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Medical studies have shown that EEG of Alzheimer's disease (AD) patients is “slower” (i.e., contains more low-frequency power) and is less complex compared to age-matched healthy subjects. The relation between those two phenomena has not yet been studied, and they are often silently assumed to be independent. In this paper, it is shown that both phenomena are strongly related. Strong correlation between slowing and loss of complexity is observed in two independent EEG datasets: (1) EEG of predementia patients (a.k.a. Mild Cognitive Impairment; MCI) and control subjects; (2) EEG of mild AD patients and control subjects. The two data sets are from different patients, different hospitals and obtained through different recording systems. The paper also investigates the potential of EEG slowing and loss of EEG complexity as indicators of AD onset. In particular, relative power and complexity measures are used as features to classify the MCI and MiAD patients versus age-matched control subjects. When combined with two synchrony measures (Granger causality and stochastic event synchrony), classification rates of 83% (MCI) and 98% (MiAD) are obtained. By including the compression ratios as features, slightly better classification rates are obtained than with relative power and synchrony measures alone.

Alzheimer's disease (AD) is the most common form of dementia; it is the sixth leading cause of death in the United States. More than 10% of Americans over age 65 suffer from AD, and it is predicted that the prevalence of AD will triple within next 50 years [

The progression of AD can be categorized into three different stages: mild, moderate, and severe AD; there is also a stage known as Mild Cognitive Impairment (MCI) or predementia, that characterizes a population of elderly subjects who are not compromised in their daily living, but have a subclinical and isolated cognitive deficit and are potentially at risk of developing Alzheimer's disease [

Diagnosing MCI and Mild Alzheimer’s disease is hard, because most symptoms are often dismissed as normal consequences of aging. To diagnose MCI or mild AD, extensive testing is required, to eliminate all possible alternative causes. Tests include psychological evaluations such as Mini-Mental State Examination (MMSE), blood tests, spinal fluid, neurological examination, and imaging techniques [

Several research groups have investigated the potential of electroencephalograms (EEGs) for diagnosing AD in recent years. Since EEG recording systems are nowadays relatively inexpensive and mobile, EEG may potentially be used in the future as a tool to screen a large population for the risk of AD, before proceeding to any expensive imaging or invasive procedures. To date, however, EEG does not have sufficiently high specificity and sensitivity to assume the role of reliable and reproducible method of screening AD.

In recent years, several studies have shown that AD has at least three major effects on EEG (see [

In this paper, we investigate the relation between slowing and reduced complexity in AD EEG. Those two phenomena are often silently assumed to be independent. However, since low-frequency signals are more regular than signals with high-frequency components, one would expect that slowing and reduced complexity in AD EEG are strongly related to each other. Nevertheless no study so far has analyzed the relation between both phenomena on a statistical basis though.

In order to investigate the slowing effect in AD EEG, we compute relative power in the standard EEG frequency bands (see Table

Overview of statistical measures: relative power, Lempel-Ziv complexity, and lossless compression ratio.

Measure | Description | References |
---|---|---|

Relative power | Power within specific EEG frequency band normalized by total power | [ |

Frequency bands: 0.5–4 Hz (delta), 4–8 Hz (theta), 8–10 Hz (alpha 1), 10–12 Hz (alpha 2), 12–30 Hz (beta) | ||

Lempel-Ziv complexity | Number of different patterns present in an EEG signal (complexity measure) | [ |

Lossless compression ratio | Reduction of the size of EEG data after lossless compression (regularity measure) | [ |

Compression algorithms considered here: 1D SPIHT, 2D SPIHT, and 2D SPIHT followed by arithmetic coding |

We consider two EEG datasets: (1) EEG of predementia patients (a.k.a. Mild Cognitive Impairment; MCI) and control subjects; (2) EEG of mild AD patients and control subjects. The two datasets are from different patients, different hospitals and obtained through different recording systems.

We will show that the theta band (

The paper is structured as follows. In Section

Readers who are not interested in the technical and mathematical details of our data analysis may skip Sections

The spectrum of EEG is helpful in describing and understanding brain activity. The EEG spectrum is commonly divided in specific frequency bands: 0.5–4 Hz (delta), 4–8 Hz (theta), 8–10 Hz (alpha 1), 10–12 Hz (alpha 2), 12–30 Hz (beta), and 30–100 Hz (gamma) [

The EEG spectrum can be computed by means of the Discrete Fourier Transform (DFT) of the EEG [

A variety of complexity measures have been used to quantify EEG complexity, stemming from several areas ranging from statistical physics to information theory. We refer to [

As mentioned earlier, we quantify EEG complexity by a standard measure, that is, Lempel-Ziv complexity. In addition, we use lossless compression ratios as regularity measures. In the following, we describe Lempel-Ziv complexity, and next we elaborate on lossless compression and its use as measure for regularity.

