Brain Topography, Volume 3, Number 1, 1990

137

Global Field Power and Topographic Similarity Wolfgang Skrandies*

Summary: Multichannel recordings are commonly presented as topographic maps series displaying the change of the potential distribution over time. When reviewing a sequence of potential maps it becomes obvious that there are epochs with only little activity (few field lines; small extrema values) while at other times the fields display high peaks and deep troughs with steep gradients. The measure of global field power (GFP)corresponds to the spatial standard deviation, and it quantifies the amount of activity at each time point in the field considering the data from all recording electrodes simultaneously resulting in a reference-independent descriptor of the potential field. Global field power is plotted as a function of time, and the occurrence times of GFP maxima are used to determine the latencies of ~oked potential components. The topographical change occurring in subsequent potential field distributions may also be quantified by computing an index of global dissimilarity. Global field power and global dissimilarity show a complementary behavior over time: in general high GFP is associated with similar fields while during periods between GFP peaks the topographic patterns of successive field distributions change rapidly accompanied by high dissimilarity values. The topographic changes, however, are best recognized by a segmentation procedure that considers field structure independent of GFP and global dissimilarity. The principles and practical applications of GFP computation, component latency determination and global dissimilarity of potential field distributions as well as a topographical time segmentation procedure will be illustrated with multichannel data evoked by visual stimuli. Key words: GFP;Global dissimilarity; VEP topography; Ssgmentation; Human electrophysiology.

Introduction E l e c t r o p h y s i o l o g i c a l brain activity r e c o r d e d f r o m m a n y scalp locations simultaneously typically is disp l a y e d as a s e r i e s o f e q u i p o t e n t i a l m a p s . S u c h topographic data s h o w the spatial distribution of brain electric activity at successive time points. In e v o k e d potential (EP) studies one aims at identifying so-called c o m p o n e n t s w h i c h constitute subsets of the r e c o r d e d brain activity that are related to discrete steps in information processing following stimulus presentation. Conventional w a v e s h a p e s of EPs s h o w peaks and troughs which c o m m o n l y are interpreted as components. W a v e s h a p e analysis, h o w e v e r , suffers from the ambiguity inherent in time series information. Electrical activity m a y only be r e c o r d e d as potential differences between pairs of electrodes (i.e., as voltages). It is evident that such voltage information d e p e n d s on the electrical activity at b o t h the recording and the reference electrode. Different electrode locations as well as the change of the *Max-PIanck-Institutefor Physiologicaland ClinicalResearch,FRG. Accepted for publication: June 24,1990. Correspondence and reprint requests should be addressed to Wolfgang Skrandies, Max-Planck-Institutefor Physiologicaland Clinical Research, 6350Bah Nauheim, F.R.G. Copyright © 1990 Human SciencesPress, Inc.

recording reference will drastically influence the voltage signals r e c o r d e d as time series. In a quantitative s t u d y on the effect of the reference location, Skrandies (1987) illustrates a set of visual e v o k e d potential (VEP) data w h e r e different w a v e s h a p e peak latencies are f o u n d in an identical data set w h e n the location of the recording reference is changed off-line systematically by a simple computational procedure. It is i m p o r t a n t to note that it is practically impossible to predict w h i c h changes will occur in a set of multichannel waveforms. For a further discussion and examples of the ambiguity of w a v e s h a p e c o m p o n e n t identification the reader is referred to Lehm a n n and Skrandies (1980a) and Skrandies (1987). W h e n inspecting a series of potential distribution m a p s it becomes evident that the electrical landscape changes over time. A series of brain electric activity maps e v o k e d b y a contrast reversing vertical grating stimulus is displayed in Figure 1. The spatial distribution of VEP activity at different poststimulus time points is obvious f r o m this figure w h e r e the occurrence of an occipital positivity b e t w e e n 82 and 111 ms can be seen. There are periods displaying high peaks and deep troughs with steep gradients while at other times shallow field distributions prevail. It is i m p o r t a n t to note that the information contained in such potential m a p s is i n d e p e n d e n t of the recording reference electrode. W h e n a different reference is used,

138

Skrandies

SIIMIARY NAP Si ne i avex a e a ea un le ¢u ve.

