Magnetoencephalography signals are influenced by skull defects

Clinical Neurophysiology xxx (2014) xxx–xxx

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Magnetoencephalography signals are influenced by skull defects S. Lau a,b,c,d,⇑, L. Flemming b,e, J. Haueisen a,b a

Institute of Biomedical Engineering and Informatics, Ilmenau University of Technology, P.O. Box 100565, D-98684 Ilmenau, Germany Biomagnetic Center, Department of Neurology, Jena University Hospital, Erlanger Allee 101, D-07747 Jena, Germany c NeuroEngineering Laboratory, Department of Electrical & Electronic Engineering, The University of Melbourne, Parkville 3010, Australia d Department of Medicine – St. Vincent’s Hospital, The University of Melbourne, Fitzroy 3057, Australia e Department of Traumatology and Orthopedics, Robert-Koch-Hospital, Jenaer Straße 66, D-99510 Apolda, Germany b

a r t i c l e

i n f o

Article history: Accepted 17 December 2013 Available online xxxx Keywords: Magnetoencephalography Skull hole Breach rhythm Biomagnetism Electroencephalography Volume conduction

h i g h l i g h t s  We present the first in vivo experimental evidence of the substantial influence of skull defects on

MEG.  The MEG signal amplitude deviates more if the source is central under the skull defect, whereas the

EEG signal amplitude deviates more if the source is under the edge of the defect.  Dense spatial sampling reveals high spatial frequencies in MEG and EEG signals due to skull defects

that are not detectable with current human helmet-type MEG devices and standard EEG setups.

a b s t r a c t Objective: Magnetoencephalography (MEG) signals had previously been hypothesized to have negligible sensitivity to skull defects. The objective is to experimentally investigate the influence of conducting skull defects on MEG and EEG signals. Methods: A miniaturized electric dipole was implanted in vivo into rabbit brains. Simultaneous recording using 64-channel EEG and 16-channel MEG was conducted, first above the intact skull and then above a skull defect. Skull defects were filled with agar gels, which had been formulated to have tissue-like homogeneous conductivities. The dipole was moved beneath the skull defects, and measurements were taken at regularly spaced points. Results: The EEG signal amplitude increased 2–10 times, whereas the MEG signal amplitude reduced by as much as 20%. The EEG signal amplitude deviated more when the source was under the edge of the defect, whereas the MEG signal amplitude deviated more when the source was central under the defect. The change in MEG field-map topography (relative difference measure, RDM⁄ = 0.15) was geometrically related to the skull defect edge. Conclusions: MEG and EEG signals can be substantially affected by skull defects. Significance: MEG source modeling requires realistic volume conductor head models that incorporate skull defects. Ó 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

1. Introduction The signals acquired by electroencephalography (EEG) and magnetoencephalography (MEG) are due to the electric currents generated by brain activity. The volume current through the tissues inside the head modifies the sensor signals at the head surface. The flow of electric current through the tissues influences ⇑ Corresponding author at: Institute of Biomedical Engineering and Informatics, Ilmenau University of Technology, Gustav-Kirchhoff-Str. 2, 98684 Ilmenau, Germany. Tel.: +49 3677 69 2860; fax: +49 3677 69 1311. E-mail address: [email protected] (S. Lau).

the potentials observed at the electrodes in EEG. To a lesser degree, the volume current also influences the magnetic flux observed in MEG. The skull has the most resistive tissue of the head, and therefore has the strongest influence on these techniques. The neurological term breach rhythm describes an increase in the amplitude of alpha, beta, and mu rhythms of the brain that occurs proximal to or over post-surgical skull defects (Cobb et al., 1979). At these locations, the absence of skull tissue allows volume currents to reach the electrodes largely unfiltered and unattenuated. The sharper features of breach activity are easily mistaken for interictal epileptic discharges (Brigo et al., 2011). MEG is reported to be less sensitive than EEG to skull defects (Lee et al., 2010).

1388-2457/$36.00 Ó 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.clinph.2013.12.099

Please cite this article in press as: Lau S et al. Magnetoencephalography signals are influenced by skull defects. Clin Neurophysiol (2014), http://dx.doi.org/ 10.1016/j.clinph.2013.12.099

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Theoretically, EEG and MEG signals should both be distorted by the skull and any defects in it. The degree of distortion depends on the depth, orientation, and extent of the source, as well as the geometry and composition of the skull and the skull defect (Meijs et al., 1987; Hämäläinen and Sarvas, 1989). However, the influence of the skull is estimated to be much less on components of MEG signals than on those of EEG signals, based on considerations under simplified conditions of a flat, layered, inhomogeneous volume conductor (Cohen and Hosaka, 1976) and using a concentric, multilayered, spherical, homogeneous volume conductor (Geselowitz, 1970; Grynzpan and Geselowitz, 1973). A small number of in vivo animal and post-mortem phantom experiments have examined the influence of skull defects on MEG and EEG signals. Barth et al. (1986) used a physical coaxial dipole to simulate intracerebral currents in a formalin-fixed human cranial specimen that had been filled with conducting jelly. Their visual inspection found the MEG signals above a craniotomy to be qualitatively indistinguishable from those above intact skull. Okada et al., (1999b) conducted EEG and MEG measurements associated with somatic evoked responses in anaesthetized piglets, first over intact skull and then over the dura after a large section of skull was removed (skull on versus skull off). They found no significant difference in MEG signal amplitude or morphology, except for an attenuation of the MEG signal when the skull was removed, which was stronger for deeper sources (25% for a 14 mm-deep source). The limitations of existing experiments are that (1) the skull defect was filled with non-conducting air (except in (Flemming et al., 2005) for EEG); (2) the skull defect was large compared with the sensor planes (skull-on versus skull-off); and (3) that evoked responses were used, which have a high variability with regard to source position, extent, orientation, and amplitude. Therefore, the objective of this study is to experimentally investigate the influence of conducting skull defects on EEG and MEG signals above and around a skull defect, using a well-defined current source under the middle and edge of the defect and next to it, in an in vivo rabbit model.

