Frequency source analysis in patients with brain lesions

Brain Topography, Volume 8, Number 2, 1995 109

Frequency Source Analysis in Patients with Brain Lesions

Thalia Harmony*, Antonio Fern6ndez-Bouzas @, Erzs&bet Marosi*, Thalia Fern6ndez*, Pedro Vald('.=s #, Jorge Bosch #, Jorge Riera #, Jorge Bernal*, Mario Rodriguez*, Alfonso Reyes*, Juan Silva*, Mario Alonso @, and Jos(~ M. S~nchez Cabrera @

Summary: In a previos study (Harmony et al. 1993) we observed that the volume of lesions was correlated only with delta power, while the volume and density of edema showed a significant correlation with theta and alpha power, suggesting two independent origins of activity in the delta and theta bands in patients with space-occupying lesions. Our goal in this paper is to show, through a different technique, in a narrow band spectral analysis, that brain lesions are characterized by activity in the delta domain and that edema is better correlated with activity within the theta range. Frequency source analysis based on the Maximum Likelihood (ML) test for rejection of isotropicity was applied to the EEG at rest of 36 patients with space-occupying intracranial lesions. The ML test was rejected at frequencies below 1 Hz and in the low range of the delta rhythm in 31 patients. The origin of the equivalent dipoles at these frequencies was within the volume of the lesion in 27 patients. In 15 patients out of 19 with vasogenic edema the ML test was rejected at frequencies in the theta range. The equivalent dipoles at these frequencies were all within the volume of the edema.

Key words: Delta rhythm; Theta rhythm; Slow rhythm; Brain lesions; Dipole analysis; Frequency source analysis; Vasogenic edema.

Introduction

A c o m m o n view in clinical e lectroencephalography is that in the presence of brain lesions, the boundaries be tween the delta and theta bands are arbitrary and do not d e n o t e a n y f u n d a m e n t a l b io logica l d i f ference. Therefore, a c o m m o n origin for delta and theta activity in the presence of brain lesions is usual ly assumed. Thus, it is impor tan t to establish if localized delta or theta activity represents degrees of the same process or if each f requency band is related to a different mechanism.

In a previous s tudy (Harmony et al. 1993), we correlated a g roup of compu ted tomography (CT) parameters with absolute (AP) and relative power (RP) in the delta, theta, alpha and beta bands in a group of patients with space-occupying lesions. It was observed that the volume of the lesion was correlated only wi th delta absolute and relative power , and that the vo lume and densi ty of the edema showed a significant correlation with delta,

*ENEP Iztacala, Universidad Nacional Aut6noma de M6xico. @Hospital Jufirez de M6xico. #Centro de Neurociencias de Cuba. Accepted for publication: September 14, 1995. This study was supported in part by DGAPA, UNAM, Project

1N202492. Correspondence and reprint requests should be adressed to Thalfa

Harmony, ENEP Iztacala UNAM, Apartado 314, 54090 Tlanepantla, Estado de M@xico.

Fax: (525) 390-5900 and (525) 623-1193 Copyright �9 1995 Human Sciences Press, Inc.

theta, and alpha AP calculated from EEG potentials and only with theta and alpha AP in the Laplacian. Since EEG potentials tend to p roduce a more extensive and diffuse picture of abnormality, whereas the Laplacian acts as a spatial filter emphas iz ing local sources over distant sources, we concluded that edema is related not to delta activity but to theta and alpha power. In that s tudy we suggested independent origins of activity in the delta and theta bands in patients with space-occupying lesions.

