Chapter I
Introduction

The measurement of small potential differences at the scalp was first performed by Hans Berger in 1924 (Berger, 1929).  He used two large sheets of tinfoil which served as electrodes, one on the forehead and one on the back of the head.  Such a registration is called an electroencephalogram (EEG) and it became routine clinical practice some thirty years later, albeit with more and smaller electrodes.  These potential differences are generated by currents inside the brain.  Since any current also generates a magnetic field, it should be theoretically possible to measure the magnetic field outside of the head due to this brain activity.  Because very sensitive sensors are needed to measure this field, it was not possible to do so until the development of the so-called superconducting quantum interference device (SQUID).  The measurement of the magnetic equivalent of the EEG was first carried out successfully by Cohen (1968).  He showed that the alpha rhythm, a spontaneous brain activity, could also be detected magnetically.  Such magnetic measurements are called magnetoencephalograms (MEG).  Brenner et al. (1975) were the first to present magnetic measurements of visually evoked responses (VEF's).  Since then, these types of measurements have been used for fundamental and clinical brain research.
The field of research that deals with the measurement and interpretation of magnetic fields generated in biological tissue is called biomagnetism.  Although biomagnetism can be applied to muscles, heart and other organs, this thesis will only deal with brain research.  In this chapter the generation of biomagnetic signals will be briefly discussed, as well as how they can be measured.  The measuring device that is used at the University of Twente is discussed.  The last paragraph discusses how the work described in the other chapters fits into other developments in the field of biomagnetism.

1.1 The origin of the signals

The origin of the electrical currents, and hence that of the electrical potentials and the magnetic fields lies in the neurons of the brain. Like any other biological cell they have a membrane around them, which is selectively permeable for ions.  Normally, the concentration of these ions, like potassium, sodium and chloride, is different inside the call  from that at the outside.  Due to this difference in concentration the inside of the cell has a potential around -70 mV with respect to the outside of the cell.  This is close to the equilibrium potential for potassium ions, for which the neurons have a relatively large permeability (Ganong, 1987).

When the cell is excited, the permeability for certain ions changes, allowing mainly sodium to travel freely through the membrane.  The potential of the cell then rises to positive values.  After a short period of time, the permeability returns to normal and the flow of potassium restores the resting potential.  The moving ions give rise to a current within the cell, which can be described by a current dipole, giving rise to currents in the surrounding tissues, the so-called volume currents (Plonsey, 1981; Karp, 1981).

Two types of neuronal activity can be discriminated.  First, the action potential, which is associated with the propagation of signals along neuronal fibers, as depicted in Figure I.I. Second, the postsynaptic potential or PSP.  Two types of PSPs can be distinguished.  In one case, the postsynaptic potential is a depolarisation of the cell due to the arrival of action potentials at a synapse.  Once the transmembrane potential rises above a critical value, the cell triggers a new action potential.  In the other case, the synaptic activation leads to a current of opposite sign causing a hyperpolarisation of the postsynaptic neuron.  The former is called an excitatory PSP (E) and the latter an inhibitatory PSF1 (1) (see Figure 1.2). The postsynaptic potential can be described by a current dipole which can exist for several tens of milliseconds.  The action potential can be described by a quadrupole (Wikswo, 1983), whose magnetic and electric fields decay more rapidly than those of a dipole.  Consequently, the EEG and the MEG mainly register the PSPs (Lopes de Silva and Van Rotterdam, 1987).

The cortex is organized in layers parallel to the surface of the cortex.  Each layer contains different types of neurons.  Six layers can be discriminated, with layer I being the most superficial.  The connections between neurons are mainly in a direction perpendicular to the surface of the cortex.  Layers 11, IV and VI are populated with so-called stellate cells, which have a star-shaped form and cannot generate a significant resulting magnetic field.  However, pyramidal cells have a linear structure with dendrites that are arranged parallel to each other and perpendicular to the surface the cortex.  Therefore they do generate magnetic fields when activated.  These pyramidal cells can be found mainly in layer V (Okada, 1983).

