Shannon entropy of brain functional complex networks under the influence of the psychedelic Ayahuasca

This within-subjects study (n=10) investigated the effect of ayahuasca on brain activity. Resting-state fMRI data was broadly consistent with the entropic brain hypothesis which holds that the effects of psychedelics are partially explained in terms of increased entropy of the brain’s functional connectivity.

Abstract

“The entropic brain hypothesis holds that the key facts concerning psychedelics are partially explained in terms of increased entropy of the brain’s functional connectivity. Ayahuasca is a psychedelic beverage of Amazonian indigenous origin with legal status in Brazil in religious and scientific settings. In this context, we use tools and concepts from the theory of complex networks to analyze resting state fMRI data of the brains of human subjects under two distinct conditions: (i) under ordinary waking state and (ii) in an altered state of consciousness induced by ingestion of Ayahuasca. We report an increase in the Shannon entropy of the degree distribution of the networks subsequent to Ayahuasca ingestion. We also find increased local and decreased global network integration. Our results are broadly consistent with the entropic brain hypothesis. Finally, we discuss our findings in the context of descriptions of “mind-expansion” frequently seen in self-reports of users of psychedelic drugs.”

Authors: Aline Viol, Fernanda Palhano-Fontes, Heloisa Onias, Draulio B. de Araujo & Gandhimohan M. Viswanathan

Summary

Neuroimaging techniques such as functional magnetic resonance imaging have allowed noninvasive investigation of global brain activity in a variety of conditions. Recent studies have shown that the entropy of the brain’s functional connectivity increases during the psychedelic experience. This increase can be explained by the complex spatiotemporal cortical activation pattern during anesthesia with ketamine and by the appearance of many transient low-stability structures after administration of psilocybin. Here we directly measure the Shannon entropy of the functional networks of the human brain under the influence of a psychedelic.

Ayahuasca is a beverage of Amazonian indigenous origin that contains the powerful psychedelic N,N- dimethyltryptamine (DMT), together with harmala alkaloids that are known to be monoamine oxidase inhibitors (MAOIs). It has been shown to be effective in treating mental disorders such as depression and behavioral addiction.

We use tools and concepts from the field of complex networks for analysis, which was started in the 1960s by Harary. These tools and concepts have found successful application in the study of diverse phenomena, such as air transportation networks, terrorist networks, gene regulatory networks, and functional brain networks.

Ten healthy volunteers were submitted to two distinct fMRI scanning sessions: before and 40 minutes after Ayahuasca intake.

Data analysis consists of two main steps. In the first step, we use fMRI data to generate complex networks, and in the second step, we calculate network characteristics using techniques from the theory of complex networks.

The main result of this study is that the functional brain networks become less connected globally but more connected locally after Ayahuasca ingestion.

Our method for studying the brain experimentally is grounded in two strong theoretical traditions: graph theory and complex networks, and information theory and statistical physics. It is the first time this specific approach has been applied to characterize functional brain networks in altered states of consciousness.

We find evidence of significant changes in the functional brain networks of subjects after Ayahuasca intake. The degree distributions become less peaked and wider after Ayahuasca intake.

Figure 3 shows that the average Shannon entropy of the degree distributions increases after Ayahuasca intake. Figure 4 shows that the average Shannon entropy increases subject-by-subject, and that there is a Pearson correlation coefficient of 0.005 between entropy increases and motion.

The degree distribution of a network does not completely define a network, however it can have great influence over other network properties. The Maslov algorithm can be used to generate iso-entropic randomized networks, which can be used to study the effects of Ayahuasca intake.

We generated 30 iso-entropic randomized networks for each original network, and compared the original networks with the randomized networks to determine the extent to which the degree distributions explained the changes in network properties.

After Ayahuasca ingestion, the global integration of networks increased and the global efficiency decreased. However, the change in degree distribution cannot explain the entire change.

Figure 2 shows that the degree distributions of the networks change shape after Ayahuasca ingestion, and that the Shannon entropy is higher after Ayahuasca.

Significant changes are observed in geodesic distance and global efficiency, which are measured as the ratio D/Drand and similarly for the global efficiency.

Ayahuasca ingestion increases local integration. The ratio of clustering coefficients to crand is close to zero, indicating that degree distribution can account for most of the change in clustering and local efficiency.

