336 Electroencephalography and clinical Neurophysiology , 1988, 71:336-347 Elsevier Scientific Publishers Ireland, Ltd.

EEG 03535

Three-dimensional human somatosensory evoked potentials

V e r n o n L. Towle , R i c h a r d M u n s o n , T a k a y u k i Ohira , L o u Ivanovic ,

J o h n C. W i t t a n d J e a n - P a u l Spire

Department of Neurology, and Brain Research Foundation, Unioersity of Chicago, Chicago, IL (U.S.A.)

(Accepted for publication: 18 December 1987)

Summary Median nerve somatosensory evoked potentials were recorded from 30 normal adults using conventional scalp derivations and an orthogonal bipolar surface electrode montage. This allowed the determination of the spatial orientation of the hypothetical centrally located equivalent dipole derived from the evoked response recorded in 3-dimensional voltage space. The 3-dimensional voltage trajectory describing changes in equivalent dipole orientation and magnitude revealed 4 major apices between 5 and 25 msec, 3 of which corresponded to the traditional P14, N20 and P25 peaks. A fourth apex at 17 msec was not as evident in the conventional recordings and signaled a transition from a vertical P14-N18 generator process to a horizontal N20 generator process. The normal within- and between-subject variability of trajectory apices, segments and planes are described, along with the theoretical and practical implications of this recording technique.

Key words: Somatosensory evoked potential; Three-dimensional evoked potential; Three-channel Lissajous' trajectory

Three-dimensional bipolar recordings of human cerebral evoked potentials have been described for auditory evoked potentials (Mizoi et al. 1978; Gardi et al. 1980; Ino and Mizoi 1980; Williston et al. 1981; Pratt et al. 1983, 1985, 1986b; Martin et al. 1986; Sininger et al. 1987) and for diffuse flash visual evoked potentials (Pratt et al. 1986a). When recorded in this manner the dynamic evolu- tion of the brain response to stimulation is mod- eled as changes in the orientation and magnitude of a centrally located equivalent dipole. The 3-di- mensional (3-D) nature of the neural response is emphasized with this technique in a way that is difficult to appreciate with conventional voltage/ time plots. Unlike conventional recordings in which peak latency, amplitude and wave form

Correspondence to." Vernon L. Towle, Ph.D., Department of Neurology, Box 425, University of Chicago, 5841 South Mary- land Avenue, Chicago, IL 60637 (U.S.A.).

morphology may differ depending on which scalp derivation is employed (Cracco 1972; Starr and Squires 1982), 3-channel Lissajous' trajectories (3=CLTs) are reported to be largely independent of electrode location (Pratt et al. 1984, 1986b; Martin et al. 1986, 1987c).

Auditory 3-CLTs representing the brain-stem response from cat, guinea pig and human have all been reported to have a planar structure (Willis- ton et al. 1981; Pratt et al. 1983, 1985, 1986b; Martin et al. 1982, 1987b). As many as 10 planes have been described in the human auditory 3-CLT (Sininger et al. 1987), the normal orientation of which varied by about 50 o across subjects. It has been reported that the planar structure is dis- rupted in patients with brain-stem lesions (Pratt et al. 1983, 1987), suggesting new and more sensitive measures of physiologic dysfunction.

We have recorded 3-dimensional median nerve somatosensory evoked potentials (3-D SEPs) using a similar technique and here describe their mor- phology and normal variability.

0168-5597/88/$03.50 © 1988 Elsevier Scientific Publishers Ireland, Ltd.

