Connectivity of EEG synchronization networks increases for Parkinson's disease patients with freezing of gait

Abstract

Freezing of gait (FoG), a paroxysmal gait disturbance commonly experienced by patients with Parkinson's disease (PD), is characterized by sudden episodes of inability to generate effective forward stepping. Recent studies have shown an increase in beta frequency of local-field potentials in the basal-ganglia during FoG, however, comprehensive research on the synchronization between different brain locations and frequency bands in PD patients is scarce. Here, by developing tools based on network science and non-linear dynamics, we analyze synchronization networks of electroencephalography (EEG) brain waves of three PD patient groups with different FoG severity. We find higher EEG amplitude synchronization (stronger network links) between different brain locations as PD and FoG severity increase. These results are consistent across frequency bands (theta, alpha, beta, gamma) and independent of the specific motor task (walking, still standing, hand tapping) suggesting that an increase in severity of PD and FoG is associated with stronger EEG networks over a broad range of brain frequencies. This observation of a direct relationship of PD/FoG severity with overall EEG synchronization together with our proposed EEG synchronization network approach may be used for evaluating FoG propensity and help to gain further insight into PD and the pathophysiology leading to FoG.

Fig. 1. Construction of brain wave synchronization matrices based on EEG electrode position.

a Data were recorded by a 32-channel EEG montage according to the international 10−20 standard system (the four midline electrodes Fz, Cz, Pz, Oz, and the two reference electrodes M1 and M2 were excluded from the analysis). Electrodes were grouped according to different brain lobes (as indicated by the dashed lines): frontal motor left—FML (including electrodes FP1, F7, F3, FC5, and C3); frontal motor right—FMR (FP2, F8, F4, FC6, and C4); temporal left—TL (FT9, T3, TP9, and T5); temporal right—TR (FT10, T4, TP10, and T6); parietal occipital left—POL (CP5, P3, O1, and PO9); and parietal occipital right—POR (CP6, P4, O2, and PO10). b Matrix of the averaged synchronization indexes ${⟨R^{j_1,j_2}⟩}_{\nu }$ for all combinations of α-amplitude signals j₁ and j₂ from all 26 electrodes of a single PD+FoG⁺ subject. Averaging was done over all normal walking segments ν. Note that we exclude electrodes with high impedance or high standard deviations from our analysis (e.g., the two dark blue lines in panel (b) corresponding to electrode CP6). c The matrix elements of panel (b) are averaged according to the definition of brain lobes shown in (a) to obtain a brain wave synchronization matrix. Matrix elements that correspond to the same electrode interaction (i.e., the diagonal elements in (b)) have been excluded from the average.

Fig. 2. Brain lobe interaction matrix calculated from synchronization and fraction matrix.

Element-wise multiplication of a synchronization matrix R and b fraction matrix χ yields c the total brain lobe interaction matrix R × χ that is used as the adjacency matrix of the underlying physiological network of brain lobe interactions (Fig. 3). In this figure, all matrices are derived for α−α interactions during normal walking epochs. Group average matrices for EC, PD-FoG, PD+FoG⁻ and PD+FoG⁺ (from top to bottom) are shown. Note, there is a dramatic increase in brain lobe interaction with the severity of Parkinson’s disease which is represented by (i) higher levels of α−α synchronization, as well as (ii) higher fractions of significant interactions.

Fig. 3. Physiological networks of brain lobe interactions for different EEG frequency bands.

The brain lobe interaction matrices R × χ are used to construct physiological networks for each frequency band and for each group during normal walking (cp. Fig. 2c for α−α interactions for all four groups). Network nodes correspond to the six brain lobes and the color-coding of the nodes is according to the intra-lobe interaction values obtained from the diagonal matrix elements of the lobe-averaged R × χ matrices. Weighted network links reflect inter-lobe interaction as given by the value of the non-diagonal matrix elements, and darker gray color and thicker lines represent stronger interactions. Subjects with Parkinson’s disease (PD) generally exhibit higher levels of brain lobe interactions, and the highest values are observed for PD+FoG⁺ consistently across all EEG frequency bands.