In the last years considerable progress has been made in dipole source localization procedures. At the beginning only temporal aspects of data were used in the localization procedure, as for example the computa t ion of the intracraneal sources of scalp-recorded momenta ry maps of brain electrical activity (Lehmann 1987; Fender 1987) or the calculation of dipole source potential wave- forms (Scherg 1990). In recent years, Lehmann and Michel (1989,1990) and Lutkenhoner (1992) described the localization of dipoles based upon f requency-domain aspects of the data. According to Lehmann and Michel (1989), in addit ion to these findings' theoretical interest, diagnostically useful results in patients with localized brain pathology are expected from these procedures. For this reason in this s tudy we have appl ied the procedure described by Vald6s et al. (1992) to calculate the equivalent dipoles for each f requency of the cross-spectral matrix in a group of patients with space-occupying lesions, in order to determine whether the dipoles that reflect the location of the lesion were within a f requency corresponding to the delta band, and whether dipoles reflect-

110 Harmony et al.

ing the location of the edema were within the theta band. Our approach has been based on the theory devel-

oped for a type of covariance matrix known in the statistical literature as a linear structure matrix. Vald6s et al. (1992) have shown that it is possible to construct a test for the hypothesis of isotropicity by means of Maximum Likelihood (ML) procedures in the frequency domain using multivariate complex valued statistics. The test is applied to each individual frequency of the spectra, and in those frequencies where the ML test for isotropicity is rejected, the position and normalized moment for each equivalent dipole at that frequency is calculated. The method differs from that proposed by Lehrnann and Michel (1990), which fits one dipole for least square (LS) methods to the FFT for a single frequency, as well as the extension to several dipoles made by Lutkenhoner (1992), in two main aspects: a) the estimation procedure takes into account background noise, and b) it uses spectral and cross-spectral information for estimation; therefore the dipoles describe the activity at each specific frequency as well as their correlations.

Material and Methods

Thirty-six patients with space-occupying lesions were studied. After giving their informed consent, all patients underwent clinical neurological examinations, CT scans and EEG recordings. CT scans obtained the day before the EEG recording were the reference for the lesions' anatomy. CT scans were performed with and with- out contrast medium. EEG recordings were obtained (10/20 system) using linked ear lobes as reference: Fpl, Fp2, F3, F4, C3, C4, P3, P4, O1, 02, F7, F8, T3, T4, T5, T6, Fz, Cz, and Pz. In all cases the resistances of A1 and A2 were measured before and after the recording; these were very similar and fell between 2 and 4 kohms. Subjects were awake, at rest and with eyes closed. The amplifier bandwidth was set between 0.5 and 30 Hz. Ten minutes of EEG were recorded. The EEG was sampled every 10 msec and edited off-line by visual inspection in order to select 24 artifact-free segments of 2.56 secs for the analysis.

EEG analysis

EEG analysis was done off-line. The cross-spectral matrices S(w) of all 19 leads were obtained for frequencies between 0.39 and 19.11 Hz with a spectral resolution of 0.39 Hz. The S(w) were calculated by means of the FFT and segment averaging (Brillinger 1975). Each S(w) con- sists of the crosspectra between all pairs of channels, the diagonal of these matrices containing the spectra. Spec- tra and crosspectra are esentially measures of the vari- ance and covariance respectively of complex valued Fourier coefficients. They contain all the relevant infor-

mation in the case of stationary Gaussian linear signals and are the first approximation to other types of phenom- ena. Models that explain linear properties of approxi- mately stationary EEG segments may be fitted by using complex valued multivariate statistics. Maximum likelihood (ML) procedures both for fitting models and testing the goodness of their fitting are statistically optimal but computationally expensive. Faster Least Square (LS) methods that yield good approximations have been used in this paper. Based. upon this approach, the method used for equivalent dipole fitting in the frequency domain was targeted to describe the S(w) rather than to fit individual FFTs as in other approaches (Lehrnann and Michel 1990; Lutkenhoner 1992). A complete description of the theory and implementation of the procedures used can be found in Vald6s et al. (1992). A short summary follows:

Elimination of reference effect

A reference exerts an effect on S(w) by means of an additive component that can distort magnitudes of spectra and crosspectra as well as phases of crosspectra. This component may be estimated, and S(w) may thereby be corrected for it. It is easily shown that use of the LS method is equivalent to subtracting the average reference from the original EEG data.