3-D SEPs 337

Method and material

Thirty normal adults (11 females) were studied (ages 19-48, median = 27 years) after giving in- formed consent. Twenty-five subjects were fully right-handed as assessed with the Edinburgh Handedness Inventory (Oldfield 1971). Four sub- jects were studied on 10 separate days each, with electrode locations determined on each occasion by different experimenters. Each recording session lasted about 1 h. SEPs were elicited by electrical stimulation of the median nerve at the wrist with 0.2 msec duration pulses of sufficient intensity to elicit a small twitch of the thumb. Two or 3 reproducible wave forms from 1000 stimuli pre- sented to each wrist at 6 /sec were averaged using a 1 Hz-3 kHz bandpass for 20.44 msec starting 5 msec after the onset of the stimulus (0.04 msec resolution), using a Nihon-Kohden Neuropack 8 signal averaging system. Eight channels were simultaneously recorded: 3 conventional electrode derivations (Q'-Erb's Pt¢, Fz-cervical 7, EPi-EPc) and 3 bipolar electrode placements approximating the 3 orthogonal dimensions of space: nasion-O z (x-axis), T3-T 4 (y-axis), and Cz-submentum (z-axis) (Fig. 1). Two additional 'rotated' horizontal chan- nels were recorded with electrodes placed 50% of the distance between Nz-T 3, T3-Oz, O~-T 4 and T 4- Nz. The wave forms were transferred to an Apple

+7 +7'

' / 1 Fig. 1. Modified spherical coordinate system used to describe the orientation of a segment of trajectory in 3-D voltage space in terms of its deviation (phi) from the vertical z '-axis (0 < < 180) and its deviation (theta) from the nasion in the horizon-

tal x-y plane ( - 1 8 0 < 0 <180).

l ie microcomputer for off-line analysis using software developed in this laboratory.

Voltage-voltage-voltage trajectories (Williston et al. 1981; Martin et al. 1987a) were constructed by plotting the 3 wave forms as a function of each other, such that the voltage at each point in time (Ei) for the 3 orthogonal bipolar recording deriva- tions Ex, E y , E z defined a point of the trajectory Ei~,~ in 3-D voltage space, where latency (i) in- creases at each successive point along the trajec- tory. Such trajectories depict the evoked potential in terms of changes in the magnitude and orienta- tion of a hypothetical centrally located equivalent dipole. Major bends in the trajectory (apices) were identified by visual inspection of the trajectories using cursors (0.08 msec resolution) on a display which allowed the trajectories to be rotated in 3 dimensions under manual control. Final de- terminations of apex latency were made after slowly rotating the cursored 3-D Lissajous' trajec- tories in 3 dimensions with a joystick. These mea- surements agreed with apices identified geometri- cally with an objective index of curvature (Har'E1 and Pratt 1984). Apex magnitude (distance from the origin) and orientation (see below) were mea- sured in reference to zero voltage, specified by subtracting the average voltage of the epoch be- tween 6 msec and the latency of N10 from each point in the wave form of each axis (i.e., the centroid of the 3-D baseline). The orientation of trajectory apices, segments and planes were quan- tified in terms of a spherical coordinate system where phi (~) represented the deviation from the (corrected) z-axis (0 < • < 180), and theta (@) represented the deviation from the positive x-axis ( - 1 8 0 < O < 180) in the horizontal (x-y) plane (Fig. 1). The x- and original z-axis deviated from orthogonality by approximately 18 °. The voltage along the z-axis was corrected using the formula,

z' = (z + x sin 18)/cos 18 o.

The orientation of the approximately linear por- tions of trajectory between apices (curvilinear seg- ments) was estimated from a line joining the 2 apices. A typical curvilinear segment consisted of approximately 30 data points. Planar segments (Pratt et al. 1984) were identified in a sample of the wave forms.

338 V.L. TOWLE ET AL.

Results

W e focus here on the 4 ma jo r apices and 3 in te rvening curvi l inear segments of the 3-D SEP be tween 14 and 25 msec. A l imi ted desc r ip t ion of

Left medion nerve sep I I ~ I I ' = = I I m I I I I l I I 1

N20

C 4- EP 2

Nz-O X

Y :1

Cz- SM ~ ' ~ 1 ~ ; ~

EPl_ EP2 ~ I mu ~

5 10 15 2O 25 Latency (msec)

Fig. 2. Left median nerve somatosensory evoked potentials (SEPs) derived from conventional electrode derivations (top and bottom wave forms) and 3 orthogonal electrode deriva- tions (X, Y, Z) approximating the 3 dimensions of space. The P14 brain-stem peak is better visualized in the vertical deriva- tion (C~-submentum) but the N20 peak is seen better in the 2 horizontal derivations (nasion-Oz, 1"3-1"4). Ten replications ob- tained on different days from subject 1 are superimposed. Calibration: 1 pV; C, O, T: central, occipital, and temporal scalp; EP: Erb's point; Nz: nasion; SM: submentum; N, P:

surface negative and positive.