2. Materials and Methods 2.1. Electroencephalography We constructed a miniaturized 64-channel EEG array (Fig. 1A) with electrodes 1.4 mm apart to achieve sufficient spatial sampling density. Ag/AgCl ball electrodes of 0.6 mm diameter were arranged in a regular grid embedded in silicone. The EEG signals were amplified using two synchronized SynAmps (Compumedics NeuroScan, Charlotte, NC, USA) amplifiers. A sampling rate of 1 kHz was used with an analog 0.3–300 Hz band-pass filter and a 50 Hz notch filter. The EEG array position within a stereotactic coordinate system was registered for each recording (Fig. 1B).

2.2. Magnetoencephalography The magnetic flux density was measured using the 4  4-channel MicroSQUID device (Fig. 1C) developed by Nowak et al. (1999). The thickness of the cryostat wall between the gradiometers and the measurement object was only 3 mm, which allowed the sensors to be as close as 7 mm to the animal skull. MEG signals were recorded via a third SynAmps amplifier, which was synchronized with the two amplifiers used for the EEG. The sampling rate was 1 kHz, using an analog 0.3–300 Hz and a 50 Hz notch filter. The MEG sensor locations were coregistered into the stereotactic coordinate system using a set of coils arranged permanently under the base of the stereotactic device. Each gradiometer position was fitted individually using Levenberg–Marquardt optimization. To minimize any localization inaccuracies, a regular 4  4 grid was fitted to the 16 positions. 2.3. Artificial current source An implantable physical coaxial dipole was constructed from platinum material and polytetrafluoroethylene insulation (Fig. 2A). The coaxial design minimized electromagnetic interference by the dipole stem. The inner and outer poles were 0.5 mm wide and set 1 mm apart. The tip and the outer insulation were sufficiently durable to allow reuse of the dipole. The dipole was connected to a constant-current source (20 Hz, 0.1 mA) with a sinusoidal waveform, to balance the charges. The voltage over the dipole was recorded simultaneously to EEG and MEG using a voltage divider (101:1) that scaled the amplitude to the dynamic range of the amplifier. The input impedance of the amplifier was 10 MO. A strong change in the dipole voltage between two consecutive recordings during observation of a given animal indicated a change in the properties of the volume conductor surrounding the artificial dipole; such recordings were rejected. The artificial dipole was inserted through a hole drilled in the posterior lateral skull close to the ear canal. The dipole was fixated with a device (Fig. 2B) that enabled movement of the dipole along its axis in steps of 0.3455 mm over a range of 28 steps, equating to 9.67 mm. This device was constructed solely from plastic materials to be non-magnetic. The position of the dipole was determined from post-experimental, high-resolution computed tomography (CT) with 0.4 mm voxels. The CT was coregistered to the stereotactic coordinate system (Fig. 1B) using a rigid-body transformation based on a set of four spherical CT markers (Ø 2.3 mm, Beekley Corp., Bristol, CT, USA) glued to the superior skull surface (Fig. 2C). 2.4. Skull defect material The skull defects were filled with different materials to represent different conductivity values. The materials were designed so that their ion concentrations were balanced with those of the

Fig. 1. (A) A 64-channel EEG array for bioelectric measurements composed of Ø 0.6 mm Ag/AgCl electrodes placed 1.4 mm apart; (B) Stereotactic device with orthogonal axes and digital coordinate measurements are mounted on a device for physical fixation of the rabbit’s head; (C) Arrangement of 16 asymmetric first-order gradiometers of a MicroSQUID device. The centers of the pick-up coils in the measurement plane are 8.41 mm apart.

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Fig. 2. (A) Implantable coaxial physical dipole. The inner and outer platinum poles are 1 mm apart. (B) Device for fixating the implanted dipole (left) on the skull (right) and shifting it along its axis in steps of 0.3455 mm by turning the screw. (C) Intensity-rendered CT (0.4 mm voxels) of an animal model with the four CT markers clearly visible and the artifact of the implanted artificial current source visible as a bright bar under a darker skull defect.