One activated neuron does not render a measurable magnetic field.  However, an area of several mm2 is usually excited almost synchronously.  About 100.000 neurons are present below 1 mm2 of cortical surface (Rockel et al. 1980).  Although only half of this number are pyramidal cells, which mainly contribute to the electric and magnetic fields measured at a distance, this still leaves an enormous number of neurons which are active at the same time.  However, the resulting magnetic fields are still very weak (see Figure 1.3). The measurement of neuromagnetic fields thus requires extremely sensitive sensors.  Furthermore, the fluctuations in the earth's magnetic field, or the magnetic disturbances from electrical appliances, power cables and traffic are of an order many times higher than the magnetic field generated by the brain.  Special care must be taken to reduce these disturbances as much as possible.

1.2 Measuring the MEG

1.2.1 The SQUID

An extremely sensitive sensor for magnetic fields is found in the SQUID.  It consists of a superconducting ring with one or two weak links (Josephson, 1962).  The most common type nowadays is the DC-SQUID with two junctions.  In order to operate the SQUID a bias current is fed through the ring.  If this current is higher than the critical current of the SQUID a voltage appears across the weak links.  When a magnetic flux is applied an additional supercurrent starts to run through the ring in an attempt to compensate the change in flux, giving rise to a higher voltage across the SQUID.  The voltage as a function of the bias current thus changes with a change in flux.  However, if the flux has changed by exactly one flux quantum ((0), the I-V characteristic is the same as it was before.  The bias current has to be selected to give a high voltage change with changing flux.  It then follows that the voltage is periodic with changing flux (see figure Figure 1.4) (Tesche and Clarke, 1977, Swithenby, 1980).

Usually, the SQUID is used as a zero-detector, i.e. the flux in the SQUID is kept constant by compensating the change in the magnetic flux by coupling it back through an integrator (Clarke, 1977).  The output of the integrator is a measure for the change in the magnetic flux. Usually the SQUID is operated in a flux-locked loop, whereby a modulation frequency is applied to it. Phase-sensitive detection is used to retrieve the output voltage of the SQUID (see figure 1.5).

 
1.2.2 Flux transformers

Since a SQUID is very sensitive to magnetic field changes, it must be shielded.  The flux is fed into it by means of a flux transformer.  This consists of pick-up coils and a signal coil which is inductively coupled to the SQUID.  Usually the flux transformer is constructed as a gradiometer to measure gradients of the magnetic field instead of the magnetic field itself (see Figure 1.6). The principle of the gradiometer is that two loops both register the magnetic field at slightly different locations.  By winding these loops in opposite directions, the homogeneous part of the field is canceled out.  Since sources which are far away from the gradiometer produce magnetic fields which can be considered homogeneous, they no longer disturb the measurement. Gradiometers make the measuring device particularly sensitive to nearby sources (Carelli et al, 1983).

Normally gradiometers are oriented more or less perpendicular to the surface of interest, i.e. the head. The maximum and minimum values are found on either side above the source location. It is interesting to note the approach of the Finnish group, where they use planar gradiometers (Hämäläinen, 1989). These measure the spatial gradient along the head, and therefore yield the highest output directly above a single source.

The flux transformers are, just like the SQUIDs, superconducting, which means that they have to be immersed in liquid helium, which has a temperature of 4.2 K.

1.2.3 Electronics

Part of the electronics consists of circuits to drive the SQUID, i.e. to generate the feedback current, and the driver for the bias current. Furthermore, amplification and filtering of the SQUID output is necessary. A high-pass filter is applied to get rid of the 1/f noise. A notch or comb filter can be applied to filter out the mains frequency and a low-pass filter may be used to attenuate frequency components which are not of direct importance for the investigations. A low-pass filter is also used as an anti-aliasing filter. Afterwards, the signal is sampled and stored in a computer for further processing.

