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Nonlinear Dynamic Analysis of the EEG in Patients with Alzheimer’s Disease and Vascular Dementia

Jeong, Jaeseung*; Chae, Jeong–Ho; Kim, Soo Yong; Han, Seol–Heui§

Journal of Clinical Neurophysiology: January 2001 - Volume 18 - Issue 1 - p 58-67
Original Contributions

Summary To assess nonlinear EEG activity in patients with Alzheimer’s disease (AD) and vascular dementia (VaD), the authors estimated the correlation dimension (D2) and the first positive Lyapunov exponent (L1) of the EEGs in both patients and age-matched healthy control subjects. EEGs were recorded in 15 electrodes from 12 AD patients, 12 VaD patients, and 14 healthy subjects. The AD patients had significantly lower D2 values than the normal control subjects, (P < H > 0.05), except at the F7 and the O1 electrodes, and the VaD patients, except at the C3 and the C4 electrodes. The VaD patients had relatively increased values of D2 and L1 compared with the AD patients, and rather higher values of D2 than the normal control subjects at the F7, F4, F8, Fp2, O1, and O2 electrodes. The L1 values of the EEGs were also lower for the AD patients than for the normal control subjects, except in the O1 and the O2 channels, and for the VaD patients at all electrodes. The L1 values were higher for the VaD patients than for the normal control subjects (F3, F4, F8, O1, and O2). In addition, the authors detected that the VaD patients had an uneven distribution of D2 values over the regions than the AD patients and the normal control subjects, although the statistics do not confirm this. By contrast, AD patients had uniformly lower D2 values in most regions, indicating that AD patients have less complex temporal characteristics of the EEG in entire regions. These nonlinear analyses of the EEG may be helpful in understanding the nonlinear EEG activity in AD and VaD.

*Department of Diagnostic Radiology, School of Medicine, Yale University, New Haven, Connecticut, U.S.A.; Department of Psychiatry, College of Medicine, The Catholic University of Korea, Seoul, Korea; Department of Physics, Korea Advanced Institute of Science and Technology, Taejon, Korea; and §Department of Neurology, Chungbuk National University Hospital, Korea

Address correspondence and reprint requests to Dr. Jaeseung Jeong, P.O. Box 208042, 333 Cedar Street, Department of Diagnostic Radiology, School of Medicine, Yale University, New Haven, CT 06520.

Two of the most common kinds of dementia in the elderly are Alzheimer’s disease (AD) and vascular dementia (VaD). Although AD is a leading cause of dementia in the Western world, VaD prevails in Asian countries (Jorm, 1991; Kase, 1991). It is important to diagnose AD and VaD accurately, because this enables the clinician to provide demented patients and their families with a more reliable prediction of the disease’s course, and it facilitates planning for necessary social resources. However, the differential diagnosis is complicated by the fact that a co-occurrence of AD and stroke is common. There have been substantial efforts to differentiate AD from VaD using various diagnostic modalities, including neuropsychological tests (Bowler et al., 1997; Sultzer et al., 1993; Swanwick et al., 1996), neuroimaging techniques (Mielke et al., 1994; O’Brien et al., 1997), quantitative EEG (Dunkin et al., 1994; Signorino et al., 1995; Szelies et al., 1994), and transcranial Doppler sonography (Ries et al., 1993).

Quantitative EEG analyses have been used in attempts at differential diagnosis in dementia studies. A higher incidence of focal abnormalities in VaD has been observed repeatedly (Erkinjuntti et al., 1988; Soininen et al., 1982). Progressive deterioration of the background rhythms and sequential changes in serial studies are usually helpful in confirming the existence of a progressive degenerative dementia (Markand, 1984). Spectral analysis of the EEG has shown an increased power of the lower frequency bands and a decrease of high frequencies in AD patients (Brenner et al., 1988; Coben et al., 1985, 1990; Hooijer et al., 1990; Penttilä et al. 1985; Schreiter–Gasser et al., 1993; Soininen et al., 1991). A positive linear relationship between slowing of the average EEG frequency and the degree of cognitive impairment has been reported in AD patients (Coben et al., 1985). Signorino et al. (1995, 1996a, b) and others (Pucci et al., 1998) showed that EEG spectral parameters can offer enough data to discriminate between the subtypes of AD and VaD. EEG coherence studies demonstrated that long-distance coherence seems to be more affected than local coherence in AD patients, whereas the opposite occurs in VaD patients (Comi et al., 1998; Leuchter et al., 1992). In AD patients, local changes of coherence of the α band have been reported to affect selectively the left temporoparietal–occipital areas (Leuchter et al., 1992; Locatelli et al., 1998) or the anterior areas (Besthorn et al., 1994).

