MEG and ECoG localization accuracy test

ELSEVIER

Electroencephalography and clinical Neurophysiology 94 (1995) 109-114

o

MEG and ECoG localization accuracy test Sina Gharib a,b William W. Sutherling b,c,g,* Nobukazu Nakasato d Daniel S. Barth e Christoph Baumgartner f, N. Alexopoulos at Steve Taylor g, Robert L. Rogers g Departments of ~ Electrical Engineering and b Neurology, University of California and c Brain Research Institute, Los Angeles, CA, USA d Department ofNeurosurgery, Tohoku University, Sendai, Japan e Department of Psychology, University of Colorado, Boulder, CO, USA f Neurological Unit,ersi~ Clinic, Vienna, Austria g Neuromagnetism Laboratory, Epilepsy and Brain Mapping Center, Hospital of the Good Samaritan, 1245 Wilshire Blvd., Suite 810. Los Angeles, CA 90017, USA Accepted for publication: 6 October 1994

Abstract

We tested the localization accuracy of magnetoencephalography (MEG) and electrocorticography (ECoG) for a current dipole in a saline filled sphere at depths ranging from 1 to 6 cm at 1 cm intervals. We used standard neuromagnetometer placements and subdural electrode grids, previously employed for patient studies, with precise measurements of sensor and electrode locations with a 3-dimensional spatial digitizer. MEG and ECoG had comparable accuracy with mean errors of 1.5 and 1.8 ram, respectively. It appears that use of the spatial digitizer increases accuracy for both MEG and EGoG localizations. The larger errors in the ECoG with increasing depths could be attributed to under-sampling of the spatial pattern of the field which spreads out with deeper sources. It should be noted that in clinical applications a grid of the dimensions used here would most typically be used for superficial sources on the cortex with depth recordings being preferred for investigations of deep epileptogenic activity. Results are encouraging for continued development of non-invasive MEG methods for further definition of epileptogenic zones in the brain. Kevwords: Magnetoencephalography (MEG); Electrocorticography (ECoG); Localization accuracy

1. Introduction

Surgical implantation of subdural grid and strip electrodes (ECoG) is increasingly utilized in cases where neocortical epileptogenic regions are to be delineated for subsequent surgical resection (Engel and Ojemann, 1993). The advantages gained by subdural recordings over surface EEG come from circumventing the electric resistivity of the dura, skull and scalp which at best attenuates the EEG signal and at worse distorts or prevents adequate definition of the underlying currents. This is evidenced by the fact that only a fraction of seizures recorded from implanted grids and strips are seen on surface EEG recordings (Devinsky et al., 1989). The major disadvantages of ECoG recording stems from the risks associated with as well as

* Corresponding author at address given under g. Tel.: (213) 481-1777.

the extensive costs accompanying the surgery and extended hospitalization with long-term monitoring. Magnetoencephalography (MEG) non-invasively records magnetic fields which are relatively unaffected by the various tissue layers of the human head (Barth et al., 1986). Additionally, magnetic flux circles the dipolar layer generating the electric current but does not conduct through the brain parenchyma. Although secondary currents also produce magnetic flux these tend to cancel in the spherical model and generally are not taken into account (Meijs et al., 1987). The major disadvantages of MEG include large start-up costs, high sensitivity to external sources of artifacts and the fact that not all sources are amenable to MEG analysis. The present experiment was undertaken to contrast the relative effectiveness of MEG and ECoG grids for source localization for precisely known dipolar sources in a saline filled sphere. We contrasted the comparative solutions using MEG and ECoG models at conditions as closely resembling epileptogenic activity as possible.

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EEG 93090

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S. Gharib et al. / Electroencephalography and clinical N eur ophysiology 94 (1995) 109-114 f

2. Methods

Theory A current dipole placed inside a homogeneous sphere generates a potential distribution on its surface which can be determined by solving Poisson's equation in spherical coordinates. The general solution consists of a series of weighted Legendre and associated Legendre polynomials for radial and tangential components of the dipole. Let a current dipole p(p,, py, Pz) be placed a distance d on the z-axis of a homogeneous conducting sphere with radius R~ and conductivity s. The general solution of the electric potential is thus (Stok, 1986):

V(Op, dgp) 4rr°'R2 (1 + +

2f/z +f2)

3/2 -

1

Pr cos(~b)p +py sin(~b)p 4 7ro'fR 2 sin(0)p

f - 3f2# + 3 f - / z X (1 + f 2 _ 2f/z) 3/2

(1)

where theta (0) is the declination angle and phi (~b) is the

Fig. 1. Coordinate system for theoretical dipole equations and current dipole in a sphere. The nomenclature corresponds with equations (1), (2) and (3). Phi is azimuthal and theta is declination angle; p is the dipole; and f is the sensor site for measurement in both MEG and EEG.

