Measurement of excitation-inhibition ratio in autism spectrum disorder using critical brain dynamics

Abstract

Balance between excitation (E) and inhibition (I) is a key principle for neuronal network organization and information processing. Consistent with this notion, excitation-inhibition imbalances are considered a pathophysiological mechanism in many brain disorders including autism spectrum disorder (ASD). However, methods to measure E/I ratios in human brain networks are lacking. Here, we present a method to quantify a functional E/I ratio (fE/I) from neuronal oscillations, and validate it in healthy subjects and children with ASD. We define structural E/I ratio in an in silico neuronal network, investigate how it relates to power and long-range temporal correlations (LRTC) of the network's activity, and use these relationships to design the fE/I algorithm. Application of this algorithm to the EEGs of healthy adults showed that fE/I is balanced at the population level and is decreased through GABAergic enforcement. In children with ASD, we observed larger fE/I variability and stronger LRTC compared to typically developing children (TDC). Interestingly, visual grading for EEG abnormalities that are thought to reflect E/I imbalances revealed elevated fE/I and LRTC in ASD children with normal EEG compared to TDC or ASD with abnormal EEG. We speculate that our approach will help understand physiological heterogeneity also in other brain disorders.

Conflict of interest statement

K.L.-H., S.-S.P. are shareholders of NBT Analytics BV, which provides EEG-analysis services for clinical trials. H.B., K.L.-H., and S.-S.P. are shareholders of Aspect Neuroprofiles BV, which develops physiology-informed prognostic measures for neurodevelopmental disorders. R.H., K.L.-H. have filed the patent claim (PCT/NL2019/050167) “Method of determining brain activity”; with priority date 16 March 2018. The rest of the authors have no competing interests to declare.

Figures

Figure 1

Amplitude and long-range temporal correlations of oscillations strongly depend on structural E/I. (a) Number of connections between neuron types for five different networks with increasing structural E/I. (b) Network activity filtered in the 8–13 Hz band shows increasing oscillation amplitude with increasing structural E/I. (c) Z-scored activity of (b) shows differing temporal structure of oscillation amplitude for balanced and unbalanced networks. (d) Power spectrum for networks in (b). (e) Spectral amplitude in the 8–13 Hz band increases with structural E/I. Running mean amplitude values of 300 networks (thick line) +/− 1 standard deviation (thin lines). (f) Detrended fluctuation analysis (DFA) applied to the amplitude envelope of 8–13 Hz filtered signals in b shows increasing scaling exponents for balanced (green) compared to unbalanced networks (blue, red). (g) DFA exponents show an inverse u-shaped relationship with structural E/I.

Figure 2

Joint fluctuations in the amplitude and scaling of oscillations enable estimation of the excitation-inhibition ratio of a neuronal network. (a) Similar LRTC (quantified by DFA) can be produced by two networks with different sE/I. In the blue area, increasing LRTC correspond to increasing amplitude of oscillations, in the orange area decreasing LRTC correspond to increasing amplitude of oscillations. (b) The mean fluctuation (log10 < F(t)>) for a window size of 5 seconds is a poor predictor of the DFA exponent. Each dot represents one network realization simulated for 1000 seconds, and the mean fluctuation and the DFA exponent are derived from the entire signal. (c) Mean fluctuation values (log10 < F(t)>) for a window-size scale proportionally with signal magnitude and with LRTC. Therefore, if we normalize the amplitude of the signal for a certain window size then the fluctuation in that window size would be an estimate of the DFA exponent. (d) After normalizing the signal profile windows, the DFA exponents can be estimated by their mean fluctuation, log10 < nF(t)> (shown for a window size of 5 seconds). Each value represents the average of 20 networks for each combination of excitatory and inhibitory connectivity parameters. (e) Method to calculate fE/I. (i) The model signal filtered in the alpha range (dark thin green), and the same signal with double the magnitude (thick light green). (ii) Amplitude envelope of the two signals. (iii) Signal-profile deviations are greater for the larger-magnitude signal (light green). (iv) Dividing each window by its original mean amplitude, removes any effect of original magnitude on the signal profile. (v) Subtract the linear trend. (vi) Calculate the standard deviation for each window to get the normalized fluctuation function, nF(t). (vii) fE/I is calculated by correlating the mean windowed amplitudes calculated from ii and the windowed nF(t) calculated in (vi). (f) Correlation between windowed values for nF(t) and amplitude is used to create the estimate of fE/I, shown for three example networks with low (1.82, left), medium (2.05, middle), and high (2.25, right) sE/I, respectively. (g) The sE/I index is shown in color scale for the phase space of inhibitory and excitatory connectivities with E-I combinations producing oscillations with DFA > 0.6 indicated with black squares. (h) For networks close to the critical state, fE/I correctly assigns their activity to be either inhibition dominated (blue), excitation dominated (red) or in balance (white squares). For strongly inhibition- or excitation-dominated networks, DFA is not significant and the presented method is not applicable (gray regions, where DFA ≤ 0.6). (i) fE/I is associated strongly with sE/I (calculated for networks between sE/I = 1–3 that pass the inclusion criterion of DFA > 0.6). (j) fE/I exhibits stronger correlation with κ than with sE/I.