Recent progress in the theory of nonlinear dynamics has provided new methods for the study of time-series data from human brain activities. Babloyantz et al. (1985) first reported that EEG data from the human brain had chaotic attractors for sleep stages II and IV. Much research using nonlinear methods revealed that the EEG is generated by a deterministic neural process (Babloyantz, 1988; Rapp et al., 1985; Rochke and Basar, 1988; Soong and Stuart, 1989). According to these reports, the EEG has a finite correlation dimension (D2) and a positive Lyapunov exponent (L1). Furthermore, distinct states of brain activity produce different chaotic properties quantified by nonlinear invariant measures such as D2 and L1 (Babloyantz, 1988; Babloyantz and Destexhe, 1987; Fell et al., 1993; Pijn et al., 1991; Rochke and Aldenhoff, 1991; Wackermann et al., 1993).

By contrast, there is some evidence that an EEG is not a chaotic signal of low dimension (Osborne and Provenzale, 1989; Palus, 1996; Pritchard et al., 1995; Rapp et al., 1993; Theiler and Rapp, 1996; Theiler et al., 1992). Research has shown that the normal resting human EEG is nonlinear but does not represent low-dimensional chaos, and it may be generated from 1/f-like linear stochastic systems. Our previous study also failed to detect any determinism in the EEG with the smoothness method (Jeong et al., 1999).

Although no compelling evidence for a deterministic nature of the EEG has been adduced, nonlinear dynamic analyses of the EEG to estimate D2 and L1 have proved to be useful in differentiating normal and pathologic brain states (Rapp, 1993). Many studies using nonlinear methods presented possible medications (Lehnertz and Elger, 1998) for nonlinear analysis and the possibility that nonlinear analysis of the EEG may be a useful tool in differentiating physiologic brain states (Babloyantz and Destexhe, 1986, 1987; Fell et al., 1995; Frank et al., 1990; Jeong et al., 1998a, b; Kim et al., 2000; Lehnertz and Elger, 1998; Pritchard et al., 1994).

There are several studies of the EEG in AD patients using nonlinear methods. D2 and L1 from EEG data were estimated (Besthorn et al., 1995; Jelles et al., 1999; Jeong et al., 1998a; Pritchard et al., 1991, 1993, 1994; Stam et al., 1995, 1996). Their results indicated that AD patients had significantly lower values in D2 and L1 than age-matched normal subjects, indicating that the dynamic processes underlying the EEG recording are less complex for AD patients than for normal subjects.

The aim of the current study was to examine nonlinear EEG activity in AD and VaD, and to compare the nonlinear properties of the EEGs in AD and VaD. D2 and L1 were estimated from the EEGs with the optimal embedding dimension. We regarded these nonlinear parameters as operationally defined measures of complexity. They may not be appropriate measures for differentiating between periodic, chaotic, or stochastic dynamics in the formal sense. Because this study focuses on comparing nonlinear EEG activity in AD and VaD, we do not use the surrogate-data method to detect nonlinearity and determinism of the EEG.

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One-dimensional EEG data were transformed into multidimensional phase space. The concept of phase space is central to the analysis of nonlinear dynamics. In a hypothetical system governed by n variables, the phase space is n-dimensional. Each state of the system corresponds to a point in phase space with n coordinates that are the values assumed by the governing variables for this specific state. If the system is observed for a period of time, the sequence of points in phase space forms a trajectory. This trajectory fills a subspace of the phase space, called the system’s attractor.