tissues present in bone. The conductivity in the defect was controllable via the ionic-current-resistance properties of the filling material. This minimized the exchange of ions over time, which would otherwise have significantly altered the conductivity toward the boundary to the bone. Balanced electrolyte solution (BES) acted as the source of ions; the solution was diluted with distilled water as needed. The solution was solidified in an agarose gel (Agarose Broad Range, Carl Roth GmbH + Co. KG, Karlsruhe, Germany), which itself had a low resistance to ionic currents. The resistance was adjusted by adding D()-fructose, which was chosen over glucose and sucrose because it is most neutral to the cell metabolism. In a preliminary experiment, the conductivity of a BES-agarose material without fructose was empirically determined that forms an equilibrium with the surrounding cancellous bone tissue; i.e., its conductivity remains constant within measurable accuracy for at least 70 min. Fresh porcine bone specimens (obtained from a butcher) were used because their large size enabled accurate measurement and fast diffusion. First, a 6  6  6 mm hole in the cancellous bone was filled with a BES-agarose material of high conductivity (1.57 S/m@30 °C). After 70 min, the conductivity of the agarose cube was significantly reduced, indicating a flow of ions into the bone. A similar test in a fresh hole using agarose of conductivity 0 S/m (based on distilled water) led to increased conductivity, indicating a flow of ions out of the bone. Iterative bisection narrowed the conductivity range of the equilibrium conductivity to 1.0 ± 0.3 S/m@30 °C. A similar value was found using fresh bovine bone (own measurements; data not shown). To quantify the influence of material conductivity, materials of four conductivities were investigated (Table 1; Geddes and Baker, 1967). The ion equilibrium with 1.0 S/m@30 °C (E) was chosen because of its time stability. By adding fructose, the conductivity could be lowered close to that of skin or brain (i.e., about 0.33 S/ m@30 °C) (S) while retaining the same ion concentration, and thereby preserving the time stability of the material. The lowest feasible conductivity of approximately 0.1 S/m, close to that of bone (B), was obtained using distilled water instead of BES and a maximal amount of fructose. A high conductivity of approximately 1.57 S/m (C), similar to that of cerebrospinal fluid (CSF), was achieved by adding sodium chloride; however, this addition increased the ion concentration. 2.5. Experimental protocol Ethical approval was obtained (Freistaat Thüringen, Germany, 02–034/08) for the study. Adult New Zealand White rabbits were

anaesthetized with an intravenous infusion of 10 mg Ketamine + 1 mg Xylacine per kg body weight per hour throughout the experiments. The scalp of the animal above the superior skull surface was removed to capture the EEG signal influences of the skull independent of that of the scalp. The artificial dipole was inserted into the brain through a plastic guide cannula that was glued at the desired angle into a burr hole in the postero-lateral skull anterior to the ear canal, resulting in a mainly tangential orientation relative to the superior inner skull surface. In one animal, we simulated a source radial to the skull surface by inserting the artificial dipole through the inferior skull base after euthanizing the animal. In the tangential cases, the dipole was fixated with the shifting device initially set at its outer-most position. EEG&MEG recordings with the skull intact were then obtained at regular intervals of 0.691 mm (one full screw rotation) as the dipole was moved deeper into the brain. In the case of radial dipole fixation, the dipole was set in one position only. The 64-channel EEG array was placed on filter paper that was placed on the skull surface superior to the artificial dipole. The filter paper was soaked with a solution (diluted BES) of 1.0 S/ m@30 °C (equilibrium) conductivity. Two interconnected reference electrodes were placed in two tissue pockets at the left and right sides of the anterior rostrum. The MEG sensor array was placed above the skull as close as possible without the cryostat touching the EEG array. Each recording was for 80 s with the active dipole and for 10 s with the inactive dipole for background noise estimation. The 80 s interval was chosen to allow for the setup to become stationary. For each recording, all landmarks were digitized and an MEG sensor coregistration was performed. As reference recordings, EEG and MEG of the artificial dipole beneath intact skull were performed. In the first set of experiments, a rectangular hole of approximately 4  4 mm was then created in the skull above the implanted source. The dura mater was left intact. To simulate tissue of different conductivities, the hole was filled with each of the materials sequentially, and measurements were repeated under each condition. A second, smaller, circular hole of Ø 2 mm was then created near the first hole. Each hole was filled with the same conducting material, and measurements were repeated for each of the materials. In the second set of experiments, both holes were filled with material E (because its conductivity is most stable over time) and a series of measurements were taken starting with the dipole at its most deeply inserted position, and the dipole extracted stepwise along its axis until its outermost position.

Table 1 Skull defect material mixtures and conductivities. Material

Tissue equivalent

Ratios

Estim. conductivity in skull at 30 °C

B S E C

Bone Skin/brain Ion equilibrium CSF

Agarose:dist. water:fructose = 3:100:50 Agarose:diluted BES:fructose = 3:100:45 Agarose:diluted BES = 2:100 Agarose:BES + NaCl to meet cond. = 2:100

0.1 0.33 1.00 1.57

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sffiffiffiffiffiffiffiffiffiffiffiffiffi m X

2.6. Preprocessing

m2i;s

EEG and MEG signals were band-pass filtered (15–25 Hz). Bad or non-stationary time intervals at the beginning and end of the recording as well as artifact-corrupted intervals during the recording and bad channels were manually excluded. Using template matching, approximately 300 consecutive trials (sinusoidal waves) were identified and averaged. Principle component analysis was performed; to remove minor signal distortions, all components except the first, strongest component were rejected. The peak-amplitude time-point was selected for analysis. Isolated noise-corrupted channels and field-maps were excluded from further analysis, using the signal-to-noise ratio thresholds described in Supplementary Material A. To make the MEG recordings fully comparable, the small gradual change in the distance between the dipole and the MEG sensors across the shift recording sequence was compensated for in the data, as described in Supplementary Material A (Knösche, 2002). 2.7. Field-map measures To quantify the topographical deviation caused by the first skull defect and by the combination of the first and second skull defects, we determined the relative difference measure (RDM⁄) (Meijs et al., 1989):