SENSOR PLACEMENTS 64 CHANNEL ECoG GRID

COMBINED MEG ARRAY

Z

Z

OOO0 OO0 OOOODOOO O OO

Y

X

Fig. 2. Diagram illustrates positions of the 64-channel ECoG grid and location of the 29 MEG sensors in the saline filled sphere.

Y

S. Gharib et al. / Electroencephalography and clinical Neurophysiology 94 (1995) 109-114

MEG

azimuthal angle in spherical coordinates as demonstrated in Fig. 1. The magnetic field of the dipole can be derived from the Biot-Savart law: H=(p×R')/(47rR

3)

l 11

EEG --2~de~h~

(2)

where R' is the vector from the current dipole to the point of measurement and R is the magnitude of the vector from the origin to that point. Since only the radial component of the magnetic field is measured, we are interested only in this component which is given by: ~

p ~ d sin(0) sin(&)

=

. 0.5 sec.

0.5 sec.

(3)

.

~

. ~

.

.

~

~

.

. ~

~

47r[R ~ + d ~ - 2 d R cos(&)] 3/~ 6 o ' n deplh ~

Experimental procedure

An acrylic sphere of inner radius 10.0 cm was designed and built to model a human brain. Current dipoles were constructed from twisted copper wires inserted inside serological pipettes in a T formation with total length of 0.5 cm. Signals were generated from a solid state square wave stimulator (Grass Instruments Model $88, Quincy, MA) and sent through a photoelectric stimulus isolator which produced a constant current output. The electric field was measured using 64 ECoG platinum-iridium grid electrodes placed inside the sphere. The potential at each electrode was measured relative to ground and a reference electrode distant from the dipole and the ECoG grid. The dipole was near the center of the ECoG grid. Data obtained from each electrode were independently amplified, filtered (bandpass 1-100 Hz), digitized at a sampling rate of 256 Hz (12 bits) and stored for further analysis. The magnetic field was measured in a shielded environment using a 7-channel magnetometer with a DC-SQUID (Superconducting QUantum Interference Device) and coplanar second derivative gradiometers (coil diameter 1.5 cm; coil baseline 4.0 cm; coil center to center distance 2.7 cm; Biomagnetic Technologies, Inc., San Diego, CA). MEG was recorded from 29 sites on the sphere surface and the coil locations for the channels were determined using a digitizing probe position indicator. The dipole was at the center of the MEG matrix. Data obtained were filtered (bandpass 1-100 Hz), digitized at a sampling rate of 256 Hz and stored for further analysis. The locations of the MEG sensor sites and the ECoG electrodes were determined using a spatial digitizer and a probe position indicator (PPI, Polhemus 3-space tracker) as illustrated in Fig. 2. We tested the accuracy of the digitizer which had a measured error of about 0.2 mm in comparison to the width of a 20 cm diameter cylinder, measured by a ruler which was graduated in millimeters. ECoG sensor site location was measured using a head digiziting stylus of the PPI to estimate the center of each electrode position. The stylus was placed perpendicular to the outer surface of the sphere and then the thickness of the sphere

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r

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>=

--

St.._

0.5 sec. F i g . 3. O r i g i n a l

,

0.5 sec. tracings

of MEG

and ECoG

wave

forms

for a superficial

dipole (1 cm) and deep dipole (6 cm).

of 2 mm was subtracted to the center to obtain the locations of the electrodes. The spatial digitizer gave the exact locations of each of the sensor sites relative to the center of the sphere, the origin of the coordinate system, and to the dipole. Electric and magnetic fields were measured for a single current dipole varied from a depth of 1 - 6 cm in 1 cm increments toward the center of the sphere. We checked that the slight difference in centering the MEG and ECoG matrices did not significantly change localization accuracy by localizing each of 2 dipoles separated by 2 cm, one centric and the other eccentric. There was no apparent difference in the localization errors between the centric and eccentric dipoles. We used the amplitude at the first peak of the spiky wave forms (Fig. 3) for localization of the dipole source. Data analysis T h e " d i p o l e s o u r c e " . We estimated the localization of

the current dipole by the method of an "equivalent source." This assumes that the location of electric current can be represented as a "current dipole" source at its center. The current dipole is a good approximation of a focal source and is the first approximation to the description of any source (Darcey et al., 1980).