Reconstruction of the attractor in phase space was carried out through the technique of delay coordinates. To unfold the projection back to a multivariate state space that is a representation of the original system, we use the delay coordinates y(t) = [xj(t), xj(t + T), . . . , xj (t + [d − 1]T)] from a single time series xj and perform an embedding procedure, where y(t) is one point of the trajectory in the phase space at time t, x(t + iT) are the coordinates in the phase space corresponding to the time-delayed values of the time series, T is the time delay between the points of the time series considered, and d is the embedding dimension (Eckmann and Ruelle, 1985; Takens, 1981).

The choice of an appropriate time delay T and embedding dimension d are important to the success of reconstruction with finite data. For the time delay T, we used the first local minimum of the average mutual information between the set of measurements v (t) and v (t +T) in the current study. Mutual information measures the general dependence of two variables (Fraser and Swinney, 1986).

We used the minimum (optimal) embedding dimension in the reconstruction procedure (Kennel et al., 1992). The algorithm is based on the idea that in the passage from dimension d to dimension d +1, one can differentiate between points on the orbit that are true neighbors and those that are false. A false neighbor is a point in the dataset that is a neighbor solely because we are viewing the orbit (the attractor) in too small an embedding space (d < dmin). When we have achieved a large enough embedding space (d ≥ dmin), all neighbors of every orbit point in the multivariate phase space will be true neighbors.

We defined the embedding rate as the ratio of true neighbors to neighbors in the embedding dimension. Figure 1 shows a typical example of the embedding rate as a function of the embedding dimension for 16,384 EEG data points in a normal control subject. The proper minimum embedding dimension was selected as 11 in this case. The detailed algorithm was reported in our previous paper (Jeong et al., 1998a). We also showed the increase in the efficiency and accuracy of our method relative to the old one.

FIG. 1

FIG. 1

One of the important mathematical quantities characterizing an attractor is its correlation dimension (D2), which is a metric property of the attractor that estimates the degree of freedom. It determines the number of independent variables that are necessary to describe the dynamics of the original system. For instance, in the case of steady-state behavior, D2 of the attractor is zero and D2 of the periodic attractor is one. In chaotic states, D2 usually takes on noninteger values. The larger the D2 value of the attractor, the more complicated the behavior of the nonlinear system. D2 is thus a measure of the complexity of the process being investigated, and it characterizes the distribution of points in phase space (Hornero et al., 1999).

We evaluate the D2 values of the attractors from the EEG using the Grassberger–Procaccia algorithm (Grassberger and Procaccia, 1983). With this algorithm, D2 is based on determining the relative number of pairs of points in the phase-space set that are separated by a distance less than r. It is computed from the followingMATHwhere the correlation integral C(N, r) is defined by theMATHwhere x i and x j are the points of the trajectory in the phase space, N is the number of data points in the phase space, the distance r is a radius around each reference point x I, and θ is the Heaviside function, defined as 0 if x < 0, and 1 if x ≥ 0. For small r, a scaling property is exhibited: C(N, r) ∝ rD2. For a self-similar (fractal) attractor, the local scaling exponent is constant, and the region is called a scaling region. If this plateau is convincing enough, the scaling exponent can be used as an estimate of D2. One plots C(N, r) versus r on a log–log scale, and D2 is given by the slope of log C (r) versus the log r curve over a selected range of r. The slope of the correlation integral curve in the scaling region is estimated by a least-squares fitting method.

A slightly modified version of the Grassberger–Procaccia algorithm was used to prevent overcontributing early terms from the start in the correlation integral and to compensate for the oscillation of the scaling region caused by the lacunarity of the attractor or finite sample oscillations caused by the limited amount of data (Jeong et al., 1998a). Figure 2 shows that our method yields a larger scaling region of the correlation integral than the conventional method.

