IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 37, NO. I, JULY 1990
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An Improved Method for Localizing Electric Brain Dipoles YEHUDA SALU, LEONARD0 G. COHEN, DOUGLAS ROSE, SUSUMU SATO, CONRAD KUFTA, MARK HALLETT
Abstract-Methods for localizing electrical dipolar sources in the brain differ from one another by the models they use to represent the head, the specific formulas used in the calculation of the scalp potentials, the way that the reference electrode is treated, and by the algorithm employed to find the least-squares fit between the measured and calculated EEG potentials. The model presented here is based on some of the most advanced features found in other models, and on some improvements. The head is represented by a three-layer spherical model. The potential on any point on the scalp due to any source is found by a closed formula, which is not based on matrix rotations. The formulas will accept any surface electrode as the reference electrode. The least-squares procedure is based on optimal dipoles, reducing the number of unknowns in the iterations from six to three. The new method was evaluated by localizing five implanted dipolar sources in human sensorimotor cortex. The distances between the locations of the sources as calculated by the method, and the actual locations were between 0.4 and 2.0 em. The sensitivity of the method to uncertainties encountered whenever a real head has to be modeled by a three-layer model bas also been assessed.
I. INTRODUCTION HE ELECTRICAL activity of a small brain region can be modeled by an equivalent dipolar source. The surface EEG generated by this active region contains information about the location and orientation of that equivalent dipole, which in turn can provide information about ongoing processes in the brain tissue that it represents. The equivalent dipole is a good approximation only for small active brain regions. The head itself can be modeled by three concentric spheres [l]. This is a simplification that preserves some important electrical features of the head, while keeping the mathematical complexity of the problem manageable. In the past, there have been several reports of methods for noninvasive localization of equivalent dipolar sources in the brain, utilizing three layer head models [2]-[6]. The purpose of this paper is to present and to evaluate an improved method for noninvasive localization of equivalent dipoles in the brain. The proposed method has been tested and evaluated on human in vivo.
T
Manuscript received January 17, 1989; revised November 7, 1989. This work was supported in part by Grant 1 R03 MH 4 3050-01 from The National Institute of Mental Health. Y. Salu is with the Department of Physics and Astronomy, Howard University, Washington D C 20059. L. G. Cohen, D. Rose, S . Sato, C . Kufta, and M. Hallett are with Human Motor Control Section, Medical Neurology Branch, NINDS, NIH, Bethesda, M D 20892. IEEE Log Number 9035442.
AND
THEORY The Equivalent Dipole The basic idea of most dipole localization methods is to look for an equivalent dipole, such that V ( i )tal, the calculated potentials that it generates at N scalp locations, best fit V ( i )&, the observed EEG potentials at those points. Best fit is defined as a least-squares-fit. The equivalent dipole is then the one for which SUM is minimum. N
The SUM of any other dipolar source would be greater then the SUM of the equivalent dipole. The calculated potentials depend on the dipolar parameters, and on the head model being used. A common head model, which includes sufficient details, but which is not too complicated to be handled mathematically, is the three-layered spherical head model.
Spherical Three-Layer Model In the spherical three-layer model, the head is modeled by three concentric spheres. The inner sphere represents the brain, the intermediate layer represents the skull, and the outer layer represents the scalp. Consider first a dipole located on the Z axis, and the potential that it generates at scalp point P , located in the X Z plane (Fig. 1). Two of the components of the dipole moment which lie in the XZ plane, m, in the radial direction, and m,in the tangential direction, are shown in Fig. 1 . The third component, which is perpendicular to the XZ plane, does not contribute to the potential on that plane, and is not shown in the figure. The potential V generated by the dipole at the scalp point P is given by [7], [8], [5]
+ m,P; (cos a) cos /3]
(2)
where (Fig. l), R = outer radius of head, S = soft tissue conductivity, X = (skull conductivity)/S, b = (distance of dipole from center)/R, a = polar angle of surface point, /3 = azimuth of surface point, not shown in Fig. 1 , and not used in this work.
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Z
Any point on the scalp may serve as the reference electrode. Once such a point has been chosen, the appropriate adjustments have to be made in (3), which becomes
4
+
+
V' = v;, vy vi. (34 A detailed discussion of this matter is given in the Appendix [see A. 61 .
+X
Fig. 1 . A cross section through the spherical three-layer model. The center of the spheres is at the origin.
1 r
d,, = [ ( n + l ) X
-
+ n]
7
nX + l j n + l
P,, ( ) and P!,( ) are Legendre and associated Legendre polynomials n l = 2n 1, rl and r2 are inner and outer radii of skull, f l = r i / R , fi = r 2 / R , m,., and m, radial and tangential dipole moments. Equation (2) gives the scalp potentials generated by a dipole located on the Z axis, with zero dipole moment in the Y direction. To find the scalp potentials generated by an arbitrary dipole, the coordinate system has to be rotated accordingly, using rotation transformations [3], [4]. Simple closed formulas, which generalize (2) for any arbitrary dipole are derived in the Appendix, and can be written as (Fig. 2)
+
vx =
Tx12
Dx
(3) The potential
at R2due to a dipole D located at R1 is:
v=
vx
+ v y + v,
Equation (3) is a condensed form of (A.5). TXl2,Tyl2, and TZl2are called transfer coejicients. TXl2 gives the potential that a unit dipole, located at R1 and pointing in the X direction, will generate at scalp point R2.The meaning of the other coefficients is similar. Their detailed expressions can be inferred by comparing (3) and (A.5); they are the expressions inside the corresponding curled brackets { >. The transfer coefficients depend on the geometrical properties of the head, and on the location of the dipole. They do not depend on the orientation of the dipole.
The Least-Squares-Fit The least-squares-fit searches for a dipole that minimizes SUM in (1). The observed potentials in ( 1 ) are measured with respect to the arbitrarily chosen reference Ro, and the theoretical potentials are calculated according to equations (A.6). There are six parameters that specify the equivalent dipole: three spatial coordinates, and three components of the dipole moment. When (A.6) is substituted in (l), the equations for those six parameters are nonlinear. The minimization of ( 1 ) is usually carried out by an iterative algorithm 131, [41. In the following, a different approach is employed. It is based on the concept of the optimal dipole [9]. Any point inside the sphere has its own optimal dipole. An optimal dipole fits the observed data better than any other dipole, which has the same location but different orientation. The unknown parameters of an optimal dipole are D,, Dy, and D,. The transfer coefficients for any optimal dipole can be calculated directly by (A.5) and (A.6). Therefore, finding an optimal dipole is a linear least squares problem with only three parameters. It can be solved easily [lo]. There are two possible ways for finding the equivalent dipole, utilizing optimal dipoles. First, few optimal dipoles are found in an arbitrary region. The steepest slope with respect to the spatial coordinate is found, and a new search region is obtained. Optimal dipoles in that region are found, a new slope is determined, and so on, till the best of all optimal dipoles is found. This is a minimization iteration, that depends only on three parameters, compared to the six parameters being used in other dipole localization methods. The second way, which was used in this study, is to find optimal dipoles at a dense grid of points, that covers the volume in which the dipolar source is expected to be. The best of all the optimal dipoles is the equivalent dipole. Since using optimal dipoles reduces the number of unknown parameters from six to three, such dense grids can be handled easily by today's computers. The grid spacing in this work was 3 mm.