The subjective states of the subjects were evaluated using two psychometric scales. The correlations between CADSS scores variation and entropy before Ayahuasca intake reach r = 0.91 and r = 0.71, respectively.

Discussion

We interpret the findings of this study in the context of some well understood prototypical classes of networks. We find that the degree distribution of Ayahuasca networks becomes broader, and that the Shannon entropy of the node degree distribution increases in parallel with clustering and geodesic distance.

Figure 3 shows that the entropy of the distribution of node degrees increases after Ayahuasca ingestion. This increase is the main result that we report.

Ayahuasca intake decreased global integration and increased local robustness in functional brain networks, which could be explained by a variation in modular structure of the networks.

The entropic brain hypothesis holds that the mental state induced by psychedelics (termed “primary-state”) presents relatively elevated entropy in some features of brain organization, compared to the ordinary waking state (termed “secondary”).

Figure 4 shows the entropy growth per subject after Ayahuasca ingestion, and the significant increase in entropy after Ayahuasca ingestion is indicated by the asterisks (*) in the bottom rows of both plots.

We believe that the increase in entropy observed in a brain that has been temporarily freed from constraints may be related to the mind becoming more flexible and less identified with the reality it represents.

Ayahuasca ingestion decreased global efficiency and integration in the complex networks of all 7 subjects, as well as in their corresponding iso-entropic randomized networks.

Several studies have investigated the role of entropy in brain functional networks. Tagliazucchi et al.14, Yao et al.66, Schröter et al.4, and Lebedev et al.15 have shown that entropy may be correlated to brain function and perhaps also its development.

After Ayahuasca ingestion, clustering coefficient C and local efficiency E l increased, as well as the mean degrees of the networks for all 7 subjects.

We comment on the limitations of our method, such as the small number of subjects, the fact that all were experienced with Ayahuasca, and that the chosen range of correlation values automatically limits the networks’ behavior to a small-world network.

We calculated the Shannon entropy of the degree distribution of complex networks generated from fMRI data and found that psychedelics increase the entropy in brain functions.

10 healthy right-handed adult volunteers (mean age 31.3, from 24 to 47 years) underwent fMRI and T1-weighted imaging with a 1.5 T scanner (Siemens, Magneton Vision) using an EPI-BOLD like sequence comprising 150 volumes and 156 contiguous sagittal slices.

The volunteers were not under medication for at least 3 months prior to the scanning session, were abstinent from caffeine, nicotine and alcohol prior to the acquisition, and ingested 120 – 200 mL of Ayahuasca known to contain 0.8 mg/mL of DMT and 0.21 mg/mL of harmine.

Methods

Complex network metrics include node degree, geodesic distance, clustering coefficient, and local and global network efficiencies. Non-weighted undirected networks are isomorphic to a binary symmetric matrix known as the adjacency matrix.

A network’s degree distribution is the normalized histogram of degrees over all nodes, and its geodesic distance is the number of links in the shortest geodesic path between two nodes. Its clustering coefficient is defined by .

The efficiency of a network is measured by the reciprocal of the harmonic mean of geodesic distances.

We calculate the Shannon entropy of a network with N nodes by taking the normalized probability distribution for node degree k and dividing it by the number of nodes in the network.

The Maslov algorithm generates randomized networks by unlinking and relinking non-overlapping pairs of linked nodes. The degree of each node remains the same.

We segmented the brain images into 110 brain regions, calculated the average fMRI time series for each region, and applied a band-pass filter to reduce confounders. We then calculated the Pearson correlation between these wavelet coefficients from all possible pairs, and considered only reliable values.

We use a thresholding function to create non-weighted networks from correlation matrices. We create a number of networks for each fMRI sample, all with the same number of nodes (104 nodes), and analyze the behavior of the network properties over a range of values.

We choose common upper and lower thresholds for all correlation matrices to ensure the networks were fully connected but also relatively sparse. These thresholds are identical to those adopted by refs 4, 54.

We excluded two subjects from the analysis because they had different threshold ranges, and a third subject was excluded due to excessive head movement. We generated networks with mean degree in the range 24 k – 39, and showed network properties as a function of mean degree.