1.2.4 Shielded room

By using higher-order gradiometers it is possible to measure the MEG in a noisy environment, although it is much more convenient to use a magnetically shielded room, which is designed to keep out external magnetic disturbances. The walls of such rooms contain a layer of aluminum which shields mainly higher-frequency fields by eddy-currents which are induced in the material. Furthermore, the walls of the room may contain one or more p-metal layers which absorb the magnetic field lines, and thereby give the room a basic level of shielding (Mager, 1981).

An overview of the various components of the experimental set-up can be seen in figure 1.7. A subject is positioned under the dewar, containing the liquid helium, the gradiometers and the SQUIDs.  The dewar and subject are inside the shielded room.  The signals from the SQUID are amplified and fed to the SQUID control electronics (which include filters) and the signals are then sampled and stored in a computer.

1.3 The Twente blomagnetic facility

The sensors used in the 19-channel magnetometer system that is used in the Biomagnetic Centre Twente (BCT) are DC-SQUIDs which were made by the Low Temperature group of the University of Twente, using thin-film techniques. Their fabrication is based on Nb/Al technology. The SQUIDs are either resistively or inductively shunted. Two configurations are used in the 19-channel system. The first is a Tesche-Clarke type DC-SQUID with a SQUID inductance of 270 pH, an input inductance of 0.1 pH, and a coupling factor of O.S. The forward transfer is generally about 70 pVADO. The second configuration is a resistively shunted type with a SQUID inductance of 85 pH, an input inductance of 0.1 pH, a coupling factor of 0.8 and a transfer of 110 pV/00. Both types of SQUIDs have a white-noise spectral density below 10-5 (0/(Hz (Houwman, 1990). Each SQUID is placed on a solid niobium body that fits into a cylindrical lead shield and which is divided into several compartments. Apart from the SQUID chip a feedback inductor, an output transformer and a tuning capacitor are also placed in such a compartment. One compartment has screws to connect the sensing coil to the input coil on the SQUID. The output transformer is tuned to a modulation frequency of 100 kHz by means of the tuning capacitor which is shunted across the transformer. The gain of the tuned transformer is 10 at 100 kHz, with a quality factor of about 2.

The SQUID module is designed to operate the sensor in an external feedback mode. This means that the current in the sensing coil is compensated, instead of the flux through the SQUID. In this way, crosstalk between channels can be eliminated (Ter Brake et al, 1986).

If a channel is not in operation, currents in its gradiometer are not compensated and therefore do cause a crosstalk contribution in other channels.  It is possible to correct for this contribution, but measurements have shown this not to be necessary as long as the majority of the channels are correctly operating in external feedback mode.

The magnetic flux changes to be measured are picked up by first-order, wirewound, gradiometers and are coupled into the SQUID. The gradiometers have a diameter of 20 mm, and a baseline length of 40 mm which separates the centres of the two coils which each have three turns. The distance between the turns of the lowest coil is 0.5 mm and that of the compensation coil is 6 mm. The 19 gradiometers are distributed in rings around the centre coil on the bottom of a CTF-SST 140 cryostat. This bottom has a concave shape having a curvature with a radius of 125 mm. The wire used for the gradiometers is Formvar-insulated single-core niobium wire with a diameter of 0.1 mm, manufactured by California Fine Wire Co. The calculated self-inductance of the gradiometers is 0.73 pH. In combination with the SQUIDs, the intrinsic noise is about 5 fT/(Hz. Apart from the gradiometers, a reference coil unit is placed at a distance of about 25 cm from the gradiometers. This unit consists of three orthogonal 1 cm loops which are connected to three SQUID systems. Their output can be used as a reference for the three orthogonal components of the magnetic field, and therefore for electronic balancing or active shielding purposes.

The cryostat is suspended in a wooden gantry, which allows coverage of the head from all angles, while remaining perpendicular to a sphere with a constant radius. The gantry is placed in a magnetically shielded room manufactured by Vacuumschmelze GmbH, type AK3B. This room has two (-metal layers and one aluminum layer, and the shielding factor for DC-fields is about 1200 while that for AC fields at 0.1 Hz is 70 (Ter Brake et al, submitted).