L R L R 15 .5 15 .5

T~ ~ T 4

Fig. 3. Stereo view of the average 3-D SEP trajectory resulting from the wave forms shown in Fig. 2. The left (L) and right (R) median nerve trajectories are viewed from the negative x-axis of voltage space which parallels the anatomical view from behind. The small crossed lines indicate the location of the 0 pV origin of 3-D voltage space for each trajectory. The early baseline portion of the trajectories have been omitted for clarity in this and subsequent figures. Calibration: 1.7 #V

(~ = 55 °, O = 45°); latencies in msec.

p l a n a r segments will also be presented . Conven- t ional recordings of the 10 rep l ica t ions for subject 1 are shown in Fig. 2. E x a m i n a t i o n of the raw wave forms shows an ini t ia l ver tex ( + z-axis) pos i -

tive c o m p o n e n t at 15 msec co inc iden t wi th the conven t iona l P14 peak, fo l lowed by a t empora l - occip i ta l negat iv i ty co inc iden t in t ime with N20. The 3-D na tu re of the cerebra l evoked response is be t te r seen in Fig. 3, in which the 10 rep l ica t ions have been averaged and d i sp layed as a 3-D SEP for left and r ight med ian nerve s t imula t ion . The ini t ia l vertex pos i t iv i ty was seen as a ver t ical de- f lect ion of the t ra jec tory which was m a x i m u m at 15.5 msec. The t ra jec tory then decreased in magni - tude unt i l 17.7 msec, af ter which it increased in magn i tude wi th in the hor izon ta l x-y p lane unt i l 20.3 msec, at which t ime it moved back toward the origin and changed d i rec t ion again at 23.8 msec. These changes in t ra jec tory a m p l i t u d e and or ien- ta t ion def ined 4 apices, l abe led A, B, C and D in Fig. 4. The la tencies of each of these apices are shown in Tab le I a long with the la tency of con- vent iona l SEP peaks for the 4 extensively s tud ied subjects and the 30 no rma l subjects.

The typica l in te r -subjec t d i f ferences of 3-D SEP t ra jector ies is i l lus t ra ted in Fig. 4, in which the average t ra jec tor ies of the 4 extensively s tud ied subjects are shown. Apex A was p r o m i n e n t in the

3-D SEPs 339

A A A A

B B , , , subject C

D A A

C ,~,~ C subject

Fig. 4. Three-dimenstonal SEPs lrom 4 normal subjects show- ing the 4 apices (A-D) and 3 intervening segments. Each trajectory is viewed from near the negative x-axis which paral- lels the anatomical view from behind, with a slight horizontal

rotation to allow optimal viewing of the B-C segment.

Sub i. 4

D RIGHT

t r a j ec to ry of subjec t 2; apex C d o m i n a t e d the

t r a jec to ry of sub jec t 4. A l t h o u g h they var ied in la tency , m a g n i t u d e a n d o r i e n t a t i o n , apices A, B, C a n d D were i den t i f i ed in the t ra jec tor ies of each of

the 30 subjects . F o r m a n y subjec ts apex C was

obse rved to be a t the e n d of a smal l ' h o o k ' of va r i ab l e o r i e n t a t i o n . Th e m e a n d i r ec t i on of each

apex f rom the o r ig in a n d the m e a n o r i e n t a t i o n of each s e g m e n t was ca l cu l a t ed b y averag ing their c a r t e s i an c o o r d i n a t e s a n d c o n v e r t i n g the m e a n

vec to r i n to spher ica l c o o r d i n a t e s (Tab le II). T h e

3-D sep segment

A -B B-C C-D

Between-

Fig. 5. The average within- and between-subject variability for all wave forms in the experiment. The data are displayed so that the central tendency of each data set lies in the plane of the page. Segment A-B was the least variable, having com- parable within- (top) and between-subject variability (bottom). The between-subject variability of segment B-C was greatest. The between-subject differences for subjects 1-4 (top) have been removed. Data from the left and right arms have been

superimposed.