•

".~

S( AI t:: 8

÷

e

100, ,

Figure 1, Maps series between 70 and 135 ms of potentials elicited by a contrast reversing vertical grating stimulus of 1.0 c/d presented monocularly as a 17.1 by 13.4 deg arc test field to the central retina. Head seen from above; average reference data recorded from 21 electrodes with the most anterior electrode row at 40% of the nasion-inion distance above the inion and the most posterior electrode row at the inion (see inset). For color-coded amplitude values in the maps refer to color scale on the right.

the location of the zero baseline and the labeling of the potential values change while the locations of potential maxima and minima, as well as the potential gradients remain unaffected. This means that the shape of a given map does not change. In this way topographic mapping allows one to assess unambiguously the brain's electrical fields whose configurations do not depend on electrode locations or reference sites.

Potential Field Strength: Global Field Power Lehmann and Skrandies (1980a) and Skrandies and Lehmann (1982a) described the method of Global Field Power (GFP) computation. This measure allows one to quantify the integrated electrical activity in each map by computing a kind of spatial standard deviation. The underlying idea of this procedure is that fields with few field lines (for example from 118 to 129 ms in Figure 1) presumably contain little information while scalp fields displaying much activity reflect the synchronous activation of a large number of intracranial neuronal elements (for example the maps between 94 and 105 ms in Figure 1). The latency of an evoked component may reasonably be associated with the occurrence time of maximal activity in the potential distributions, reflecting the

s y n c h r o n o u s activation of a m a x i m a l n u m b e r of neurones. Global Field Power is used to quantify the amount of activity, and it is computed as the mean of all absolute~otential differences in the field corresponding to the spatial standard deviation (Lehmann and Skrandies 1980a~, Figure 2A illustrates the GFP function computed over 256 ms for the complete maps series of the data shown in Figure 1. Until about 70 ms following stimulus presentation, and after 200 ms, the integrated activity in the potential fields is low, and at 98 ms GFP reaches its maximum. The occurrence time of this maxim u m defines the latency of the conventional P100 component of the VEP. We note that this strategy of latency determination is based on the features of the scalp field, and it considers all recording points in a given potential field distribution simultaneously; thus it is unambiguous and identifies components topographically independent of the reference location. The determination of component latency is one of the first steps in topographic data analysis• Subsequently, scalp potential fields may be further investigated at these latencies allowing statistical comparisons of component latencies, or of m a x i m a a n d m i n i m a locations, amplitudes, and potential gradients obtained in different subjects or in different experimental conditions• Complete maps at component latency elicited in different

GFP and Topographic Similarity 100

A

139

I .,/~"

Q_ 50

, -f i i ,

I

I

I

I

I

I

I

....

"L.~/ I

I

I

I

ill

~,'~,! ~' I

I

I

I

I

I

I

I

I

~'--.

I

i

I

A 100 ~-

~. so

,,!

I

J,,,

,

0 ~

I

o~ 50 CO

\ 0

~ : 0

I

I

5O

i

t ) ~, " ~ / t I"

I~'/

I

100

II

i

I

~;%-. J,

150

I

I

I

I

I

200

I

I

/ I

j ,. i

I

250

LATENCY (ms)

Figure 2, (A) Global field power (GFP) computed from the data shown in Figure 1 as a function of poststimulus time. GFP was computed at each of the 256 individual time points as the spatial standard deviation, and values are normalized to a range between 0% and 100%, Maximal GFP occurs at 98 ms with an amplitude of 7.71 uV. (B) Global dissimilarity (DIS) computed as standard deviation between successive field distributions. Original amplitude values of the 21 electrode locations were used. The resulting curve was scaled to a range between 0°/0 and 100°/0 amplitude. (C) Global dissimilarity (DIS) computed as standard deviation between successive field distributions after scaling all maps for equal GFP. For display the curve was normalized to a range between 0% and 100% amplitude. Note a more clear-cut picture than in 2B.