Comparisons between the two conditions are obtained from paired-sample Student’s t-tests, with p values ranging from 0.05 to 0.005.

Acknowledgements

Santo Daime members provided the Ayahuasca, and the research was funded by CAPES and CNPq. AV thanks Guillermo Cecchi and Irina Rish for their hospitality and discussions.

Author Contributions

D.B.A. recruited the volunteers, A.V., F.P.-F. and H.O. performed fMRI data preprocessing, complex network construction and evaluated standard network features, A.V. and G.M.V. wrote the first manuscript draft.

The author(s) of this article have given a Creative Commons Attribution 4.0 International License to the article and the source, and have indicated if changes were made.

Summary

Neuroimaging techniques such as functional magnetic resonance imaging have allowed noninvasive investigation of global brain activity in a variety of conditions. Recent studies have shown that the entropy of the brain’s functional connectivity increases during the psychedelic experience. This increase can be explained by the complex spatiotemporal cortical activation pattern during anesthesia with ketamine and by the appearance of many transient low-stability structures after administration of psilocybin. Here we directly measure the Shannon entropy of the functional networks of the human brain under the influence of a psychedelic.

Ayahuasca is a beverage of Amazonian indigenous origin that contains the powerful psychedelic N,N- dimethyltryptamine (DMT), together with harmala alkaloids that are known to be monoamine oxidase inhibitors (MAOIs). It has been shown to be effective in treating mental disorders such as depression and behavioral addiction.

We use tools and concepts from the field of complex networks for analysis, which was started in the 1960s by Harary. These tools and concepts have found successful application in the study of diverse phenomena, such as air transportation networks, terrorist networks, gene regulatory networks, and functional brain networks.

Ten healthy volunteers were submitted to two distinct fMRI scanning sessions: before and 40 minutes after Ayahuasca intake.

Data analysis consists of two main steps. In the first step, we use fMRI data to generate complex networks, and in the second step, we calculate network characteristics using techniques from the theory of complex networks.

The main result of this study is that the functional brain networks become less connected globally but more connected locally after Ayahuasca ingestion.

Our method for studying the brain experimentally is grounded in two strong theoretical traditions: graph theory and complex networks, and information theory and statistical physics. It is the first time this specific approach has been applied to characterize functional brain networks in altered states of consciousness.

We find evidence of significant changes in the functional brain networks of subjects after Ayahuasca intake. The degree distributions become less peaked and wider after Ayahuasca intake.

Figure 3 shows that the average Shannon entropy of the degree distributions increases after Ayahuasca intake. Figure 4 shows that the average Shannon entropy increases subject-by-subject, and that there is a Pearson correlation coefficient of 0.005 between entropy increases and motion.

The degree distribution of a network does not completely define a network, however it can have great influence over other network properties. The Maslov algorithm can be used to generate iso-entropic randomized networks, which can be used to study the effects of Ayahuasca intake.

We generated 30 iso-entropic randomized networks for each original network, and compared the original networks with the randomized networks to determine the extent to which the degree distributions explained the changes in network properties.

After Ayahuasca ingestion, the global integration of networks increased and the global efficiency decreased. However, the change in degree distribution cannot explain the entire change.

Figure 2 shows that the degree distributions of the networks change shape after Ayahuasca ingestion, and that the Shannon entropy is higher after Ayahuasca.

Significant changes are observed in geodesic distance and global efficiency, which are measured as the ratio D/Drand and similarly for the global efficiency.

Ayahuasca ingestion increases local integration. The ratio of clustering coefficients to crand is close to zero, indicating that degree distribution can account for most of the change in clustering and local efficiency.

The subjective states of the subjects were evaluated using two psychometric scales. The correlations between CADSS scores variation and entropy before Ayahuasca intake reach r = 0.91 and r = 0.71, respectively.

Discussion

We interpret the findings of this study in the context of some well understood prototypical classes of networks. We find that the degree distribution of Ayahuasca networks becomes broader, and that the Shannon entropy of the node degree distribution increases in parallel with clustering and geodesic distance.

Figure 3 shows that the entropy of the distribution of node degrees increases after Ayahuasca ingestion. This increase is the main result that we report.

