Connectome-harmonic decomposition of human brain activity reveals dynamical repertoire re-organization under LSD

Atasoy and colleagues situate their work in a context where modern neuroimaging has begun to reveal the correlates of the psychedelic state but the spatio-temporal dynamics that underlie LSD's effects on whole-brain activity remain incompletely understood. Previous fMRI and MEG studies reported increased visual cortex blood flow, greater whole-brain functional integration and broad decreases in oscillatory power under LSD, and theoretical accounts have proposed that psychedelics broaden the repertoire of brain states. However, the field has lacked mathematical tools tailored to characterise how cortical activity patterns, constrained by structural connectivity, reconfigure under psychedelics. This study introduces and applies a connectome-harmonic decomposition method to resting-state fMRI data collected under LSD and placebo in order to test whether LSD alters the energy and power of frequency-specific brain states, whether it expands the repertoire of active brain states, how cross-frequency interactions change, and whether these changes move whole-brain dynamics closer to criticality (the balance between order and disorder). The authors aim to link these objective dynamical measures to subjective experience and to network-level functional connectivity changes.

The study used a within-subject, single-blind design in which participants attended two scanning sessions 14 days apart and received either 75 μg LSD (intravenous) or placebo (saline). Scanning began 70 minutes after infusion; each session contained two non-music BOLD runs and one music run, each 7 minutes long. Twenty subjects were scanned overall but the present analysis used data from 12 participants (mean age 30.5 ± 8 years, four female) after exclusions for early termination, excessive head motion and technical problems with sound delivery. Participants provided brief visual analogue scale (VAS) ratings after each scan probing five experiential dimensions: complex imagery, simple hallucinations, emotional arousal, positive mood and ego-dissolution. The central methodological advance is the use of connectome harmonics as a basis set of spatial brain states. Connectome harmonics are the eigenmodes (harmonic modes) of a graph Laplacian computed on an averaged structural connectivity (adjacency) matrix derived from an independent sample of 10 subjects from the Human Connectome Project. Each harmonic is a spatially synchronous cortical pattern associated with a wavenumber k (spatial frequency); representing fMRI activity as a linear combination of these harmonics provides a spatial-frequency decomposition that is anatomically informed and independent of the analysed fMRI data. From the time-resolved projection coefficients onto each connectome harmonic, the authors defined power as the instantaneous strength of activation of a harmonic and energy as the power weighted by the harmonic's intrinsic frequency-dependent energy (eigenvalue squared). Total power and total energy were computed by summing across harmonics and time points. The connectome-harmonic spectrum was discretised for some analyses (e.g. 15 logarithmic bins of wavenumber) to probe frequency-selective effects. Cross-frequency correlations were estimated as Pearson correlations between time courses of pairs of harmonics. Power-law behaviour across the harmonic spectrum was assessed by plotting maximum power, mean power and power fluctuations versus wavenumber on log10-log10 axes, performing logarithmic binning and fitting a line to estimate the critical exponent β; goodness of fit was quantified as the root mean squared error ε. Statistical tests included two-sample t-tests across subjects, Kolmogorov–Smirnov tests for distribution differences, Monte Carlo simulations with Bonferroni correction for bin-wise comparisons, and correlation analyses between energy changes and subjective ratings. Resting-state networks (RSNs) were estimated from an independent HCP-derived sample; multiple correlation analyses related RSN connectivity changes to subjective ratings both directly and indirectly via the harmonic-energy correlates of RSN changes.