experimental conditions may be compared directly using t-tests (or z-tests) which results in the spatial distribution of significant differences (e.g., Lehmann and Skrandies 1980b; Duffy et al. 1981; Skrandies, Dodt, Kofmel and Michel 1989), and multivariate statistical procedures like principal component analysis may be applied to the data decomposing field distributions into basic components which are defined mathematically (Skrandies and Lehm a n n 1982b; Skrandies 1989; Harner and Riggio 1989).

Topographic Changes: Global Dissimilarity As evident from Figure I the configuration of the scalp field distributions changes over time: around 100 ms the fields are dominated by an occipital peak with a frontal m i n i m u m while around 135 ms an occipital trough prevails. It is of interest to investigate how these changes come about. Is there a gradual change from one pattern

of field distribution to another over longer timer intervals, or do large changes occur rapidly ? This question may be answered w h e n potential distributions are compared quantitatively over time by computing the global dissimilarity (Lehmann and Skrandies 1980a; Skrandies and Lehmann 1982a) as the standard deviation between successive maps (i.e., global dissimilarity is determined for map (1) and m a p (2), m a p (2) and map (3), map (3) and map (4), etc.). We obtain a measure of global dissimilarity each time point between successive maps resulting in global dissimilarity values that may be plotted as a function of time. This time function represents the overall topographical changes occurring in a given maps series. Since we are interested only in topographical changes of field configuration but not in changes of field strength or amplitude between successive maps, the data must be scaled to equal GFP at each time point before global dissimilarity is computed. The effect (and advantage) of scaling the field distributions at each recording time point to equal GFP may be observed in Figure 2: the curve in Figure 2B shows h o w global dissimilarity varies over time w h e n the raw data are used. Around 100 ms the dissimilarity function shows a local minimum, preceded and followed by several peaks of h i g h global dissimilarity. The curve in Figure 2B displays many changes over the whole recording period indicating variation of the evoked potential fields over time. In this case, however, it is impossible to decide whether high global dissimilarity is caused by fields that have different strength (different amplitudes but similar topographies) or w h e t h e r high global dissimilarity v a l u e s are p r o d u c e d by the fact that m a i n l y the topographical features of the field distributions change from one m a p to the next. The only way to detect shape changes independent of amplitude variations is possible w h e n all data are scaled to identical GFP at each time point. Any changes that are n o w found cannot be accounted for by simple differences in amplitude or field strength. Figure 2C illustrates the resulting global dissimilarity function computed on the data of Figure 1 scaled for equal GFP (i.e., all 256 maps have identical field strength). N o w a m u c h clearer picture emerges: global dissimilarity remains high until about 70 ms, and drastically decreases in the interval between 75 and 115 ms. This indicates that the topography of the potential distributions r e m a i n stable d u r i n g this period while amplitude variations may take place as Figure 2B suggests. Between 120 and 130 ms global dissimilarity displays a maximum, and it remains on a low level from about 140 ms on. Thus, periods of high GFP (Figure 2A) a p p e a r to c o i n c i d e w i t h p e r i o d s of similar field topographies while major changes in the fields occur rapidly during times of low GFP. We note, however, that

140

Skrandies

1 ... 13

14 . . 21

2 2 ... 3 8

3 9 ... 4 2

4 3 ... 7 4

7 5 ... 116

117 ... 117

118 ... 118

119 ... 119

120 .., 124

136 ... 177

178 ... 180

181 ... 2 3 5

2 3 6 ,.. 2 3 8

125 .,. 135 Q

MAXIMUM

0

ms

MINIMUM

Figure 3. Segments found for the data of Figure 1 during the first 238 ms following the stimulus. Numbers indicate staff and end time points for e a c h segment in milliseconds, Location changes of the field extrema of more than one electrode location in the anterior-posterior or left-right direction or simultaneous changes of both maximum and minimum locations by one electrode define segment borders. Filled circles show maximum locations, open circles correspond to minimum locations. In order to enhance the basic field configurations the extrema locations are joined by a line. The numbers in e a c h frame correspond to the 21 electrodes of the array shown in Figure 1.

