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 psychedelics16. 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 in10.

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. 1f–h). The brain states are defined as spatial patterns formed by fully synchronized activity, each associated with a different spatial wavelength; i.e. connectome harmonics15 (Fig. 1f). 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.

LSD increases power and energy of brain states

We first estimated the power of activation for each brain state by measuring the strength of its contribution to cortical activity pattern of the fMRI volume acquired at each time instance. By combining the power of activation with the intrinsic, frequency-dependent energy of each harmonic brain state, we calculate the energy of a particular brain state (Methods).

Based on these introduced fundamental measures, enabled by connectome-harmonic decomposition of fMRI data, we first investigated global effects of LSD over the complete spectrum of brain states. To this end, we measured the total power and total energy over the whole connectome-harmonic spectrum for all 6 conditions; LSD, PCB, LSD with-music, PCB with-music, LSD after-music, PCB after-music (Methods). This analysis revealed that the total power and energy of all brain states averaged across all time points significantly increases under LSD (p < 0.0001, two-sample t-test between each pair of LSD vs. PCB conditions) (Fig. 2a,b).

Figure 2 Changes in energy of brain states under LSD. Total power (a) and total energy (b) of all harmonic brain states for all 6 conditions, where stars indicate significant differences (p < 10−4, two-sample t-test) between each pair of LSD vs. PCB conditions with indicated p-values. (c) Probability distribution of total energy values (sum over all harmonics) for all 6 conditions. (d) Probability distribution of the occurrence of projection values (the amount of contribution) of connectome harmonics after normalization of each harmonic’s contribution by the maximum value of the baseline (PCB) condition, shown for all 6 conditions; LSD, PCB, LSD with-music, PCB with-music, LSD after-music, PCB after-music. (e) Energy of connectome harmonics quantized into 15 levels of wavenumbers k (in the log-scale) for conditions (left) LSD vs. PCB, (middle) LSD with-music vs. PCB with-music, (right) LSD after-music vs. PCB after-music. Stars indicate significant differences (p < 0.01, Monte-Carlo simulations after Bonferroni correction). (f) and (g) show the mean (μ) and standard deviation (σ) of the fit of the energy distribution of frequencies shown in (e) to normal distribution for all conditions, respectively. (h) shows the energy differences for each bin between the conditions LSD and PCB, LSD with-music and PCB with-music, LSD after-music and PCB after-music with stars indicating significant differences between conditions of no music, with music and after music (p < 0.01, Monte-Carlo simulations after Bonferroni correction). Mean (i) and standard deviation (j) of energy values of connectome harmonics \(({\{{\psi }_{k}\}}_{k=1}^{n})\) shown as a function of the wavenumber k. Full size image

To further characterize the energy spectrum of each of the 6 conditions, we estimated the probability distribution of their energy values. We observed significantly different probability distributions of energy values (p < 10−85, two-sample Kolmogorov-Smirnov test, Fig. S2) between each pair of LSD vs. PCB conditions and reassuringly no significant difference was found between any pair of LSD or any pair of placebo conditions, even in the case where one condition involved listening to music (i.e. only LSD vs. placebo, between-condition differences were found to be significant and not within condition differences). A clear shift to higher energy values was observed at the peak of the probability distribution in all three LSD conditions \({{\rm{E}}}_{\{\mathrm{LSD},\mathrm{LSDwith}-\mathrm{music},\mathrm{LSDafter}-\mathrm{music}\}}^{\ast }=1203\) in comparison to the energy probability distributions of PCB conditions \({{\rm{E}}}_{\{\mathrm{PCB},\mathrm{PCBwith}-\mathrm{music},\mathrm{PCBafter}-\mathrm{music}\}}^{\bigstar}=1156\) (Fig. 2c). In both, the LSD and PCB conditions, with music, we also found a higher probability of reaching this maximum likely (characteristic) energy state (\({\rm{\Pr }}({{\rm{E}}}_{\mathrm{PCBwith}-\mathrm{music}}^{\ast })=0.2247\) vs. \({\rm{\Pr }}({{\rm{E}}}_{{\rm{PCB}}}^{\ast })=0.2185\)) and (\({\rm{\Pr }}({{\rm{E}}}_{\mathrm{LSDwith}-\mathrm{music}}^{\ast })=0.2104\) vs. \({\Pr ({\rm{E}}}_{{\rm{LSD}}}^{\ast })=0.1809\)). In the placebo condition, this effect of music - increased probability of reaching the characteristic energy state - was also found in the after-music session (\({\Pr (E}_{\mathrm{PCBwith}-\mathrm{music}}^{\ast })=0.2247\) vs. \({\Pr (E}_{\mathrm{PCBafter}-\mathrm{music}}^{\ast })=0.2250\)). In the LSD after-music condition, the higher probability of reaching the characteristic energy state induced by music, slightly decreased (\({\Pr (E}_{\mathrm{LSDafter}-\mathrm{music}}^{\ast })=0.1878\) vs. \({\Pr (E}_{\mathrm{LSDwith}-\mathrm{music}}^{\ast })=0.2104\)), although it still remained higher than in the initial LSD condition (\({\Pr ({\rm{E}}}_{{\rm{LSD}}}^{\ast })=0.1809\)), (Fig. 2c). These results indicate that LSD renders brain dynamics more likely to reach higher energy states, in particular in response to music, which in turn suggests an increased sensitivity of cortical dynamics to the effect of music. Our results reveal that this amplified effect of music on cortical dynamics was also more rapidly reversed after the offset of music under the influence of LSD compared with the placebo condition. These changes are highly suggestive not only of an increased sensitivity to music, as found in previous studies16, but also more rapidly changing cortical dynamics with increased flexibility, which may potentially underlie the enhanced sensitivity to the environment and context observed under the influence of LSD16,17,18. We explore these dynamical changes of cortical activity in further detail in our criticality analysis.