FIG. 2

FIG. 2

As another measure of complexity, Lyapunov exponents estimate the mean exponential divergence or convergence of nearby trajectories of the attractor in the phase space. This reflects the sensitive dependence on the initial conditions (Fell et al., 1993). A system possessing at least one positive Lyapunov exponent value is chaotic. Lyapunov exponents are usually ordered in a descending fashion from L1 (the highest value) to Ln (the lowest value), where n is equal to the dimensionality of the phase space. Thus, positive L1 of the time series means that it is chaotic or complex. The larger the positive L1 of the attractor, the more complicated the behavior of the nonlinear system.

We calculated L1 by applying a modified version of the Wolf algorithm (Wolf et al., 1985) and by following a proposal by Frank et al. (1990). Essentially, the Wolf algorithm computes the initial vector distance di of two nearby points and evolves its length at a certain propagation time. If the vector length df between the two points becomes too large, a new reference point is chosen with properties that minimize the replacement length and the orientation change. Now, the two points are evolved again, and so on. After m propagation steps, the first positive Lyapunov exponent results from the sum over the of the ratios of the vector distances divided by the total evolving time:MATHwhere dt is the sampling interval, EVOLV is the evolving time, and di and df are the initial and the final separations between the points in the fiducial trajectory and in the nearest-neighbor trajectory separated in time by i th EVOLV step respectively (Principe and Lo, 1991; Wolf et al., 1985).

By using the weight function proposed by Frank et al. (1990), we improved the L1 estimate by widening the search to allow replacements to be well-aligned points lying farther apart but still within the region of linear dynamics. This more detailed algorithm is also reported in a previous paper (Jeong et al., 1998a).

A consecutive series of patients with AD and VaD who attended the Department of Neurology, Chungbuk National University Hospital, Korea, were screened for inclusion in this study. All patients had undergone a thorough clinical evaluation that included clinical history, physical and neurologic examinations, routine laboratory tests, electrocardiogram, EEG, and brain MRI.

Twelve AD patients (four men and eight women; mean age, 68.7 ± 5.1 years) met the criteria for AD as mandated in the Diagnostic and Statistical Manual of Mental Disorders, 4th edition (American Psychiatric Association, 1994), and probable AD established by the National Institute of Neurologic Disorders and Stroke Association and Alzheimer’s Disease and Related Disorders Association (McKhann et al., 1984). The probable AD patients had a Mini-Mental State Examination–Korean version (MMSE-K) score (Kwon and Park, 1989) of less than 12 points (mean MMSE-K score, 9.2 ± 3.5 points), indicating a severe degree of dementia. The average age at onset of dementia was approximately 64.9 ± 3.1 years, and the average length of illness was approximately 46.0 ± 7.3 months.

Twelve VaD patients (four men and eight women; mean age, 67.9 ± 4.9 years) met the National Institute of Neurologic Disorders and Stroke Association–Internationale pour la Recherche et l’Enseignement en Neurosciences criteria (Roman et al., 1993). The patients with VaD also had MMSE-K scores less than 12 points (mean MMSE-K score, 9.9 ± 4.2 points). Additionally, they either had experienced the onset of cognitive impairment after a clinical stroke or had shown clear focal neurologic signs on examination. They had a Hachinski ischemic score of more than 7 points. MRI revealed large-vessel stroke, multiple subcortical lacunar infarcts, and/or extensive white matter lesions in each VaD patient. Although it is impossible to be certain that no patients had coexisting AD and VaD, patients with evidence of both disorders were excluded.

Fourteen age-matched, healthy, elderly control subjects (five men and nine women; mean age, 66.9 ± 5.0 years) were recruited from a senior community club in Taejon, South Korea. The control subjects had a mean score of 27.1 ± 0.7 points on the MMSE-K.

All subjects were excluded from each group if there was a history of psychotic disorder unrelated to dementia, a history of head trauma with loss of consciousness, a psychoactive substance use disorder, a systemic illness, or other neurologic illness that could account for the cognitive impairment. The local ethics committee approved the study. All subjects and all caregivers of the demented patients gave informed consent for participation in the current study.