S. Gharib et al. / Electroencephalography and clinical Neurophysiology 94 (1995) 109-114

112

The MEG and ECoG data were independently analyzed by a computer program that used an exhaustive brute force search to obtain initial start values and then estimated the dipole location with a downhill simplex algorithm of Nelder and Mead (Press et al., 1986) which utilized least-squares fit to obtain best fitting equivalent dipole source. Finally, the computer's solution was compared to the actual physical location of the current source. We used least-squares modeling which fits observed map patterns to patterns derived from experimental or computer model sources with known locations. We corrected for the effects of gradiometer baseline (Barth et al., 1986) and for the tangential component of the magnetic field (Stok, 1986, 1987) in an improved version of MEG source localization from our previous work.

3. R e s u l t s

Fig. 3 shows the recorded ECoG potential and MEG wave forms for 64 ECoG electrodes and 29 MEG sensor locations at depths of 1 and 6 cm. Although the configuration of the apparatus produced biphasic spikes, this was

considered desirable since they more closely resemble clinically recorded spikes seen in epileptic patients than would square wave patterns. The isocontour maps at each depth for both potential and magnetic field patterns are depicted in Fig. 4. These isocontour maps and the traces in Fig. 3 were constructed from normalized data which circumvent problems associated with determining magnetic fields in absolute values and also emphasize the spreading associated with increasing depth. The raw amplitudes decreased with greater depth as expected. Table 1 summarizes the results of the dipole localizations. The physical location of the dipole is compared to the source estimation by the computer; the percentage of data variance explained by the dipole model is also determined. The Euclidean error defined as the distance between the physical location of the source and the location predicted by the computer model is shown in both MEG and ECoG cases. MEG localized the current dipole at 6 different depths with an average error of 0.15 cm (__+0.08). The MEG model explained a high percentage of data variance (97.5% + 2.2). The ECoG localized the dipole with an average error of 0.18 cm (+0.06) and explained an even higher

MEG

'NI Iii~}~i~i~::!~*~ ........................ 1 cm

/ 2 cm

3 cm

4 cm

5 cm

6 cm

4 cm

5 cm

6 cm

8 cm

ECoG

1 cm

L

2 cm

3 cm

I

4crn Fig. 4. Isocontour maps at the peak of dipole stimulus signal for MEG and ECoG. Maps are shown for each depth. Note the tight field pattern for 1 cm depth and the gradually expanding pattern for increasing depth. MEG covers both field extrema for all depths, whereas ECoG covers both field extrema only for 1 cm and 2 cm. All maps are based on normalized data.

S. Gharib et al. / Electroencephalography and clinical Neurophysiology 94 (1995) 109-114

113

Table 1 M E G and E C o G localizations of a current dipole in a sphere Dipole location ( c m ) x

y

Location ( c m ) z' b

x

Euclidean error ( c m )

Var(%) a

y

MEG 0.00

- 0.06

1.00

- 0.03

0.02

0.99

0.09

93.0

0.00

- 0.04

2.00

0.02

0.17

2.02

0.22

97.2

0.00

- 0.03

3.00

- 0.02

0.11

3.01

0.15

99.4

0.00

- 0.01

4.00

0.06

0.23

3.99

0.26

98.1

0.00

0.00

5.00

- 0.01

0.00

4.95

0.05

98.6

0.00

0.00

6.00

- 0.05

0.09

6.04

O. 11

98.4

Mean = 0.15 ECoG 0.00

- 0.06

1.00

0.08

- 0.24

0.99

0.20

98.2

0.00

- 0.04

2.00

0.06

- 0.18

2.00

0.14

97.4

0.00

- 0.03

3.00

0.06

- 0.22

3.01

0.19

98.8

0.00

- 0.01

4.00

0.08

- 0.22

3.90

0.24

98.6

0.00

0.00

5.00

0.08

- 0.21

4.89

0.25

99.0

0.00

0.00

6.00

0.02

- 0.36

5.86

0.39

98.8

Mean = 0.23 a Var ( % ) = percent of data variance of data explained by one dipole model. b Z' = depth below surface of sphere = ( 1 0 - z )

cm on coordinate s y s t e m in Fig. 2.

percentage of data variance (98.4% __+0.7). A univariate F test of the differences between MEG and ECoG error scores was not statistically significant. ECoG Euclidean errors demonstrated a tendency to increase with depth. Since MEG errors in x and y were often of opposite sign compared with ECoG errors in x and y, we tested MEG + ECoG localization accuracy compared with MEG accuracy. We averaged MEG and ECoG localizations together to obtain an MEG + ECoG localization. There was a significant trend for MEG + ECoG to have a smaller error (mean 0.07 cm, S.E. 0.01) than MEG (mean 0.15, S.E. 0.03) ( P = 0.05). 4. Discussion The results of this experiment confirm that MEG and ECoG are both highly accurate methods of localizing current sources within a couple of millimeters. Interestingly, the error appeared due largely to systematic inaccurate localizations in the y direction for both MEG and ECoG, but in opposite directions. Errors seen here could have resulted from several potential causes. One potential source of error in ECoG could be in the estimate of sensor site locations. Our determination of ECoG sensor site location assumed that the electric potential was recorded at the centroid of the electrode geometry. The actual recording electrolyte interface or double ion layer is more complex and location of the actual ECoG sensor site may be more difficult to determine. This estimate of ECoG electrode center and the layer is inherently less accurate than the automatic estimates of the center of fixed coils in the neuromagnetometer and may explain part of the error. Another potential source of error in ECoG could have