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12 u 0 u u B C u B C uX C m m u m B i;r i;s  B RDM ¼ u Bvffiffiffiffiffiffiffiffiffiffiffiffiffi  vffiffiffiffiffiffiffiffiffiffiffiffiffiC C uX u BuX m m C u u i¼1 @u t m2 t m2 A t j;r

j¼1

i¼1

MAGrel ¼ 1  sffiffiffiffiffiffiffiffiffiffiffiffiffi : m X

ð2Þ

m

2 i;r

i¼1

The reference map for computing MAGrel and RDM⁄ values of the shift map series was the intact skull recording obtained with the dipole positioned close to the center of the subsequently introduced defect 1. During preprocessing, the stationarity of the signal within a selected time interval was evaluated using the instantaneous RDM⁄ and MAGrel curve. The curve represents the RDM⁄ and MAGrel values between every maximum of the sine wave (one per trial) and the maximum of the average of all the trials. These curves indicate gradual and sudden changes in field-map topography, amplitude, and inter-trial variability. For evaluation of the shift experiment and for cross-animal comparisons, the field-maps were restricted to circular evaluation environments around defect 1 of radius 4.5 mm for EEG and 12 mm for MEG. Accordingly, field-map sections distant from the structures of interest were excluded. The environment for EEG mostly excluded the second defect, and the metrics focused on defect 1. The majority of excluded measurements were EEG signals that did not sufficiently cover the chosen circular environment. In the same way, field-map comparisons in which the overlap of both maps did not sufficiently cover the circular environment were also excluded.

ð1Þ 2.8. Geometric measures

j;s

j¼1

where i and j the channel indices, mi;r is the value of the reference signal with intact skull, and mi;s is the value of the signal measured with either one or two defects. To quantify the magnitude deviation caused by these two conditions, we determined the relative magnitude difference (MAGrel):

Fig. 3. Schematic view of the geometry of the shift experiment.

The geometries of the skull defects were manually segmented from the CT images. To accurately represent the shape of each defect, the outer edge, inner edge, and the middle of the cut surface (between the outer and inner edges) were sampled finely. The position of the artificial dipole was obtained from the same CT images. The stepwise positions were reconstructed from the positions given in the CT images by adding or subtracting multiples of the step length (0.3455 mm) along the axis of the artificial dipole. Supplementary Material B describes the geometric calculation of the center of the defect, equivalent radius, skull thickness, dipole depth, and the distance between the dipole and the MEG and EEG sensor locations. In two-dimensional field-map view, the eccentricity of the dipole relative to the skull hole was defined as the ratio of two distances: the distance between the defect center and the dipole, and the distance between the defect center and the point on the middle edge of the defect crossed by a ray from the defect center through the dipole. To make the repeated shift experiments comparable, we defined the shift eccentricity of a point along the shift line as 0 at the normal projection of the defect center on the shift line, and as +1 or 1 at the normal projections of the outermost edge points onto the shift line (Fig. 3). The eccentricity of the shift

Table 2 Geometric measures of experimental setup during agar experiments (D1 = defect 1, D2 = defect 2). Skull and skull defects

Setup during agar experiments

No.

Skull thickness at D1 in mm

Equiv. radius D1 in mm

Equiv. radius D2 in mm

Distance dipole to MEG in mm

Distance dipole to EEG in mm

Dipole depth from inner skull surface in mm

Orientation in degrees (90° = radial)

Dipole eccentricity D1

Dipole eccentricity D2

1 2 3 4 5

2.4 2.0 1.9 2.3 2.0

1.6 2.2 1.9 1.9 2.3

1.1 1.2 1.1 1.0 1.2

20.6 14.0 10.9 13.5 12.1

7.2 7.1 3.9 6.6 4.7

4.4 4.9 1.8 3.7 2.2

56.3 7.0 0.3 0.1 3.2

2.04 0.93 0.41 0.76 0.71

2.3 3.90 4.50 4.21 2.94

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line itself was defined as the eccentricity of the point closest to the center of the defect along this line (Fig. 3). 3. Results 3.1. Setup geometries Successful recordings were made in five animals: four in vivo with a source oriented tangentially to the skull surface, and one post mortem with a radially oriented source. The skull thickness around defect 1 was comparatively homogeneous (Table 2). The CT images confirmed that the three layers of the skull around the defects were differentiable and fully developed. The skull defects were of similar sizes. Among the animals, sources were located at different depths from the inner skull surface (range, Table 3 Geometric measures of experimental setup during shift experiments (D1 = defect 1, D2 = defect 2). No.