EEGs were recorded from the 15 scalp loci of the International 10–20 System. The EEG reading from the T5 channel was not recorded because of a hardware problem. With the subjects in a relaxed state with their eyes closed, 32,768 seconds of data (16,384 data points) were recorded with a sampling frequency of 500 Hz, digitized by a 12-bit analog–digital converter in an IBM personal computer. Recordings were made under the eyes-closed condition to obtain as many stationary EEG data as possible. Potentials from 15 electrodes (F7, T3, Fp1, F3, C3, P3, O1, F8, T4, T6, Fp2, F4, C4, P4, and O2) against “linked earlobes” were amplified on a Nihon Kohden EEG-4421K using a time constant of 0.1 second. All data were filtered digitally to remove residual electromyographic activity at 1 to 35 Hz. Each EEG record was judged by inspection to be free from electro-oculographic and movement artifacts, and to contain minimal electromyographic activity.

All analyses were carried out using the Statistical Package for the Social Sciences (SPSS version 7.0; SPSS, Inc., Cary, NC USA) for Windows. One-way of analyses of variance (SPSS General Linear Models module) were used to test group-specific effect. If significant effects between groups were found, the effects were analyzed additionally using Duncan’s post hoc test. The results of group data are expressed as mean ± standard deviation. A two-tailed probability of less than 0.05 was considered to be significant.

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During the reconstruction procedure, time delays of 34 to 50 msec and embedding dimensions of 11 to 18 were used for the AD patients, and time delays of 26 to 46 msec and embedding dimensions of 13 to 19 were used for the VaD patients. The normal control subjects had time delays of 28 to 34 msec and embedding dimensions of 11 to 19.

The average D2 values and standard deviations for the AD patients, VaD patients, and normal control subjects for the 15 electrodes identified earlier are summarized in Table 1, which shows that each group had distinctly different D2 values in all electrodes. The AD patients had significantly lower D2 values than the normal subjects except at the F7 and O1 electrodes, and lower than the VaD patients except at the C3 and C4 electrodes. The differences between the D2 values in the F4, F8, Fp1, Fp2, O1, and O2 channels were approximately 1.5 to 2.2 U. The VaD patients had significantly higher D2 values than the normal control subjects in six channels (F7, F4, F8, Fp2, O1, and O2). In addition, the VaD patients had a less uniform distribution of D2 values over the regions than the AD patients and the normal control subjects, although statistics do not confirm this (Fig. 3).

Table 1

Table 1

FIG. 3

FIG. 3

Another nonlinear measure, L1, was calculated for all subjects at all electrodes. The evolving time was selected using the 1/e spectral frequency, and was approximately 180 to 240 msec. The calculation of L1 depended on the time over which the trajectory was evaluated. After 200 propagation steps, the values converged in an interval of ±0.92% around the final value of L1.

The average L1 values and standard deviations for all subjects at all electrodes are summarized in Table 2. It shows that the average L1 values were higher for the normal control subjects than for the AD patients (F7, T3, Fp1, P3, F8, T4, T6, Fp2, C4, P4, P < 0.01; F3, C3, F4, P < 0.01), just as the D2s were. The L1s of the AD patients in channels O1 and O2 were not significantly different from those of the normal control subjects. The differences between the values of L1 in the F7, T3, Fp1, P3, F8, T4, T6, Fp2, C4, and P4 channels were very significant—approximately 1.0 to 1.8 U. The results for L1 were consistent with those for D2, except in the F7 and O2 channels. AD patients had significantly lower L1 values than VaD patients (P < 0.001) in all channels. The L1 values for the VaD patients were higher than for the normal control subjects (F3, F4, F8, O1, O2, P < 0.01).

Table 2

Table 2

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Our results indicate that AD patients have significantly lower D2 and L1 values than VaD patients and the age-matched healthy control subjects over all regions except at a few electrodes. By contrast, VaD patients have relatively higher D2 and L1 values than AD patients. VaD patients have an uneven distribution of D2 values over the channels than other groups, whereas AD patients have uniformly lower values of D2 and L1, indicating that EEGs in AD patients are less complex than those in other groups.