n o r m a l wi th in - a n d b e t w e e n - s u b j e c t va r i ab i l i ty ( the m e d i a n i n c l u d e d ang le b e t w e e n each o b s e r v a t i o n a n d the m e a n vector) of apex a n d s e g m e n t o r ien- t a t i on is s u m m a r i z e d in T a b l e III . I n genera l , the va r i ab i l i ty of apex o r i e n t a t i o n was grea ter t h a n

tha t of segments , pos s ib ly due to the m a n n e r in wh ich we specif ied the or ig in . S e g m e n t A - B was the least va r i ab le of all of the measures . T h e

TABLE I

The latency (msec, + 1 S.D.) of conventional SEP peaks (C~'-EPc) and 3-D SEP apices for the 4 subjects 10 times each and the 30 subjects studied 1 time each. Values for the 2 arms have been averaged. The cases in which there were statistically significant differences between the responses from the 2 limbs are indicated with asterisks.

Within subject Between subject

1 2 3 4 1 - 3 0

Peak latency N10 11.25 (0.15) P14 15.73 (0.19) N20 20.04 (0.25) P25 23.59 (0.38)

Apex latency A 15.50 (0.26) B 17.71 (0.26) C 20.29 (0.33) D 23.78 * (0.35)

10.77 (0.14) 10.81 (0.13) 9.03 (0.16) 9.93 (0.74) 15.43 (0.27) 15.95 (0.16) 13.22 (0.12) 14.63 (1.00) 20.45 (0.25) 20.33*(0.28) 17.94 (0.14) 19.19 (1.00) 25.44 23.04 (0.49) 21.24 (0.18) 22.20 (1.06)

14.88 (0.27) 15.64 (0.21) 13.30 (0.19) 14.07 (1.02) 17.85 (0.28) 18.34"(0.31) 15.06 (0.14) 16.77 (1.06) 20.50 (0.39) 20.30 (0.34) 18.32"(0.24) 19.23 (1.05) 22.73 (0.42) 23.28 (0.35) 21.13 (0.57) 22.56 (1.05)

340 V.L. T O W L E ET AL.

TABLE II

Orientation of the centrally located equivalent dipole and intervening segments in degrees at the latency of the 4 major apices A, B, C and D. Values for the 2 l imbs have been combined by averaging phi and the absolute value of theta from each limb. Asterisks indicate a statistically significant difference in orientation between the responses from the 2 limbs.

Subject

1 2 3 4 1-30

Apex A Phi 19 33 37 23 22 Theta 32 21 48 90 21

Apex B Phi 148 145 130 74 117 Theta 153 177 140 169 178

Apex C Phi 92 145 142 69 * 105 Theta 32 96 82 36 * 69

Apex D Phi 141 157 153 * 65 141 Theta 148 * 159 140 91 166

Segment A - B Phi 159 147 148 150 152 Theta 149 166 168 * 133 162

Segment B - C Phi 78 87 * 103 73 * 82 Theta 26 47 58 * 30 * 47

Segment C - D Phi 115 113 132 109 * 124 Theta 149 119 131 147 * 144

between-subject variability in orientation was usu- ally greater than the within-subject variability (Fig. 5). Exceptions were apex A and segment A-B

variability, for which the within- and between-sub- ject variabilities were comparable. The 3 outliers of the within-subject variability of segment C - D

TABLE III

The normal variability in orientation (deg) of 3-D SEP parameters in terms of the included angle between the average vectors and each replication that contributed to them (median and inter-quartile range). Values for the 2 limbs have been pooled.

Within subject Between subject

1 2 3 4 1-30

Apex A 10 (8) 11 (113) 14 (15) 12 (16) 13 (13) B 29 (24) 19 (14) 21 (28) 35 (22) 43 (40) C 17 (13) 16 (24) 19 (14) 10 (7) 52 (28) D 14 (11) 16 (13) 6 (9) 54 (29) 20 (22)

Segment A - B 5 (4) 5 (4) 7 (5) 10 (7) 10 (8) B - C 8 (4) 16 (14) 10 (18) 7 (5) 32 (27) C - D 6 (5) 22(21) 9 (5) 6 (6) 18(13)

3-D SEPs 341

were from subject 2, for whom apex D latency was sometimes beyond the end of the sampling epoch.

