By: Sheng H. Wang
J Matias Palva Lab
HiLife, University of Helsinki, Finland
NBE, Aalto University, Finland
Neuronal activity exhibits power-law dynamics throughout the scales of the nervous system. This has been thought to reflect conventional brain criticality, i.e., the brains operating near a continuous second-order phase transition between disorder and order. However, when neuronal activity is constrained by resource depletion or limiting mechanisms, the phase transition may become discontinuous (first-order) and lead to bistable dynamics. Nonetheless, observations of bistability in awake human brain activity have remained scarce, and its functional significance and relationship to brain criticality unclear. We assessed the emergence of bistability in neuronal amplitude dynamics first using a generative model with state-dependent noise representing a positive local feedback . We found that bistability occurred exclusively within the critical regime so that the first-order phase transition emerged progressively with increasing state dependency. We then measured resting-state brain activity with magnetoencephalography (MEG) and intra-cranial stereo-encephalography (SEEG). Bistable critical dynamics were, in fact, a robust large-scale phenomenon in the amplitude dynamics of local neuronal oscillations from delta (3-7 Hz) to high-gamma (100-225 Hz) frequencies. As predicted by the model, we found a positive correlation with bistability and long-range temporal correlations. As evidence for functional significance, we found that moderate bistability was positively correlated with executive functions in healthy subjects. Conversely, excessive bistability was associated with epileptic pathophysiology and predictive of the epileptogenic zone. Critical bistability thus characterizes spontaneous human brain dynamics in awake resting-state with both physiological and pathophysiological roles. We suggest that these findings expand the framework of brain criticality and imply that near-critical neuronal dynamics involves both first- and second-order phase transitions in a frequency- and neuroanatomy-dependent manner.
Bistability is unambiguously caused by high state-dependent noise. (A) Kuramoto model order parameter (R), (B) long-range temporal correlation (LRTC) estimated with detrended fluctuation analysis (DFA), and (C) bistability as functions of noise state-dependency (r) and the intrinsic coupling parameter (k). Each pixel is the mean of 50 independent model realizations. (D) Overlapping regimes based on observations of (A–C). The normal criticality is associated with low degree of r (black dashed line) whereas bistable criticality is caused by mid-to-high degree of r (red dashed line); (E) The probability density of R as a function of k in bistable (top) and normal (bottom) critical regime; the LTRC peak (black overlaid lines) coincided with the phase transitions. (F) Probability density (pdf) of R and (G) scaling of the DFA fluctuation function in unimodal and bistable critical regime marked in (D–E)colour coded. (H) Exemplary order parameter (R) time series.
Bistability and LRTC are robust, large-scale phenomena in the brain. (A–B) Five minutes of broad band and narrow band time series showing (A) SEEG electrode contact and (B) MEG source level evidence of bistability; insets: switching between “up” and “down” states; mFG: middle frontal gyrus; Vis: visual area. (C–D) Topological similarity (i.e., Spearman’s correlation) between narrow-band LRTC and bistability estimates of MEG and SEEG parcels (Schaefer 100-parcels); red boxes demarcate frequency-band clusters in which cortical maps are topologically similar. Note: SEEG parcel data exclude contacts sampled from subcortical areas and epileptogenic zones. (E) Frequency-collapsed a- and g-band metrics (normalized); white-out SEEG parcels are excluded due to insufficient sampling. (F–G) Group-level cortical maps of a-band (F) MEG and (G) SEEG bistability.
Frequency-specific MEG and SEEG bistability exhibit functional significance. (A) Correlation between individual neuropsychological scores (zoo map time) and a-band mean-parcel LRTC (black dots) and bistability (red triangles) estimates, each marker represents one subject. (B–C) Significant correlations (FDR corrected) between zoom map time and a-band individual parcel (B) LRTC and (C) bistability estimates. (D) The effect size of differences between band-collapsed LRTC (black) and bistability (red) estimated for SEEG contacts recorded from epileptogenic zones (EZ) and non-EZ (nEZ); dashed line: 99%-tile of 1,000 label-shuffled surrogates. (E) Feature importance (SHAP values) estimated for random forest classifier. (F) The area under curve (AUC) of receiver operating characteristics (ROC) derived from pooled (blue) and within individuals (black) when using LRTC alone, bistability (BiS) alone, combined LRTC and BiS (L&B), L&B plus contact loci in Yeo systems (L&B(Y)). Dashed lines: 99%-tile of AUC observed from 1,000 surrogates generated independently for each of the four feature sets. (G-H) Post-hoc inspection of classification outcome using the L&B(Y) feature set that is indicated by the black marker in (F). (G) Spearman’s correlation (p < 10-6, n=55) between individual AUC and within-subject mean Cohen’s d between EZ and nEZ in band-collapsed LRTC and BiS. (H) Within-patient prediction precision as a function of true positive rate (magenta box); the red marker indicates the population mean. Precision = true positive num ÷ reported positive num. (I) ROC of classification within individuals (thin lines) and mean ROC (thick)