The LSD-induced energy increase of brain activity can be attributed to two possibilities. Firstly, more brain states may be contributing to brain activity leading to an expanded repertoire of brain states, and secondly, the same active brain states may be contributing with more power and energy under LSD. Next, we investigated which of these factors contributed to the observed energy increase under LSD.

LSD extends the repertoire of active brain states

Theoretical and computational studies indicate that spontaneous brain activity explores a dynamic repertoire of brain states and predict a variation in the size of this repertoire in different states of consciousness19. Furthermore, studies exploring psilocybin-induced psychedelic state found greater diversity in functional connectivity motives accompanied by increased variance in temporal oscillations, which indicates an enhanced repertoire of active brain states under the effect of psilocybin, i.e. the main psychoactive compound in magic mushrooms20. To quantify the size of the repertoire of active brain states under LSD and placebo conditions, we estimated the probability distribution of the occurrence of projection values (the amount of contribution) of connectome harmonics for all 6 conditions; LSD, PCB, LSD with-music, PCB with-music, LSD after-music, PCB after-music, after normalizing each harmonic’s contribution by the maximum value of the baseline (placebo) condition. Figure 2d demonstrates that the probability distribution of conditions under LSD shows a clear decrease (height of the normal distributions: μ LSD = 0.0355, μ PCB = 0.0388, μ LSDwith−music = 0.0358, μ PCBwith−music = 0.0387, μ LSDafter−music = 0.0356, μ PCBafter−music = 0.0385) for small magnitude activations (0 value signifying no-activation coincides with the peak of the normal distribution). This decrease signifies that more brain states contribute (with a non-zero weight) to brain dynamics under the influence of LSD. Figure 2d further illustrates the slight increase for higher magnitude activations (towards the tails of the normal distribution, −1 and 1), which indicates that a stronger activation of brain states is observed more frequently under the effects of LSD. The increase in active brain states under LSD is further reflected by the increased width of the normal distribution of projection values (σ LSD = 0.3731, σ PCB = 0.3416, σ LSDwith−music = 0.3710, σ PCBwith−music = 0.3432, σ LSDafter−music = 0.3729, σ PCBafter−music = 0.3447) in Fig. 2d. These results demonstrate that the increased power and energy of brain activity under LSD is caused by both an extended repertoire of active brain states over time as well increased activity of certain brain states.

LSD increases high frequency activity

Next we investigated which brain states demonstrate increased activity under the effect of LSD. To this end, we explored frequency-specific alterations in brain dynamics induced by LSD, by first discretising the connectome-harmonic spectrum into 15 levels of wavenumbers k in the log-space and then analysing the energy changes within each of these parts of the harmonic spectrum for each of the 6 conditions and each subject separately (Methods).