All SQUIDs are connected to preamplifiers, which are placed in an aluminum box on top of the cryostat. They consist of Toshiba FETs (2SK146) in a cascade configuration, loaded with an RCL network, resonating at 100 kHz. The quality factor is about 3.5 and the preamplifier gain is 400.

The control and detection electronics are realised on one Eurocard per channel. Several parameters are fixed. The sensitivity can be set to 1 V at an output of I 00 in the SQUID. The dynamic range of 10 V corresponds then to an effective field of about 0.5 nT in the gradiometer. The frequency bandwidth is fixed at 5 kHz. There are separate power and bias-current supplies for each channel, whereas the 100 kHz modulation is obtained for all channels from one external oscillator.

The control and detection electronics contain a 50 Hz adaptive notch filter, which suppresses the mains frequency by more than 60 dB with a bandwith of 1 Hz.  High-pass and low-pass filters are applied.  The low-pass filters also act as anti-alias filters.  A block diagram of the filters and amplifiers is shown in Figure I.8.
The signal goes from the electronics to the data-acquisition system, where the signals are sampled and stored (see chapter II).  Data can be sent through a computer network to a Vaxstation 5320 running under VMS.  This computer is equipped with three 340 Mb disks, 16 Mb of memory and two graphical workstations.  The system supports a variant of the X-Windows system, called Dec-windows.  This computer is used to process the data.  It can be accessed from outside the University through the network, and this allows people who carry out measurements at the Biomagnetic Centre to process the data remotely, or to transfer them to a local computer.  Various data-processing software packages are available on the Vax-station.  One of them, the software to integrate the MEG signals with MRI scans will be discussed later.

1.4 Scope of this thesis

Magnetoencephalography can lead to a better understanding of the functioning of the brain because of its ability to localize sources of electric and magnetic activity with a reasonable spatial resolution and an excellent resolution in time (1 ms). In the field of biomagnetism researchers from various disciplines do combine their forces to cover the mathematical, physical, technical, (neuro-) physiological and medical aspects of this field. In this multi-disciplinary approach it is the task of the physicist to optimize the measurement equipment, the measuring procedure and the processing and presentation of the data in order to allow the physicians and psychologists to conduct experiments in order to obtain information about the location and the strength of the sources within the brain which are active under certain conditions. The localizations have to be presented with reference to anatomical and physiological information known from other means. In order to enable the physicians and psychologists to appreciate the results, but also to understand the restrictions of the methods used, an estimation of the errors has to be given. It is important that the results are validated whenever possible. This can be done by comparing the results with known physiological facts, or by comparing the results with data from other types of measurements like PET or SPECT.

Presently, many multi-disciplinary teams are doing research in the field of biomagnetism (cf., Hoke at al., 1992). The state-of-the-sensors are DC-based SQUIDs with an intrinsic noise which is as good as 5 fT14Hz or lower (Drung et al., 1991; Ter Brake et al., 1991; Kajola et al., 1991; Heiden, 1991; Foglietti et al., 1991; Flokstra et al., 1991). Present instruments still use SQUIDs which operate at liquid Helium temperature (4.2 K), alithough first measurements of magnetic fields using high T, Squids have already been carried out (Tavrin et al., 1993). Currently, biomagnetic measuring devices are coming into operation which measure the magnetic field simultaneously over the whole scalp, as with the 122 channel system in Helsinki (Ahonen et al., 1992) or the 64 channel system of CTF (Cheyne et al., 1992). More helmet-type systems are under development (Yamasaki et al., 1992; Romani, 1992). Other systems measure the magnetic field over one hemisphere of the head such as the commercial systems from BTI (37 channels) (c.f. Pantev et al., 1991), Philips (31 channels) (Dössel et al., 1993) or the system from Siemens (37 channels) (Abraham-Fuchs et al., 1990). Other systems have a number of channels which requires sequential re-positioning of the system with respect to the subjects head, like the system used in Twente (19 channels) (Ter Brake et al., 1992), Birmingham (19 channels), Berlin (37 channels) (Drung et al., 1991) or Rome (28 channels) (Foglietti, 1991). The general layout of such a system has been depicted in this chapter. Recently, an excellent overview article has appeared, dealing with the various aspects of magnetoencephalography (Hämäläinen et al., 1993).