METHODS In order to evaluate the accuracy of the method described above, it was used in the localization of dipolar sources whose positions and orientations could be also determined by other independent means. Informed consent was obtained from the patient, male, 23-years old. The patient had matrices of subdural platinum electrocorticography electrodes, that were implanted for locating epileptic foci. The diameter of these disk electrodes was 6 mm, and their spacing was 1 cm center to center. Five pairs of
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t
rRZ
Fig. 2. Vectors involved in expressing the potential generated by an arbitrary source onto an arbitrary scalp point, in Cartesian coordinates. RI is the location of the source. R, is the point at which the potential is calculated. D = ( D x ,D,, D,)is the dipole moment, RR is a unit vector in the radial direction of R I , and T i s a tangential unit vector in the major plane.
those electrodes were chosen to simulate cortical dipoles. Those electrodes were over the sensorimotor cortex. The distance between the electrodes forming each dipole was 1 cm. A positive current pulse of 40 pA and duration of 5 ms followed by a negative pulse of the same size was delivered to each dipole. The delay between the pulses was 20 ms. This was repeated 200 times for each dipole, at a frequency of 1 Hz. The EEG’s generated by those currents were picked up by 30 surface electrodes. The electrodes were needle electrodes that were placed in a 5 x 6 lattice over the left scalp area anteriorly and posteriorly to the Cz-T3 line of the international 10-20 system. The inter electrode impedance for the tests was less then 2 kfl. Reference electrode was at right earlobe. The separation between the scalp electrodes was 2.5-3.0 cm. The signals from the electrodes were amplified by a bank of amplifiers, band width 1 Hz to 1 kHz, and gain of 2000 or 5000, as needed. The amplified signals were digitized at 4.1 kHz per channel, 12 b, and stored on a disk. This digitizing rate provided 20 samples per channel for every current pulse. The square shape of the pulse could be clearly seen in the recordings (Fig. 3). Averages of 200 sweeps were then calculated for each scalp electrode and each dipolar source, to further reduce the noise. Those averaged potentials at the center of the square, i.e., 2.5 ms after the onset of the current pulse, were used as the V ( i ) &s in (1). The x , y, z coordinates of the scalp electrodes and of landmarks on the head were measured by a three-dimensional digitizer (3Space digitizer, Polhemus). MRI of the patient with markers for scalp electrodes Cz, C3, Pz,and P 3 were taken before the implantation of the subdural electrodes. The subdural electrodes were surgically positioned as required clinically, and their exact relationships with the scalp markers was determined. X rays of the patient with the implanted electrodes were taken from several angles. The x , y, z coordinates of the subdural electrodes, that were used as dipoles, were determined based on the MRI markers, the X rays, and the coordinates of the scalp electrodes.
0.1 sec
U Fig. 3. Recordings of scalp potentials generated by dipolar source 3. Each trace corresponds to a surface electrode. Cz, C3, P:, P 3 . T3, and Ts indicate traces at those locations of the international 10-20 system. The positive and negative square pulses are seen in each of the 30 traces. All ordinates use the same normalized scale.
The center of the sphere that represents the head was in the coronal cross section that contains surface electrodes Cz, C3, and C4. The contour of the upper head in this cross section is semicircular, and the center of the sphere was the center of this contour. The distance of each surface electrode from this center was calculated, and the average of those distances was chosen as the radius of the outer sphere. The locations of the 30 scalp electrodes were then projected by spherical projection onto the sphere. The outer radius of the sphere was 10.45 cm, and the distances of the scalp electrodes from its center, before being projected, were in the range 9.5-1 1.5 cm. The conductivity ratio [Xin (2)] of skull to soft tissue was taken as 0.0125, and the relative radii of the inner spheres [ f, and fi of (2)] were 0.87 and 0.92 El]. The location and orientation of each dipole were determined by using ( l ) , (A.5), and (A.@, as described above, and compared with those obtained from the MRI’s and the X rays. RESULTS Fig. 3 shows typical averaged scalp potentials as recorded by the 30 surface electrodes, for dipolar source
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! Fig. 4. Locations and orientations of calculated and real dipoles for the five dipolar sources D1 through D5.Each dipolar source is displayed in two projections: coronal (left panels), and lateral (right panels). The center of the sphere representing the head, and 1 cm scale are given in each panel. Large circles (one per panel) denote real dipolar sources, smaller circles denote calculated dipoles. Numbers next to the dipoles indicate the type of model used in their calculation: 1's are for models with standard parameters. 2's are for head model in which the center of the sphere was moved 2 cm to the front. 3's are for center moved 2 cm to the back. 4's are for skullisoft tissue conductivity of 0.019. 5 ' s are obtained when only 20 out of the 30 scalp electrodes were included in the calculation. 6's are found without adjustment for the ground electrode. 7's are for a homogeneous head model.