Elimination of the isotropic component

An additional additive component has been described that accounts for a substantial part of the total power in the EEG at some w. This component has a correlation structure that falls off as a function of in- terelectrode distance. A covariance matrix of this type may be generated by an isotropic stochastic process on a sphere, and probably explains the topography of some spatial principal components of the EEG (Silberstein 1992). Simulations have shown that such an isotropic stochastic process might be generated in the EEG by widespread sets of weak cortical generators and the additional effect of spatial blurring. Fitting dipoles to an isotropic stochastic process on the sphere produces arti- ficial central dipoles and their presence in S(w) may bias dipole estimation in the frequency domain. Previous work has shown that S(w) for normal resting EEGs is probably isotropic except at frequencies in which localized sets of generators are present. For this reason the goodness of fit statistic for an isotropic model is first found for the whole frequency range. Sharp peaks of this statistic above the general level were considered as evi- dence for more localized sources at those w that required equivalent dipole fitting.

Frequency Source Analysis in Brain Lesions 111

CT Slice

ss,oo I

7• ~ L % I y=-y,

h: alice's level P:sJice's sngle X = X' * Cos(pJ - h * Sen(p)

h Z = X * TsniP] + -

Cos(p)

Figure 1. Calculation of the X, Y, Z coordinates of the center of the lesion from the CT images and correction of the angle of the CT slide to the horizontal position.

Frequency domain dipole fitting

Any number of equivalent dipoles may be fitted to a S(w) by minimizing a goodness of fit criterion between this matrix and the crosspectrum reconstructed by the dipoles (as well as the reference and the isotropic component). The model parameters are the position of the equivalent dipoles for each frequency and the crosspec- tral matrix of these equivalent dipoles. They are estimated by means of a numerical optimization procedure. The number of dipoles to be fitted was increased until no further improvement of the goodness of fit criterion was possible. However, the experience in this study was that a single equivalent dipole for each frequency was enough to explain the topography of the lesion.

Fitting goodness

This section describes the methodology used to as- sess the goodness of the fitting method. The mathemathi- cal procedure used to obtain the distance from the tumor and the edema to the equivalent dipole is described. The only available information from the subjects was the tomographic (CT) images in which the lesion, the edema and some other significant points like nasion, inion, vertex and left and right external auditory channel were located. Normally, all these points appeared in different CT images. Using the header of the tomograph, which always appeared at the same position in all images, as a reference, the CT images containing the relevant points were superimposed and all the points were marked on a single sheet of paper. The level of the CT slice where the points appeared was also recorded.

On the sheet of paper, two arbitrary axes (X and Y) were marked and the corresponding coordinates of every point were recorded. However, the unity of measure- ments of the slice's level were in real coordinates. It was then necessary to transform them in order to make them

compatible with the X and Y coordinates, which were rescaled by the projection procedure. A scale factor was determined by a linear comparison of the real head's measurement with the X and Y coordinates taken from the CTs. Using this factor, the slice's level was rescaled. To calculate the Z coordinate of the lesion and the edema, it was necessary to take into account that the CT slices were not recorded in the horizontal position, but with an angle of 20 degrees with respect to the ear's horizontal plane. To correct the X, Y and Z coordinates according to the horizontal plane, the following equation system was used:

Y1 = Y0

X1 = X0 * Cos(rho) - h * Sen(rho)

Z1 = X * Tan(rho) + (h / Cos(rho))

where: X0, Y0 are the X and Y coordinates of the points from the paper's sheet; h: the level of the slice's tomography; rho: the angle of the CT slice with respect to the horizontal plane.

The X axis was taken from the inion to the nasion. The origin of the axis was in the center of the head and the positive direction was towards the nasion.

The Y axis was taken along the line between the left and right ears, with the positive direction towards the left ear.

The Z axis was set perpendicular to the XY plane, following from the center of the head to the vertex, with the positive direction towards the vertex. See figure 1.

The (X,Y,Z) coordinates for the inion, nasion, vertex and left and right external auditory channels were used to calculate the best fitting sphere to these points, using the procedure described by Lutkenhoner (1992).