1.4.1 Measurements

In classical EEG measurements, the signals of the various channels were directly written to paper. However, in order to calculate the source of magnetically or electrically measured brain activity the data needs to be measured by a computer and stored for later processing. A data-acquisition system is necessary which allows the acquisition of many channels simultaneously at a sample-rate which is high enough to measure the brain-activity of interest. The system has to be capable of acquiring data over long periods of time, specially in the case of the measurement of spontaneous brain-activity. The system should also be capable of registering information about time-instants at which stimuli are presented, or responses from a subject detected. Many groups have constructed such a system (Ross et al., 1989; Voskamp et al., 1989; Gonnelli et al., 1991; Cumming and Wells, 1992; Marlow et al., 1993). Our solution is discussed in chapter II and has the advantage of a long continuous measurement time, low cost and easy expendability.

An important aspect in the measurement of the weak magnetic fields is the noise in the signals.  Due to the weakness of the signal it is important to find methods to reduce environmental disturbances.  One of the first methods used to reduce these disturbances was the use of first or higher-order gradiometers as pick-up coils for the magnetic field (Vrba et al., 1982; Carelli et al., 1983; Bruno et al., 1987; Node et al., 1987).  These gradiometers can not be made perfectly insensitive to these homogeneous fields, and a mechanical balancing method was developed to reduce these imperfections (Overweg and Walter-Peters, 1978).  However, with the advent of multi-channel systems, mechanical balancing turned out to be a very impractical method.  An alternative in the form of electronic balancing was suggested (Hansen et al., 1983, Ter Brake et al., 1986).  We performed measurements, using an electronic balancing method which is carried out by the computer, which automatically calculates the proper balancing factors.  We discovered that this method does not work well in combination with an other method to reduce environmental disturbances, namely the magnetically shielded room.  This is discussed in chapter II.  A different approach to reduce disturbances is the method of actively compensating disturbances.  This has already been suggested by Marzetta (1961) , and applied for biomagnetic measurements by Donnely et al. (I 988) and Kelhä et al. (1982) . It turns out that in this case, the combination with a magnetically shielded room is very beneficial.  Our approach in this matter is also discussed in chapter II.  An important difference with the approach taken by Kelhä et al. is that they measured the disturbances outside the shielded room with a fluxgate magnetometer while we measure the disturbances inside the room using a SQUID magnetometer.

1.4.2 Modelling the head

Because the solutions of the inverse problems of the MEG and the EEG are not unique, a model is needed both for the sources and the head (Morse and Feshbach, 1953). In other words a "constrained inverse solution" has to be solved, in which information about neurophysiology and anatomy is used to limit possible source distributions (Nunez et al. 1991). A common model for the sources are equivalent current dipoles. It can be assumed that one or more dipoles are at a fixed position during a given time-interval and that their strength and orientation varies over time. The orientation can also be fixed. This is called the fixed dipole model. A different approach is to allow the dipoles to change their position as well as their strength and orientation. Basically, this method fits one or more dipoles at each time-instant independently. This is the moving dipole model (Lopes de Silva and Spekreijse, 1991). A third approach is to try and estimate current distributions in the brain (Kuhlman et al., 1989; loannides et al., 1990; Wang et al., 1992; Okada et al., 1992). Basically, the result of this method is a fixed dipole solution with very many dipoles fixed at discretized points in the region of interest. Due to the nonuniqueness of this solution it is only possible to use a two-dimensional surface as the region of interest.