For all 3 conditions, i.e. before, during and after-music sessions, with LSD vs. PCB, a significant change was observed in the energy of all quantized levels of wavelenths (p < 0.01, Monte-Carlo simulations after Bonferroni correction, Fig. 2e). Notably, the energy distribution over quantized levels of wavenumbers also followed a log-normal distribution for all conditions (Fig. 2e), where both, the mean (μ[E]), (Fig. 2f) and the width (σ[E]), (Fig. 2g) of the normal distribution increased in all LSD conditions, although slightly less for LSD with-music condition. Note that the number of divisions of the connectome-harmonic spectrum did not alter the log-normal distribution and the observed energy differences. This increase of the mean and width of the normal distribution suggests that LSD increases the energy (activity) of the brain states corresponding to high frequency wavenumbers. This energy increase for high frequency brain states (connectome harmonics with larger wavenumber k > 2 ⋅ 102 corresponding to 0.01–1% of the whole spectrum) is also clearly observed in Fig. 2h demonstrating the energy difference between LSD and PCB conditions before, during and after-music sessions. Critically, a significant decrease of energy is found for all low frequency brain states, connectome harmonics with wavenumer k < 2 ⋅ 102 corresponding to 0–0.01% of the whole spectrum (p < 0.01, Monte-Carlo simulations after Bonferroni correction, Fig. 2h). For both effects, increased energy of high frequencies and decreased energy of low frequencies, the differences between each pair of conditions were found to be significant (p < 0.01, Monte-Carlo simulations after Bonferroni correction). Figure 2i shows the mean energy across all subjects for the discretised spectrum of connectome harmonics and illustrates the increased energy of brain states with larger wavenumbers k > 2 ⋅ 102. Furthermore, for high frequency brain states (k > 103 corresponding to 0.05–1% of the whole spectrum) an increase was also found in energy fluctuations over time for all 3 LSD conditions (Fig. 2j). Taken together, our results reveal that LSD increases the total energy of brain activity and expands the repertoire of active brain states by significantly increasing the activity of high frequency brain states.

Cross-frequency correlations between brain states

We next sought to understand whether LSD-induced expansion of the repertoire of active brain states occurred in a structured or random fashion. To this end, we investigated LSD-induced changes in cross-frequency interactions in brain dynamics. We examined the degree of co-activation of different frequency brain states by exploiting the spectra-temporal representation enabled by the connectome-harmonic decomposition. As this harmonic decomposition of fMRI data yields the strength of activation of different frequency brain states over time, the correlation between the time courses of different connectome harmonics reveals the degree to which these two frequency brain states co-activate within the complex cortical dynamics. In this manner, we estimated cross-frequency correlations between each pair of brain states across all LSD and placebo conditions. Under the influence of LSD for all three conditions; before music, with music and after music, we observed a significant decrease in cross-frequency correlations within the low-frequency brain states (k ∈ [0–0.01%] of connectome-harmonic spectrum) (effect size; Cohen’s d-value \(\ast > 0.2\), Fig. 3a). Notably, this range of brain states is the same as that in which a significant decrease in energy was observed (Fig. 2h). In a higher frequency range k ∈ [0.01–0.1%], the only significant difference was found between LSD and PCB conditions with music (effect size; Cohen’s d-value \(\ast > 0.2\), Fig. 3b) indicating the influence of music on the co-activation of brain states within this frequency range. For increasing frequency, k ∈ [0.1–0.2%] of the spectrum, no significant differences were found in cross-frequency correlations (Fig. 3c). Finally, for higher frequency range k ∈ [0.2–1%], we found a significant increase in the cross-frequency correlations between LSD and PCB conditions, while this effect was not significant for conditions with and after-music (Fig. 3d). Also, over the complete spectrum of brain states, LSD significantly increased cross-frequency correlations (Fig. 3e).

