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1 Introduction

Alzheimer’s Disease (AD) is a progressive neurodegenerative disorder with high prevalence [1]. Its symptoms include cognitive impairment, memory loss and attention deficit, among others. The gold standard for AD diagnosis is the histological examination of brain tissue to confirm the presence of A\(\beta \) peptide plaques and tau protein fibril tangles [2]. Mild cognitive impairment (MCI) is considered a prodromal state in AD development [3]. MCI is a crucial pathological entity for an early AD diagnosis.

Spectral entropy (SpecEn) is a measure of the disorder relying on the signal power spectrum [4]. It is widely applied to many biomedical signal processing problems. However, a single scale is often not enough to reveal the complex behavior of a physiological system [4]. Besides, AD is characterized by abnormal brain physiology behavior, which can be observed in high scales [5]. For these reasons, in our study SpecEn method was calculated from a multiscaled approach.

Multiscale spectral entropy (MSSE) quantifies irregularity patterns of the underlying system at different scales, and it may be related with its structural complexity. To the best of our knowledge, this is the first time that MSSE is applied to electroencephalographic (EEG) data in order to characterize brain dynamics in AD. This technique can show new insights to categorize AD neurodegeneration evolution. In this regard, the aim of this study is to analyze spectral components from EEG signals in order to characterize abnormal neural dynamics in AD and MCI.

2 Materials and Methods

2.1 Materials

Sixty subjects took part in the study: 18 controls with a median age of 76 (interquartile range (IQR) = [73, 82]) years, 10 mild cognitive impaired (MCI) subjects with a median age of 81.5 (IQR = [78, 87]) years and 32 AD patients with a median age of 80 (IQR = [75, 87]) years. Patients were diagnosed according to the criteria of the National Institute on Aging and Alzheimer’s Association (NIA-AA).

EEG signals were recorded with a 19-channel Nihon Kohden Neurofax JE-921A EEG System, at electrodes F3, F4, F7, F8, Fp1, Fp2, T3, T4, T5, T6, C3, C4, P3, P4, O1, O2, Fz, Cz and Pz of the International 10’20 System. Sampling frequency was established to 500 Hz. Five minutes of resting state activity were acquired while the subjects stayed with their eyes closed in a noise-free environment.

Afterwards, EEG data were preprocessed according to the following steps: (i) bandpass filtering with a Hamming window between 0.4 and 98 Hz, (ii) independent component analysis (ICA), (iii) segmentation into 2 s epochs and visual rejection of epochs contaminated by artifacts.

2.2 Methods

MSSE was calculated for each artifact-free epoch. The algorithm to compute MSSE entropy is the following. Given a one-dimensional discrete time series, [\({x_1,\ldots ,x_i,\ldots ,x_N}\)], successive coarse-grained time series [\({Y^{(\tau )}}\)] are built according to the scale factor \(\tau \) [5]:

$$\begin{aligned} Y_j^{\tau } = \frac{1}{\tau }\sum _{i=(j-1)\tau +1}^{j\tau }x_{i}, \quad 1 \le j \le \frac{N}{\tau }=N^{(\tau )}, \end{aligned}$$
(1)

It is important to note that for scale \(\tau \) = 1, [\({Y^{1}}\)], the resulting coarse-grained sequence is equal to the original sequence. The maximum analyzed scale was \(\tau _{MAX}\) = 20.

Fig. 1.
figure 1

Median spectral entropy values for each scale factor and each group (controls, MCI subjects and AD patients). On the top of the figure, p-values (Kruskal-Wallis test) for each scale factor are displayed.

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Afterwards, normalized PSD function is computed for each coarse-grained time series. Normalized PSD is finally used to calculate SpecEn according to the following equation [6]:

$$\begin{aligned} SpecEn = -\frac{1}{ln(N)}\sum _{f = f1}^{f2} PSDn(f)ln[PSDn(f)] , \end{aligned}$$
(2)

where PSDn is the power spectral density of a coarse-grained sequence with frequency limits at f1 and f2. Notably, higher SpecEn values correspond to higher irregularity of the associated PSD [6].

3 Results and Discussion

MSSE was applied to the EEG data from 32 AD patients, 10 MCI subjects and 18 controls. Kruskal-Wallis test and Mann-Whitney U-test were used to determine statistical differences among the groups. Median MSSE profiles for each group, averaged for all trials and channels, are displayed in Fig. 1. Kruskal-Wallis p-values were obtained for each scale, represented on the top of Fig. 1.

This study reveals important differences in lower scales between MSSE profiles of controls and AD patients (\(p{\text {-}}values < 0.01\) at scales 1 to 6, Mann-Whitney U-test), whilst MCI subjects were indistinguishable from controls. For low scales, MSSE values were smaller in AD patients than in MCI subjects and controls. These results agree with other studies [7] that revealed a SpecEn decrease in AD patients in comparison with in controls.

Fig. 2.
figure 2

3D ROC surface (\(TC_{CON}\): true class for controls; \(TC_{MCI}\): true class for MCI subjects; \(TC_{AD}\): true class for AD patients).

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MSSE exhibited an increasing tendency for each group as factor scale augmented. At higher scales, MCI patients become distinguishable from controls (p-values < 0.01 at scales between 15 and 20, Mann-Whitney U-test). This point is crucial in early AD diagnosis, as MCI often is linked with the first steps at AD neural degeneration.

In order to study the discrimination power of MSSE, a 3D receiver operating characteristic (ROC) surface was used (Fig. 2). A 3D ROC allows to express a three-way classification according to two changing discriminating thresholds. These results were applied for a scale factor of 3, since it revealed the highest volume under the surface (VUS): 0.6. For each pairwise comparison, we obtained the following values of area under the ROC curve (AUC): 0.8 for controls vs. AD comparison, 0.6 for controls vs. MCI, and 0.8 for MCI vs. AD. Since a random two-way classifier would obtain an AUC of 0.5 and a three-way classifier would obtain a VUS of 0.167 [8], we can conclude that MSSE at scale factor 3 provides a good discrimination among groups.

In summary, MSSE analysis provides a complementary point of view to other multiscale entropy studies, such as multiscale approximate entropy and multiscale sample entropy, since it evaluates the EEG in the spectral domain. Power spectrum shape is altered and the dominant frequency shifted as the AD develops to further stages [8]. Our methodology may be useful to distinguish between healthy subjects and AD patients, even in incipient stages of the disease. However, further studies with a large number of subjects are needed to confirm these results.