The head is always delineated by a compartment model where each compartment has its own electrical conductivity.  Usually, the compartments are described by a set of concentric spheres (Schneider, 1974; Hosek et al., 1978; Kavanagh et al., 1978; Cuffin and Cohen, 1979; Gutman and Shimoliunas, 1980; Sencaj and Aunon, 1982; Stok, 1986; De Munck, 1989).  A problem with the use of a spherical model is that the sphere has to be fitted to the head in a way that it is a good description for the curvature of the head, nearest to the source and therefore the parameters of the best fitting sphere are not uniquely defined.  Since the choice of the best fitting sphere is, to some degrees, arbitrary, we would like to fit the sphere by computer, using MRI scans, as described in chapter IV.  In that case, it is also possible to fit the sphere to the inner surface of the skull instead of the scalp, or to fit all the spheres to their proper surface in case of a multi-compartment model.  Furthermore, the use of a sphere fitted from MRI yields more accurate results than a sphere fitted to, for instance, the position of the electrodes, in case that the resulting source location is displayed in that MRI.  This is shown in chapter VII.  When EEG measurements are used to estimate the location of a source, an additional problem arises with the use of the sphere model; positions at which the potential is measured do not lie on the surface of the model, although this is exactly what has to be assumed in the inverse procedure.  This is an intrinsic problem of the use of the sphere model in processing EEG measurements.

For a spherically symmetric model analytical expressions can be found for the magnetic field and the electric potential.  The basic theory for these expressions is discussed in chapter III.  From simulation studies based on realistically shaped multi-compartment models, however, it follows that the shape of the compartments can significantly influence the magnetic field and the electric potential (He et al., 1987; Mails et al., 1988; Hämäläinen and Sarvas, 1989; Ishiyama and Kanai, 1992; Menninghaus et al., 1992).  These simulations are based on the boundary element method, where the contribution of the volume currents is represented by that of equivalent sources at the interfaces between regions with a different conductivity, which includes the outer-surface of the head.  Since the skull is poorly conducting, the main contribution to the magnetic field outside the head is from currents flowing in the brain tissue.  The secondary sources at the outside of the skull counteract those at the surface of the head (Meijs et al., 1988).  Hence, the MEG lends itself to the use of a simpler model than that needed for the EEG when deducing source localizations.  Hämäläinen and Sarvas (1987) estimated that for the MEG a homogeneous model shaped as the inner surface of the skull will approximate within 5% a realistically shaped three-compartment model of the head, describing the brain, the skull and the scalp.  The shape of the skull's inner-surface was obtained from CT scans (Hämäläinen and Sarvas, 1987) or from an anatomically accurate plastic model (Hämäläinen and Sarvas, 1989) and was manually divided into triangles.  However, for EEG such a homogeneous model is not adequate as the influence of the other compartments is large and the outside of the scalp has to be included in the model anyway since the measurement points are located on this surface.

In electrocardiography (ECG) and magnetocardiography (MCG) the use of standard multi-compartment models of the torso has been shown to produce reasonably accurate localization results (Oosterom and Huiskamp, 1992; Nenonen et al., 1992). Huiskamp and van Oosterom (1989) described the use of an individualized model for the solution of the inverse problem in electrocardiography. They used realistically shaped multi-compartment models of the human torso for three individuals. The models were derived from MRI scans of the subjects. They showed that using a realistic, yet inaccurate, geometrical description of a subject proves to be insufficient. Even when the torso shape and size of a subject is about the same as that of the applied standard realistic torso model. Stroink et al. (1992) found the same results, they suggest that scaling of the standard torso may be a cost effective compromise between the accuracy of the solution and the time and expense of creating an individual torso model. Especially, since the manual tesselation of the interfaces is such a cumbersome procedure.

In order to decide if a tailored standard model of the head is sufficient in MEG some simulations were carried out, as described in chapter V. From these simulations it follows that the use of a standard realisitically shaped inhomogeneous model of the brain used in solving the inverse problem of MEG and EEG will also give less reliable solutions then tailored models.  However, if indeed an individualized model is needed to obtain a precise localization from MEG and/or EEG, such a model has to be constructed from CT or MRI images of each subject separately.