Dipole depth when most centrally under D1 in mm

Shift line eccentricity D1

Shift line eccentricity D2

2 3 4 5

4.7 1.8 3.7 2.2

0.56 0.30 0.66 0.36

3.67 3.28 3.05 3.01

5

1.8–4.9 mm) (Table 2). The source was approximately 11–14 mm from the MEG sensor plane except in animal 1 (radial dipolar source; 20.6 mm). During the agar recordings, the dipole was located at a range of eccentricities relative to defect 1. During the shift recordings in the four tangential experiments, the shift line crossed defect 1 at shift eccentricities of 0.3–0.66 (Table 3). 3.2. Intact skulls versus skulls with defects The potential map of a tangential dipolar source (Fig. 4A, left) under an intact skull shows a dipolar pattern, which changes strongly following the introduction of a skull defect above the source. In animal 5, for example, the positive potential dominates the potential map mainly above the skull defect (RDM⁄ 0.86), but also extending beyond its edges (Fig. 4A, center). The positive EEG signal amplitude is notably increased above the defect and across the potential map (MAGrel 1.75). A second defect closer to the negative pole strongly changes the potential map topography (RDM⁄ from single to double defect 0.27) (Fig. 4A, right) by introducing a negative signal component above and proximal to the second defect. This only influences the potential map amplitude to a small degree (MAGrel between single and double defect 0.14) in this case. The flux density map amplitude above the intact skull in the same experiment (Fig. 4B, left) is reduced (MAGrel 0.11) when a skull defect is introduced (Fig. 4B, center), and a further amplitude

Fig. 4. Animal 5: Potential maps (A) and flux density maps (B) of the dipolar source (black bar with two spheres marking the poles) at peak amplitude with intact skull (left), with a single skull defect (inner, middle, and outer edges drawn in black) filled with agar of conductivity 1.57 S/m, (center) and with two skull defects (right). EEG electrode positions are marked with gray dots. The minimum and maximum values and isoline difference are displayed above each map.

Fig. 5. Animal 1: Potential maps of a radial dipolar source (black dot) at peak amplitude with intact skull (left), with a single skull defect (inner, middle, and outer edges drawn in black) filled with agar of conductivity 1.1 S/m (center) and with two skull defects (right). Figure structure and labels equivalent to Fig. 4.

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In the radial source experiment (Fig. 5), the potential map increases in amplitude with the introduction of the first defect (MAGrel 0.80) and the second defect (MAGrel 1.03), similar to the tangential experiments. The peak amplitude of the potential map with a single defect is found above that defect (RDM⁄ 0.15) (Fig. 5, center), but is attracted to the second defect upon its introduction (RDM⁄ 0.24). The dipole tip contact in this setup is closer to the skull and to the defects than is the base pole, and points toward the location of the second defect. The MEG signal in this mainly radial source experiment is of low signal-to-noise ratio and has an unstable topography (not shown). 3.3. EEG signal changes relative to source position In the dipole shift experiment, the influence of a skull defect is measured across a range of source positions relative to the defect (Fig. 6). The potential map of a tangential source can experience a reversal of polarity above defect 1 (Fig. 6A versus E) depending on which pole is closer to it. When the source is approximately central under the defect (Fig. 6C), the overall topography is most similar to that observed for the intact skull (Fig. 4A, left), but with distortions above the skull defect. The potential map magnitude (Fig. 7B) shows an overall elevation due to skull defects. The magnitude is most similar to that observed for the intact skull condition when the tangential source is approximately central under the defect (Fig. 7B). In these experiments, a magnitude increase by more than nine times (MAGrel > 9.0) is observed when the source is close to the defect edge. MAGrel decreases with increasing distance between the source and the defect. The projected edge contact points of the shift lines indicated at the tops of Figs. 7B–E show that in animal 5, the dipole is shifted centrally beneath defect 1 (shift line eccentricity 0.36); whereas in animal 4, it is shifted more peripherally beneath the edge of defect 1 (shift line eccentricity 0.66). However, the peak amplitude change is always observed at a shift eccentricity closer to 1 than at the edge contact points. The potential map topography change due to a skull defect (Fig. 7D) is least when the source is approximately central under the defect. The degree of topography change shows an increase toward the edge of the defect. In each animal, the change in topography is greater on one side of the defect than on the other. 3.4. MEG signal changes relative to source position

Fig. 6. Animal 5: Potential maps (left) and flux density maps (right) of the source at different positions relative to defect 1. An intact skull recording of the same animal is given in Fig. 4 left column (annotations equivalent to Fig. 4).

reduction (MAGrel between single and double defect 0.16) occurs with the second skull defect (Fig. 4B, right). In the subtraction map (Fig. 8, Shift pos. 16), this amplitude reduction is further qualified as a mainly dipolar component of approximately, but not exactly, opposing orientation. The topographic difference due to the first defect corresponds to an RDM⁄ of 0.06, and that from the single to the double defect corresponds to an RDM⁄ of 0.06.