With regard to the ratio and the center of the sphere, two transformations were applied. First the origin of the system axes was translated to the center of the sphere, subsequently the coordinates of all the points were rescaled according to the ratio of the sphere to the unity ratio. Finally, all the points, including the center of the lesion and the edema, were rescaled and translated to a sphere of center in the origin (0,0,0) and unity ratio, the same conditions which the dipole coordinates fulfill.

The volume of the lesion and the edema was also available. From a visual observation of the cases, an assumption of an spheric shape for both lesion and edema was considered valid. By means of the following relation: volume of the sphere = 4 /3 * Pi * Radius 3 the radius of the lesion and the edema were calculated.

The dipoles at the frequencies where the isotropicity test was rejected were selected. Then the distance from the center of the lesion and the edema to the dipoles in

112 Harmony et ak

Table I.

Case 08 19 27 32 33 41 58

115 16 46 49 13 17 40

114

Diagnosis Left TO glioblastoma Right TP astrocytoma Left TO astroc~oma Pineal astroc~oma Left thalamic glioblastoma Left frontal astroc~oma Left frontal astrocytoma Left TP glioblastoma Pituitary adenoma Sa~ittal dis~erminoma Intrasellar l~r Prechiasmatic metastasis 3 right hem. metastasis Right parietal metastasis Right frontal metastasis

02 Left frontobasal menin~ioma 05 Right frontobasal menin~ioma 10 Left frontobasal meningioma 29 Left frontal menin~ioma 30 Left FTP menin$ioma 35 Ril~ht frontal meningioma 38 Right parietal meningioma 44 Left frontal rnenin~ioma 48 Right TP meningioma 55 Left temporal menin~ioma 01 Cysticercus right gyrus rectus 11 Right TP cysticercus 45 Right frontal ~stieercus

108 Left parietal cysticercus 110 Left temporal cysticercus 117 ~ Right temporal cysticercus

1482 Right putaminal hematoma Left frontal hematoma

47 52 23!

Left putaminal hematoma Left putaminal hematoma Left P hemorrha~,ic infarct

LESION Freq. Radius Center Border

0.39 0.91 0.35 0.00 0.78 0.92 0.15 0.00 0.78 0.82 0.37 0.00 1.17 0.41: 0.44 0.03 1.56 0.60 0.40 0.00 1.17 0.33 0.87 0.54 3.90 0.53 0.45 0.00 3.90 0.72 0.40 0.00 4.68 0.71 0.12 0.00 2.73 0.57 0.12 0.00 0.78 0.41 0.14 0.00 6.63 0.35 0.44 0.09 0.78 0.39 0.31 0.00 2.73 0.31 0.47 0.16 1.56 0.74 0.32 0.00 1.17 0.73 0.22 0.00 1.17 0.40 0.25 0.00 1,17 0,74 0.28 0.00 1_56 0.50 0.52 0.02 195 0.71 0.41 0.00 2.73 0.86 0.43 0.00 3.51 0.82 0.65 0.00 2.731 0.37 0.77 0.40 0,39 0.40 1.33 0.93 4.29 0.67 0.24 0.00 0.39! 0.16 0.27 0.11 1.17 0.68 0.36 0.00 2.73 0.87 0.45 0.00 0.39 0.12 0.48 0.36 0.781 0,87 0.49 0.00 1.56 0.43 0.40 0.00 0.78 0.56 0.25 0.00 1.56 0.37 0.44 0.07

. . . . =

0.78 0.43 0.35 0.00 078 0.54 0.28 0.00 1.95 0.44 0.27 0.00

EDEMA Freq. [Radius] Center I Border

3.901 0.79 0.24 1 0.00

1.17 0.58 0.00! 0.00 3.90 0.34 0.40 0.06 6.24 0.62 0.21 0.00

3.121 0.72 0.441 0.00

4.29 0.96 0.13! 0.00 3.51 0.93 0.22 0.00 5.85 0.94 0.22 0.00 4.29 0.71 0.37 0.00 5,85 0.58 0.52 0.00 5.85 0.94 0.15 0.00 5.85 0.74 0.19 0.00 4.68 0.80 0.18 0.00 3.51 0.89 0.00 0.00

6.241 0.47 0 .29 , 0.00 6.24[ 0.59 0.34 0.00

5185 0.60 0.24 0.00 6.63 0.60 0.21 0.00 3190 0.53 0.26 0.00

those frequencies were calculated, as well as the distance from the the dipoles to the "borders" of the lesion and the edema. The m i n i m u m distance to the center of the lesion or the edema was selected.