Consequently, it is of importance to develop a procedure to extract points on the interface of the compartments which can be carried out fully automatically. From these points (triangulated) surface descriptions can be obtained which can be used in the boundary element method or as basis for a finite element model. The automated procedure is even more important with the improvement in scan-techniques, where a dataset of one subject can consist of more than 200 images, each of which would otherwise have to be examined manually. To enable the extraction of the various surfaces, the data from the scan has to be segmented. This has also to be performed fully automatically, for the same reasons as mentioned above. Various groups in the world work on the automatic segmentation of medical images (Udupa, 1982; Kubler et al., 1987; Ortendahl and Carlson, 1988; Lifshitz and Pizer, 1988; Farrell and Zappulla, 1989; Bornans et al., 1990; Gevins et al., 1990) with varying results. We designed a dedicated method, with an accuracy sufficient for our purposes. This method and the generation of the realistically shaped model is described in detail in chapter IV.

The current density method, also often referred to as minimum norm estimate of the sources, restricts the solution to a two-dimensional surface.  An obvious choice for this surface would be the cortex itself.  If the geometry of the cortex is known and if it is known that the sources of measured fields and potentials are located in the cortex, it is possible to uniquely delineate the pattern of electrical activity (Wang et al., 1993).  Wang et al. suggest that an accuracy of better than 4 mm in knowledge of cortical geometry may be required.  With the method described in this thesis the geometry is smoothed and the gyri and fissures are not given in detail, although it is possible to extract the cortical tissue in each slice.

1.4.3 Visualization and evaluation of results

The goal of an inverse procedure is, obviously, to obtain an equivalent dipole for which the model predicted distribution is closest to the measured distribution in a least square error sense.  A small residue is a necessary but not sufficient condition for the validity of the model used.  Examples of insidious errors due to misspecification of the models used for EEG in the case that multiple sources are active were reported by Zhang and Jewett (1993).  Thence, we are in favour of combining MEG and EEG.  By using them both the non-uniqueness associated with the inverse problem is reduced.  If the sources of MEG and EEG, for instance, would coincide within the error estimate, it would strengthen our faith in the models used.  Such a confrontation was used by Sutherling et al. (1988).  Oostendorp et al. (1990) compared the results from ECG and MCG in order to decide if, instead of a uniform current dipole layer, a single dipole could be used as a cardiac source model.  Their measured ECGs were almost as good described by a moving dipole as by spreading uniform dipole layers.  The measured MCGs, however, were much better described by dipole layers.  Therefore they concluded that the dipole layer is to be preferred as a model because it seems to represent the actual sources more closely.  A singular value decomposition of the data matrices of both MEG and EEG can help us to estimate the number of equivalent dipoles with more confidence.  Assuming that there are sources which are magnetically "silent" ("radial" dipoles) and electrically not and that there are no sources which are electrically silent and magnetically not, the number of equivalent dipoles estimated from MEG has to be equal or less than those obtained from EEG.  A Second argument for combining MEG and EEG is that the amount of information obtained is larger than that of EEG or MEG alone.  A third argument is that when the inverse algoritm for minimalization of the difference between observed and simulated data is performed for MEG and EEG simultaneously that the results are better (Stok, 1986; Stok, 1987).  A fourth argument is that the combination of MEG and EEG can give us an estimate of the strength of the equivalent dipole as discussed in chapter V.