The flux density map (Fig. 6, right column) of a tangential source shows much smaller (but observable) changes due to skull defects at different positions relative to the source than does the potential map. When the source is under the edge of defect 1 (Fig. 6A and E), the flux density gradient is strong (the distance between iso-fluxdensity lines is small) compared with MEG conducted with the source central under the defect (Fig. 6C). Small topographic distortions, such as a slight displacement of the zero-flux-density line, are observed across the shift positions (Fig. 6C). Comparison across the animals shows that the magnitude of the flux density map is approximately 20% lower (MAGrel 0.2) when the source is central under defect 1 than for the intact skull MEG (Fig. 7C). When the source is closer to the defect edge, this reduction in magnitude is less. When the source is approximately beneath the edge, the magnitude is slightly larger (approximately +5%) than observed in the intact skull condition for animals 3 and 5. The magnitude difference is reduced further when the source is next to and distant from the defect. The variability between animals and measurements is more prominent for MEG signals than for EEG signals because of the smaller magnitude of the MEG signals. Note that EEG and MEG signals show qualitatively different behaviors: the EEG signal magnitude deviation is largest when the source is under

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Fig. 7. (A) Geometric relations (parallel projection into EEG plane) of defect 1 and the dipole positions during the shift experiment (black line with dots), the reference shift position (diamond), the shift position of minimal magnitude deviation with respect to the intact skull reference recording for EEG (circle) and MEG (square), and the dipole position at which the agar conductivity experiment was performed (plus). Note that the defect is slightly funnel-shaped: e.g., the smallest edge polygon is the inner-most, closest to the source. (B)–(E) Change in Potential map (left column) and flux density map (right column) magnitude (top row) and topography (bottom row) for different source positions along the shift lines shown in (A) relative to a reference recording with intact skull at a position most centrally under defect 1 (diamond). MAGrel and RDM⁄ were evaluated in a circular environment around defect 1. Animals are color-coded; depth d of the source when most centrally under defect 1 is annotated in top diagrams; gray background indicates source positions next to defect 1. Bars at the top of each diagram indicate the projected contact points of the shift line with the edge of defect 1 for each animal.

the defect edge, whereas the MEG signal magnitude deviation is largest when the source is central under the defect. The change in flux density map topography due to the presence of skull defects is approximately consistent among the rabbits (RDM⁄ 0.1–0.2) (Fig. 7E). The RDM⁄ metric does not differentiate the topographic changes well, relative to the source position. To evaluate this aspect, we subtracted the flux density map for intact skull from the flux density map with the skull defects (Fig. 8). A gradual flux density map topography change is observable that is geometrically related to the curvature of the skull defect edge. The main orientation of the defect-related flux density map component appears to rotate as the dipole is moved from one side of the defect to the other. 3.5. Defect conductivity The influence of defect conductivity was investigated by repeating the EEG and MEG measurements with agars of varying conduc-

tivities. The data, described in detail in Supplementary Material C, show that the deviations of potential map and flux density map magnitude and topography become stronger with increasing defect conductivity. 4. Discussion 4.1. Skull defects in MEG 4.1.1. Amplitude A conducting skull defect has much less influence on flux density map than on potential map; however, the influence is substantial, with a field-map amplitude reduction of approximately 20% compared with intact skull (Fig. 7C). If we consider the deviation at a particular point in the sensor plane, such as the peak amplitude in the difference map (Fig. 8, shift pos. 16, peak negative amplitude 5 127 fT), then this deviation constitutes a 49.2% change in the intact skull MEG signal amplitude at the same point

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Fig. 8. Animal 5: Difference of reference intact skull flux density maps and skull defect flux density maps across a range of shift positions.

(+10 416 fT) under otherwise similar conditions. This means that if the magnetic flux density were sampled at that point, then the resulting signal channel would experience an amplitude deviation of 49.2% due to the proximal skull defect. Because MEG sensors integrate over a certain pick-up coil area, this peak deviation would be spatially smoothed in practice, and signal differences between 20% and 50% would be observable. This amplitude decrease can be explained by the presence of a defect volume having conductivity higher than that of the skull. The volume current extends farther into the defect volume, which is known as the shunting effect (Haueisen et al., 1997; Rush and Driscoll, 1968; Brody, 1956). The volume current is therefore closer to the MEG sensors. Because the volume current flows in a direction opposite to that of the impressed current in the dipole implant, it generates a magnetic field of opposing orientation, thus producing a reduction in MEG signal amplitude. Consequently, the MEG signal amplitude reduction should be maximal if the source is fully under the defect, as observed in the present data. Barth et al. (1986) conducted MEG recordings of an implanted dipole in a gel-filled, formalin-fixed, human cranial specimen, first 2 cm beneath intact skull, and then after a craniotomy of 7 cm in which the bone flap was placed in its original position to leave an air-filled gap of 1–2 mm. Compared with our results, their observation of an unaffected MEG signal can be understood given that the skull defect consisted of non-conducting air. The volume currents would flow through the highly conducting gel inside the head, rather than the low-conducting skull. The air gap would only slightly affect the volume currents, and therefore the MEG signal difference should be minimal (Ilmoniemi, 1995). In addition, the air gap was distant from the source. Okada et al. (1999b) conducted a skull-on versus skull-off MEG experiment in swine in vivo, using an averaged somatically evoked source. They observed no clear differences in the MEG signal waveform or amplitude between the two conditions. This result can also be understood given that the skull hole was filled with air. The removal of the already weakly conducting skull would be expected to have a minimal influence on the volume currents. Okada et al. also noted MEG signal attenuation for sources deeper than 7 mm, which became stronger with depth; up to 25% attenuation was found for a depth of 14 mm. Our results agree in terms of the magnitude of the MEG signal change that volume conduction can cause, and our experimental setup is similar to the setup of Okada