The Lempel-Ziv complexity measure (LZ complexity) computes the number of different patterns present in a sequence of symbols [

To compute LZ complexity, the time series is first reduced to a symbol list. For the sake of simplicity, we convert the EEG signals into binary sequences

In this section, we briefly explain the lossless compression algorithms applied in this study (see Figure

Biomedical signals such as EEG often have a

First the EEG signal

A wavelet transform decomposes a given signal into different frequency bands; it allows to represent the signal in multiple resolutions (coarse to fine) [

Wavelet transform realization via lifting scheme (a) Forward transformation. (b) Inverse transformation. The boxes labeled by

Lossless EEG compression algorithms apply wavelet transforms followed by Set Partitioning in Hierarchical Trees (SPIHT).

Algorithm A: EEG compression using 1D SPIHT

Algorithm B: EEG compression using 2D SPIHT

Algorithm C: EEG compression using 2D SPIHT (at optimal rate

In a lifting scheme, the pair of lifting steps, that is, prediction

The lifting wavelet transform provides a sparse, multiresolution representation, that is well suited for effective compression (e.g., by means of SPIHT, to be explained in next section);

As the last step in the process, the wavelet-transformed signals are compressed. We use a widely known wavelet-based compression scheme, that is,

Wavelet decomposition of the 2D matrix and associated tree-based set originating from the low-frequency band. The root node (black) branches towards horizontal, vertical, and diagonal higher-frequency bands (H, V, D).

The integer wavelet transform, in conjunction with SPIHT, yields a quality and resolution scalable bitstream: the quality and resolution of the signal improve as bitstream progresses. This is a very desirable property for real-time applications. Moreover, the output bitstream is embedded: the bitstream can be truncated at any point to approximately reconstruct the signal. When the bitstream is fully decoded, we obtain a lossless representation.

Though this coding scheme is specifically developed for images, it can be applied to all data sources with decaying spectrum [

The three compression algorithms are depicted in Figure

The first EEG data set has been analyzed in previous studies concerning early diagnosis of AD [

Ag/AgCl electrodes (disks of diameter 8 mm) were placed on 21 sites according to 10–20 international system, with the reference electrode on the right earlobe. EEG was recorded with Biotop 6R12 (NEC San-ei, Tokyo, Japan) at a sampling rate of 200 Hz, with analog bandpass filtering in the frequency range 0.5–250 Hz and online digital bandpass filtering between 4 and 30 Hz, using a third-order Butterworth filter. We used a common reference for the data analysis (right earlobe) and did not consider other reference schemes (e.g., average or bipolar references).

The subjects comprise two study groups. The first consists of 25 patients who had complained of memory problems. These subjects were diagnosed as suffering from mild cognitive impairment (MCI) when the EEG recordings were carried out. Later on, they all developed mild AD, which was verified through autopsy. The criteria for inclusion into the MCI group were a mini-mental state exam (MMSE) score = 24, though the average score in the MCI group was 26 (SD of 1.8). The other group is a control set consisting of 56 age-matched, healthy subjects who had no memory or other cognitive impairments. The average MMSE of this control group is 28.5 (SD of 1.6). The ages of the two groups are 71.9 ± 10.2 and 71.7 ± 8.3, respectively. Finally, it should be noted that the MMSE scores of the MCI subjects studied here are quite high compared to a number of other studies. For example, in [

The second EEG data set also has been analyzed in previous studies [

In both datasets, all recording sessions were conducted with the subjects in an awake but resting state with eyes closed, and the length of the EEG recording was about 5 minutes, for each subject. The EEG technicians prevented the subjects from falling asleep (vigilance control). After recording, the EEG data has been carefully inspected. Indeed, EEG recordings are prone to a variety of artifacts, for example, due to electronic smog, head movements, and muscular activity. For each patient, an EEG expert selected one segment of 20 s artifact-free EEG by visual inspection, blinded from the results of the present study. Only those subjects were retained in the analysis whose EEG recordings contained at least 20 s of artifact-free data. Based on this requirement, the number of subjects of EEG Dataset 1 was further reduced to 22 MCI patients and 38 control subjects; in EEG Dataset 2 no such reduction was required. From each subject in the two datasets, one artifact-free EEG segment of 20 s was analyzed.

We compute relative power, compression ratios, and LZ complexity for the EEG signals of all subjects. More specifically, we calculate those measures for all individual EEG channels, and then the measures are averaged over all channels; this results in average measures for all subjects. Our results are summarized in Tables

Mean and standard deviation values of compression ratio, LZ complexity, relative power, and synchrony measures. Sensitivity of the measures in discriminating between MCI and mild AD is given in last column. Uncorrected ^{†} Indicates

MCI versus control | |||

Measure | Control | MCI | |

1D SPIHT CR | .3077 | ||

2D SPIHT CR | .3778 | ||

2D SPIHT+AC | .4477 | ||

LZ complexity | .0830 | ||

^{**†} | |||

ffDTF | ^{**†} | ||

delta | .2934 | ||

theta | ^{**†} | ||

alpha-1 | .1698 | ||

alpha-2 | .9939 | ||

beta | |||

Mild AD versus control | |||

Measure | Control | Mild AD | |

1D SPIHT CR | ^{**†} | ||

2D SPIHT CR | ^{**†} | ||

2D SPIHT+AC | ^{**†} | ||

LZ complexity | ^{**†} | ||

^{**†} | |||

ffDTF | ^{**†} | ||

delta | ^{**†} | ||

theta | ^{**†} | ||

alpha-1 | ^{**†} | ||

alpha-2 | ^{**†} | ||

beta | ^{**†} |

Classification rates for discriminant analysis (DA) of the lossless compression ratios, LZ complexity and relative power in theta band.

