EEG Fractal Analysis Reflects Brain Impairment after Stroke

Abstract

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.

Keywords: EEG; fractal analysis; neurophysiology; neuroplasticity; stroke.

Figure A1

Example of $log\left(\mathbf{L}\right(k\left)\right)$ versus $log\left(k\right)$ curve (referred to $l_k$ in the paper) computed from a cosine with 7.5 Hz of frequency. The slope of the linear part of the curve stands for the FD Higuchi (in green), the changes in the curvature sign for values greater than ${\mathrm{k}}_{\mathrm{l}\mathrm{i}\mathrm{n}}$ (in red) stands for the FD Tortuosity (in light blue) and the deviation of the curve from the regression line computed in its linear region stands for the FD Residuals (in violet).

Figure A2

Topographic maps of the median values of FD Residuals in healthy controls (first row, colormap range is from 165 to 195) and during acute (second and third row) and sub-acute (fourth and fifth row) phase in stroke survivors (colormaps range is from 200 to 350). Second and fourth rows refer to stroke survivors with right-hemisphere lesion, third and fifth rows to stroke survivors with left-hemisphere lesion. Second and fourth columns report Wilcoxon test statistic (stroke survivors vs. controls, colormaps range is from 0 to 0.016 for Dataset 1, i.e., Acute Phase, and from 0 to $1.7\ast {10}^{-4}$ for Dataset 2, i.e., Subacute Phase).

Figure A3

Results of averaged FD measures—respectively of Higuchi, Residuals and Tortuosity—at T0 (in green) and T1 (in violet) in acute phase (first row) and between $\widetilde{T1}$ (in violet) and T2 (in yellow) in subacute phase (third row). Clinical recovery was estimated through NHISS and FMA scores at T0 and T1 (in acute phase—second row) and through ARAT, BBT and N-HPT scores at $\widetilde{T1}$ and T2 (in sub-acute phase—fourth row). Results for participants with right hemisphere lesion (first two columns in each plot) and participants with left hemisphere lesion (last two columns in each plot) are reported on separate columns for the sake of clarity. On each box, the central line indicates the median, and the bottom and top edges of the box indicate the 25th and 75th percentiles, respectively. The whiskers extend to the most extreme data points not considered outliers, and the outliers are plotted individually using the ‘o’ symbol.

Figure A4

Results in acute phase (first and second row, colormap range from 1.042 to 1.058) and sub-acute phase (third and fourth row, colormap range from 1.05 and 1.065) for Fractal Dimension Higuchi. Topographic map of: (1) the median values of the Fractal Dimension Higuchi among survivors with right hemisphere (non-dominant) lesion and left hemisphere (dominant) lesion (first and second column) and (2) Wilcoxon test statistic (T0–T1 in acute phase and $\widetilde{T1}$–T2 in subacute phase) where crosses stand for significant increase ($p_{value}$ < 0.05; colormap range from 0 to 1) (third column).

Figure A5

t-maps representing Wilcoxon test statistic (T1 in acute phase vs. $\widetilde{T1}$ in subacute phase) where non-white colors stand for significant difference ($p_{value}$ < 0.05; colormap range from 0 to 0.05). A significant decrease between T1 in acute phase vs. $\widetilde{T1}$ in subacute phase was observed only for participants with left-hemisphere lesion.

Figure 1

Histograms reporting the timing of EEG recording and clinical and behavioral data collection for the two datasets recorded in Padova (PD) and in Villa Beretta (VB). On the x-axis the days after the event in which the EEG recording and clinical evaluation were performed and on the y-axis the number of participants that were evaluated at that day. The distribution of the participants evaluated at T0 at the Stroke Unit of Padova is represented in green; the distribution of the same participants evaluated at T1 is represented in violet; the distribution of the participants evaluated at $\widetilde{T1}$ at the Neurorehabilitation Unit of Villa Beretta is represented in violet too and the distribution of the same participants evaluated at T2 is represented in yellow. A Gamma distribution gamma(α, β) was fitted to each subset of data: Hyper-acute phase represented in green was quantified as T0_UNIPD∼gamma(2.13, 0.59); Acute phase in violet as T1_UNIPD∼gamma(9.58, 0.7), T1_VB∼gamma(4.57, 3.29); Early subacute phase in yellow as T2_VB∼gamma(38.28, 1.42).

Figure 2

Schema of data analysis.

Figure 3

Fractal (i.e., $log\left(\mathbf{L}\right(k\left)\right)$ versus $log\left(k\right)$) curve computed for three representative subjects at EEG channel location Fz. The red line represents the median of the curves computed from the 41 EEG epochs of 2 s in one healthy control. The green and violet lines stand for the median of the curves computed from the 41 EEG epochs of 2 s at T0 (green) and at T1 (violet) for one stroke survivor of Dataset 1. The dark violet and yellow lines stand for the median of the curves computed from the 41 EEG epochs of 2 s at $\widetilde{T1}$ (dark violet) and at T2 (yellow) for one stroke survivor of Dataset 2. Shaded areas represent ± standard deviation for each curve.

Figure 4

Topographic maps of the median values of FD Higuchi and Tortuosity during resting-state in healthy controls (first row) and during acute (second and third row) and sub-acute (fourth and fifth row) phase in stroke survivors. Second and fourth rows refer to stroke survivors with right-hemisphere lesion, third and fifth rows to stroke survivors with left-hemisphere lesion.