et al. in that it captures volume conduction in a conducting skull defect. Our experiments included source depths of up to 4.9 mm, and within this range the influence of source depth on the MEG signal amplitude could not be established. In a simulation study, Lew et al. (2013) found that the MEG signal magnitude simulated with fontanels and sutures as natural skull defects can be measurably different to the MEG signal magnitude simulated for a closed skull. In agreement with the present results, the MEG signal amplitude change was strong when a tangential source was under a skull defect and weak otherwise. When evaluating the MEG signal magnitude difference due to skull defects over the whole head surface, they found maximum values of absolute MAGrel of 7.2–7.9%. Considering that in their infant model the skull was very thin and had comparatively high homogeneous conductivity of 0.03–0.05 S/m, and that the absolute MAGrel was calculated over the whole head, including large field-map areas distant from the primary skull defect, these absolute values are in accordance with our results of approximately MAGrel 20%. In the radial experiment, the MEG signal amplitude was low and the topography was inconsistent across recordings. This is in agreement with previous experimental observations by Melcher and Cohen (1988), who used an implanted artificial dipolar source in a rabbit head. They found that the MEG signal amplitude is approximately six times smaller when the source is radial to the skull surface than when tangential. Measurements with varying skull defect conductivities (Supplementary Material C) showed that the flux density map magnitude deviation increased with increasing defect conductivity. For example, in animal 5, the flux density map deviated from the intact skull recording by MAGrel 0.07 for bone-like agar conductivity, by MAGrel 0.13 for brain-like conductivity, and by MAGrel 0.25 for CSF-like conductivity. 4.1.2. Topography The topographic influence of a conducting skull defect is much smaller on the flux density map than on the potential map, but of a consistent degree of an RDM⁄ of 0.1–0.2. Subtraction of the intact skull reference map (Fig. 8) reveals a gradual flux density map topography change as the source is moved beneath the defect, and this change is geometrically related to the edge of the skull defect. The gradual rotation of the main orientation of the defectrelated MEG signal component provides further insight into the

Please cite this article in press as: Lau S et al. Magnetoencephalography signals are influenced by skull defects. Clin Neurophysiol (2014), http://dx.doi.org/ 10.1016/j.clinph.2013.12.099

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diminishing amplitude reduction toward the defect edge. If the defect-related MEG signal component has opposing orientation, then it maximally reduces the amplitude. As the component changes its orientation, positive field-map sections will coincide with positive field-map sections of the non-defect-related field, and therefore increase the local amplitude (equivalently for negative field-map sections), therefore counteracting the signal amplitude reduction. The neonatal simulation study of Lew et al. (2013) found flux density map topography differences due to fontanels of up to RDM⁄ 0.017–0.022. Considering (1) the very thin, higher conducting skull and comparatively lower conductivity of the defects (0.3 S/m) in their model and (2) that RDM⁄ was evaluated including large field-map areas distant from the skull defect, their results concur with ours in that skull defects cause a measurable topography difference when the source is beneath the defect. The comparatively high spatial sampling density of the MicroSQUID system (8.4 mm coil center distance) enabled us to detect topographic flux density map changes related to the geometry of a skull defect. However, the skull defect edges had higher spatial frequencies that could not have been detected with this MEG sensor array. Therefore, we consider that higher MEG sampling density could be beneficial in the presence of skull defects. 4.2. Skull defects in EEG 4.2.1. Amplitude The potential map amplitude can be increased by a factor of 2–10 if the source is beneath a conducting skull defect (Fig. 7B). This is consistent with the finding of Okada et al. (1999a), who found an increase in amplitude by a factor of 4–10 between the EEG signal of a somatic evoked potential at the cortical surface compared with that at the skull surface of a juvenile swine. The potential map amplitude increase also matches clinical findings in humans, which are reported as factors of up to 3 (Cobb et al., 1979; Radhakrishnan et al., 1999) and of up to 5 (average, 1.5) in 30 patients (Kendel, 1970). For the tangential source (Fig. 7B), this peak amplitude increase is reached when the dipole is beneath the edge of the defect, while the amplitude change is minimal when the dipole is approximately central under the defect. This can be explained by a current that flows at the interior side of the highly conducting defect if both poles are beneath the defect. If only one pole is beneath the defect, then its potential extends to the exterior surface of the defect, and the current flows through the defect edge surface. We observed a weaker increase in amplitude when the source was located farther from the defect, although our sampling range was limited to the vicinity of the defect. Consistent with our measurements, Kendel (1970) observed an increase in breach rhythm amplitude close to the edges of skull defects of post-surgical patients. The peak amplitude change decreases with increasing source depth (Fig. 7B), which can be explained by less current reaching the skull and the defect. Meanwhile, the shift eccentricity of the peak magnitude change is higher with increasing depth, indicating that the defect has its greatest influence when the source is outside, but close to, the defect area for deeper sources. Measurements with varying skull defect conductivities (Supplementary Material C) showed that the potential map magnitude deviation increases with increasing defect conductivity. For example, in animal 5, the potential map deviates from the intact skull recording by MAGrel 0.54 for bone-like conductivity, by MAGrel 1.06 for brain-like conductivity, and by MAGrel 1.37 for CSF-like conductivity. 4.2.2. Topography In contrast to the flux density map topography, the potential map topography is highly dependent on the position of the source relative to a skull defect. The local potential map topography can

