Serotonergic psychedelics LSD & psilocybin increase the fractal dimension of cortical brain activity in spatial and temporal domains

This fMRI study (2020) found that LSD and psilocybin increased the fractal dimension of cortical brain activity, which is suggested to serve as a direct measure to validate current theories of psychedelic neural mechanisms.


“Psychedelic drugs, such as psilocybin and LSD, represent unique tools for researchers investigating the neural origins of consciousness. Currently, the most compelling theories of how psychedelics exert their effects is by increasing the complexity of brain activity and moving the system towards a critical point between order and disorder, creating more dynamic and complex patterns of neural activity. While the concept of criticality is of central importance to this theory, few of the published studies on psychedelics investigate it directly, testing instead related measures such as algorithmic complexity or Shannon entropy. We propose using the fractal dimension of functional activity in the brain as a measure of complexity since findings from physics suggest that as a system organizes towards criticality, it tends to take on a fractal structure. We tested two different measures of fractal dimension, one spatial and one temporal, using fMRI data from volunteers under the influence of both LSD and psilocybin. The first was the fractal dimension of cortical functional connectivity networks and the second was the fractal dimension of BOLD time series. In addition to the fractal measures, we used a well-established, non-fractal measure of signal complexity and show that they behave similarly. We were able to show that both psychedelic drugs significantly increased the fractal dimension of functional connectivity networks and that LSD significantly increased the fractal dimension of BOLD signals, with psilocybin showing a non-significant trend in the same direction. With both LSD and psilocybin, we were able to localize changes in the fractal dimension of BOLD signals to brain areas assigned to the dorsal-attention network. These results show that psychedelic drugs increase the fractal dimension of activity in the brain and we see this as an indicator that the changes in consciousness triggered by psychedelics are associated with evolution towards a critical zone.”

Authors: Thomas F. Varley, Robin Carhart-Harris, Leor Roseman, David K. Menon & Emmanuel A. Stamatakis


Psychedelic drugs increase the complexity of brain activity by moving the system towards a critical point between order and disorder, creating more dynamic and complex patterns of neural activity. We used fMRI data from volunteers under the influence of both LSD and psilocybin to study how these changes in complexity affect consciousness.

Author summary

Psychedelic drugs produce a unique state of consciousness that can be measured using measures of “fractal-quality” of brain activity. These measures behave similarly to a well established, non-fractal measure of signal complexity frequently used in previous studies of consciousness.

1. Introduction

Since the turn of the century, there has been a renewal of interest in the science of serotonergic psychedelic drugs, including LSD, psilocybin, mescaline, etc. This is because of the potential medical applications of these drugs, as well as what they might tell us about the relationship between activity in the brain and consciousness.

Neuroimaging studies using fMRI and MEG have suggested that the psychedelic state is caused by an increase in entropy in the brain, which brings the system closer to a critical zone between order and disorder. The hypothesis that the brain operates in the critical zone is well-established, and systems near the critical point tend to take on particular, highly stereotyped structures.

Studies with psilocybin have shown that the patterns of functional connectivity in the brain undergo dramatic reorganization, and that the repertoire of possible states functional connectivity networks can occupy is increased, which is interpreted as an increase in the entropy of the entire system.

Many measures of brain complexity have been tested, but none of them directly address the phenomenon of criticality. The only study that has directly addressed the criticality aspect of the EBH is the study of LSD and connectome harmonics. There are many ways to assess the complexity of a time-series, and each one provides different information about system dynamics. Fractal dimension is an additional measure that can be related to critical processes.

To address the relative lack of studies testing criticality directly, we propose a measure of complexity called fractal dimension.

Fractals are ubiquitous in nature and are defined by the property of having a non-integer dimension. If the brain is moving closer towards a state of criticality, then we might expect any fractal character in brain activity to become more pronounced. When consciousness is lost, the fractal dimension of brain activity drops significantly, with the exception of REM sleep, during which the fractal dimension rises again. The fractal dimension is also sensitive to subtler changes in cognition, such as attentional states and hypnosis.

The physical structure of the brain and the patterns of activity measured by neuroimaging paradigms display pronounced fractal character. This fractal character may play an important role in regulating how information is propagated through the brain.