Not only the surface of the brain but also the inside of the brain can be made visible by making "cut-away" views. Such a view is of importance when the inverse solution is confronted with a-priori information obtained from electrophysiological, neuroanatomical, neuropathological and neurosurgical studies about, for example, the orientation and density of pyrimidal cells. The composition of a database which will contain such information has been started within the EC program AIM (Anogianakis et al., 1992). The methods discussed above are part of the contribution of the research group in Twente to that program. Hence, it is important to be able to show the sources of brain activity calculated from MEG and/or EEG with respect to anatomical information obtained from the MRI. Various groups working with the MEG and EEG have shown sources depicted in MRI scans (Pantev et al., 1990; Suk et al., 1991; Gallen at al., 1992; Nomura et al., 1992; Peresson et al., 1992), but often without any exact information on how the calculated sources were transferred to the MRI. Chapter V discusses the methods we developed to accurately locate the source in the MRI. Usually, the dipole is displayed in the appropriate transversal slice of the MRI-dataset but it can also be depicted in arbitrary chosen planes. However, it is still difficult to envision the source position with respect to the complete head. To facilitate this task, 3D images of the head and brain can be constructed. This has already been done by various groups working on medical images (Lobregt and Kleine Schaars, 1987; Zonneveld et al., 1987; Wallis et al., 1989; Bomans et al., 1990; Tiede et al., 1990; Valentino et al., 1991) and raytracing (Phong, 1975; Robb and Barillot, 1989; Levoy, 1990). We have implemented these methods, as described in chapter IV. By cutting parts away from the 3D head, through the source location, and indicating the source location in the resulting image, it is much easier to envision the position of the sources. Examples can be seen in chapters IV and V. Another useful 3D image is that of the brain. It is possible to project the sources directly onto the 3D image of the brain, thereby allowing the researcher to directly view their location with respect to important anatomical landmarks like the central fissure or the sylvian fissure. This is especially useful in the case of very superficial sources. We have used this in chapter VI.

It is important to confirm the findings of MEG and EEG localizations as much as possible.  The first check on the position of the dipole is if it is located within the cortex and if the direction of the dipole is consistent with the local shape of the cortex.  One step further would be the use of different imaging techniques which also give functional information of the brain, like Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT), even when it is not yet clear if they should indicate the same areas to be active as MEG and EEG.  Information from a PET scan is first of all complementary to the information obtained from the MEG (Bartenstein and Schober, 1992).  To enable the direct comparison of PET and the MEG/MRI, it is necessary to translate the position of a voxel in the MRI to the corresponding position in the PET dataset and vice versa.  In this way it is possible to merge these two images together.  The merging of images from different modalities, also called registration or fusion, is a major topic in the field of medical image processing where the emphasis is placed mainly on the combination of PET, MRI and CT (Levin et al., 1988; Pelizzari et al.,1989; Neiw, 1991; Valentino et al. 1991; Van den Elsen et al., 1992).  The combination of PET data with MRI and MEG data has been demonstrated already by Walter et al. (1992), where they localized sources from magnetic responses due to voluntary movement of the right foot, the right thumb, the right index-finger and the right cheek.  We constructed an algorithm to automatically establish a transformation from PET coordinates to MRI coordinates, and to display the PET data in colour in a transparent way over the MRI scan.  Dipole positions can be added to the MRI scan at the proper locations.  Alternatively, the PET data can also be displayed on the 3D brain surface, which is useful when areas of the brain are investigated which are located on the outer brain-surface.  This is discussed in chapter VI.  To demonstrate the method we used somatosensoric stimuli, since the various measurements had to be conducted on different days and at different locations and therefore the measurements needed to be consistently reproducible.  As shown by Schwartz et al. (1992) the somatosensory source localizations are highly repeatable from session to session.  Moreover, with these stimuli it is not necessary to average the data over subjects in order to get results with PET.

1.4.4 Errors

If a source localization is to have any scientific or clinical value an estimate in the error of its position is imperative.  The influence of different aspects of source localizations have been investigated in the past.  These aspects include the influence of noise on the data (Kuriki et al., 1989), the parameters of the compartments in the concentric sphere model (Stok, 1986), the measurement position (Buchanan, 1989; Peters and De Munck, 1991) and the influence of the volume conductor model itself (Meijs et al., 1988; Cohen et al., 1990; Menninghaus et al., 1992).  In chapter VII we try to take al these factors into account and also assess those errors which are generated by combining the data from MEG and EEG with the MRI.

(c) MEG, EEG and the integration with Magnetic Resonance Images, H.J. Wieringa, 1993

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