Fig 1.
(A) The phase difference estimated from the BOLD signals of brain regions n and p at time point t, obtained by applying the Hilbert transform to the BOLD signals. The dashed lines represent the BOLD signals, while the solid lines indicate the corresponding phases, with both line types using the same color for each brain region. (B) The phase-lock matrix calculated for a subject at t= 0, t= 1, and t= 2. (C) The 6 cluster centroids obtained from k-means clustering of the leading eigenvectors of the phase-locking matrices across all time points for all subjects under both LSD and placebo conditions, reduced to a 3-dimensional space, where each cluster centroid corresponds to a brain state. (D) Probabilities of occurrence of each brain state. (E) The average structural connectivity matrix. (F) Brainnetome Atlas (https://atlas.brainnetome.org/download.html) used for delineating brain regions; (G) Schematic of the neural mass model, which consists of differential equations governing the dynamics of excitatory (E) and inhibitory (I) neuron populations for each brain region. The structural connectivity, brain atlas, and dynamical model collectively determine the digital twin brain model, with the ratio of the time-averaged values of excitatory and inhibitory synaptic gating variables () representing the E/I ratio.
Fig 2.
Visualization of BOLD signals and Kuramoto order parameter for subject 001 and results of paired t-test.
(A) The Kuramoto order parameter (OP) of Subject 001 under LSD (red solid line) and placebo (black solid line) conditions across 216 time points. The dashed lines represent the mean OP over time for each condition, with a red dashed line indicating the LSD condition and a black dashed line indicating the placebo condition. (B) Boxplots of OP (left panel) and the standard deviation of the OP, STD(OP), (right panel) under LSD and placebo conditions. Each boxplot shows the distribution of data, with the central horizontal line representing the median, the box indicating the interquartile range (IQR) between the first (Q1) and third (Q3) quartiles, and the whiskers extending to the minimum and maximum values within 1.5 times the interquartile range from Q1 and Q3. Statistical details: OP (LSD vs. placebo), p = 0.0101, Cohen’s d = 0.7671; STD(OP) (LSD vs. placebo), p = 0.0140, Cohen’s d = 0.7246.
Fig 3.
Repertoire of spatially distributed phase-locking patterns (PL states) obtained using the Leading Eigenvector Dynamics Analysis (LEiDA).
Each column corresponds to a distinct brain state. (A) The bar plot showing the cluster centroid vectors (i.e., PL states), where each element of the centroid vector Vc represents the projection of the BOLD phase of each region onto Vc. If the BOLD phase of a region aligns with the direction of Vc, the corresponding element is positive (colored red); otherwise, it is negative (colored blue). (B) The representation of brain regions based on their contributions, where the magnitude of each element in Vc indicates the contribution of that brain region to the respective PL state, with color intensity reflecting the value. (C) The PL states are represented in matrix format by computing the outer product of Vc × VcT, as depicted in the bottom panel.
Fig 4.
Spatial overlap of six PL states with seven resting-state networks (RSNs).
The bar chart illustrates the Pearson correlation coefficients between the six PL states and the seven RSNs [28]. The length of each bar represents the magnitude of the Pearson correlation coefficient. Red circles indicate significant correlations with p-values less than 0.05 (FDR corrected). The radar plots further depict the relationships, with red dots marking the points where the p-values are less than 0.05, highlighting the significant overlaps between the PL states and RSNs in spatial representation. VIS, Visual; SOM, Somatomotor; DAT, Dorsal Attention; VAT, Ventral Attention; LIM, Limbic; FPN, Frontoparietal; DMN, Default.
Fig 5.
Probability of occurrence, dwell time, and transition probabilities between 6 PL states.
(A) The first row shows the transition probabilities of the 6 PL states under LSD and placebo conditions, while the second row displays the dwell time. PL states marked with asterisks indicate significant differences assessed by permutation tests, with one asterisk representing FDR uncorrected p < 0.05 and two asterisks representing p < 0.05/k, where k = 6. (B) The matrix of transition probability for PL states under LSD and placebo conditions. Compared to the placebo condition, all probabilities of transitioning out of PL state 3 decreased under LSD (highlighted in the blue box), while all probabilities of transitioning into PL state 3 increased (highlighted in the red box), with significant changes indicated by asterisks. (C) Changes in transition probabilities between PL states under LSD compared to the placebo condition. Red/blue arrows indicate higher/lower transition probabilities in the LSD condition compared to the placebo condition, with significant differences marked by asterisks.
Fig 6.
Distribution of E/I Ratio Differences on the Cortex.
(A) The distribution of the E/I ratio rendered onto the cortical surface. (B) The administration of LSD induces a compression of the global E/I ratio towards the center along the principal functional gradient. (C) The distribution of E/I ratios across the 7 RSNs under LSD and placebo conditions shows that the peak E/I ratio in the primary cortex under LSD is situated to the left of the corresponding peak observed under placebo, whereas the peak in the associative cortex under LSD is located to the right of the placebo peak. (D) Pearson correlation between the E/I ratio difference and the densities of 5-hydroxytryptamine-2A (5-HT2A) receptors and glutamate receptors.