Using connectome-harmonic decomposition, the authors show that LSD selectively alters the energy and power of harmonic brain states, expanding the repertoire of active states and increasing non-random cross-frequency co‑activation. The frequency distribution of these active states follows power laws, indicating a reorganisation of brain dynamics towards the edge of criticality.
Recent studies have started to elucidate the effects of lysergic acid diethylamide (LSD) on the human brain but the underlying dynamics are not yet fully understood. Here we used ’connectome-harmonic decomposition’, a novel method to investigate the dynamical changes in brain states. We found that LSD alters the energy and the power of individual harmonic brain states in a frequency-selective manner. Remarkably, this leads to an expansion of the repertoire of active brain states, suggestive of a general re-organization of brain dynamics given the non-random increase in co-activation across frequencies. Interestingly, the frequency distribution of the active repertoire of brain states under LSD closely follows power-laws indicating a re-organization of the dynamics at the edge of criticality. Beyond the present findings, these methods open up for a better understanding of the complex brain dynamics in health and disease.
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.
Papers cited by this study that are also in Blossom
Tagliazucchi, E., Roseman, L., Kaelen, M. et al. · Current Biology (2016)
Carhart-Harris, R. L., Muthukumaraswamy, S., Roseman, L. et al. · PNAS (2016)
Carhart-Harris, R. L., Leech, R., Shanahan, M. et al. · Frontiers in Human Neuroscience (2014)
Schartner, M., Carhart-Harris, R. L., Barrett, A. B. et al. · Scientific Reports (2017)
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.
Ethics statement. This study was approved by the UK National Health Service research ethics committee, West-London. Experiments were performed in accordance with the revised declaration of Helsinki (2000), the International Committee on Harmonization Good Clinical Practice guidelines, and National Health Service Research Governance Framework. Imperial College London sponsored the data collection, which was conducted under a Home Office license for research with schedule 1 drugs. All participants gave informed consent.
Here we recorded fMRI data from 12 subjects in 6 different conditions; LSD, placebo (PCB), LSD and PCB while listening to music, LSD and PCB after the music session. Exploring the combined effects of music and the psychedelic state induced by LSD provided us an opportunity to reveal not only the LSD-induced dynamical changes in the brain but also how these dynamics are affected by the presence of a complex, natural stimuli like music. Furthermore, music is also known for its capacity to elicit emotions, which is found to be emphasized by the effect of psychedelics. This was a within-subjects design in which healthy participants (mean age 30.5 ± 8, 4 females) received 75 μg LSD in 10 mL saline (intravenous, I.V.) or placebo (10 mL saline, I.V.), 70 minutes prior to fMRI scanning. LSD and placebo sessions were separated by 14 days and occurred in a counter-balanced order, as in. To study the LSD-induced changes in cortical dynamics, we decomposed fMRI recordings of 12 subjects in 6 different conditions into the activity of frequency-specific brain states (cortical patterns) (Fig.). The brain states are defined as spatial patterns formed by fully synchronized activity, each associated with a different spatial wavelength; i.e. connectome harmonics(Fig.). We firstly investigated two fundamental properties of these harmonic brain states: 1) power of activation; i.e. the amount of contribution of each harmonic brain state to cortical dynamics, and 2) energy of each of these brain states that combines their intrinsic, frequency-dependent energy with the strength of their activation. Furthermore, to characterize dynamical changes in the repertoire of active brain states, we explored cross-frequency correlations across different harmonics brain states. Finally, to assess the proximity of brain dynamics to criticality, we evaluated power-law distributions across the whole power spectrum of these brain states.