been the slightly shifted position of the grid in relation to the underlying dipole, as seen in Fig. 3. However, since we tested localization accuracy for ECoG for a dipole at the center and shifted by 2 cm along the y-axis and found no significant differences in the localization errors, we believe that the difference between MEG and ECoG in precise centering of the matrix over the dipole is unlikely to be an explanation of a difference in MEG and ECoG accuracy (Weinberg et al., 1986). Furthermore, the effect on error from precise centering of the matrix over the dipole would be expected to be larger for sources near the matrix. MEG, however, had small errors for both 1 cm and 5 cm depths and ECoG had the smallest error at a superficial depth and the largest error at the largest depth. It should be also noted that in clinical settings intraoperative placement of electrode grids is not likely to approach the accuracy in precise placement over the source that was achieved here since the location of the dipole will be unknown. However, theoretically, localization accuracy should not depend on placing the grid exactly over the dipole as long as adequate sampling is achieved. The primary cause of increased inaccuracy in the ECoG model at greater depths may have resulted from the inability of the grid electrodes to cover the full extrema of the electric field pattern (Fig. 4). Since the maxima and minima of the electric potential field were not recorded, the ECoG computer model may not have been able to obtain reasonable start values or to fit the pattern as precisely as in MEG. Inadequate field sampling has been a criticism of some studies reporting larger MEG localization errors (Cohen et al., 1990; Williamson, 1991). We used the 64-grid ECoG electrode array because it is the same type of array used in our patients evaluated for surgical treatment of medically intractable epilepsy and most large

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S. Gharib et al. / E lectroencephalography and clinical Neurophysiology 94 (1995) 109-114

arrays used for clinical subdural recording have similar electrode spacing and spatial extent. We could have added more ECoG electrodes inside the sphere to cover the maxima and minima of the electric potential field; however, the relevance of this for clinical studies is not apparent. ECoG grids are restricted in number due to considerations of mass effect and intracranial pressure. Furthermore, in the human head, the addition of larger grid arrays and more electrodes increase the non-sphericity of the electrode matrix. Another cause for MEG localization errors in this study may be the inclusion for the effects of the tangential component of the magnetic field. Although it was relatively simple to place the 7-channel neuromagnetometer approximately perpendicular to the surface of the sphere visually, the coils of our gradiometers are coplanar. This could have introduced a component of the tangential field (Stok, 1986). Large MEG arrays with fixed sensor locations will likely give more accurate results. We also found that there was a trend for MEG + ECoG to be more accurate than MEG alone. This is similar to our previous findings in the somatosensory evoked response where MEG + EEG had smaller errors than either MEG or EEG alone (Sutherling et al., 1988) consistent with the theory (Stok, 1987). The cause of this improvement appeared to be due to different deviations of the MEG and EEG localizations in the x and y directions. The advantage of MEG + EEG appears to be useful for absolute localization accuracy as well as for separation of sources with different orientations (Wood et al., 1985). Some improvement using combined MEG + EEG could be due to the additional number of samples used. It is also possible that combined MEG, EEG and ECoG could degrade the results of one of the measures if the other is considerably less accurate. This study did not directly compare MEG and EEG accuracies. In conclusion, these results indicate that MEG and ECoG have similar abilities to localize a single equivalent dipole source in a physical model and that any small differences seen here are likely to be minimal in clinical relevance. Most important to determining clinical usefulness of MEG and ECoG are their abilities to locate actual abnormal biological signals in patients. This represents additional challenges associated with such parameters as background brain noise, non-sphericity of the human head, inhomogeneities of the various tissues especially the variations of skull thicknesses, and the simultaneous activation of multiple areas as frequently seen in the brain (Fender, 1987). Multiple source models are currently being tested and appear to provide accurate localization of two or more concurrent sources (Weinberg et al., 1986; Baumgartner et al., 1991). Future investigations and refinements of both MEG and ECoG localization models appear promising.

Acknowledgments Supported by Grant NS20806 from the National Institute of Neurological, Communicative Disorders and Stroke, Epilepsy Branch. Dr. Sutherling is a recipient of a Teacher-Investigator Development Award (NS00678). We thank Tony Fields for technical assistance.

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