Figure 3 Cross-frequency correlations. (a–d) Distributions of cross-frequency correlation values within [0–0.01%], [0.01–0.1%], [0.1–0.2%] and [0.2–1%] of the spectrum, respectively. (e) Distribution of cross-frequency correlations across the complete spectrum of connectome harmonics. Significant differences between cross-frequency correlation distributions are marked with stars (effect size; Cohen’s d-value \(\ast > 0.2\)) for pairs of condition LSD, PCB, LSD with-music, PCB with-music, LSD after-music, PCB after-music. (f–n) Illustrate differences in mean cross-frequency correlations in 10 × 10 partitions across the complete spectrum of connectome harmonics evaluated between all pairs of 6 condition; LSD, PCB, LSD with-music, PCB with-music; LSD after-music, PCB after-music. Full size image

Considering the sequential acquisition of the scans in conditions before music, with music and after music, the insignificant differences of the cross-frequency correlations within the high frequency range between LSD and PCB with music and after music can be attributable to both, the effect of music and the fading effect of LSD over time. To distinguish the effect of these two factors, we compared the average cross-frequency correlations across the whole connectome-harmonic spectrum between each pair of the 6 conditions (Fig. 3f–n). Figure 3f clearly demonstrates the decreased cross-frequency correlations among the low frequency brain states (k∈[0–0.1%] of the spectrum) accompanied by increased correlation between all frequencies in the range k∈[0.1–1%] of the spectrum. Over time, the LSD-induced increase in cross-frequency co-activation gradually diminished (Fig. 3f–h), which was also confirmed by the comparison of the sequentially acquired LSD scans (Fig. 3i–k). These changes were not found in the sequential comparison of PCB scans (Fig. 3l–n). Music under the influence of LSD decreased the cross-frequency correlations also within the frequency range k ∈ [0.01–0.02%] of the spectrum (Fig. 3g), which remarkably coincides with the range of brain states whose energy changes were altered under the influence of music (Fig. 2h). Notably, this effect of music was observed only in the LSD but not the PCB condition (Fig. 3m). This analysis confirms that both factors, the fading effect of LSD and the influence of music, contribute to observed changes in cross-frequency correlations over the three scans (LSD/PCB, LSD with-music/PCB with-music and LSD after-music/PCB after-music). However, while music affected the communication within the low to mid range frequencies k∈[0.01–0.02%] in particular under the influence of LSD, the isolated effect of LSD was apparent in the increased cross-frequency correlations throughout the connectome-harmonic spectrum.

These results demonstrate that for the low-frequency range, where the energy of brain states decrease under the influence of LSD, there is also a decrease in the “communication” (co-activation) of these brain states. The exact opposite effect, i.e. increased communication along with increased energy and power, is observed among a large part (k∈[0.01–1%]) of the spectrum under the influence of LSD. Such increased cross-frequency correlations strongly suggest that LSD causes a re-organization rather than a total randomization of brain dynamics. This type of non-random expansion of the state repertoire naturally occurs in dynamical systems when they approach criticality - the boundary of an order-disorder phase transition21,22. As a logical next step, we therefore investigated whether the dynamics of harmonic brain states show other characteristics of criticality and how these may be altered under the effect of LSD.

Power laws and whole-brain criticality

With a growing body of experimental evidence23,24,25,26,27,28,29,30 and theoretical findings31,32,33,34,35,36,37, it has become increasingly apparent that neural activity shows characteristics of criticality - a delicate balance between two extreme tendencies; a quiescent order and a chaotic disorder-where complexity increases and certain functional advantages may emerge38,39. Theoretical and computational studies identify that criticality enables the essential dualism necessary for complex dynamics; i.e. a certain level of stability (order) is required for coherent functioning and certain degree of disorder is needed for functional flexibility and adaptability34. These studies also highlight some important functional advantages of criticality; e.g. that greater diversity in the repertoire of brain states22 enables a larger capacity for information encoding22 and faster information processing22,30.

Supporting the hypothesis that brain dynamics reside at the edge of criticality, experimental studies reveal a key characteristic of critical dynamics - the power-law distributions - in large scale brain networks in fMRI24,27, electroencephalography (EEG)23,26,28, MEG23,24,28,29 and intracranial depth recordings in humans40 as well as in numerical simulations of computational models of brain dynamics33,35, mostly with small deviations from criticality to the subcritical (ordered) regime.

The power-laws, although observed consistently across wakefulness40, deep-sleep40, REM sleep40 and during anaesthetics induced loss of consciousness25, are found to slightly deteriorate in wakefulness30,37,40, tend to diminish in cognitive load41 and recover during sleep32,37,40,42. These findings suggest that even though power-laws are likely to be a feature of neural dynamics, which transcends levels of consciousness, differences in power-law distributions are characteristic of different states and the proximity of these states to critical dynamics. Furthermore, such deviations and subsequent re-emergence of power-laws with changing states of consciousness and cognitive-load strongly indicate that they originate from critical network dynamics, ruling out alternative explanations such as filtering or noise37.