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change from a dipolar to a monopolar pattern and invert its polarity due to a skull defect (Fig. 4A). Concordant with this observation, Van Burik and Peters (2000) reported strong potential map distortions with large gradients in the proximity of burr holes in a surgical patient. The observation of potential map polarity inversion depending on which pole of the source is closer to the defect is in agreement with data from a phantom experiment (Heasman et al., 2002). This can significantly impair clinical interpretation of the EEG signals, during which the location of the EEG signal maxima and minima are central features (Brigo et al., 2011). The potential map topography is most similar to the dipolar intact skull potential map when the tangential source is approximately central under the defect. This is consistent with the clinical observation that in the center of a skull defect the potential map may look unsuspicious (Kendel, 1970). The topography change increases rapidly toward the edge of the skull defect. This transition appears to be sharper for superficial, and therefore closer, sources (Fig. 7D). 4.3. Interpretation for human MEG and EEG We expect that our results are transferable to humans. Specifically, the influence of a human skull defect on the MEG signals should be strongest if the source is central beneath the defect. A neonatal simulation study supports this finding (Lew et al., 2013). In the following, we evaluate the differences between our experiment and potential human recordings. (1) Defect conductivity: The main factor modulating the magnitude of MEG and EEG signal changes is the skull defect conductivity relative to the conductivity of the skull, and the compacta layers in particular. While a defect conductivity of 1.0 S/m in our shift experiment resulted in reductions of flux density map magnitude of greater than 20%, a more physiological defect conductivity of 0.33 S/m decreased the flux density map magnitude by approximately 13% (Supplementary Material C). This indicates that the local flux density map magnitude change due to a skull defect in humans may be between 10% and 20% and subject to geometric and anatomical factors. (2) Defect size: The experimental skull defect of approximately 4  4 mm, equivalent to a burr hole, enabled us to assess the influence of a skull defect on MEG and EEG signals for different source positions. The qualitative observations should be transferable to burr holes in humans. This is supported by a neonatal simulation study (Lew et al., 2013) that showed that the MEG and EEG signals of sources beneath neonate thin sutures are influenced by these sutures. Larger skull defects should cause a wider spread of signal changes. Larger defect volumes cause more volume currents to be displaced closer to the MEG sensors, which could increase the influence of the skull defects. (3) Skull thickness: Humans skulls, being thicker than those of rabbits, are likely to show stronger attenuation of EEG signals. A skull defect with higher conductivity than the skull would eliminate this attenuation locally, and cause a strong signal change. MEG signals would be affected by a thicker skull through showing a slightly stronger amplitude reduction because the volume current passing through the skull defect would extend a few millimeters farther in the direction of the sensors. (4) Source depth: The amplitude of the magnetic flux density diminishes rapidly with distance. However, the currents in the defect are closer to the MEG sensors, and therefore are less attenuated. This distance advantage would become even more pronounced for a deeper source and the influence of

Please cite this article in press as: Lau S et al. Magnetoencephalography signals are influenced by skull defects. Clin Neurophysiol (2014), http://dx.doi.org/ 10.1016/j.clinph.2013.12.099

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skull defects would be magnified. A deeper source would also cause the volume current at the skull and any skull defects to be weaker. However, experimental evidence (Okada et al., 1996) indicates that subcortical sources at depths of 4–5 cm in the brain of juvenile swine contribute substantially to electric potential at the cortical surface. Therefore, the volume current at the skull due to a 4–5 cm deep source may still be substantial. The influence of these opposing effects and their interrelation should be investigated further. 5. Conclusion For both MEG and EEG, we observed substantial signal amplitude and topography changes due to a skull defect. The changes were dependent on the exact geometry of the skull defect and the relative orientation and position of the source. The conductivity of the skull defect had a modulating influence on the local amplitude. We conclude that a realistic representation of the skull and skull defects in volume conductor models of the head is important for the forward simulation of not only EEG but also MEG, a novel finding. We expect flux density map magnitude changes of up to 20% due to skull defects in humans, such as in patients with post-surgical skull conditions. The extent, to which skull defects influence human MEG and EEG signals, as well as source reconstruction from MEG and EEG in the presence of skull defects, requires further investigation.

Conflict of interest disclosure All funding sources supporting this work are acknowledged. The authors will disclose to the editor any pertinent financial interests associated with the manufacture of any drug or product described in this manuscript. Acknowledgments This work was supported by the German Research Foundation [Ha2899/14-1]; the Australian National Health and Medical Research Council [558425]; the German Academic Exchange Service [D/08/13928, 54388947]; and the Australian Group of Eight. We wish to thank Stefan Clauss, Hannes Nowak, Ralph Huonker, Frank Gießler, Daniel Güllmar, Eric Lopatta, Simon Vogrin, Levin Kuhlmann, David Grayden, and Mark Cook for their support. We thank the Research Workshop of the Jena University Hospital for the production of the high-density EEG array, the physical dipole model, and the stereotactic device.

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.clinph.2013.12. 099.

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Please cite this article in press as: Lau S et al. Magnetoencephalography signals are influenced by skull defects. Clin Neurophysiol (2014), http://dx.doi.org/ 10.1016/j.clinph.2013.12.099