L - R differences There were several statistically significant

asymmetries in apex and segment orientation when the 3-D SEPs from the left and right hands of subjects 1-4 were compared (Mann-Whitney U test, P < 0.01). These are indicated by asterisks in Tables I and II, the entries of which represent the average of the two limbs. In general, apices A and B were symmetric about the midline, with some asymmetry beginning with the B-C segment. The largest number of asymmetries was seen in subject 4, a left-handed female. Many of these asymme- tries in orientation were recorded in the presence of symmetric latencies, suggesting that peak latency is independent of orientation. When the 5 left-handed subjects were compared to the 25 right-handed subjects, no statistically significant

- - - W , ' l ,

_

1 Torsion i

I ~_~.

Fr - l i ,anes I

I I d

i I I I I I I I I I I I I I I I I I

5 10 15 20 25 Latency (msec)

Fig. 6. Trajectory amplitude (the distance from the origin), curvature and absolute torsion as a function of latency for the left median nerve response of subject 1. Apices A - D , which were identified by visual inspection of the trajectories, corre- sponded to peaks in the curvature function. The vertical axes are arbitrary scales. The trajectories included 4 planar seg-

ments.

Segment B-C

Between-subject variability

Fig. 7. A comparison of the between-subject variability ix orientation of segment B - C and plane b. When viewed from the central axis of the distribution, the B - C segment variability was approximately circular. The same view was approximately

elliptical for plane b.

differences were observed for any of the measures listed in Tables I and II (Mann-Whitney U test, P > 0.1).

Geometric analysis In addition to identifying trajectory apices by

visual inspection, trajectory structure was analyzed using objective indices of amplitude, curvature and absolute torsion. Curvature is a local mea- surement of deviation from linearity; torsion is an index of departure from the locally best-fitting plane. The results of these analyses, applied to the left median nerve response from subject 1, are shown in Fig. 6. Apices A, B, C and D were all associated with increases in curvature, indicating that the experimenters could correctly identify them by visual inspection of the trajectories. The relatively low absolute torsion between the A-B, B-C and C - D segments suggested that they formed planar segments, similar to those de- scribed for auditory 3-CLTs.

The global planarity (Har'E1 and Pratt 1984) surrounding apices A, B, C and D was evaluated using an arbitrary termination criterion of 2 S.D. of baseline noise (Martin et al. 1987a). The in- creased amplitude associated with apex A was coincident with a plane (a) which ended before

342 V.L. TOWLE ET AL.

apex B. Apex B was associated with a plane (b) which began and ended during the A - B and B-C segments, respectively. A third plane (c) started at the termination of plane b and ended before apex D. A fourth plane began during the B - C segment and extended to the end of the trajectory. The planarity surrounding apex B was evaluated for the left median nerve 3-D SEP trajectories of all subjects. The between-subject variability of the orientation of this plane (calculated from the sight vector to the plane: 4 = 1 1 7 ° , O = - 2 6 ° ) is compared to the variability of the B-C segment in Fig. 7. The 32 ° median variability of the B -C segment was nearly twice the 17 o median variabil- ity of plane b. Although the variability of segment B - C was approximately circular, that of plane b was elliptical, with more variability in the horizon- tal than vertical direction.

Rotated montage In order to assess the possible local influence of

electrode position, simultaneous recordings were obtained from the rotated montage placed within the horizontal x-y plane of electrodes, the axes of which were rotated counter-clockwise from the primary montage by approximately 45 o. The de- gree to which the trajectories recorded from the rotated 3-D montage deviated from those ob- tained from the primary 3-D montage mainly indi- cated the effects of local fields specific to dec-

TABLE IV

Angular difference (deg) in orientation for apices and segments recorded from the primary and rotated electrode montages after back-rotating the trajectories from the rotated montage 45 o.