Ayahuasca intake decreased global integration and increased local robustness in functional brain networks, which could be explained by a variation in modular structure of the networks.

The entropic brain hypothesis holds that the mental state induced by psychedelics (termed “primary-state”) presents relatively elevated entropy in some features of brain organization, compared to the ordinary waking state (termed “secondary”).

Figure 4 shows the entropy growth per subject after Ayahuasca ingestion, and the significant increase in entropy after Ayahuasca ingestion is indicated by the asterisks (*) in the bottom rows of both plots.

We believe that the increase in entropy observed in a brain that has been temporarily freed from constraints may be related to the mind becoming more flexible and less identified with the reality it represents.

Ayahuasca ingestion decreased global efficiency and integration in the complex networks of all 7 subjects, as well as in their corresponding iso-entropic randomized networks.

Several studies have investigated the role of entropy in brain functional networks. Tagliazucchi et al.14, Yao et al.66, Schröter et al.4, and Lebedev et al.15 have shown that entropy may be correlated to brain function and perhaps also its development.

After Ayahuasca ingestion, clustering coefficient C and local efficiency E l increased, as well as the mean degrees of the networks for all 7 subjects.

We comment on the limitations of our method, such as the small number of subjects, the fact that all were experienced with Ayahuasca, and that the chosen range of correlation values automatically limits the networks’ behavior to a small-world network.

We calculated the Shannon entropy of the degree distribution of complex networks generated from fMRI data and found that psychedelics increase the entropy in brain functions.

10 healthy right-handed adult volunteers (mean age 31.3, from 24 to 47 years) underwent fMRI and T1-weighted imaging with a 1.5 T scanner (Siemens, Magneton Vision) using an EPI-BOLD like sequence comprising 150 volumes and 156 contiguous sagittal slices.

The volunteers were not under medication for at least 3 months prior to the scanning session, were abstinent from caffeine, nicotine and alcohol prior to the acquisition, and ingested 120 – 200 mL of Ayahuasca known to contain 0.8 mg/mL of DMT and 0.21 mg/mL of harmine.

Methods

Complex network metrics include node degree, geodesic distance, clustering coefficient, and local and global network efficiencies. Non-weighted undirected networks are isomorphic to a binary symmetric matrix known as the adjacency matrix.

A network’s degree distribution is the normalized histogram of degrees over all nodes, and its geodesic distance is the number of links in the shortest geodesic path between two nodes. Its clustering coefficient is defined by .

The efficiency of a network is measured by the reciprocal of the harmonic mean of geodesic distances.

We calculate the Shannon entropy of a network with N nodes by taking the normalized probability distribution for node degree k and dividing it by the number of nodes in the network.

The Maslov algorithm generates randomized networks by unlinking and relinking non-overlapping pairs of linked nodes. The degree of each node remains the same.

We segmented the brain images into 110 brain regions, calculated the average fMRI time series for each region, and applied a band-pass filter to reduce confounders. We then calculated the Pearson correlation between these wavelet coefficients from all possible pairs, and considered only reliable values.

We use a thresholding function to create non-weighted networks from correlation matrices. We create a number of networks for each fMRI sample, all with the same number of nodes (104 nodes), and analyze the behavior of the network properties over a range of values.

We choose common upper and lower thresholds for all correlation matrices to ensure the networks were fully connected but also relatively sparse. These thresholds are identical to those adopted by refs 4, 54.

We excluded two subjects from the analysis because they had different threshold ranges, and a third subject was excluded due to excessive head movement. We generated networks with mean degree in the range 24 k – 39, and showed network properties as a function of mean degree.

Comparisons between the two conditions are obtained from paired-sample Student’s t-tests, with p values ranging from 0.05 to 0.005.

Acknowledgements

Santo Daime members provided the Ayahuasca, and the research was funded by CAPES and CNPq. AV thanks Guillermo Cecchi and Irina Rish for their hospitality and discussions.

Author Contributions

D.B.A. recruited the volunteers, A.V., F.P.-F. and H.O. performed fMRI data preprocessing, complex network construction and evaluated standard network features, A.V. and G.M.V. wrote the first manuscript draft.

The author(s) of this article have given a Creative Commons Attribution 4.0 International License to the article and the source, and have indicated if changes were made.