MCI versus control | |||

Measure | Linear DA | Quadratic DA | SVM |

theta | 76.67% | 76.67% | 76.67% |

ffDTF | 63.33% | 71.67% | 78.33% |

75% | 75% | 76.67% | |

ffDTF + | 76.67% | 80.00% | |

Theta + | 78.33% | 80.00% | |

Mild AD versus control | |||

Measure | Linear DA | Quadratic DA | SVM |

1D SPIHT CR | 80.49% | 80.49% | 80.49% |

2D SPIHT CR | 82.93% | 82.93% | |

2D SPIHT+AC CR | 75.61% | 80.49% | 82.93% |

LZ complexity | 68.29% | 68.29% | 68.29% |

theta | |||

ffDTF | 58.54% | 78.05% | 82.93% |

56.10% | 63.41% | 63.41% | |

ffDTF + | 65.85% | 70.73% | 78.05% |

theta + ffDTF | |||

theta + ffDTF + | |||

1D SPIHT CR |

In Table

Theta relative power is significantly larger in MCI patients compared to reference subjects, whereas beta power is significantly smaller. In the MiAD patients the perturbations on EEG relative power are stronger: delta and theta relative power is significantly larger than in the reference subjects, whereas alpha and beta power is significantly smaller. In other words, slowing occurs in both the MCI and MiAD patients, which is in agreement with earlier studies (see [

Relative power distribution in various frequency bands for all the datasets. (a) Control group. (b) Mild cognitive impaired subjects.

Relative power distribution in various frequency bands for all the datasets. (a) Control group. (b) Mild Alzheimer’s disease subjects.

Correlation between the lossless compression ratios, LZ complexity, relative power in different bands, Granger causality (ffDTF), and stochastic event synchrony (

MCI (Dataset 1)

Mild AD (Dataset 2)

Pearson correlation test between the lossless compression ratios, LZ complexity, relative power in different bands, Granger causality (ffDTF), and stochastic event synchrony (

MCI (Dataset 1)

Mild AD (Dataset 2)

No significant effect on the complexity and regularity measures can be observed in MCI patients. On the other hand, the regularity measures and complexity measures are significantly larger and smaller, respectively, for MiAD patients than for control subject; in other words, the EEG signals of MiAD patients are significantly less complex than in healthy subjects. This observation is in agreement with several earlier studies (see [

We also try to classify patients versus control subjects by means of the most discriminative EEG measures (

In order to gain more insight in the relationship between the different measures, we calculate the correlation between those measures (see Figure

As expected, the compression measures are significantly mutually correlated as all the schemes are based on the same principle; they are also significantly anticorrelated with LZ complexity in the MiAD dataset (Dataset 2).

Interestingly, the compression ratios are significantly correlated with low-frequency relative power (delta and theta; MiAD) and anticorrelated with high-frequency relative power (beta; both datasets). Likewise LZ complexity is strongly anticorrelated with low-frequency relative power (delta and theta; both datasets) and correlated with high-frequency relative power (beta; MiAD). Taken together, this observation strongly suggests that slowing and loss of complexity in AD EEG are

Perhaps surprisingly, Granger causality (ffDTF) [

Stochastic event synchrony (

In this study, we investigated the use of relative power, LZ complexity, and lossless compression ratio as EEG markers for MCI and mild AD. Lossless compression ratio is shown to be discriminative for mild AD, whereas it is not discriminative for MCI. On the other hand, theta band relative power was observed to be statistically larger in MCI and mild AD patients than in control subjects. Maximum discrimination is obtained by combining the compression ratio, relative power, and synchrony measures (Granger causality and/or stochastic event synchrony).

We would like to reiterate, however, that the two datasets analyzed (MCI and MiAD) were obtained through different recording systems and at different hospitals; a direct comparison of the results obtained from MCI with those from mild AD is therefore difficult. On the other hand, since the datasets are independent, our observations are probably not dependent on particularities of the recording systems and/or procedures at the hospitals.

Interestingly, compression ratios were found to be significantly correlated to delta and theta band relative power, showing their strong correlation with relative power at low frequencies; also strong anti-correlation between compression ratios and beta relative power was observed. Therefore, slowing and loss of complexity in the EEG of MCI and MiAD patients may be strongly related phenomena.

More generally, this study also underlines the importance of analyzing MCI and AD EEG by means of a variety of statistical measures (relative power, complexity/regularity measures, synchrony measures), in order to detect potential correlations between various observed phenomena associated with MCI and AD.