Results The results obtained with this procedure are shown

in table L The first two fields of the table correspond to case identification and diagnosis. Then the same fields are presented for both the lesion and the edema, sepa- rately: FREQ is the dipole 's best-fitting frequency (Hz)

for the lesion or the edema. RADIUS is the radius for the spherical vo lume assumed for the lesion or the edema. CENTER is the distance f rom the origin of the dipole to the center of the lesion or the edema at the given frequency. BORDER is the distance f rom the origin of the dipole to the "border" of the lesion or the edema at the given frequency. RADIUS, CENTER and BORDER are referred to as the sphere of unity ratio. Considering that the average ratio for the sphere which best fits the head is about 10 cm, a factor of 10 could be used in order to refer to all of these measures as corresponding to a "real head."


1 0 /

S

8

6

4

21 �84

tnLesion

[mEdema ]

. . . . . . . . . . . . . . . . . . . . .

0.39 0.78 t,17 1.56 1.95 2.34 2.73 3.12 3.51 3.9 4.29 4.68 5.07 5.85 6.24 6.63

Figure 2. Distribution of frequencies where the best dipole was found for the lesion and for the edema. The dipoles for the lesions were in the low and delta frequencies and the dipoles that localized the edema were within the thefa range.

The frequencies at which the LS test for isotropicity was rejected and the equivalent dipole had its origin at a minimum distance from the center of the lesion were, in the majority of cases, within the delta band: in 31 out of 36 patients (86%) the optimum dipoles were in frequencies between 0.39 and 3.51 Hz. In the remaining 5 patients the dipole nearest to the center of the lesion was found in frequencies within the theta band (from 3.9 to 5.63 Hz). Figure 2 shows the distribution of frequencies which correspond to the dipoles nearest to the center of the lesion and of the edema.

When the volume of the lesion was taken into account, in 27 patients out of 36 (75%) the origin of the dipole was inside the lesion. However, in 4 patients (11%) the distance from the origin of the dipole to the border of the lesion was less than 0.1 units, which corresponds to less than i cm. In 5 patients (14%) the distance was bigger, corresponding to lesions of smaller size.

Nineteen patients also presented edema. In 15 out of 19 (79%) cases the frequencies at which the isotropicity test was rejected and the equivalent dipole had the minimum distance to the center of the edema were within the theta band (3.9 to 6.63 Hz). In the remaining 4 cases, the optimum dipoles were within the delta band (1.17 to 3.51 Hz), as shown in figure 2. In all patients with edema the origin of the optimum dipole was within the volume of the edema.

We illustrate these results in figures 3 and 4. Figure 3(a) shows the CT of a patient (08) with a left temporo- occipital glioblastoma and a large area of edema occupying the left frontal lobe. In figure 3(b) the V(t) spectra

(red), the spectra for the isotropic model (blue) and for the isotropic model plus one dipole (green) are shown for each lead. At the bottom the values of the LS test for rejection of isotropicity at each frequency are shown. The maximum value was observed at 0.39 Hz. The right portion of the figure shows top, posterior and left views of the head, with white and yellow areas showing the highest power at this frequency. The heads at the left correspond to the distribution of power at this frequency, those at the right to the distribution of power according to the model using one dipole. The position of the equivalent dipole at 0.39 Hz is shown. Its origin is placed in the left temporo-occipital area, within the volume of the lesion.