S A L U et al.: IMPROVED METHOD FOR L O C A L I Z I N G B R A I N DIPOLES
no. 3. The potentials that were used in the calculations were the differences between the measured potentials due to the first current pulses (positive), and the seCond pulses (negative). That reduces the effects of undesired baseline shifts that may occur in each recording electrode. The location of the center of each dipole and its orientation, as determined from the MRI’s and the X rays are shown by heavy circles in Fig. 4. Panels are marked with 0 1 to 0 5 , corresponding to the five dipolar sources. Left panels show projections on the coronal plane, and the right panels projections on the lateral plane. Thick dots represent the real dipoles, and the other dots represent calculated results. The locations and orientations of the equivalent dipoles, as calculated by the method described above, are denoted by 1’s in those panels. The error ranges of those dipoles are summarized in Table I. The normalized variances (variance divided by the range of the observed potential in that potential map) are given in the last column. The equivalent dipoles, denoted by 1 , were obtained for a standard set of model parameters: The center of the sphere was in the coronal plane defined by Cz, C3, and C4; the skull/soft tissue conductivity ratio was 0.0125, and the inner and outer radii of the skull were 0.87 and 0.92 of the outer head radius [I]. The outer radius of the head, as calculated from the coordinates of the 30 scalp electrodes was 10.45 cm. Those are typical values, but there is a reasonable range to those parameters. In order to evaluate the susceptibility of the method to changes in those parameters, the dipoles were localized in models that used different sets of parameters. The equivalent dipoles as found in those cases are also included in Fig. 4. They could be identified by the numbers next to the dots. Equivalent dipoles 2 are for head model in which the center of the sphere was moved 2 cm to the front. Dipoles 3 are for center moved 2 cm to the back. Dipoles 4 are for skull/soft tissue conductivity of 0.019. Dipoles 5 were obtained when only 20 out of the 30 scalp electrodes were included in the calculation. Those results demonstrate that equivalent dipoles 2, 3, 4, and 5 were always less then 2 cm away from equivalent dipoles 1 . The importance of treating the reference electrode in a consistent way was explained in the theory section. Equivalent dipoles 6 were calculated when no adjustment for the reference point was taken. Equations (3) were used instead of (A.6). It can be seen that for dipolar source 0 1 , equivalent dipole 6 was 3.3 cm away from the true location while equivalent dipole l , which was found by using (A.6), was only 1.4 cm away. For dipolar sources 0 2 and 0 3 , the discrepancy between equivalent dipoles 1 and 6 is smaller, and for dipolar sources 0 4 and D5,equivalent dipoles 1 and 6 were at the same location. Those results demonstrate that, in some cases, the adjustment for the reference point may not be needed, but as a rule, it should be included in the computations. A frequently asked question is how does a homogeneous head model compare with an inhomogeneous model, like the one used here. Equivalent dipoles 7 were local-
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TABLE I DIFFERENCES BETWEEN REALA N D CALCULATED EQUIVALENT DIPOLES FOR EQUIVALENT DIPOLE 1. COLUMNS 2, 3 , AND 4 ARE COMPONENTS OF THE THE CENTERS OF THE DIPOLES, COLUMN 5 IS THE SEPARATIONS BETWEEN TOTALDISTANCE, COLUMN 6 IS THE ANGLE,IN DEGREES, BETWEEN THE REALAND THE CALCULATED DIPOLES. COLUMN 7 IS THE VARIANCE BETWEEN CALCULATED AND OBSERVED POTENTIALS DIVIDED BY THE RANGEOF THE POTENTIAL IN THAT MAP Dipole
AX
AY
1
0.3
-1.0
1.0
1.4
3
2 3
0.0 1.2 1.0
0.2 -0.8
0.4
0.4
31
20
1.1
0.7 -0.6 -0.2
1.6
0.8 0.5
0.7
-0.1
0.3
4 5
Average
A2
Distance
Angle
1.4
53
1.2 1.2
47 32
Variance 0.05 0.06 0.05
0.09 0.03 0.06
ized for a homogeneous head model [Xas defined in (2) was set to one in (A.5)]. It is seen that, as expected, those equivalent dipoles are localized closer to the center of the sphere. The ratio between the eccentricities of the calculated dipoles in the homogeneous head model, and the eccentricities of the sources themselves were: 1.67, 1.43, 1.42, 1.37, and 1.63, for dipolar sources 1 through 5 , respectively. Those results are within the range of the theoretical predictions [5].
DISCUSSION In the past, various approaches have been used for selecting the reference electrode. An approach different from the one used here assumed that electrodes far from the area of interest automatically have zero potential. Another different approach used a special hardware “ghost” electrode that averages potentials from several scalp points [ 1 13. Unlike these approaches, which are only approximation to the accurate treatment, the approach used here is mathematically accurate and simple to implement. The experimental results have demonstrated that the method, even with its present accuracy, has a great potential for clinical use. Small gaps remained in the skull of the subject of this study because of the craniotomy. Those gaps are smaller than other normal deviation of the intact skull from a spherical shell, as used by the model. It is therefore anticipated that slightly better results may be obtained when the method is applied to subjects with intact skulls. In order to further reduce the uncertainty range due to the susceptibility to head parameters, more patients will have to be studied similarly to the one reported here. It may turn out that in order to reduce the error in the localization of the dipole, more accurate modeling of the head will be required. The equations used in the model assume a dipole of zero length. The experimental dipoles that served as sources were of 1 cm length. In reality, biological sources are not point sources, and 1 cm is a reasonable size for an isolated small brain source, whose signals can be detected on the scalp. There have been reports about localization of real biological sources [12], [13], but it is not known what were the actual brain volumes that contributed to the observed potentials.
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 37. NO. 7, JULY 1990
When only a small area of the brain is active, it may be modeled by an equivalent dipole. If a larger area of the brain is active, it may be modeled by an array of equivalent dipoles. The way to localize those equivalent dipoles would be to use (A.6) for each dipole of the array, and substitute it into ( I ) . The major obstacle is the noise in the system. If two or more dipolar sources are too close to each other, the system cannot separate them, and may give erroneous results [lo]. If the separation between the sources is greater then the error range with which the system localizes single dipolar sources, it might be possible to apply the method for localization of arrays containing several dipolar sources. In cases where there is no prior knowledge about the nature of the source, combined magnetic and electric recordings [14] seems to be a very promising tool for verification of the dipolar or the multidipolar nature of the brain source. APPENDIX The Potential of a General Dipole Consider a dipole with a dipole moment D = (D,, D,, 0,)located at RI = ( X I ,Y1, Z1), and a point on the scalp R2 = ( X , , Y2,Z,), (Fig. 2 ) . The radius vectors RI and R2 define a plane in space, which will be called the major plane. The cross product N = R1 X R2 is perpendicular to the major plane. The cross product t = N X R I is in the major plane, and perpendicular to R I . Based on an identity from vector algebra, t = R2(R I R I ) - Rl( R I * R 2 ) ,or by components tl
=
x, - p t; =
-
-
XI
z, p
q; t, -
Yz
=
*
p
-
Y,
*
ZI . q
q:
(‘4.1)
where p = X:
+ Y: + 2:
v, =
(A.2)
i
5
. bn-l[nR, P,,(cos a )
v, =
i ~
*
where b potential
The unit vector RR R I is
/I 1;
R , = x, R I where
=
b”-I[nR~Pr,(cos a)
/I RI 1 ;
(A.5 1 and cos a is given by (A.4). The I/ at R2 due to D at RI is I/ = V , + I/, + V,.
=
I RI l / R ,
+ Yl
. Y,
+ Z1 -
= (X:
/I I
(A.3)
Vi
lR2l
where
CIO)
*
-
q.10)
*
(T-12 - TzI,)
+
(A.4)
4, 4,. D;
(A.6)
+
REFERENCES [ I ] S . Rush and D. A. Driscoll, “EEG electrode sensitivity-An application of reciprocity,” IEEE Trans. Biorned. Eng., vol. BME-16, pp. 15-22, Jan. 1969. 121 M . Schneider. “Effects on inhomoeeneities on surface sienals coming from a cerebral dipole source,” f E E E Trans. Biorned. Eng., vol. BME-21, pp. 52-54, Jan. 1974. .
1 R2( = ( X z + Y i + Z;)1’2.
=
-
where TXl0,T v l 0 ,Tzl0are the transfer coefficients from a dipole at RI onto surface point Ro. V ’ , the theoretical potential at R2 with respect to Ro due to a dipole at R I is given by V ’ = v;, v, V i .
The cosine of the angle between R1 and R2, used in ( 2 ) is
-
(Tx12
Vi, = ( q 1 *
+ Y: + Z:)”’.
cos a = 9/IRll
Z2.
respect to the earlobe) should be subtracted from the measured potential at each point). 2 ) Equations (3) are corrected for the new reference point, and become
.