We created 1000-node functional connectivity networks from fMRI data from subjects under the influence of either LSD or psilocybin, and used a network-specific variation of the box-counting algorithm to extract the fractal dimension. We also used the Higuchi fractal dimension to test the temporal fractal dimension. Previous work has shown that both of these measures are sensitive to changes in level of consciousness following traumatic or anoxic brain injury.

We used a Lempel-Ziv complexity analysis to check the validity of the fractal dimension measures and hypothesized that the patterns observed in previous studies should be apparent here as well.

2.2. Calculating network fractal dimension

When calculating the fractal dimension of a naturally occurring system, researchers commonly use a box-counting algorithm. This algorithm captures the distribution of elements across multiple scales, and can be used to estimate the length of a shape in space.

Because of the logarithmic relationship between box-size and fractal dimension, the highest-resolution parcellation that is computationally tractable is required to achieve modest increases in the measured fractal dimension.

We used the CBB method to analyze the fractal dimension of human FC networks, and found that the network had a power-law structure. The results should not be interpreted as proof that a power-law structure exists, but rather as a preliminary result.

2.3. Calculating BOLD time-series fractal dimension

The Higuchi fractal dimension algorithm can be applied to two-dimensional images, such as histological photographs, to test whether the spacial distribution of cortical activity follows a fractal pattern.

2.4. Lempel-Ziv complexity of temporal BOLD series

The Lempel-Ziv algorithm creates a dictionary of binary patterns from a time-series, and returns a value LZC jDj . This value is normalised by dividing the “true” value of LZC by LZCrand .

2.5.1. LSD data

20 healthy volunteers underwent two scans, 14 days apart, with a placebo and an active dose of LSD. The scans were eyes closed, resting state without any in-ear auditory stimulation.

The following pre-processing stages were performed: removal of the first three volumes, de-spiking, slice time correction, motion correction, brain extraction, registration to anatomical scans, non-linear registration to 2 mm MNI brain, scrubbing, spatial smoothing, and 9 nuisance regressors.

2.5.2. Psilocybin data

We scanned 15 healthy volunteers and infused psilocybin (2 mg in 10-mL saline) in the active scan. We used the psilocybin-positive scan to compare the pre-infusion condition to the post-infusion condition for control.

All data was preprocessed using the following pipeline: de-spiking, slice time correction, motion correction to best volume, brain extraction using the BET module in FSL, registration to anatomy, scrubbing, smoothing, linear and quadratic detrending, and regression of 6 motion regressors and 3 nuisance regressors.

2.6. Formation of functional connectivity networks

We extracted BOLD time-series data from each brain, segmented the cerebral cortex into 1000 distinct ROIs, and used the Schaefer Local/Global 1000 Parcellation to achieve an optimal balance between network resolution and computational tractability.

Every time-series was transformed using the norm of the Hilbert transform, and the Pearson Correlation was used to correlate every time-series with every other time-series.

No significance testing was done, because significance filtering would have resulted in an uneven distribution of edges and degrees between graphs. The correlation matrices were filtered to remove self-loops, ensuring simple graphs.

A 95% threshold was chosen to ensure that only positive values survived thresholding, and that any surviving edges became ones. This resulted in a marginally less sparse network than what might have occurred if negative values had been thrown out prior to thresholding.

2.6.1. Specific-network analysis

We used the 1000 ROI parcellation and the mapping proposed by Yeo et al. (2011) to group individual time-series into seven networks. We then used the Higuchi fractal dimension method to measure the average time-series fractal dimension of each network.

2.6.2. Statistical analysis

The analysis was carried out using the Python 3.6 programming language in the Spyder IDE, using the packages provided by the Anaconda distribution. The significance tests were non-parametric, and the Benjamini-Hochberg procedure was used to correct for multiple comparisons within a single analysis.

3. Results

3.1. LSD & psilocybin network fractal dimension

These results are consistent with the EBH, which posits that criticality will increase during psychedelic states. The difference in base-line fractal dimension between LSD and psilocybin is intriguing, and may be a result of differences in data acquisition and processing specifications.

3.2. LSD & psilocybin BOLD time-series fractal dimension

In the LSD condition, a correlation between the network fractal dimension and the temporal fractal dimension was found, but not meaningful.

The results suggest that the activity of the brain tends towards increased fractal character in the temporal as well as spatial dimension, and that this is consistent with the EBH. The difference between the two non-drug conditions is most likely explained by the significant difference in dataset lengths.