Subject

1 2 3 4

Apex A 6 4 15 6 B 26 6 16 23 C 7 9 17 7 D 5 5 9 37

Segment A - B 3 2 8 9 B - C 7 13 14 11 C - D 7 28 8 10

C

1 2 3 4 Subject

Fig. 8. Comparison of the 3°D SEP trajectories recorded from the primary (x, y, z ' ) and rotated (x ' , y ' , z ' ) electrode montages. The trajectories from the rotated montage (thin lines) have been back-rotated 45 o to aid in the comparison. The trajectories are viewed from the positive z'-axis, which

parallels the anatomical view from above.

trode position. The angular error, defined as the subtended angle between trajectories at identical latencies (after back-rotating 45°) , averaged 12 ° for apices and 7 o for segments (Table IV), indi- cating that the horizontal electrode locations em- ployed in this study were not a major factor in determining the shape of the trajectories. There was a tendency for apices C and D to be shifted clockwise when recorded using the rotated montage for the 4 extensively studied subjects (Fig. 8).

Patient data An example of an abnormal 3-D SEP is shown

in Fig. 9. The patient was a 74-year old woman with a hemorrhage of the fight thalamus and internal capsule. Evoked potential studies were requested to assess her neurologic status. Her con- ventional wave forms showed a loss of N20 fol- lowing left median nerve stimulation and a normal response to right median nerve stimulation. The simultaneously obtained 3-D SEP trajectory re- vealed a clearly identifiable apex A only. The trajectory remained in a vertical orientation dur- ing the time that apices B, C and D normally occur, as determined from the response from her opposite limb. The failure of the trajectory to return immediately to the origin and the failure of

3-D SEPs 343

Thalamic hemorrhage

L R

T a T 4

N20 I

P14

NIO 1,uV I ÷

| I I I I I I I I I

5 25 Latency (msec)

Fig. 9. Abnormal conventional median nerve SEPs and abnormal 3-D SEPs from a patient with a hemorrhage of the right thalamus and internal capsule. The effects of the horizon- tal N20 generator are missing on the trajectory obtained from stimulation of the left limb, causing an 'unmask ing ' of the

vertical N18 generator.

it to change from a vertical to horizontal orienta- tion suggest a loss of the horizontal N20 generator and an 'unmasking' of the vertical N18 generator (Gardi et al. 1987).

Discussion

In addition to revealing peak amplitude and latency, 3-D evoked potentials display the orienta- tion of each component in 3-D voltage space. They reflect the complex spatial nature of cerebral evoked potentials in a manner that has previously

been appreciated only by careful comparisons of wave form differences across several derivations (Desmedt and Cheron 1981) or through topo- graphic mapping techniques (Goff et al. 1977). Like topographic mapping, a standard montage can be used to collect all modalities of evoked potentials, but unlike that technique only 3 chan- nels are required, and quantitative 3-D measure- ments can be made with relatively simple trigono- metric calculations easily performed on a micro- computer. The present analysis defines the funda- mental evoked potential components in a manner that is relatively unaffected by electrode location (Pratt et al. 1984, 1986b; Martin et al. 1986, 1987c).

A comparison of the conventional SEP compo- nents obtained from right median nerve stimula- tion of a normal subject with the simultaneously obtained 3-D SEP trajectory is shown in Fig. 10. P14, N20 and P25 correspond to apices A, C and D. Apex A was not merely a simple reversal of trajectory direction, but was usually observed to be made up of 2 or 3 smaller inflections reflecting the multiple generators of N / P 1 3 and P14 (Kaji and Sumner 1987). It was preceded by inflections corresponding to the cervically generated P l l and N12 peaks (Fig. 4), which were not systematically examined here. There was no clear inflection cor- responding to the N10 commonly recorded at Erb's point. The nearly 90 ° change in dipole orientation forming apex B was not coincident with a well-defined peak in the conventional somatosensory evoked potential wave forms (C'- Fz). In several subjects apex B was defined by a gradual change in orientation. Apex B coincided in latency with the onset of N20 as defined by the beginning of the parietal asymmetry of the con- ventional median nerve SEP (Desmedt and Cheron 1981). The small complex inflection near the mid- dle of the B-C curvilinear segment coincided with the peak of N18. Clear recognition of these aspects of the trajectory may be of value in the char- acterization of possible thalamic or cortical le- sions, where the separation of the temporally over- lapping N18 and N20 components is clinically important (Maugui+re et al. 1983). Because apex B is not easily identified in conventional recordings, alteration of the shape and orientation of the B-C