RL = ZI R I
1
+ T;Pi,(cos a ) ] D;
Assigning a Reference Electrode 1) An arbitrary convenient point on the surface, denoted by Ro, is declared as the reference. All potentials are measured with respect to the electrode at this point. (If the potentials have already been measured with respect to a different point, such as left earlobe, they have to be adjusted accordingly. The measured potential at Ro (with
(R,, R,, R,) in the radial direction
R,. = yl
1 RI1
I/,
1
+ T, PA( cos a ) ] D,
I ~ ( 2 +n I)’ 4rSR’ri=I d,,(n + 1 ) .
=
+ t ; + t.?)
1
+ T,Pf,(cosa ) ] D,
and similarly, the potential due to D, and D; would be
where / t i = (t.!
+
I ~ ( 2 n q3 4aSR2 n = I d,(n + 1 ) . -
bfl-I[nRYPn(cosa )
and q = X I X ,
T = (T,, T,, T z )is the unit vector in the t direction, which is the tangential direction to R1 in the major plane. Its components are T, = tl./ltl; T,. = t,./ltl; T: = t ; / ( t l
The potential that the dipole D generates at the scalp point R2 is the sum of the potentials contributed by D , , D,., and D,. When these expressions are substituted in ( 2 ) , the potential at R2 due to D,turns to be
1
SALU er
(I/..
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I M P R O V E D METHOD FOR LOCALIZING BRAlK D1POL.k.S
1.31 R . N. Kavanagh. T . M . Darccy. D. Lehniann. and D. H . Fender.
Leonard0 G . Cohen received the M . D . degree
"E\ aluation of method5 for three dimensional localization of electri-
and neurology training at the University of Buecal \ource\ in the human brain." / € € E T r t i m . E r o r r i d E J , I , ~iol. .. no5 Aires, Argentina. BME-25. pp. 421-429. Sept. 1978. He is currently a Visiting Scientist i n the Hu141 R . D.Sidmen. V . Giambalvo. T . Allison, and P Bergej. "A inethod man Motor Control Section of the Medical Neufor localization o f sources in huinan cerebral potentials evoked by rology Branch at the National Institute of Neurosensory \timuli." Scrisor~Proc.c,\.\.. vol. 2. pp. 116-129. 1978. logical Disorders and Stroke. National In\titute\ 151 J . 0. Ary. S . A . Klcin. and D . H . Fender. "Location of sources o t of Health. Bethesda, M D . His work in clinical evoked scalp potentials: Corrcctions for h k u l l and scalp thicknesses." neurophysiology includes the stud) of evoked po/ € € E Trcim. Biorric~/.O i g . . \oI. BME-28. pp. 447-452. June 1981. tentials and transcranial magnetic stimulation and 161 D. B. Smith. R . D . Sidmun. H . Flanigin. J . Henke. and D.Labiner. a particular interest in the noninvasive evaluation "A rcliablc method tor localizing deep intracranial source\ of the of plastic changes in the human central nervous system. He had fellowships EEG." Ncirro/o,q!. v o l . 35. pp. 1702-1707. 1985. in clinical neurophysiology at the University of California. Irvine. and at 171 D . B. Gcselouitr and H . Ishiuatari. "A theoretical study o l t h e ctfcct the National Institutes of Health. He has been approved for a tenured poof the intracavity blood mass on the dipolarity o f an cquivalent heart sition at NIH and is now studying the reorganization of human motor and generator." in P r o ( , . Lorig /.\/uric/ J e , i t ~ i . s / i Hosp. S ~ m p .Vec.forc.tir- sensory pathways following different lesions and the experimental treate / i o , y r . c i p / i ~Anisterdaiii. . The Netherlands: North Holland. 1966. pp. ment of focal dystonias of the hand with botulinum toxin injections. 393-402. 181 R . M . Arthur and D.B. Geselowitz, "Etfccts 0 1 inhomogeneities on the apparent locution and magnitude o f a cardiac current dipole gcnerator." / E E E Trcir7.5. Biorwtl. t r i g . . vol. BME- 17. pp. 14 1 - 146. Apr. 1970. Douglas Rose, photograph and biography not available at thc tinic of pub[ 9 ] Y . Salu and P. Mehrotra. "A computerized sy\tem for localizing i ;,.,, t i ,\" ''c''L'"'' sources of cardiac activation." C'oirip. H i o m c , e / . Re.\.. \ o l . 17. ppl 2 2 2 - 2 2 8 . 1984. W . H. Pre\\. B. P. Flannery. S. A . Teukol\ky. and W . T . Vetterling. N i m e r i u i / Rc(.r/w\. Cainbridse, Cambridzc U n i i . Pre\s. 1986. pp. 51-64. F , F , 0tfner, . . ~ EEG h ~ as nlapping: ~h~ vlllue the i , \ , ~ Susumu Satu, photograph and biography not available at the time of puberagc monopolar reference," E/ec./roeric'f,/~/iii/o~qr. c,/irr. ~ r i i r o p / 1 ~ ~lication. s i o l . \01. 2 . pp. 213-214. 1950. C . C . Wood. "Application of dipole localization methods to source identitication of human evoked potentials." -1,iu. N Y A t , d Sci.. \oI. 388. pp. 139-155. 1982. Conrad Kufta, photograph and biography not available at the time of pubW . W . Sutht.1-ling. P. H . Crdndall. T . M . Darccy. D. P. Becker. M . lication. F. LeLcsquc. and D . S. Bart. "The magnetic and electric fields agree with intracranial localization\ o f somatosensory cortex." Ncio.o/o,qx. vol. 38. pp 1705-1714. 1988. C . C. Wood. D. Cohen. B. Neil Cutfin. M . Yarita. and Truett Allison. "Electrical sources in human soniatoscnsory cortex Idcntitication bq combined magnetic and potential recordings." Sc,ir,rce,. vol Mark Hallett received the M . D . degree at Har227. pp. 1051-ICt53. 1985. vard Medical School. interned at Peter Bent Brigham Hospital, Boston. and did a neurology residency at the Massachusetts General Hospital. Boston. Yehuda Salu received the M.Sc. degree in physHe is currently Clinical Director and Director ics from The Hebrew University. Jerusalem. in of the Clinical Neurosciences Program at the Na1964. and the Ph.D in physics from Tel-Aviv tional Institute of Neurological Disorders and University, Tel-Aviv, Israel. in 1973. Stroke. National Institutes of Health. Bethesda. I He was a research scientist at the Department M D . He has had a long-standing interest in clinof Physics and at the Cardiovascular Research ical neuroohvsiologv Center at the University of Iowa. Iowa City. He , _. -,and human motor control. He had fellowships in physiology at the National Institutes of Health and the is currently a professor of physics at Howard UniInstitute of Psychiatry in London. Before assuming his current position. he versity. Washington. DC. His research interests was Director of the Clinical Neurophysiology Laboratory at the Brigham include applications of electromagnetic theory to and Women's Hospital, Boston, and in the Department of Neurology at the study of biological systems. and designing and Haward Medical School. modeling neural n e t u o rks .