many small changes that repeatedly occur between successive m a p s c o u l d also f i n a l l y r e s u l t in large topographic changes that may not be detected by global dissimilarity. If changes are gradual and smooth over time a modified field structure may occur as a final result while the standard deviations between neighbouring maps remain small throughout the analysis epoch. Such a gradual development may be detected only by the direct examination of the topographic features of the scalp potential field distributions as described below.

Topographically Defined Segments In evoked potential or spontaneous EEG data, time segments may be found that show a stable topography (Lehmann and Skrandies 1984, 1986). In contrast to the results obtained with the segmentation of time series data (e.g., Michael and Houchin 1979), such segments may be determined topographically independent of the recording reference and the absolute field strength by examining the locations of the potential m a x i m u m and minimum in the field at each recording time point. This appears feasible since most scalp potential maps have a

simple organization, in general displaying not more than one maximum and minimum at a given time point. This holds true also w h e n potential distribution data are obtained from up to 47 scalp sites simultaneously (Lehmann and Skrandies 1980a). Thus, the locations of the maxima and minima in the field are an adequate description of the major topographic features of a potential distribution map. Stable topography implies that identical neuronal generators are activated over some time during which the extreme values of the scalp potential field remain in circumscribed areas. On the other hand, different locations of maxima and minima in the surface recorded fields must be caused by the activation of nonidentical neural generating processes. Topographically stable segments are obtained when sequential maps are scanned for location changes of potential maxima and minima (Lehmann and Skrandies 1984, 1986). In general, the locations of the extreme field values stay constant for several sampling time points, and change within a brief interval to a new field configuration. Topographic segmentation is based on the recognition of identical (i.e., stable) potential field configurations by determining whether the maxima and minima locations remain unchanged or not. We note that this approach disregards amplitude changes within the fields and stresses the topographical aspects of the multichannel data. In addition, this is a reference-independent procedure as the locations of potential maxima and minima in the fields do not depend on the potential values at the reference site. Figure 3 illustrates 15 field configurations (reduced to the loca~ons of the potential maxima and minima in the field) that constitute all segments determined for the data of Figure Kduring the first 238 ms following the stimulus (the whole recording epoch of 256 ms consisted of 18 segments). A segment was defined as an epoch during which the maximum and minimum of the field remained in a small area surrounding the electrode that sees an extreme value in the field. Starting at poststimulus time point 1, a spatial window of one electrode distance in the anterior-posterior and in the left-right direction was set. As soon as the maximum or the minimum left this spatial window or when both the maximum and minimum moved simultaneously by only one electrode distance, the segment was terminated, and an other spatial window was set around the locations of the field maximum and minimum of the new segment. This procedure was repeated throughout the recording epoch and resulted in the segments illustrated in Figure 3. It is evident from this figure that there occurs only a small number of differently organized field distributions over the whole recording period. Several segments result at early or late time points where also low GFP values are observed (see Figure 2A). A long segment

GFP and Topographic Similarity

of 41 ms occurs around 100 ms where the maximum remains occipitally in the midline and the minimum in the left frontal area from 75 to 116 ms. This stable field configuration coincides with high GFP and low global dissimilarity (see Figure 2A and C) which start to change at the segment borders of 75 and 116 ms. Three other segments cover the time periods from 136 to 177 ms, from 178 to 180 ms, and from 181 to 235 ms during which the minimum remains stable over 99 ms (at electrode 16, see Figure 3) while segments are terminated and new segments are defined by location changes of the field maxima. During this late interval again high GFP and low global dissimilarity are observed but we note that slight configuration changes may occur during such periods. Topographically stable configurations that can be found over subjects and are influenced by experimental stimulus conditions are associated with the activation of different (or differently oriented) intracranial neuronal generators. Thus segments of scalp field distributions may be interpreted as steps in information processing. Skrandies (1988) and Brandeis and Lehmann (1989) present additional data on the segmentation of electric brain activity that are related to visual input conditions as well as to visual attention.