344 V.L. TOWLE ET AL.

(P14) A

;P13) ~ ( N18 onset)

( N 1 8 ) ~ g (N20 onset) /

(N20) C , ~ . ~ . . A

~ - - D (P25)

N20

c 'c- Fz - - - - P2~ Onset of N 2 0 \ Onset of N18 \

C-NC

P-NC ~ I , ~ / P22 I

Cv7 - Fz ~ ~ N 1 0

Ep i - Ep c ~ ~

A B C D Fig. 10. Comparison of conventional right median nerve SEP wave form peaks with 3-D SEP apices. Electrophysiologic events such as the onset of N18 and N20 and the peak of N18 are difficult to identify in many conventional wave forms but are clearly seen in the 3-D SEP trajectory. Dashed lines are

recorded from scalp ipsilateral to stimulation.

curvilinear segment in the presence of normal conventional peak amplitude and latency is a pos- sibility in some stroke patients (Pratt et al. 1987). The common practice (and resulting controversies, Celesia 1985) of analyzing evoked potential wave form peaks that are specific to certain derivations (e.g., N /P13) underscores the undue emphasis placed upon this aspect of conventional wave form analysis (Har'E1 and Pratt 1984; Pratt et al. 1984; Jewett et al. 1987).

Putative generators A fundamental question concerns the biological

significance of the reported structure of 3-D SEP and auditory 3-CLT trajectories. They have been analyzed in terms of apices and curvilinear and planar segments. It follows from dipole theory that the activation and decline of a single sta- tionary dipolar generator would manifest itself as a linear segment of trajectory which begins at the origin, increases in magnitude, and then returns along the same path to the origin, regardless of the location of the generator. One possible source of the surface recorded 3-D SEP trajectories de- scribed here are the fields of single or multiple stationary grey matter generators. Jewett (1987) has argued from theoretical grounds that a planar trajectory structure can result from 2 differentially activated generators which are summating, caus- ing otherwise linear segments to curve. The partial temporal overlapping of more than one generator has been observed in both the ascending auditory and somatosensory systems of humans (Hashimoto 1984; Katayama and Tsubokawa 1987) and animals (Arezzo et al. 1979; Achor and Starr 1980).

A second possible source of the surface re- sponse is the afferent volley. Action potentials have been modeled as quadrupoles (Wikswo et al. 1980; Nunez 1981) which can appear under some circumstances as a dipole oriented parallel to the direction of the white matter pathway (Plonsey 1974). That the extracellular field of the afferent volley is oriented parallel to the pathway and can be recorded from the surface of the scalp is con- sistent with the 'open field' structure of subcorti- cal afferents (Lorente de N6 1947; Klee and Rail 1977). An example of this is the P14 peak, which is generally thought to reflect activity in the me- dial lernniscus. P14 is observed in the (vertical) scalp to non-cephalic reference derivation, but not in the (horizontal) Cc-F z derivation (Fig. 10), The orientation of apex A was within 7 ° of the anatomical orientation of the lemniscal-thalamic pathway, estimated by superimposing our coordi- nate system on a stereotaxic atlas (Shaltenbrand and Wahren 1977) and on MRI scans. That a planar trajectory structure can result from action potentials traversing a curved white matter

3-D SEPs 345

pathway has been demonstrated both in vitro (Chimento et al. 1987) and mathematically (Shah 1987). We suspect that both of these possible explanations may account for the planarity ob- served in the 3-D SEP trajectories. Clarification of this issue will determine whether apices, segments, planes, or as yet undescribed aspects of trajectory structure are biologically meaningful.