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An Improved Method for Localizing Electric Brain Dipoles YEHUDA SALU, LEONARD0 G. COHEN, DOUGLAS ROSE, SUSUMU SATO, CONRAD KUFTA, MARK HALLETT
Abstract-Methods for localizing electrical dipolar sources in the brain differ from one another by the models they use to represent the head, the specific formulas used in the calculation of the scalp potentials, the way that the reference electrode is treated, and by the algorithm employed to find the least-squares fit between the measured and calculated EEG potentials. The model presented here is based on some of the most advanced features found in other models, and on some improvements. The head is represented by a three-layer spherical model. The potential on any point on the scalp due to any source is found by a closed formula, which is not based on matrix rotations. The formulas will accept any surface electrode as the reference electrode. The least-squares procedure is based on optimal dipoles, reducing the number of unknowns in the iterations from six to three. The new method was evaluated by localizing five implanted dipolar sources in human sensorimotor cortex. The distances between the locations of the sources as calculated by the method, and the actual locations were between 0.4 and 2.0 em. The sensitivity of the method to uncertainties encountered whenever a real head has to be modeled by a three-layer model bas also been assessed.
I. INTRODUCTION HE ELECTRICAL activity of a small brain region can be modeled by an equivalent dipolar source. The surface EEG generated by this active region contains information about the location and orientation of that equivalent dipole, which in turn can provide information about ongoing processes in the brain tissue that it represents. The equivalent dipole is a good approximation only for small active brain regions. The head itself can be modeled by three concentric spheres [l]. This is a simplification that preserves some important electrical features of the head, while keeping the mathematical complexity of the problem manageable. In the past, there have been several reports of methods for noninvasive localization of equivalent dipolar sources in the brain, utilizing three layer head models [2]-[6]. The purpose of this paper is to present and to evaluate an improved method for noninvasive localization of equivalent dipoles in the brain. The proposed method has been tested and evaluated on human in vivo.
T
Manuscript received January 17, 1989; revised November 7, 1989. This work was supported in part by Grant 1 R03 MH 4 3050-01 from The National Institute of Mental Health. Y. Salu is with the Department of Physics and Astronomy, Howard University, Washington D C 20059. L. G. Cohen, D. Rose, S . Sato, C . Kufta, and M. Hallett are with Human Motor Control Section, Medical Neurology Branch, NINDS, NIH, Bethesda, M D 20892. IEEE Log Number 9035442.
AND
THEORY The Equivalent Dipole The basic idea of most dipole localization methods is to look for an equivalent dipole, such that V ( i )tal, the calculated potentials that it generates at N scalp locations, best fit V ( i )&, the observed EEG potentials at those points. Best fit is defined as a least-squares-fit. The equivalent dipole is then the one for which SUM is minimum. N
The SUM of any other dipolar source would be greater then the SUM of the equivalent dipole. The calculated potentials depend on the dipolar parameters, and on the head model being used. A common head model, which includes sufficient details, but which is not too complicated to be handled mathematically, is the three-layered spherical head model.
Spherical Three-Layer Model In the spherical three-layer model, the head is modeled by three concentric spheres. The inner sphere represents the brain, the intermediate layer represents the skull, and the outer layer represents the scalp. Consider first a dipole located on the Z axis, and the potential that it generates at scalp point P , located in the X Z plane (Fig. 1). Two of the components of the dipole moment which lie in the XZ plane, m, in the radial direction, and m,in the tangential direction, are shown in Fig. 1 . The third component, which is perpendicular to the XZ plane, does not contribute to the potential on that plane, and is not shown in the figure. The potential V generated by the dipole at the scalp point P is given by [7], [8], [5]
+ m,P; (cos a) cos /3]
(2)
where (Fig. l), R = outer radius of head, S = soft tissue conductivity, X = (skull conductivity)/S, b = (distance of dipole from center)/R, a = polar angle of surface point, /3 = azimuth of surface point, not shown in Fig. 1 , and not used in this work.
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Z
Any point on the scalp may serve as the reference electrode. Once such a point has been chosen, the appropriate adjustments have to be made in (3), which becomes
4
+
+
V' = v;, vy vi. (34 A detailed discussion of this matter is given in the Appendix [see A. 61 .
+X
Fig. 1 . A cross section through the spherical three-layer model. The center of the spheres is at the origin.
1 r
d,, = [ ( n + l ) X
-
+ n]
7
nX + l j n + l
P,, ( ) and P!,( ) are Legendre and associated Legendre polynomials n l = 2n 1, rl and r2 are inner and outer radii of skull, f l = r i / R , fi = r 2 / R , m,., and m, radial and tangential dipole moments. Equation (2) gives the scalp potentials generated by a dipole located on the Z axis, with zero dipole moment in the Y direction. To find the scalp potentials generated by an arbitrary dipole, the coordinate system has to be rotated accordingly, using rotation transformations [3], [4]. Simple closed formulas, which generalize (2) for any arbitrary dipole are derived in the Appendix, and can be written as (Fig. 2)
+
vx =
Tx12
Dx
(3) The potential
at R2due to a dipole D located at R1 is:
v=
vx
+ v y + v,
Equation (3) is a condensed form of (A.5). TXl2,Tyl2, and TZl2are called transfer coejicients. TXl2 gives the potential that a unit dipole, located at R1 and pointing in the X direction, will generate at scalp point R2.The meaning of the other coefficients is similar. Their detailed expressions can be inferred by comparing (3) and (A.5); they are the expressions inside the corresponding curled brackets { >. The transfer coefficients depend on the geometrical properties of the head, and on the location of the dipole. They do not depend on the orientation of the dipole.
The Least-Squares-Fit The least-squares-fit searches for a dipole that minimizes SUM in (1). The observed potentials in ( 1 ) are measured with respect to the arbitrarily chosen reference Ro, and the theoretical potentials are calculated according to equations (A.6). There are six parameters that specify the equivalent dipole: three spatial coordinates, and three components of the dipole moment. When (A.6) is substituted in (l), the equations for those six parameters are nonlinear. The minimization of ( 1 ) is usually carried out by an iterative algorithm 131, [41. In the following, a different approach is employed. It is based on the concept of the optimal dipole [9]. Any point inside the sphere has its own optimal dipole. An optimal dipole fits the observed data better than any other dipole, which has the same location but different orientation. The unknown parameters of an optimal dipole are D,, Dy, and D,. The transfer coefficients for any optimal dipole can be calculated directly by (A.5) and (A.6). Therefore, finding an optimal dipole is a linear least squares problem with only three parameters. It can be solved easily [lo]. There are two possible ways for finding the equivalent dipole, utilizing optimal dipoles. First, few optimal dipoles are found in an arbitrary region. The steepest slope with respect to the spatial coordinate is found, and a new search region is obtained. Optimal dipoles in that region are found, a new slope is determined, and so on, till the best of all optimal dipoles is found. This is a minimization iteration, that depends only on three parameters, compared to the six parameters being used in other dipole localization methods. The second way, which was used in this study, is to find optimal dipoles at a dense grid of points, that covers the volume in which the dipolar source is expected to be. The best of all the optimal dipoles is the equivalent dipole. Since using optimal dipoles reduces the number of unknown parameters from six to three, such dense grids can be handled easily by today's computers. The grid spacing in this work was 3 mm.