In line with these findings, the tuning of brain dynamics towards or away from criticality is likely to be mediated by varying excitation/inhibition balance37,43,44, which has been shown to underlie the temporal organization of neuronal avalanches with power-law distributions43 as well as whole-brain oscillatory patterns15. In contrast, other pharmacologically induced variations in neural activity; e.g. changes in the concentration of dopamine or administration of a dopamine D1 receptor agonist45, or antagonist46, as well as application of acetylcholine47, lead to alterations of the steepness of the critical exponent without destroying the power-law distributions. As with other classic psychedelic drugs48, LSD’s principal psychoactive effects are mediated by serotonin 2A receptor (5-HT2AR) agonism, and 5-HT2AR signalling has reliably been shown to induce cortical excitation49. Increased cortical excitation via increased 5-HT2AR signalling is a plausible mechanism by which LSD may tune cortical dynamics towards criticality.

Based on LSD’s known pharmacology and related effects on cortical excitation10, as well as a prior hypothesis regarding the psychedelic state and criticality in the brain11, we investigated LSD-induced dynamical changes in the brain in the context of criticality. To this end, we evaluated the distribution of maximum power, average power as well as power fluctuations over the spectrum of connectome harmonics. Notably, all power related distributions (maximum, mean and standard deviation) of the connectome harmonics with different wavenumbers followed power-law distributions (Fig. 4). In line with previous findings30,32,40,42 and theoretical models31,32,33,34,35,36,37, we observed a slight cut-off in the tail of the power-law distributions indicative of the slight deviation to the subcritical regime. This result confirms previous studies suggesting that conscious, waking state brain dynamics reside at the edge of criticality with a slight deterioration to the subcritical regime35,37,40.

Figure 4 Power laws in connectome harmonic decomposition. Maximum power \(({\rm{\max }}(P({\psi }_{i})))\) vs. wavenumber (k) of connectome harmonics \(({\{{\psi }_{k}\}}_{k=1}^{n})\) in \({\mathrm{log}}_{10}\) coordinates for (a) LSD vs. PCB, (b) LSD with-music vs. PCB with-music and (c) LSD after-music vs. PCB after-music, respectively. Mean power \((\overline{P({\psi }_{k})}))\) vs. wavenumber (k) of connectome harmonics \(({\{{\psi }_{k}\}}_{k\mathrm{=1}}^{n})\) in \({\mathrm{log}}_{10}\) coordinates for (d) LSD vs. PCB, (e) LSD with-music vs. PCB with-music and (f) LSD after-music vs. PCB after-music, respectively. Power fluctuations (σ(P(ψ k ))) vs. wavenumber (k) of connectome harmonics \(({\{{\psi }_{k}\}}_{k=1}^{n})\) in \({\mathrm{log}}_{10}\) coordinates for all 6 conditions. In all plots, ε and β indicate the root mean squared error and the slope of the line fit, respectively. Stars indicate significant differences (p < 0.05, two-sample t-test). Full size image

In an effort to quantify LSD-induced changes to critical brain dynamics, we quantitatively evaluated the goodness of fit of power-laws, by measuring the root mean squared error ε of power-law fit for all different conditions (Methods). Critically, the root mean squared error of power-law-fits decreased significantly (p < 0.01, two-sample t-test) for maximum power (Fig. 4a,b), mean power (Fig. 4d,e) and power fluctuations (Fig. 4g,h) in LSD compared with PCB for the first two conditions (before music and with music). The decreased error of fit found for LSD vs. PCB in the after-music condition (Fig. 4c,f,i) remained insignificant, reflecting the slightly fading effect of LSD over the course of the three scans. The decreased goodness-of-fit error demonstrates that the distribution of all power-related observables (maximum power, mean power and power fluctuations) fit power-law distribution more closely under the influence of LSD. These experiments suggest that brain dynamics in both conditions, LSD and PCB, reside close to criticality with slight deviations to the subcritical regime, as also indicated in previous studies30,37,40, while the induction of LSD tunes brain dynamics further towards criticality. An additional analysis evaluated the power-law exponent for all 6 conditions. In all conditions with LSD compared to placebo, the power law exponent of maximum (Fig. 4a–c) and mean-power distribution (Fig. 4d–f) is found to decrease significantly (p < 0.01, two-sample t-test). For power fluctuations, the decrease was only significant for the first scan (Fig. 4g); LSD vs. placebo condition, coinciding with the peak of the LSD experience. This change in the power-law exponents under the influence of LSD indicates increased power and power-fluctuations of high frequency and slightly decreased power and power-fluctuations of low frequency connectome harmonics. As the decrease in power-law exponent and goodness-of-fit error both originate from the increased power of high frequency connectome harmonics, this finding confirms our earlier results regarding increased energy in high frequency states and enriched repertoire of brain states under the influence of LSD while indicating a crucial link between whole-brain criticality and the observed energy, power and repertoire changes.