Synopsis Steps in processing of incoming information by the brain are reflected in the topographic patterns of the scalp recorded field potential distributions. Mapping such activity allows for a reference-independent assessment of the electrical fields of the brain. Numerical processing of the field distributions results in statements about the strength of the evoked potential fields by determining GFP which is influenced by input parameters and globally reflects the number of neuronal elements activated synchronously. This is most evident in experimental conditions where subsets of neuronal populations process different aspects of sensory information (e.g., Skrandies et al. 1989). Global field power helps to determine component latencies independent of the recording reference by considering all recording points on the scalp simultaneously and has been applied successfully to many different sets of evoked potential data (e.g., Skrandies 1987). In general, periods of high GFP coincide with periods of low global dissimilarity w h e n the topographical features of the fields are selectively considered and amplitude changes are eliminated by scaling the field distribution data to equal field strength throughout the analysis epoch. In addition, during such periods one may also observe topographically stable segments of the potential field distributions. Such segments are defined by the locations

14t

of the field's extreme values, and there is a limited number of segments occurring over longer time periods indicating that the major topographical features of the scalp recorded electrical brain activity remain stable over some time. Further studies of such segments of electrical brain activity will certainly reveal more information contained in the electrical fields of the brain that are recorded as scalp field distributions from human subjects.

References Brandeis, D. and Lehmann, D. Segments of event-related potential map series reveal landscape changes with visual attention and subjective contours. Electroenceph. Clin. Neurophysiol., 1989, 73: 507-519. Duffy, F.H., Barrels, P.H. and Burchfiel, J.L. Significance probability mapping: an aid in the topographical analyses of brain electrical activity. Electroenceph. Clin. Neurophysiol., 1981, 51: 455-462. Harner, R. and Riggio, S. Application of singular value decomposition to topographic analysis of flash evoked potentials. Brain Topography, 1989, 2, 91-98. Lehmann, D. and Skrandies, W. Reference-free identification of components of checkerboard-evoked multichannel potential fields. Electroenceph. Clin. Neurophysiol., 1980a, 48: 609621. Lehmann, D. and Skrandies, W. Visually evoked scalp potential fields in hemiretinal stimulation. Docum. Ophthalmol., 1980b, 23, 237-243. Lehmann, D. and Skrandies, W. Time segmentation of evoked potentials (EPs) based on spatial scalp field configuration in multichannel recordings. Electroenceph. Clin. Neurophysiol., 1986, Suppl. 38: 27-29. Michael D. and Houchin, J. Automatic EEG analysis: a segmentation procedure based on the autocorrelation function. Electroenceph. Clin. Neurophysiol., 1979, 46: 232-235. Skrandies, W. The upper and lower visual field of man: electrophysiological and functional differences. Progress in Sensory Physiology, 1987, 8: 1-93. Skrandies, W. Time range analysis of evoked potential fields. Brain Topography, 1988, 1: 107-116. Skrandies, W. Data reduction of multichannel fields: global field power and principal components. Brain Topography, 1989, 2: 73-80. Skrandies, W. and Lehmann, D. Occurrence time and scalp location of components of evoked EEG potential fields. In: W.M. Herrmann (Ed.), Electroencephalography in Drug Research, Fischer, Stuttgart, 1982a: 183-192. Skrandies, W. and Lehmann, D. Spatial principal components of multi-channel maps evoked by lateral visual half-field stimuli. Electroenceph. Clin. Neurophysiol., 1982b, 54: 662667. Skrandies, W., Dodt, E., Kofmel, B.A. and Michel, Ch. Scalp potential field topography evoked by lateralized dynamic random-dot stereograms. Invest. Ophthalmol. Vis. Scie., 1989, Suppl. 30: 515.