METHODS In order to evaluate the accuracy of the method described above, it was used in the localization of dipolar sources whose positions and orientations could be also determined by other independent means. Informed consent was obtained from the patient, male, 23-years old. The patient had matrices of subdural platinum electrocorticography electrodes, that were implanted for locating epileptic foci. The diameter of these disk electrodes was 6 mm, and their spacing was 1 cm center to center. Five pairs of
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t
rRZ
Fig. 2. Vectors involved in expressing the potential generated by an arbitrary source onto an arbitrary scalp point, in Cartesian coordinates. RI is the location of the source. R, is the point at which the potential is calculated. D = ( D x ,D,, D,)is the dipole moment, RR is a unit vector in the radial direction of R I , and T i s a tangential unit vector in the major plane.
those electrodes were chosen to simulate cortical dipoles. Those electrodes were over the sensorimotor cortex. The distance between the electrodes forming each dipole was 1 cm. A positive current pulse of 40 pA and duration of 5 ms followed by a negative pulse of the same size was delivered to each dipole. The delay between the pulses was 20 ms. This was repeated 200 times for each dipole, at a frequency of 1 Hz. The EEG’s generated by those currents were picked up by 30 surface electrodes. The electrodes were needle electrodes that were placed in a 5 x 6 lattice over the left scalp area anteriorly and posteriorly to the Cz-T3 line of the international 10-20 system. The inter electrode impedance for the tests was less then 2 kfl. Reference electrode was at right earlobe. The separation between the scalp electrodes was 2.5-3.0 cm. The signals from the electrodes were amplified by a bank of amplifiers, band width 1 Hz to 1 kHz, and gain of 2000 or 5000, as needed. The amplified signals were digitized at 4.1 kHz per channel, 12 b, and stored on a disk. This digitizing rate provided 20 samples per channel for every current pulse. The square shape of the pulse could be clearly seen in the recordings (Fig. 3). Averages of 200 sweeps were then calculated for each scalp electrode and each dipolar source, to further reduce the noise. Those averaged potentials at the center of the square, i.e., 2.5 ms after the onset of the current pulse, were used as the V ( i ) &s in (1). The x , y, z coordinates of the scalp electrodes and of landmarks on the head were measured by a three-dimensional digitizer (3Space digitizer, Polhemus). MRI of the patient with markers for scalp electrodes Cz, C3, Pz,and P 3 were taken before the implantation of the subdural electrodes. The subdural electrodes were surgically positioned as required clinically, and their exact relationships with the scalp markers was determined. X rays of the patient with the implanted electrodes were taken from several angles. The x , y, z coordinates of the subdural electrodes, that were used as dipoles, were determined based on the MRI markers, the X rays, and the coordinates of the scalp electrodes.
0.1 sec
U Fig. 3. Recordings of scalp potentials generated by dipolar source 3. Each trace corresponds to a surface electrode. Cz, C3, P:, P 3 . T3, and Ts indicate traces at those locations of the international 10-20 system. The positive and negative square pulses are seen in each of the 30 traces. All ordinates use the same normalized scale.
The center of the sphere that represents the head was in the coronal cross section that contains surface electrodes Cz, C3, and C4. The contour of the upper head in this cross section is semicircular, and the center of the sphere was the center of this contour. The distance of each surface electrode from this center was calculated, and the average of those distances was chosen as the radius of the outer sphere. The locations of the 30 scalp electrodes were then projected by spherical projection onto the sphere. The outer radius of the sphere was 10.45 cm, and the distances of the scalp electrodes from its center, before being projected, were in the range 9.5-1 1.5 cm. The conductivity ratio [Xin (2)] of skull to soft tissue was taken as 0.0125, and the relative radii of the inner spheres [ f, and fi of (2)] were 0.87 and 0.92 El]. The location and orientation of each dipole were determined by using ( l ) , (A.5), and (A.@, as described above, and compared with those obtained from the MRI’s and the X rays. RESULTS Fig. 3 shows typical averaged scalp potentials as recorded by the 30 surface electrodes, for dipolar source
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! Fig. 4. Locations and orientations of calculated and real dipoles for the five dipolar sources D1 through D5.Each dipolar source is displayed in two projections: coronal (left panels), and lateral (right panels). The center of the sphere representing the head, and 1 cm scale are given in each panel. Large circles (one per panel) denote real dipolar sources, smaller circles denote calculated dipoles. Numbers next to the dipoles indicate the type of model used in their calculation: 1's are for models with standard parameters. 2's are for head model in which the center of the sphere was moved 2 cm to the front. 3's are for center moved 2 cm to the back. 4's are for skullisoft tissue conductivity of 0.019. 5 ' s are obtained when only 20 out of the 30 scalp electrodes were included in the calculation. 6's are found without adjustment for the ground electrode. 7's are for a homogeneous head model.