LSD-induced energy changes correlate with subjective ratings

We also investigated how the LSD-induced changes in brain activity relate to subjective experience. Participants were asked to perform a limited number of visual analogue scale (VAS) style ratings at the end of each scan, using a button box in the scanner. Five key facets of the LSD experience were enquired about: (1) complex imagery (i.e. eyes-closed visions of objects, entities, landscapes etc.), (2) simple hallucinations (i.e. eyes-closed visions of shapes, colours, geometric patterns etc.), (3) emotional arousal (i.e. how emotional the participant felt, regardless of whether emotions were positive or negative), (4) positive mood, and (5) ego-dissolution (i.e. a fading sense of self, ego and/or subjectivity).

To examine the relation between the activation of different brain states and subjective experiences, we explored the correlations between energy changes of different frequency connectome harmonics and subjective ratings of the five experiences. We first estimated the amount of change in energy between LSD and PCB conditions for different connectome harmonics across all 12 subjects for the two scans without music (LSD/PCB and LSD after-music/PCB after-music). Then, we evaluated the correlations between the subjective ratings and the estimated energy differences ΔE = (E PCB − E LSD ) for both, individual harmonics and different ranges of the harmonic spectrum.

For the low frequency range k ∈ 1–200 corresponding to [0–0.01%] of connectome-harmonic spectrum, we observed generally a decrease in the mean energy as well as in the energy fluctuations under LSD at an individual subject level, as indicated by the positive values of \({\rm{\Delta }}\bar{{\rm{E}}}=({\bar{E}}_{{\rm{P}}{\rm{C}}{\rm{B}}}-{\bar{E}}_{{\rm{L}}{\rm{S}}{\rm{D}}})\) and Δσ(E = (σ(E PCB ) − σ(E LSD )) denoting the differences in the mean and in the standard deviation of energy between the placebo and LSD conditions, respectively (in Fig. 5a,b,d,e). The amount of the decrease in the mean energy \({\rm{\Delta }}\overline{{\rm{E}}}\) of this frequency range significantly correlated with the subjective ratings of ego-dissolution (r = 0.55317, p < 10−3, Fig. 5a) and emotional arousal (r = 0.61063, p < 10−3, Fig. 5b). We found similar correlations also between these subjective experiences and energy fluctuations of the same range of connectome harmonics (Fig. 5d,f). These findings suggest that the deactivation of the low-frequency connectome harmonics play a crucial role in the neural correlates of ego-dissolution and emotional arousal. Remarkably, this part of the connectome harmonic spectrum also corresponds to the same frequency range in which decreased energy (Fig. 2h) and decreased cross-frequency correlations (Fig. 4) were found under LSD.

Figure 5 Correlations between energy changes of connectome harmonics and subjective experiences. (a) and (b) demonstrate significant correlations between the difference in mean energy of connectome harmonics \({\rm{\Delta }}({\bar{{\rm{E}}}}_{{\rm{P}}{\rm{C}}{\rm{B}}}-{\bar{{\rm{E}}}}_{{\rm{L}}{\rm{S}}{\rm{D}}})\) for low frequency connectome harmonics k = [1, …, 200] and the subjective ratings of ego dissolution and emotional arousal, respectively. (c) shows the correlation between the energy difference of connectome harmonics \({\rm{\Delta }}({\bar{{\rm{E}}}}_{{\rm{PCB}}}-({\bar{E}}_{{\rm{LSD}}})\) or a broader frequency range of connectome harmonics k = [1, …, 1100] and the subjective ratings of positive mood. (d) and (e) demonstrate significant correlations between the difference in energy fluctuations of connectome harmonics Δ(σ(E PCB ) − σ(E LSD )) for low frequency connectome harmonics k = [1, …, 200] and the subjective ratings of ego dissolution and emotional arousal, respectively. (f) shows the correlation between difference in energy fluctuations of connectome harmonics Δ(σ(E PCB ) − σ((E LSD )) for k = [1, …, 1100] and the subjective ratings of positive mood. (g) Illustrates multiple correlations between the functional connectivity changes of groups of resting state networks (RSNs) and subjective experiences estimated using 200 brain states, k = [1, …, 200] * p < 10−10, ** p < 10−15 after Bonferroni correction. Correlation strengths are represented by the intensity of red for each pair. Full size image

