstructed with MEG.
The inverse problem
For a given magnetic field outside the head, there are an infinite number of electrical current distributions that could have created it. This means that the MEG inverse problem is theoretically ill-posed, having many solutions to a single problem. Such ill-posed problems are however commonly encountered in everyday life. For example, watching television involves the recreation of a three dimensional scene from a two dimensional picture. This is easy for us to do as knowledge of the world, such as the size of people, helps us to mentally place the characters in their correct locations. The MEG inverse problem is therefore certainly soluble, it is simply necessary to understand more about the brain in order to do this. All source localization methods make assumptions about how the brain might work. For example one might assume that no two parts of the brain have exactly the same electrical activity (beamforming). The appropriateness of a certain approach depends on the validity of these assumptions for a particular MEG recording. Source reconstruction is comprehensively addressed elsewhere (see source localization), but it is worth mentioning the two main most popular classes of algorithm.
|Media:Retmovie.AVI||Movie shows MEG beamformer images of electrical changes in the 18-22Hz band in response to a flickering 10Hz rotating checkerboard wedge in a single recording session from one subject (data from Brookes et al. 2010). As the stimulus moves from left to right, upper to lower, visual field the evoked electrical activity in primary visual cortex traverses from right to left and inferior to superior, respectively, consistent with known human retinotopy. That is, although the inverse problem is theoretically impossible to solve, the set of assumption used here produce empirically plausible results.|
Often the underlying assumption is that only one region of cortex is strongly time-locked to an external stimulus. By averaging the brain responses across many presentations of that stimulus the signals due to all other non time-locked sources are attenuated. One can model the electrical activity using a simple dipole model and, in order to estimate the exact location of the active piece of cortex, move it around the brain until the magnetic field it produces matches the measured magnetic field. One can do this for a number of time points or time ranges and for more complex dipole models. Such methods have been used to show basic somatotopy (Baumgartner et al 1991) and even retinotopy (Supek et al. 1999) in MEG. The disadvantages are that the methods are generally poorly suited to characterising responses that do not average very well, such as responses related to higher cognitive functions. Moreover, the more dipoles one incorporates the less stable the fits become (Supek et al. 1993).
Minimum norm based approaches
If one assumes that many electrical sources are active across the cortical sheet at any one time then the number of parameters that need to be estimated are larger than the number of measurements. Additional constraints are therefore needed to obtain a unique solution. With the traditional minimum norm method this is achieved by assuming that out of all source configurations that can explain the measured data, the one that has the minimum overall source power is the optimum one. Or in other words, it assumes that the brain is efficient in terms of its energy use. However using this single assumption results in electrical source estimates that are entirely superficial (as deeper sources would need to have larger amplitude to have the same impact on the sensors), although this can be overcome by depth/noise weighting. Modifications of this approach add additional assumptions, for example that the distribution of source activity across the brain is spatially smooth (Pasqual-Marqui et al. 1994), the use of Bayesian approaches to determine the optimum source parameters (Baillet and Garnero 1997;Sato et al. 2004; Mattout et al. 2006), or the assumption that there is no perfect correlation between any two spatially distinct active brain regions (Hillebrand et al. 2005).
Statistics for MEG images
At the sensor level random field theory has been used to produce statistical images that naturally account for the comparison of multiple channels and the smoothness of the time-frequency changes (Kilner et al. 2005). Several methods have been developed to test the significance of the reconstructed source activity. At the individual level, Monte Carlo approaches are in use for dipole fitting (Mosher et. 1993) and random field and permutation/randomisation approaches for imaging methods (Pantazis et al. 2005). The latter approaches can also be used to assess the significance of results across or between different groups (Singh et al. 2003). Note that these approaches test the significance of the reconstructed activity, but not the correctness of the assumptions that were made by the source reconstruction approach. However, anatomical information may be used to test these assumptions (Barnes et al. 2006).
MEG has many inherent advantages in a clinical setting. The passive nature of the recordings means that scans can be carried out in a safe and silent environment even allowing for a patient’s companion to be present within the shielded room. In many clinical cases the relative insensitivity of MEG localization to tissue inhomogeneities (such as holes in the skull) is a considerable advantage (Flemming et al. 2005). To provide critical functional information pre-surgically MEG is regularly used to map out sensory/motor cortex (Ganslandt et al. 1996; Pang et al. 2008; Nagarajan S 2008). In situations where the dominant site for language needs to be established MEG methods have been shown to compare favourably with invasive surgical procedures such as the WADA test for language (Hirata et al. 2004; Fisher et al. 2008 ). The brain’s resting electrical state provides clear markers of certain pathologies. The localization of ictal and inter-ictal spike complexes with MEG is now widely used to identify epileptic foci for the surgical treatment of intractable epilepsy (Knowlton and Shih 2004; Tanaka et al. 2008; Stufflebeam et al. 2009). In turn focal slow wave activity is characteristic of unhealthy brain tissue. The localization of this very slow wave activity has been shown to arise from tumors or tumor boundaries (Baayen et al. 2003; Oshino et al 2006) and its amplitude has been shown to correlate with cognitive deficit in low-grade glioma patients (Bosma et al. 2008). Indeed in mild head trauma patients with cognitive complaints such low frequency oscillations seem to be diagnostically useful even though no anatomical changes are visible (Lewine et al. 2007) . More recently, graph analysis has been applied to the estimated networks of interacting neurons in order to establish the characteristics of functional networks. One particular type of functional network, the small-world network, seems to meet the dualistic requirements of the modular brain, namely that of simultaneous functional integration and segregation in neurocognitive networks. Clinically, such analysis has been shown to differentiate patient and control groups in Alzheimers (Stam et al. 2008) and Parkinsons disease (Stoffers et al. 2008), and has demonstrated disturbed functional connectivity in brain tumor patients (Bartolomei et al. 2006).
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