Primary neuroimaging results showed that LSD increased total power and total energy across the connectome-harmonic spectrum. Averaged across time points and conditions, total power and energy were significantly higher under LSD than placebo (p < 0.0001, two-sample t-test). The probability distribution of energy values differed markedly between LSD and placebo (two-sample Kolmogorov–Smirnov test, p < 10^-85), with a clear shift to higher characteristic energy states in all three LSD scan conditions. Listening to music increased the probability of reaching the characteristic energy state in both drug and placebo conditions, an effect amplified under LSD but more rapidly reversed after music in the LSD session compared with placebo. Decomposition of projection values (harmonic activation magnitudes) revealed that LSD expanded the repertoire of active brain states: the distribution of projections under LSD showed a reduced peak at zero activation and an increased width and heavier tails, indicating both more harmonics with non-zero contributions and more frequent stronger activations. Reported descriptive values included fitted means μ (e.g. μ_LSD = 0.0355, μ_PCB = 0.0388) and standard deviations σ (σ_LSD = 0.3731, σ_PCB = 0.3416), consistent with a broader activation repertoire under LSD. Frequency-selective effects were evident: after discretising the harmonic spectrum into logarithmic bins, significant energy changes were found across all quantised wavenumber levels for LSD versus placebo (p < 0.01, Monte Carlo with Bonferroni correction). Specifically, LSD produced increased energy in high-wavenumber harmonics (k > 2 × 10^2, corresponding to approximately 0.01–1% of the spectrum) and decreased energy in low-wavenumber harmonics (k < 2 × 10^2, ~0–0.01% of the spectrum). For very high wavenumbers (k > 10^3, ~0.05–1% of the spectrum) LSD also increased temporal fluctuations of energy. Cross-frequency correlation analysis indicated a structured, non-random re-organisation: under LSD, correlations among low-frequency harmonics decreased (k ∈ [0–0.01%]) while correlations among higher-frequency harmonics increased (notably k ∈ [0.2–1%]), and overall cross-frequency correlations across the full spectrum increased. The influence of music and the fading of LSD over sequential scans modulated these effects; for example, music reduced cross-frequency correlations in a mid-range band (k ∈ [0.01–0.02%]) under LSD but not under placebo. Analyses of scaling behaviour found that maximum power, mean power and power fluctuations across harmonics followed power-law distributions in both conditions, with a slight tail cut-off consistent with a near-critical, slightly subcritical regime. Crucially, goodness-of-fit of power-law models (root mean squared error ε) decreased significantly under LSD for maximum and mean power, and for power fluctuations in the first scan (p < 0.01), indicating closer adherence to power-law scaling under LSD. The estimated power-law exponent β also decreased significantly under LSD for maximum and mean power (p < 0.01), consistent with relatively increased power in high spatial frequencies and reduced power in low frequencies. Relating neural changes to subjective reports, reductions in mean energy and energy fluctuations in the low-frequency range k = 1–200 (~0–0.01% of the spectrum) correlated with higher ratings of ego-dissolution (r = 0.553, p < 10^-3) and emotional arousal (r = 0.611, p < 10^-3). Positive mood correlated with energy changes across a broader band k = 1–1100 (r ≈ 0.456, p < 10^-2). Correlations at the level of individual harmonics did not survive conservative multiple-comparison correction when the full spectrum (18,715 harmonics) was tested. In network-level analyses, direct multiple-correlation tests between RSN connectivity changes and subjective ratings were not significant, which the authors attribute to limited power (24-dimensional vectors: 12 subjects × 2 scans). An indirect approach that first mapped RSN connectivity changes onto connectome-harmonic energy changes revealed significant associations: combined visual and auditory/visual networks correlated with simple hallucinations and complex imagery (**p < 10^-15 for k ∈ [1…200]), coupled visual–left fronto-parietal connectivity correlated with simple hallucinations, and coupled visual–right fronto-parietal connectivity correlated with both imagery and hallucinations. The default-mode network (DMN) connectivity correlated with emotional arousal (**p < 10^-15), and coupled DMN–salience network (SAL) connectivity correlated with emotional arousal, positive mood and ego-dissolution (**p < 10^-15). Coupled SAL–left fronto-parietal (and SAL–FPN) connectivity also correlated with emotional arousal, positive mood and ego-dissolution (*p < 10^-10).

Using connectome-harmonic decomposition, the authors interpret their findings as showing that LSD produces frequency-selective increases in the energy and power of harmonic brain states and an expanded, non-random repertoire of active states with increased cross-frequency co-activation. They argue that these changes reflect a re-organisation rather than a randomisation of brain dynamics and that the observed enrichment of high-frequency harmonics together with altered cross-frequency structure is consistent with a tuning of whole-brain dynamics closer to criticality. Criticality is framed as a regime conferring a balance of stability and flexibility that could support greater information encoding capacity and faster processing, and the authors link their empirical observations (improved power-law fits, decreased critical exponent) to prior theoretical and experimental work on critical brain dynamics. The discussion connects these dynamical changes to LSD's pharmacology, noting that 5-HT2A receptor agonism plausibly increases cortical excitation and could be a mechanism for shifting dynamics toward criticality. Authors propose functional implications: increased sensitivity to context and stimuli ("set and setting"), potential therapeutic relevance insofar as some psychiatric disorders are associated with deviations from criticality, and a mechanistic account for how LSD might transiently restore or modulate critical balance. They also draw parallels between dynamics at criticality and creativity, suggesting that the enriched, structured repertoire under LSD resembles the increased novelty generation seen in improvisation. The authors acknowledge key caveats and limitations reported in the paper. Small sample size and the resulting dimensionality (for example 24 data points for multiple-correlation analyses) reduce statistical power in some network–subjective correlations; several single-harmonic correlations did not survive conservative multiple-comparison correction. They also note the sequential fading of LSD effects across scans and the modulatory influence of music on some measures. Finally, the authors emphasise that the connectome-harmonic approach, while applied here to fMRI, is generalisable to other modalities (MEG, high-density EEG) and that their findings open avenues for studying other psychological states and disorders using an anatomically informed harmonic decomposition.