The present findings suggest that the change in dipole orientation associated with apex B reflects the change in activation from a vertical P14-N18 dipole(s) to a horizontal N20 dipole. This is also suggested by its relatively low absolute amplitude (Fig. 6). The vertical orientation of the trajectory from the patient with a thalamic hemorrhage, during what would have been the B-C and C-D segments, implies that the vertical generator pro- cess was still active after apex B. For this patient the vertical generator was 'unmasked' by the loss of the horizontal apex C (N20) generator process. In normal subjects plane b appears to be the result of 2 temporally overlapping generator processes (Jewett 1987) associated with the conventional N18 and N20 components. The orientation of apices A and C is in good agreement with the surface distribution of the P15 (P14) and N20 components obtained from topographic mapping (Goff et al. 1977). The similar orientation and temporal symmetry of the 2 short portions of trajectory forming the apex C 'hook' that was observed in several subjects imply 2 phases of a single underlying process, possibly from the initial activation of cortex.

Trajectory variability The similar magnitude of the within- and be-

tween-subject variability of the A-B segment (Fig. 5) may reflect the relatively invariant anatomical organization of the human brain-stem. In contrast to this, the between-subject variability of the orientation of the subsequent B-C and C-D seg- ments was more than twice that of the within-sub- ject variability (Table III). This may be due, in part, to the 3 cm anatomical variability of human post-central cortex (estimated to be almost 30 o of arc measured from the thalamus) (Wahren and Braitenberg 1959; Wollsey et al. 1979), and im- plied by the functional variability of electrical

(Dinner et al. 1987) and radiographic (Fox et al. 1987) estimates of the location of human primary somatosensory cortex. The variability of the planarity described for the auditory 3-CLT (Pratt et al. 1985, Table I; Sininger et al. 1987, Table II) appears to be greater than the variability of the curvilinear segments described here. It is not pres- ently known whether this is due to inherent dif- ferences between the auditory and somatosensory systems or differences in the unit of analysis (seg- ments vs. planes). Two segments will define a plane whether or not they result from a single neural process. The elliptical character of the error of the sight vector defining plane b might be considered as evidence that the generators of the A-B and B-C segments are not closely related. We suspect that the absolute magnitude of the variability observed in this study could be further reduced by the use of narrower amplifier filter settings.

Generator eccentricity Dipole theory predicts that generators more

proximal to the recording electrodes will be em- phasized, while distant generators will contribute less to surface recordings (Nunez 1981). It might therefore be expected that the fields of generators located eccentric from the center of the head would appear distorted from their true orientation with this recording technique. A comparison of the results of the 45 o rotated montage with the primary montage (after back-rotating 45 °) re- vealed a similar trajectory morphology and orien- tation, with an average discrepancy of only 12 ° for the 4 apices recorded from the extensively studied subjects. This suggests that electrode lo- cation may not be a major distorting factor with this technique. Although the attenuating and dis- persing effects of the external layers of the skull and scalp tend to minimize local surface fields and partially 'center' the dipole (Schneider 1974; Kavanagh et al. 1978), issues related to generator eccentricity still need to be addressed. We infor- mally examined the effects of the inhomogeneities of the mouth by means of a palatal electrode and observed alterations in segment orientation no greater than 16 o.

346 V.L. TOWLE ET AL.

It should be remembered that the location of the underlying generators of the equivalent dipole cannot be directly determined from this analysis. Only the orientation of a hypothetical centrally located equivalent dipole is described. In this sense, this type of analysis is less powerful than dipole localization methods (Scherg and Von Cramon 1985; Smith et al. 1985). Even so, knowledge of the orientation of a single centrally located equiv- alent dipole may be helpful in selecting between two or more possible generators, since dipole orientation seems to be a more salient variable than dipole location in these types of studies. In spite of these inherent limitations, extension of this 3-D technique of data display and analysis to other types of evoked potentials, and even to spontaneous rhythmic activity, may permit a bet- ter understanding of the relationship between scalp-recorded electrophysiologic data and its neu- ral substrate.

This project was funded in part by the Brain Research Foundation of the University of Chicago.

We are grateful to Matthew Meriggioli, Marissa Ghez, and Adena Svingos for data collection, James J. Karaganis, Jr. for the system software, and to Drs. Barry G.W. Arnason, Michael McCaffrey and John Pofich for commenting on early versions of this manuscript.

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