Figure 3(c) shows the spectra and dipoles at 3.90 Hz of the same patient, where the LS test for isotropicity has a small peak as shown in the bottom of the figure. Now the origin of the dipole at this frequency is in the left frontal lobe, near the midline, within the volume of the edema. The position of the dipole corresponds to the circle drawn in the CT of figure 2(a) to measure the density of the edema. In the CT one also observes a midline shift due to the edema in the left hemisphere.

Therefore in this patient the dipole at 0.39 Hz corresponds to the tumor, and the dipole at 3.90 Hz to the edema. This is a good example of what happened in those patients with large areas of lesion and edema with different locations.

In patients with small lesions and large areas of edema, the frequencies at which the LS test was rejected were in the theta range. Figure 4(a) shows the CT of a

1 t4 Harmony et al.

Figure 3. Patient with a left temporo-occipital glioblastoma, as shown in the CT scan (a). An area of edema in the anterior region of the left hemisphere may be observed. Left (L) and right (R) are indicated. In the dipoles, the right hemisphere coincides with the right side of the figure. The 3 different spectra for each lead are shown. The V(t) power spectrum is in red, the spectrum calculated with zero dipoles (isotropic model) in blue and the spectrum of an isotropic model plus one equivalent dipole in green. The bottom of the figure indicates the value of the LS test for isotropicity at each frequency. The test was rejected with a maximum value at 0.39 Hz. In the right portion of the figure, top, posterior and left views of the head, white and yellow areas showing the highest power at this frequency. The heads at the left correspond to the distribution of power at this frequency, those at the right to the distribution of power according to the model with one dipole. The origin of the equivalent dipole at 0.39 Hz is shown within the volume of the tumor. In 3(c) the location of a dipole at 3.90 Hz, where the LS test for isotropicity has a small peak, as shown at the bottom of the figure: its origin is in the left frontal lobe near the midline, within the area of the edema. There is a clear peak at this frequency in the V(t) spectra (red) and the spectra of an isotropic model plus one equivalent dipole (green) in F3 and Fz.

patient (42) with a large area of vasogenic edema and a small metastasis in the right parietal lobe. In figure 4(b) the spectra and the values of the LS test at each frequency are shown. There is a clear peak at 4.29 Hz in the V(t) spectra (red) and in the spectra of an isotropic model plus one equivalent dipole (green) in P4 and T6. Isotropicity is rejected in this case; its maximum value was at 4.29 Hz. The origin of the dipole is in the right parietal lobe, within the volume of the edema.

Discussion It is well known that the "inverse problem" in EEG

has no unique solution: many different source configura- tions may give rise to the same potential distribution on the surface of the scalp. Therefore this approach has been subjected to many criticisms. We consider that patients with lesions clearly defined by CT or MRI are a valuable model for testing the usefulness of source localization


Figure 4. Patient with a small metastasis in the right parietal lobe and a large area of edema with mass effect. The LS test for isotropicity is rejected with a maximum value at 4.29 Hz, as shown in the bottom of the figure. Clear peaks at this frequency may be observed in the V(t} spectra (red) and the spectra of an isotropic model plus one equivalent dipole [green) in P4 and T6. The origin of the dipole at this frequency within the volume of the edema.

procedures. Our goal is not to incorporate new imaging techniques for the study of patients with brain lesions which are best diagnosed by CT or MRI, but rather to obtain a deeper knowledge of the potential of those procedures which may be relevant in other pathologies where it is not possible to identify any structural abnormality and where functional images are more valuable.

On the other hand, the conventional EEG mapping of power of voltage or current source densities at different frequencies has been shown to be a very powerful technique for the analysis of some forms of brain dys- function (Duffy 1985; Nuwer 1988; Prichep and John 1992; Harmony et al. 1993), and is not as complex as computation of the equivalent dipoles. However, our goal in this paper was to show, by means of a different technique and in a narrow band spectral analysis, that brain lesions are characterized by activity in the delta domain and that edema is better represented in the theta range.