S A L U et al.: IMPROVED METHOD FOR L O C A L I Z I N G B R A I N DIPOLES
no. 3. The potentials that were used in the calculations were the differences between the measured potentials due to the first current pulses (positive), and the seCond pulses (negative). That reduces the effects of undesired baseline shifts that may occur in each recording electrode. The location of the center of each dipole and its orientation, as determined from the MRI’s and the X rays are shown by heavy circles in Fig. 4. Panels are marked with 0 1 to 0 5 , corresponding to the five dipolar sources. Left panels show projections on the coronal plane, and the right panels projections on the lateral plane. Thick dots represent the real dipoles, and the other dots represent calculated results. The locations and orientations of the equivalent dipoles, as calculated by the method described above, are denoted by 1’s in those panels. The error ranges of those dipoles are summarized in Table I. The normalized variances (variance divided by the range of the observed potential in that potential map) are given in the last column. The equivalent dipoles, denoted by 1 , were obtained for a standard set of model parameters: The center of the sphere was in the coronal plane defined by Cz, C3, and C4; the skull/soft tissue conductivity ratio was 0.0125, and the inner and outer radii of the skull were 0.87 and 0.92 of the outer head radius [I]. The outer radius of the head, as calculated from the coordinates of the 30 scalp electrodes was 10.45 cm. Those are typical values, but there is a reasonable range to those parameters. In order to evaluate the susceptibility of the method to changes in those parameters, the dipoles were localized in models that used different sets of parameters. The equivalent dipoles as found in those cases are also included in Fig. 4. They could be identified by the numbers next to the dots. Equivalent dipoles 2 are for head model in which the center of the sphere was moved 2 cm to the front. Dipoles 3 are for center moved 2 cm to the back. Dipoles 4 are for skull/soft tissue conductivity of 0.019. Dipoles 5 were obtained when only 20 out of the 30 scalp electrodes were included in the calculation. Those results demonstrate that equivalent dipoles 2, 3, 4, and 5 were always less then 2 cm away from equivalent dipoles 1 . The importance of treating the reference electrode in a consistent way was explained in the theory section. Equivalent dipoles 6 were calculated when no adjustment for the reference point was taken. Equations (3) were used instead of (A.6). It can be seen that for dipolar source 0 1 , equivalent dipole 6 was 3.3 cm away from the true location while equivalent dipole l , which was found by using (A.6), was only 1.4 cm away. For dipolar sources 0 2 and 0 3 , the discrepancy between equivalent dipoles 1 and 6 is smaller, and for dipolar sources 0 4 and D5,equivalent dipoles 1 and 6 were at the same location. Those results demonstrate that, in some cases, the adjustment for the reference point may not be needed, but as a rule, it should be included in the computations. A frequently asked question is how does a homogeneous head model compare with an inhomogeneous model, like the one used here. Equivalent dipoles 7 were local-
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TABLE I DIFFERENCES BETWEEN REALA N D CALCULATED EQUIVALENT DIPOLES FOR EQUIVALENT DIPOLE 1. COLUMNS 2, 3 , AND 4 ARE COMPONENTS OF THE THE CENTERS OF THE DIPOLES, COLUMN 5 IS THE SEPARATIONS BETWEEN TOTALDISTANCE, COLUMN 6 IS THE ANGLE,IN DEGREES, BETWEEN THE REALAND THE CALCULATED DIPOLES. COLUMN 7 IS THE VARIANCE BETWEEN CALCULATED AND OBSERVED POTENTIALS DIVIDED BY THE RANGEOF THE POTENTIAL IN THAT MAP Dipole
AX
AY
1
0.3
-1.0
1.0
1.4
3
2 3
0.0 1.2 1.0
0.2 -0.8
0.4
0.4
31
20
1.1
0.7 -0.6 -0.2
1.6
0.8 0.5
0.7
-0.1
0.3
4 5
Average
A2
Distance
Angle
1.4
53
1.2 1.2
47 32
Variance 0.05 0.06 0.05
0.09 0.03 0.06
ized for a homogeneous head model [Xas defined in (2) was set to one in (A.5)]. It is seen that, as expected, those equivalent dipoles are localized closer to the center of the sphere. The ratio between the eccentricities of the calculated dipoles in the homogeneous head model, and the eccentricities of the sources themselves were: 1.67, 1.43, 1.42, 1.37, and 1.63, for dipolar sources 1 through 5 , respectively. Those results are within the range of the theoretical predictions [5].
DISCUSSION In the past, various approaches have been used for selecting the reference electrode. An approach different from the one used here assumed that electrodes far from the area of interest automatically have zero potential. Another different approach used a special hardware “ghost” electrode that averages potentials from several scalp points [ 1 13. Unlike these approaches, which are only approximation to the accurate treatment, the approach used here is mathematically accurate and simple to implement. The experimental results have demonstrated that the method, even with its present accuracy, has a great potential for clinical use. Small gaps remained in the skull of the subject of this study because of the craniotomy. Those gaps are smaller than other normal deviation of the intact skull from a spherical shell, as used by the model. It is therefore anticipated that slightly better results may be obtained when the method is applied to subjects with intact skulls. In order to further reduce the uncertainty range due to the susceptibility to head parameters, more patients will have to be studied similarly to the one reported here. It may turn out that in order to reduce the error in the localization of the dipole, more accurate modeling of the head will be required. The equations used in the model assume a dipole of zero length. The experimental dipoles that served as sources were of 1 cm length. In reality, biological sources are not point sources, and 1 cm is a reasonable size for an isolated small brain source, whose signals can be detected on the scalp. There have been reports about localization of real biological sources [12], [13], but it is not known what were the actual brain volumes that contributed to the observed potentials.
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When only a small area of the brain is active, it may be modeled by an equivalent dipole. If a larger area of the brain is active, it may be modeled by an array of equivalent dipoles. The way to localize those equivalent dipoles would be to use (A.6) for each dipole of the array, and substitute it into ( I ) . The major obstacle is the noise in the system. If two or more dipolar sources are too close to each other, the system cannot separate them, and may give erroneous results [lo]. If the separation between the sources is greater then the error range with which the system localizes single dipolar sources, it might be possible to apply the method for localization of arrays containing several dipolar sources. In cases where there is no prior knowledge about the nature of the source, combined magnetic and electric recordings [14] seems to be a very promising tool for verification of the dipolar or the multidipolar nature of the brain source. APPENDIX The Potential of a General Dipole Consider a dipole with a dipole moment D = (D,, D,, 0,)located at RI = ( X I ,Y1, Z1), and a point on the scalp R2 = ( X , , Y2,Z,), (Fig. 2 ) . The radius vectors RI and R2 define a plane in space, which will be called the major plane. The cross product N = R1 X R2 is perpendicular to the major plane. The cross product t = N X R I is in the major plane, and perpendicular to R I . Based on an identity from vector algebra, t = R2(R I R I ) - Rl( R I * R 2 ) ,or by components tl
=
x, - p t; =
-
-
XI
z, p
q; t, -
Yz
=
*
p
-
Y,
*
ZI . q
q:
(‘4.1)
where p = X:
+ Y: + 2:
v, =
(A.2)
i
5
. bn-l[nR, P,,(cos a )
v, =
i ~
*
where b potential
The unit vector RR R I is
/I 1;
R , = x, R I where
=
b”-I[nR~Pr,(cos a)
/I RI 1 ;
(A.5 1 and cos a is given by (A.4). The I/ at R2 due to D at RI is I/ = V , + I/, + V,.
=
I RI l / R ,
+ Yl
. Y,
+ Z1 -
= (X:
/I I
(A.3)
Vi
lR2l
where
CIO)
*
-
q.10)
*
(T-12 - TzI,)
+
(A.4)
4, 4,. D;
(A.6)
+
REFERENCES [ I ] S . Rush and D. A. Driscoll, “EEG electrode sensitivity-An application of reciprocity,” IEEE Trans. Biorned. Eng., vol. BME-16, pp. 15-22, Jan. 1969. 121 M . Schneider. “Effects on inhomoeeneities on surface sienals coming from a cerebral dipole source,” f E E E Trans. Biorned. Eng., vol. BME-21, pp. 52-54, Jan. 1974. .
1 R2( = ( X z + Y i + Z;)1’2.
=
-
where TXl0,T v l 0 ,Tzl0are the transfer coefficients from a dipole at RI onto surface point Ro. V ’ , the theoretical potential at R2 with respect to Ro due to a dipole at R I is given by V ’ = v;, v, V i .
The cosine of the angle between R1 and R2, used in ( 2 ) is
-
(Tx12
Vi, = ( q 1 *
+ Y: + Z:)”’.
cos a = 9/IRll
Z2.
respect to the earlobe) should be subtracted from the measured potential at each point). 2 ) Equations (3) are corrected for the new reference point, and become
.