Fig. 4. Rank distributions for the strength of brain lobe interactions.

Group-averaged values of individual brain lobe α−α interactions (i.e., 21 matrix elements of the upper triangular part of the matrices in Fig. 2c) for the different groups of subjects. The ranking follows the values of the PD+FoG⁺ group. Ranks 1 and 2 correspond to interactions within the frontal motor areas (FMR−FMR and FML−FML) that are strongest for all groups. Note that values of each R × χ matrix element are consistently highest for PD+FoG⁺ and lowest for EC, with PD-FoG and PD+FoG⁻ falling in-between. Symbols and error bars represent the group means and standard error, respectively. Error bars have been calculated using a bootstrap method.

Fig. 5. Intra-lobe brain interactions in the frontal motor lobe for the individual subjects performing different motor tasks.

a Symbols represent the average values of FMR−FMR and FML−FML α-band interactions as derived from the R × χ matrix during normal walking (blue squares), standing still (green diamonds), and hand tapping (red circles). Values for each task are arranged in columns and each symbol represents an individual subject. The different groups are marked by different background shadings. Fitting lines highlight the trend towards higher brain lobe interactions for subjects with PD and FoG, which is seen across all three motor tasks. b Scatter plots show strong cross-correlations between the different motor tasks and confirm the observation of an increase of brain interactions with PD severity. The colors of the symbols correspond to the background shadings in (a) for patients belonging to different groups. Pearson’s correlation coefficients ρ are highly significant (p < 10⁻³) and are shown in the upper left corner of each subplot. The insets confirm the significance of the results by surrogate analysis (i.e., shuffling the number tuples of the subjects by n iterations, with n = 0 being the original un-shuffled tuple series).

Fig. 6. Phase synchronization of amplitude-amplitude modulations and surrogate analysis to identify significant interactions.

Two pairs of α frequency-band signals (blue curves in (a)−(c) and (b)−(d)) from different EEG electrodes were obtained by applying a [7.8−15.59 Hz] bandpass-filter to the preprocessed EEG data. The black curves in each of these panels are the corresponding instantaneous amplitudes calculated by the analytic signal approach, Eq. (1). Red dashed lines are the corresponding averages ${⟨A^j\left(t\right)⟩}_L$ subtracted when applying the analytic signal approach to derive phases of these instantaneous amplitudes. e Phase differences of the instantaneous amplitudes of (a)−(c) are clustered on the unit circle leading to a high synchronization index of R = 0.85 (Eq. (2)). In contrast, the signals in (b)−(d) are less synchronized as can be seen in (f), where the corresponding phase differences are distributed on the unit circle yielding a low index of R = 0.38. g, h Phase synchronization index R as a function of the shift τ between the instantaneous amplitude signals (a) vs. (c) and (b) vs. (d), respectively. The phase synchronized amplitude signals from (a) and (c) yield a maximum R at shift ${\tau }^{*}={\left(\tau \right.∣}_{R\left(\tau \right)\equiv R_{\max }}^{}=0$, and R(τ) decays rapidly for ∣τ∣ > 0. For the much lower synchronized signals from (b) and (d), however, R(τ) shows fluctuating behavior without clear decay. A significance value W characterizes R(τ) by normalizing $R_{\max }$ by the mean and standard deviation of R(τ) (Eq. (3)). Correspondingly, we obtain a higher W value for panel (g) (W = 5.2) than for panel (h) (W = 1.6). We utilize W to characterize the significance of the interaction between two signals. Panel (i) indicates that the highest W values are observed for τ^* ≈ 0. In this scatter plot we show 1000 α−α samples of W vs. τ^* for real data (blue circles) and surrogate data (red dots). Real signals are taken from the same patient (using different EEG electrodes), whereas surrogate pairs were chosen randomly from different patients. Clearly, higher W values are obtained for real signals for τ^* ≈ 0. The surrogate analysis does not lead to high W values around τ^* ≈ 0 and shows a uniform W vs. τ^* distribution.