3.2.1. Localizing time-series fractal dimension to sub-networks

The Higuchi method was used to determine the fractal dimension of the fMRI time-series for the psilocybin condition. Only one significant difference in the fractal dimension of the time-series was found, in the dorsal attenion network.

We found significant increases in fractal dimension in the fronto-parietal, dorsal-attenion, and visual networks under LSD compared to the placebo condition.

The dorsal-attenion network was increased in both LSD and psilocybin, suggesting that this increase may be more robust than the increases in the fronto-parietal network or visual network that appear to be unique to LSD.

3.3. LSD & psilocybin BOLD Lempel-Ziv complexity

In the LSD and psilocybin conditions, the Lempel-Ziv complexity correlated better with the network fractal dimension and Higuchi fractal dimension than they did with each-other.

The LZC measure may be more “robust” when compared to the fractal dimension measure, at least where temporally sparse signals such as BOLD are concerned.

In the LSD condition, the fronto-parietal network, the dorsal-attenion network, and the visual network had higher complexity than in the placebo condition. In the psilocybin condition, the ventral-attenion network and the dorsal-attenion network approached significance.

Using the Higuchi fractal dimension and Compact-Box burning algorithm, we found that the fractal dimension of cortical functional connectivity networks is increased by both psilocybin and LSD, and that the fractal dimension of the BOLD time-series is increased by LSD, but not psilocybin.

The results of this study are consistent with theories of consciousness beyond the EBH, such as Integrated Information Theory (IIT) and the so-called algorithmic information theory of consciousness (KT), which both propose an entropic but hierarchically modular structure characterized by both high entropy rate and fractal character.

The 5-HT2A receptor is widely expressed in the CNS, but a specific population localized to Layer V pyramidal cells in the neocortex is both necessary and sufficient to induce psychedelic effects. This suggests that the 5-HT2A receptor serves as a kind of ‘information gate’ in neural information processing. During normal waking consciousness, areas of the brain may not be functionally connected by Layer V pyramidal neurons, but when psychedelics are introduced, this changes.

Neuron firing may be analogous to increasing the branching ratio, which may bring the process closer to the critical value of c. Furthermore, different neurotransmitter systems co-regulate each-other, and so the effects of psychedelic drugs are likely to rely on multiple systems.

The dorsal-attenion network is involved in a variety of processes related to visual processing of the environment, and has been proposed to be involved with top-down, conscious allocation of attention to environmental objects.

LSD increased the complexity of BOLD signals in the fronto-parietal network, but not in the Default Mode Network. This may be due to the sheer number of nodes assigned to the DMN being weighted equally, thus obscuring a real effect only present in a subset of DMN nodes.

LSD alters the coherence of signals in visual areas thought to be associated with the experience of hallucinations. This may be a particularly fruitful avenue of psychedelic research going forward.

This study has several limitations, including a small sample size, a low number of samples per time-series, and a low parcellation resolution. However, a replication with EEG or MEG data should be considered before these results are considered strong.

Future studies should use a higher resolution cortical parcellation, and should also strive to ensure that the subjective intensities of the experiences volunteers underwent was equivalent. This would allow researchers to more fully explore the commonalities, and differences between individual psychedelic compounds.

6. Conclusions

In this study we report that the fractal dimension of cortical functional connectivity networks and BOLD time-series is increased under the influence of two serotonergic psychedelics: LSD and psilocybin. These results are consistent with a different, non-fractal measure of complexity, Lempel-Ziv compressibility.

CRediT authorship contribution statement

Thomas F. Varley, Robin Carhart-Harris, Leor Roseman, David K. Menon and Emmanuel A. Stamatakis contributed to this work.


Authors associated with this publication with profiles on Blossom

Robin Carhart-Harris
Dr. Robin Carhart-Harris is the Founding Director of the Neuroscape Psychedelics Division at UCSF. Previously he led the Psychedelic group at Imperial College London.

Leor Roseman
Leor Roseman is a researcher at the Centre for Psychedelic Research, Imperial College London. His work focussed on psilocybin for depression, but is now related to peace-building through psychedelics.


Institutes associated with this publication

Imperial College London
The Centre for Psychedelic Research studies the action (in the brain) and clinical use of psychedelics, with a focus on depression.

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