Figure 3

fE/I is balanced in healthy populations and can detect pharmacologically induced shifts in excitation/inhibition ratio. (a) Grand average fE/I topography during eyes-closed rest (n = 176). (b) Increasing inhibitory decay rate in the model is associated with decreasing fE/I. (c) Eighteen subjects taking zolpidem, which increases inhibitory input decay constant, show a significant decrease in fE/I and a return to baseline values after 4–6 hours both relative to baseline (blue asterisks) and relative to the placebo control (black asterisks). The bipolar Oz-Pz electrode position measured is indicated on the inset. Bonferroni-corrected P-values are indicated as * <0.05. (d) Filtered signal (left column) and fE/I (right column) shown for a single subject (zolpidem condition) at four time points.

Figure 4

Alpha oscillations in ASD are characterized by strong LRTC and large variability in fE/I. Grand-average topographies for the EEG biomarkers are shown for TDC (first column), ASD (second column), and for ASD-minus-TDC (third column). (a) Relative power (RP) showed the characteristic occipito-parietal distribution both in TDC and ASD. (b) Whole-brain average and variability of LRTC quantified by the DFA exponent were both larger in ASD compared to TDC. (c) A pronounced variability of whole-brain fE/I was evident in ASD. White circles on the topographies represent significant channels (i.e., p-value < 0.05, using Wilcoxon rank-sum test and FDR correction). The fourth column shows individual-subject values, boxplots, and mean and SEM for TDC (blue circles) and ASD (red squares). Comparisons represented in boxplots were based on the average value of the EEG biomarkers across all 64 electrodes, each data point represents one subject (whole-head average; p-values are from Wilcoxon rank-sum test (mean)/Levene’s test (variability).

Figure 5

ASD without visual EEG abnormalities show strong LRTC and elevated fE/I. Compared to the children with ASD and a normal EEG (ASDnl), subjects with EEG abnormalities (ASDabn) had lower relative power in the alpha band (a), weaker LRTC (b) and lower fE/I (c). Compared to TDC, ASDabn had lower RP (d), but no significant difference in LRTC (e) or fE/I (f). In contrast, ASD subjects without any visible EEG abnormalities (ASDnl) showed higher RP than TDC (g), stronger LRTC (h) and higher fE/I (i). Grand-average topographies are shown for the cohort difference of the indicated comparisons (labels on top). The reported p-values are based on the Wilcoxon rank-sum test. White circles on the topographies represent significant channels as in Fig. 4. Comparisons at the left of the topographies were based on the average value of the EEG biomarkers across all 64 electrodes, each data point represents one subject (whole-head average, Wilcoxon rank-sum test).