Dipole locations were within the volume of the lesion in 75% of the patients, and very near to the lesion in 11% more. In 12 subjects the LS test for isotropicity was rejected with its maximum values in frequencies lower than i Hz. This was an unexpected result. In 4 patients the best location was at 0.39 Hz, a frequency which was attenuated in our recordings since we used a time con- stant of 0.5 Hz. Steriade et al. (1993a), while performing studies of thalamic and cortical neurons in cats in order to reveal the cellular basis of oscillations within the frequency band of 0.1-4 Hz, found that these rhythms do not constitute a homogeneous entity. Instead, they belong to

at least two different types of oscillatory activities: 1-4 Hz or delta rhythm and <lHz or "slow rhythm", with dis- tinct sites of genesis and dissimilar mechanisms. These authors observed the slow rhythm in 88% of the cortical cells recorded. In most neurons the slow oscillation con- sisted of long-lasting depolarizations, but in others the major events were pronounced hyperpolarizations. They concluded that the slow oscillation probably in- cludes EPSPs and IPSPs as well as intrinsic currents, the predominance of one or another aspect varying from cell to cell according to their place in the circuitry. These slow cortical oscillations survived total lesions of thalamic perikarya projecting to the recorded cortical neurons (Steriade et al. 1993b). These results were observed during slow-wave sleep in cats, but they point to the possi- bility that in brain lesions, where some areas of the cortex are frequently partially or totally isolated from the rest of the brain, the slow rhythm might be observed.

Clinical electroencephalography has shown brain lesions to be characterized by the occurrence of polymorphic delta activity. We observed this activity in the EEG records of our patients, sometimes the slow rhythm is very difficult to detect by visual inspection. In a previous paper we analyzed EEG power in the delta, theta, alpha and beta bands and observed a very high correlation between delta power and the volume of the lesion (Har- mony et al. 1993). However, in 33% of the patients, in frequencies lower than 1 Hz the test of isotropicity was rejected with higher values than it was in frequencies in the delta band. In the majority of these cases, the equivalent dipole at these slow frequencies was within the

116 Harmony et ai.

volume of the lesion, and nearer to the center of the lesion than the dipoles at frequencies in the delta band--where the LS test was rejected with values which were not so high. Therefore, we conclude that the slow rhythm plays an as yet undefined role in patients with brain lesions.

The frequencies within the delta band in which the source analysis was accurate in locating the lesions were in the low delta range. Delta activity in the presence of brain lesions has been related to a partial cortical deafferentation (Gloor et al. 1977; Goldensohn 1979). Delta sleep activity was classically regarded as a rhythm aris- ing in the cerebral cortex, since vertical source-sinks were found at different cortical layers (Ball et al. 1977; Petsche et al. 1984). However, Steriade et al. (1993c) proposed that delta polymorphic activity recorded at the scalp during slow-wave sleep may have its origin in the thalamus and be transferred to cortical neurons in different layers. Within the cortex, active excitatory-inhibitory postsynap- tic processes and long-lasting intrinsic currents produce the delta waves, as reflected at the cortical surface. In our data it was very interesting to observe that the two cases in which the LS test of isotropicity was rejected at frequencies in the theta band were patients with tumors that did not affect the cerebral cortex (a prechiasmatic metastasis and an adenoma of the hypophysis). This finding suggests that in the case of brain lesions the presence of delta waves is more related to cortical deafferentation.

In relation to vasogenic edema, our hypothesis was confirmed: the LS test for isotropicity was rejected in frequencies within the theta range with equivalent dipoles that were within the volume of the edema in 79% of the patients. Many different factors have been proposed for the generation of vasogenic edema (Harmony et al. 1993). Thus, it would be simplistic to relate the generation of theta activity to a particular factor present in such complex processes as the generation of vasogenic edema.

Our results point toward the existence of three different EEG activities in the presence of space-occupying lesions in conscious patients: a slow (<1 Hz) rhythm and a delta ( 1-4 Hz) rhythm directly related to the presence of a space-occupying lesion which usually produces partial or total cortical deafferentation, and activity in the theta range which reflects the presence of edema in hemi- spheric space-occupying lesions.

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Frequency source analysis in patients with brain lesions

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