The energy change within this low frequency range alone did not significantly correlate with ratings of positive mood under LSD. But a broader range of spatial frequencies k = [1, …, 1100] showed significant correlation with the intensity of positive mood induced by LSD (r = 0.45629, p < 10−2 for \({\rm{\Delta }}\overline{{\rm{E}}}\) and r = 0.4714, p < 10−2 for Δσ(E)). This finding implies that only a decrease of activity of low frequency connectome harmonics k = [1, …, 200] is not sufficient to account for the positive mood felt under LSD, but this decrease has to be accompanied by increased contribution of slightly higher frequency range connectome harmonics k = [201, …, 1100] for positive mood to be felt. Note that LSD generally induced a decrease in the low frequency range k = [1, …, 200] while leading to increased activation in the rest of the connectome harmonic spectrum k = [200, …, 18715], as shown in Fig. 2h.

For individual harmonics, although we observe high correlations ranging from −0.6 to 0.5 between the energy change of each harmonic and the subjective ratings, these correlations did not survive a conservative correction for multiple comparisons (Bonferroni correction), when the whole connectome-harmonic spectrum was considered (18715 comparisons, Fig. S3 shows the correlation values of the first 200 harmonics). We did not find any significant correlations between the subjective ratings of simple hallucinations and complex imagery and the energy changes of a particular frequency range of brain states.

Correlations between subjective ratings and connectivity of resting state networks

Finally, we asked whether there was a correlation between subjective ratings and connectivity of resting state networks (RSNs). Previous analyses with LSD10 and other psychedelics11,50,51 have shown changes in the functional properties of RSNs under these drugs that correlate with different psychological aspects of the experience.

Even for simple hallucinations, it is now understood that no one single brain area is responsible, but rather the interaction of multiple brain areas52. Thus, unlike previous studies focusing on the connectivity of individual networks10,11,50,51, here we investigated how the connectivity changes in groups of networks mutually relate to the intensity of subjective experience using multiple correlation analysis53. We examined the correlations between the ratings of subjective experiences of simple hallucinations, complex imagery, emotional arousal, positive mood and ego dissolution and LSD-induced functional connectivity changes of RSNs, individually, as well as in subgroups of RSNs using multiple correlation analysis53.

For the group analysis we first identified the following RSNs as described in10: medial visual network (VisM), lateral visual network (VisL), occipital pole network (VisO), auditory network (AUD), sensorimotor network (SM), default-mode network (DMN), parietal cortex network (PAR), dorsal attention network (DAN), salience network (SAL), posterior opercular network (POP), left fronto-parietal network (lFP) and right fronto-parietal network (rFP) and then defined the following subgroups of networks: fronto-parietal network (FPN by combining lFP and lFP), visual (by combining VisM, VisL, VisO), visual-AUD, PAR-pOP, pOP-rFP, DMN-SAL, DMN-lFP, DMN-rFP, DMN-FPN, DMN-pOP, SAL-lFP, SAL-rFP, lFP-visual, rFP-visual.

As connectome harmonics are spatial patterns of synchronous activity emerging on the cortex for different frequency oscillations, they are theoretically equivalent to frequency-specific functional connectivity patterns15; hence, the observed functional connectivity changes in the RSNs can be attributed to and decomposed into the changes in the activation of individual connectome harmonics. Here, we evaluated multiple correlations between groups of RSNs and subjective ratings using both, estimated functional connectivity changes of RSNs directly and their correlations with the energy changes of individual harmonics (Methods).