Here, we investigated LSD-induced changes in brain activity using a novel connectome-specific harmonic decomposition method. In particular, utilizing the connectome harmonicsas brain states -elementary building blocks of complex cortical activity -we studied LSD-induced changes in energy and power of these harmonic states as well as the dynamical changes in their active repertoire. Unlike previous techniques applied to explore brain dynamics such as dynamic functional connectivity, the estimation of harmonic brain states relies solely on the structural connectivity (human connectome) and thus is independent from the fMRI data itself. Hence, the connectome harmonics are estimated once as the harmonic modes of the human connectome and serve as a universal, anatomically informed harmonic representation to explore any functional neuroimaging data; i.e. similar to using sine and cosine functions to decompose a signal in Fourier transform. This approach allows us to use the exact same brain states to describe the brain dynamics in different conditions; i.e. LSD vs. placebo, which would not be possible with previous techniques. Furthermore, by definition, the connectome harmonics provide fully synchronous (spatial) patterns of activation, each spatial pattern corresponding purely to a different temporal frequency oscillation. This allows for a frequency-specific decomposition of the fMRI data for the first time in the spatial domain. Finally, although in this study we apply this technqiue to fMRI data in order to extract the neural signatures of the LSD state, application of the connectome-harmonic decomposition can also be easily extended to other functional neuroimaging datasets such as MEG or high density scalp EEG. Our results demonstrate that LSD alters the energy and the power of individual harmonic brain states in a frequency-selective manner and enriches the connectome-harmonic repertoire. Moreover, this expansion of the repertoire of active brain states occurs in a non-random fashion with increased co-activation across frequencies suggesting a re-organization of brain dynamics. Taken together, the expanded repertoire of brain states and increase in cross-frequency correlations under LSD demonstrate that not only do more brain states contribute to neural activity under LSD leading to a richer, more flexible repertoire of dynamics, but also their co-activation patterns are highly correlated over time, indicating a preserved stability in brain dynamics, albeit a 'stability' of a different kind with more complex dynamics. Increased diversity in the repertoire of brain states is an expected property of brain dynamics approaching criticality -i.e. balance between order and chaos. Such an expansion of brain states is thought to underlie an expanded capacity for information encodingand an enhanced efficiency of processing. In light of previous theoreticaland experimental findings, we hypothesized that this increased energy and enriched repertoire of brain states under LSD could be accompanied by a tuning towards criticality. Confirming this hypothesis, we found that LSD induced both: closer fit of power laws in the distribution and fluctuations of several observables and a slight change in the critical exponent, indicating a shift of brain dynamics towards criticality. Our results suggest that brain dynamics in both conditions, LSD and placebo, reside close to criticality, with slight deviations to the subcritical regime under placebo, as also indicated for resting state brain dynamics in previous studies, while the induction of LSD tunes brain dynamics further towards criticality. It is noteworthy that the brain dynamics at rest have been found to fluctuate near criticality rather than sitting at a singular critical point. These theoreticaland empirical findingsimply the presence of an extended critical region, which was shown to precisely stem from the hierarchical organization of cortical networks. Our results reveal that while the hallmark of critical dynamics, the power laws, were observed in both the LSD and placebo conditions, the significantly reduced goodness-of-fit error of power laws under LSD, suggests a tuning of brain dynamics further towards criticality -consistent with the so-called' entropic brain' hypothesis. The presented method goes beyond the conventional fMRI analyses previously used to measure changes in brain activity under psychedelics, by enabling the study of fundamental properties of harmonic brain states, such as energy and power, and by revealing how these introduced concepts relate to important principles of dynamical systems, such as whole-brain criticality. Criticality in the brain (i.e. the property of being optimally poised between order and disorder) has been hypothesised to reflect and underlie its advanced functionality; remarkably however, here, using the above-described connectome-harmonic decomposition, we discover a tonic brain state (the LSD state), which exhibits more pronounced signatures of criticality than the normal waking state. This finding provides the first experimental evidence for previous theoretical studies hypothesizing that brain activity in the psychedelic state may be closer to critical dynamics than the normal waking stateand has several important implications. Firstly, criticality provides the necessary conditions for optimal information processing and representation 22 for a complex system, rendering it more supple and flexible within its own intrinsic functioning but also more sensitive to incoming stimuli. Hence, a natural functional consequence of tuning brain dynamics towards criticality, as was observed here under LSD, is an increased sensitivity to both external stimuli as well as internal, intrinsic activity, which in turn leads to greater sensitivity to both the external environment and internal milieu -referred to as'setting' and'set' respectively, in relation to psychedelics. Hence, the LSD-induced shift towards criticality, presents a candidate mechanism underlying increased sensitivity to the context under LSD and psychedelics more generally. The importance of so-called 'set and setting' have been much emphasized by those working with psychedelics in humansand the very definition of the word 'psychedelic' is intended to refer to the putative ability of these compounds to allow the surfacing of normally 'unconscious' mental contents into consciousness. The present findings may therefore represent the beginnings of a mechanistic explanation of these principles, which if substantiated, would have profound implications for psychology. Secondly, various previous studies have pointed out that deviations from criticality could be symptomatic or even causative of certain psychiatric disorders. In particular, brain dynamics in depression, addictionand obsessive compulsive disorder (OCD)have been associated with the subcritical regime, whereas super-critical regime has been found to govern brain dynamics during epileptic seizuresand in conditions such as autism. Taken together with these studies, our findings highlight the potential effect of LSD to regulate brain dynamics in pathology by re-establishing the critical balance between ordered and disordered states. Such an action may explain the increasing body of evidence supporting the therapeutic potential of psychedelic drugs for treating disorders such as OCD, depressionand addictions. Finally, the balance between the complementary dynamics governing stability (ordered regime) and flexibility (disordered regime), attained at