RL = ZI R I
1
+ T;Pi,(cos a ) ] D;
Assigning a Reference Electrode 1) An arbitrary convenient point on the surface, denoted by Ro, is declared as the reference. All potentials are measured with respect to the electrode at this point. (If the potentials have already been measured with respect to a different point, such as left earlobe, they have to be adjusted accordingly. The measured potential at Ro (with
(R,, R,, R,) in the radial direction
R,. = yl
1 RI1
I/,
1
+ T, PA( cos a ) ] D,
I ~ ( 2 +n I)’ 4rSR’ri=I d,,(n + 1 ) .
=
+ t ; + t.?)
1
+ T,Pf,(cosa ) ] D,
and similarly, the potential due to D, and D; would be
where / t i = (t.!
+
I ~ ( 2 n q3 4aSR2 n = I d,(n + 1 ) . -
bfl-I[nRYPn(cosa )
and q = X I X ,
T = (T,, T,, T z )is the unit vector in the t direction, which is the tangential direction to R1 in the major plane. Its components are T, = tl./ltl; T,. = t,./ltl; T: = t ; / ( t l
The potential that the dipole D generates at the scalp point R2 is the sum of the potentials contributed by D , , D,., and D,. When these expressions are substituted in ( 2 ) , the potential at R2 due to D,turns to be
1
SALU er
(I/..
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I M P R O V E D METHOD FOR LOCALIZING BRAlK D1POL.k.S
1.31 R . N. Kavanagh. T . M . Darccy. D. Lehniann. and D. H . Fender.
Leonard0 G . Cohen received the M . D . degree
"E\ aluation of method5 for three dimensional localization of electri-
and neurology training at the University of Buecal \ource\ in the human brain." / € € E T r t i m . E r o r r i d E J , I , ~iol. .. no5 Aires, Argentina. BME-25. pp. 421-429. Sept. 1978. He is currently a Visiting Scientist i n the Hu141 R . D.Sidmen. V . Giambalvo. T . Allison, and P Bergej. "A inethod man Motor Control Section of the Medical Neufor localization o f sources in huinan cerebral potentials evoked by rology Branch at the National Institute of Neurosensory \timuli." Scrisor~Proc.c,\.\.. vol. 2. pp. 116-129. 1978. logical Disorders and Stroke. National In\titute\ 151 J . 0. Ary. S . A . Klcin. and D . H . Fender. "Location of sources o t of Health. Bethesda, M D . His work in clinical evoked scalp potentials: Corrcctions for h k u l l and scalp thicknesses." neurophysiology includes the stud) of evoked po/ € € E Trcim. Biorric~/.O i g . . \oI. BME-28. pp. 447-452. June 1981. tentials and transcranial magnetic stimulation and 161 D. B. Smith. R . D . Sidmun. H . Flanigin. J . Henke. and D.Labiner. a particular interest in the noninvasive evaluation "A rcliablc method tor localizing deep intracranial source\ of the of plastic changes in the human central nervous system. He had fellowships EEG." Ncirro/o,q!. v o l . 35. pp. 1702-1707. 1985. in clinical neurophysiology at the University of California. Irvine. and at 171 D . B. Gcselouitr and H . Ishiuatari. "A theoretical study o l t h e ctfcct the National Institutes of Health. He has been approved for a tenured poof the intracavity blood mass on the dipolarity o f an cquivalent heart sition at NIH and is now studying the reorganization of human motor and generator." in P r o ( , . Lorig /.\/uric/ J e , i t ~ i . s / i Hosp. S ~ m p .Vec.forc.tir- sensory pathways following different lesions and the experimental treate / i o , y r . c i p / i ~Anisterdaiii. . The Netherlands: North Holland. 1966. pp. ment of focal dystonias of the hand with botulinum toxin injections. 393-402. 181 R . M . Arthur and D.B. Geselowitz, "Etfccts 0 1 inhomogeneities on the apparent locution and magnitude o f a cardiac current dipole gcnerator." / E E E Trcir7.5. Biorwtl. t r i g . . vol. BME- 17. pp. 14 1 - 146. Apr. 1970. Douglas Rose, photograph and biography not available at thc tinic of pub[ 9 ] Y . Salu and P. Mehrotra. "A computerized sy\tem for localizing i ;,.,, t i ,\" ''c''L'"'' sources of cardiac activation." C'oirip. H i o m c , e / . Re.\.. \ o l . 17. ppl 2 2 2 - 2 2 8 . 1984. W . H. Pre\\. B. P. Flannery. S. A . Teukol\ky. and W . T . Vetterling. N i m e r i u i / Rc(.r/w\. Cainbridse, Cambridzc U n i i . Pre\s. 1986. pp. 51-64. F , F , 0tfner, . . ~ EEG h ~ as nlapping: ~h~ vlllue the i , \ , ~ Susumu Satu, photograph and biography not available at the time of puberagc monopolar reference," E/ec./roeric'f,/~/iii/o~qr. c,/irr. ~ r i i r o p / 1 ~ ~lication. s i o l . \01. 2 . pp. 213-214. 1950. C . C . Wood. "Application of dipole localization methods to source identitication of human evoked potentials." -1,iu. N Y A t , d Sci.. \oI. 388. pp. 139-155. 1982. Conrad Kufta, photograph and biography not available at the time of pubW . W . Sutht.1-ling. P. H . Crdndall. T . M . Darccy. D. P. Becker. M . lication. F. LeLcsquc. and D . S. Bart. "The magnetic and electric fields agree with intracranial localization\ o f somatosensory cortex." Ncio.o/o,qx. vol. 38. pp 1705-1714. 1988. C . C. Wood. D. Cohen. B. Neil Cutfin. M . Yarita. and Truett Allison. "Electrical sources in human soniatoscnsory cortex Idcntitication bq combined magnetic and potential recordings." Sc,ir,rce,. vol Mark Hallett received the M . D . degree at Har227. pp. 1051-ICt53. 1985. vard Medical School. interned at Peter Bent Brigham Hospital, Boston. and did a neurology residency at the Massachusetts General Hospital. Boston. Yehuda Salu received the M.Sc. degree in physHe is currently Clinical Director and Director ics from The Hebrew University. Jerusalem. in of the Clinical Neurosciences Program at the Na1964. and the Ph.D in physics from Tel-Aviv tional Institute of Neurological Disorders and University, Tel-Aviv, Israel. in 1973. Stroke. National Institutes of Health. Bethesda. I He was a research scientist at the Department M D . He has had a long-standing interest in clinof Physics and at the Cardiovascular Research ical neuroohvsiologv Center at the University of Iowa. Iowa City. He , _. -,and human motor control. He had fellowships in physiology at the National Institutes of Health and the is currently a professor of physics at Howard UniInstitute of Psychiatry in London. Before assuming his current position. he versity. Washington. DC. His research interests was Director of the Clinical Neurophysiology Laboratory at the Brigham include applications of electromagnetic theory to and Women's Hospital, Boston, and in the Department of Neurology at the study of biological systems. and designing and Haward Medical School. modeling neural n e t u o rks .
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