Our findings of a decreased dimensional complexity and flexibility of EEGs in AD patients supports a number of previous findings (Besthorn et al., 1995; Jelles et al., 1999; Pritchard et al., 1991, 1993, 1994; Pucci et al., 1998; Stam et al., 1995; Woyshville and Calabrese, 1994; Woyshville et al., 1987; Yagyu et al., 1997). If dynamic properties of the EEG reflect differential information processing in the brain, the states of information processing could be estimated by nonlinear measures (Rochke, 1992). Lutzenberger et al. (1992) demonstrated that human intellectual ability may be reflected in a higher complexity of the electrical dynamics of the brain. Accordingly, we may interpret our results to mean that a decrease of D2 and L1 in AD may be associated with deficient information processing in the brain injured by AD.

The finding that VaD patients have relatively higher values of D2 and L1 than AD patients and even normal control subjects, and have an uneven distribution of D2 values, may be in accord with previous findings (Johannesson et al., 1979; Saletu et al., 1991). Saletu et al. (1991) demonstrated the uneven distribution of EEG abnormality in multi-infarct dementia by multichannel EEG mapping. In mild cerebrovascular dementia, the EEG was often normal or slightly abnormal (Johannesson et al., 1979).

An uneven distribution of D2 values in VaD compared with those in AD may be the result of uneven neuronal pathology in VaD. VaD is a heterogeneous syndrome with various subtypes, including multi-infarct dementia, strategic single infarct dementia, small-vessel disease with dementia, hypoperfusion, and hemorrhagic dementia (Roman et al., 1993). VaD may exhibit cortical and/or subcortical involvement (Weiner et al., 1991). Several lines of studies using topographic EEG analysis showed the VaD group had more asymmetric findings than the AD group (Ding, 1990). Diffuse abnormality of EEG was found to increase in AD (Erkinjuntti et al., 1988). Conversely, clinical studies have linked signs and symptoms of VaD to patchy and irregular brain damage. Radiologic studies showed that VaD patients had central brain atrophy more often than AD patients or normal control subjects, indicating multiple small infarcts in the thalamus and other basal brain structures (Cumming and Beson, 1992). Fenton (1986) showed that VaD patients had the lowest coherence between the different cortical areas, indicating asymmetry of functioning, whereas patients with non-VaD had the greatest EEG coherence between the centroparietal and temporal regions within each hemisphere. The current study suggested that the distributions of lesions were more scattered in VaD than in AD. Therefore, an uneven distribution in the nonlinear measures in VaD patients may, to some extent, result from underlying etiologic heterogeneity. FIGURE

FIG. 4

FIG. 4

Similar disturbances in electrical activity may be caused by a variety of disease processes involving either damage to nerve cells or potentially reversible disturbances in cell metabolism resulting from metabolic insults. Hence, electrical patterns associated with brain dysfunction cannot be used to predict the exact nature of the underlying disease process (Fenton, 1986). Our results from the nonlinear analysis of the EEG suggest that the estimation of nonlinear measures like D2 and L1 may be helpful in diagnosing AD and VaD more accurately. Pritchard et al. (1994) found that the addition of nonlinear EEG measures improved the classification accuracy of the subjects as either AD patients or control subjects.

Several limitations of these findings merit consideration. The sample size was small, and the severity of cognitive dysfunction was not strictly controlled. The results obtained seem to depend on the clinical degree of dementia studied. The stage of dementia must affect the ability of the EEG to distinguish one type of dementia from the other or from control subjects. The relationship of EEG alterations to the severity of dementia raises an issue concerning the strict psychometric or neuropsychological evaluation in the nonlinear analysis of EEG. Additionally, we cannot explain why the VaD patients had higher D2 and L1 values in some channels than normal subjects. Our results, however, encourage further investigation of the complexity of electrocortical responses in brains injured by dementia, although the current study is quite preliminary.

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Alzheimer’s disease; Vascular dementia; EEG; Correlation dimension; Lyapunov exponent.

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