criticality, enables flexible and evolving dynamics while maintaining stability. Thus, brain dynamics at the edge of criticality have been hypothesized to constitute the neural basis of creativity. Supporting evidence of this hypothesis comes from studies revealing network correlates of creativity. Divergent thinking and creative idea production have been found to involve the cooperation of two different types of brain networks: those linked to top-down control of attention and cognition (SAL, executive control network (ECN)) and the DMN associated with spontaneous thought. This finding resonates with the above-mentioned functional advantages of a critical system, where an optimal balance between stability (cognitive control) and flexibility (spontaneous thought) may enable the generation of novel and potentially useful ideas. An intuitive understanding of the relation between creativity, critical dynamics and the connectome-harmonic decomposition method utilized here, can be gained from studies exploring neural basis of jazz improvisation. A notable finding of these studies is that the number of musical notes played during improvisation is significantly higher compared with memorized play of the same piece, hence leading to an increase of novel information; i.e. improvisation (involving creativity) introduces spontaneously generated novelty into previously known patterns of melody. Likewise, brain dynamics at the edge of criticality enable the emergence of maximally novel dynamics, where more harmonic brain states are involved in a structured (non-random) yet spontaneous manner, as demonstrated in our findings. Note that connectome harmonics, utilized as brain states in this work, are also mathematically equivalent to the patterns of standing sound waves emerging within musical instruments, where in this case the standing wave equation is solved for the particular connectivity of the human brain (connectome). Consistent with this hypothesis, our findings reveal both, an increase in the number of active brain states, accompanied by a shift towards criticality in brain dynamics under the effect of LSD. This is suggestive of increased flexibility and novelty in brain dynamics induced by LSD compared with placebo, resembling the difference between improvisation (LSD) and memorized play (placebo) of a musical piece. Taken together with previous studies associating psycho-pathology with deviations of brain dynamics from criticality, this interpretation also suggests that the same dynamics that underlie creativity when tuned to criticality, may lead to psycho-pathology when the critical dynamics are impaired. Interestingly, this interpretation is supported by the shared genetic roots of schizophrenia, bipolar disorder, psychosis and creativity, as well as by the shared network correlates of psychiatric disorders and creativity. For instance, the functional networks, whose activity and dynamic coupling is linked to creative thinking (DMN, SAL and ECN), show abnormal functional connectivity in psychiatric disorders such as schizophrenia, bipolar disorders, anxiety and depression. Notably, discussions of psychological parallels between creativity and mental illness has a long history. Surprising parallels also emerge between the crucial role of RSN's in psychiatric disorders and our multiple-correlation analysis relating the energy changes of different connectome harmonics to connectivity changes of the RSNs and to the intensity of different subjective experiences: in line with previous studies, highlighting the important role of abnormal DMN connectivity in psychiatric disorders such as depression, anxiety, bipolar disorderand schizophrenia, as well as in the psychedelic state, we found significant correlations between the DMN connectivity and the intensity of emotional arousal. This result suggests that the link between abnormal DMN connectivity and abnormal mental states may involve or even be mediated by altered emotional processing, also supporting previous studies linking DMN to emotional disregulation. Interestingly, all pairs of networks, whose connectivity changes showed significant correlation with the ratings of emotional arousal, i.e. DMN-SAL, DMN-rFP, DMN-pOP, PAR-pOP, have been previously reported to show increased between-RSN functional connectivity under LSD, suggesting a potential link between this increased between-RSN functional coupling and emotional arousal experienced in the psychedelic state. In particular, abnormal DMN-SAL functional connectivity correlating with intense subjective effects has previously been reported under LSDand psilocybin, and this coupling has been found to relate to ego-dissolution, which is experienced as a positive feeling of oneness and loss of ego-boundaries. Our results also revealed significant correlations between the changes in coupled DMN-SAL connectivity and all three experiences of emotional arousal, positive mood and ego dissolution. This finding is also in agreement with and highly relevant for previous clinicaland theoretical studieshighlighting the important role of DMN-SAL coupling in various mood disorders such as depression, anxiety, bipolar disorder 56 and schizophrenia. In patients with schizophrenia, increased connectivity was also found between the lFP and temporal and parietal regions. Although we acknowledge that chronic schizophrenia is a heterogeneous disorder (and not really a 'state' as such) with many phenomenological features that are inconsistent with the psychedelic stateand vice versa, notably our multiple correlation analysis revealed that the coupled connectivity changes of SAL with lFP alone or with FPN (lFP and rFP together) significantly correlated with the ratings of emotional arousal, positive mood and ego-dissolution, whereas connectivity changes of the SAL when coupled only with rPF did not yield the same level of significance. Moreover, the coupled connectivity of the lFP with the visual networks correlated with ratings of simple hallucinations, while the coupled connectivity of the rFP with the visual networks was found to significantly correlate with the ratings of both, complex imagery and simple hallucinations. These findings suggest that the cooperation between the visual networks and lFP and the lack of cooperation of the rFP may underlie related perceptual abnormalities seen not only in the psychedelic state but also in certain phases of psychosis, such as early psychosis. To conclude, here we have applied a new and powerful analytical methodology to the LSD state, yielding novel findings that inform not only on the neural correlates of this peculiar state of waking consciousness but also on the functioning of the brain more generally. The present findings highlight the value of viewing global brain function and related subjective states in terms of dynamic activation of harmonic brain states. Remarkably, this simple change in perspective reveals the dynamical repertoire of brain activity and suggests a shift of the brain dynamics towards whole-brain criticality under LSD. Importantly, by revealing the characteristic changes in cortical dynamics between LSD and normal awake state, the introduced method opens-up an opportunity for exploring the neural signatures of other psychological traits and states, including personality; creativity; psychiatric and neurological disorders; sleep, anaesthesia and disorders of consciousness; as well as other drug and non-drug induced altered states of consciousness.
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