Although the evaluation of the multiple correlation analysis between subjective ratings and connectivity changes of RSNs showed differences of correlations (Fig. S4a), in this direct application, no correlation was found to be significant. One limitation of this approach is that the small number of data points (12 subjects × 2 scans leading to 24 dimensional vectors to compute the multiple correlations) renders the correlation analysis poorly powered to reveal potentially ‘true’ relations between RSNs and subjective ratings (i.e. the risk of false negatives). This limitation can be addressed by firstly correlating the connectivity changes of RSNs to energy changes of individual brain states (connectome harmonics) and then evaluating the multiple correlations between the subjective ratings and individual or groups of RSNs (Methods). This approach has the advantage of enabling hidden information present in the data itself to emerge by revealing the contribution of each brain state to changes in functional connectivity. The number of brain states chosen to express the connectivity changes of RSNs will determine the sensitivity of multiple correlations (Fig. S4, Methods). Fig. S4 shows the multiple correlation values evaluated on the RSN connectivity directly, and for increasing number of brain states (30, 50, 100, 200 and 18715 (complete spectrum)). Although, similar correlation matrices emerge in the direct (on the RSN connectivity) and indirect (on the energy changes of connectome harmonics) evaluation of multiple correlations, the latter revealed significant correlations between the intensity of certain subjective experiences and groups of RSNs.

Firstly, we observed significant correlations between the connectivity changes of visual and sensory (visual-auditory) networks and ratings of simple hallucinations and complex imagery (Fig. 5g, **p < 10−15, k ∈ [1, …, 200], after Bonferroni correction). However, this significant correlation was only observed when the visual or sensory networks are considered together but not individually. This finding suggests that it is not the activity of individual networks alone but rather their joint activity that relates to the experience of hallucinations and imagery. Moreover, the coupled connectivity of the the visual networks with the left fronto-parietal network (lFP) correlated with ratings of simple hallucinations (Fig. 5g, **p < 10−15, k ∈ [1, …, 200], after Bonferroni correction). Interestingly, the coupled connectivity of the right fronto-parietal network (rFP) with the visual networks was found to significantly correlate with the ratings of both, complex imagery and simple hallucinations (Fig. 5g, **p < 10−15, k ∈ [1, …, 200], after Bonferroni correction) suggesting that the asymmetric contribution of the fronto-parietal networks may underlie the perceptual abnormalities such as visual hallucinations experienced in the psychedelic state.

Secondly, we also found significant correlations between the DMN connectivity and the intensity of emotional arousal (Fig. 5g, **p < 10−15, k ∈ [1, …, 200], after Bonferroni correction). The changes in coupled connectivity of DMN with the salience network (SAL) - a network of brain areas that plays an important role in attentional capture of biologically and cognitively relevant events52 - showed significant correlations with all three experiences of emotional arousal, positive mood and ego dissolution (Fig. 5g, **p < 10−15, k ∈ [1, …, 200], after Bonferroni correction). Importantly, abnormal DMN-SAL functional connectivity correlating with intense subjective effects has previously been reported under LSD10 and psilocybin54. We also found that the coupled connectivity changes of SAL with lFP alone or 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 (Fig. 5g, *p < 10−10, k ∈ [1, …, 200], after Bonferroni correction) for correlations with the ratings of these experiences. In particular, the coupling of the the rFP and lFP together with the SAL increased the significance of the correlations with positive mood (Fig. 5g, **p < 10−15, k ∈ [1, …, 200], after Bonferroni correction). The coupled connectivity changes of posterior opercular network (pOP) and DMN as well as pOP and the parietal network (PAR) also showed significant correlation with the ratings of emotional arousal, whereas the correlation of pOP connectivity alone was less significant (Fig. 5g, *p < 10−10, k ∈ [1, …, 200], after Bonferroni correction). All four pairs of networks, DMN-SAL, DMN-rFP, DMN-pOP, PAR-pOP, which significantly correlated with the ratings of emotional arousal, have been previously reported to show increased functional connectivity under LSD17 and the DMN specifically has been linked to mood and emotion52,55,56,57,58 as well as ego-dissolution in relation to psychedelics10,11. Our findings suggest a potential link between the increased between-RSN functional coupling, particularly in relation to high-level RSNs, and emotional arousal under the effect of LSD. Further important parallels emerge between these findings linking the RSNs to the intensity of subjective experiences in the psychedelic state and the abnormal activity of RSNs in psychiatric disorders, as explained in Discussion.