Different hierarchical reconfigurations in the brain by psilocybin and escitalopram for depression

Abstract

Effective interventions for neuropsychiatric disorders may work by rebalancing the brain’s functional hierarchical organization. Here we directly investigated the effects of two different serotonergic pharmacological interventions on functional brain hierarchy in major depressive disorder in a two-arm double-blind phase II randomized controlled trial comparing psilocybin therapy (22 patients) with escitalopram (20 patients). Patients with major depressive disorder received either 2 × 25 mg of oral psilocybin, three weeks apart, plus six weeks of daily placebo (‘psilocybin arm’) or 2 × 1 mg of oral psilocybin, three weeks apart, plus six weeks of daily escitalopram (10–20 mg; ‘escitalopram arm’). Resting-state functional magnetic resonance imaging scans were acquired at baseline and three weeks after the second psilocybin dose (NCT03429075). The brain mechanisms were captured by generative effective connectivity, estimated from whole-brain modeling of resting state for each session and patient. Hierarchy was determined for each of these sessions using measures of directedness and trophic levels on the effective connectivity, which captures cycle structure, stability and percolation. The results showed that the two pharmacological interventions created significantly different hierarchical reconfigurations of whole-brain dynamics with differential, opposite statistical effect responses. Furthermore, the use of machine learning revealed significant differential reorganization of brain hierarchy before and after the two treatments. Machine learning was also able to predict treatment response with an accuracy of 0.85 ± 0.04. Overall, the results demonstrate that psilocybin and escitalopram work in different ways for rebalancing brain dynamics in depression. This suggests the hypothesis that neuropsychiatric disorders could be closely linked to the breakdown in regions orchestrating brain dynamics from the top of the hierarchy.

Main

Neuropsychiatric disorders are devastating, incurring significant disability and stigma for individuals and a serious and growing burden for society^1,2. Major depressive disorder (MDD) has become pervasive. A major contributor to the years lost to disability worldwide, in terms of the burden of disease, by 2030 MDD is predicted to become the largest contributor³. Adding to this problem, antidepressant drugs show modest efficacy^4,5, have unpleasant side effects that impact treatment adherence⁶ and are associated with high relapse rates⁷. Problems with current treatments and the scarcity of reliable animal models mean that new research strategies are needed to treat neuropsychiatric disorders^8,9. Yet, at the present time, it is not clear how brain dynamics change when patients get better following pharmacological intervention.

Neuroimaging has identified abnormal brain dynamics in depression^10,11, with changes linked primarily to higher-order brain networks including the default mode network (DMN), executive network (EN) and salience network (SN)^11,12. Research in healthy individuals has associated these networks with higher-order functioning, including executive control and attentional switching¹³, which are often impaired in depressed patients¹⁴. There have also been neuroimaging studies investigating the effective connectivity in depression associated with treatment response^15,16,17. Successful pharmacological intervention for depression must therefore be linked to a rebalancing of these dynamics. One candidate mechanism is the role of the serotonin 2A (5-HT2A) receptor subtype, which is closely associated with serotonergic psychedelic drugs such as psilocybin^18,19. The spatial distribution of 5-HT2A receptors overlaps with the DMN, EN and SN²⁰. It has been hypothesized in the ‘relaxed beliefs under psychedelics’ (REBUS) theory²¹ that psychedelics can bring about a relaxation of the precision of high-level priors or ‘beliefs’, allowing bottom–up rather than hierarchical top–down information flow, which is consistent with more hierarchy-free system dynamics, suggesting a hierarchical reconfiguration of brain dynamics²². However, a full whole-brain quantification of hierarchical processing has not yet been attempted.

In this Article, the main aim is to study the effects of pharmacological intervention on brain dynamics and in particular to determine how this affects the hierarchy of brain processing associated with two serotonergic pharmacological interventions given to patients with treatment-resistant depression. To answer this research question, we leveraged a double-blind phase II randomized controlled trial²³, where resting-state functional magnetic resonance imaging (fMRI) scans at baseline and after treatment were obtained from all patients²². To best quantify the changes in brain dynamics, we implemented a sensitive measure of hierarchy, inspired by work in ecology capturing the hierarchical relationships between plants, herbivores and carnivores in a food web. The method uses the concept of trophic levels for each node in a directed graph, which can be thought of as the ‘height’ of a node in the hierarchy²⁴. A flat hierarchy is characterized by equal trophic levels and low directedness, which reflects low asymmetry in a network. In contrast, a strong hierarchy is associated with high directedness and strong asymmetric connections in a many-layered network. This measure of directedness (also called trophic coherence) has been related to other network properties, such as cycle structure, stability, normality and percolation²⁵.

This hierarchy measure provides the global level of directedness and regional trophic levels, which we applied to the graph of the generative effective connectivity (GEC) matrix²⁶. This was estimated from whole-brain modeling of the resting state for each session of each patient. The GEC is an extension of the classic concept of effective connectivity²⁷, but generative in the sense that the GEC is created from a whole-brain model of empirical resting-state data, where the strengths of existing anatomical connectivity are adapted iteratively until best fit, thus providing a mechanistic explanation of the resting-state data. This asymmetric measure of functional brain connectivity is fundamental for assessing hierarchy, while other simpler measures such as functional connectivity (FC) are not suitable because they are, by definition, symmetric.

The overall result was that the two pharmacological interventions gave rise to significantly different hierarchical reconfigurations following treatment, with differential, opposite statistical effect responses. In other words, we found significant differences between measures of both directedness and the trophic level, before and after intervention. These differences were found both from direct statistical tests and when using machine learning to measure the degree of pattern separation. Furthermore, we also found significant differences in trophic levels when comparing responders with non-responders for each pharmacological intervention. Importantly, pharmacological interventions were found to work best when select cortical and subcortical regions in the so-called ‘global workspace’ were re-established as being near the top of the hierarchy²⁸. These results strongly suggest that the psilocybin and escitalopram work in very different ways when used for rebalancing the hierarchical organization of brain dynamics in depression. In general, the research presented here offers a principled route to evaluate the effects of pharmacological intervention based on empirical brain dynamics data. Many obstacles remain, including replication of the results in a much larger population and for other interventions, but the results show potential for fulfilling the great expectations of using neuroimaging for understanding the underlying mechanisms of neuropsychiatric disorders.

Results

We addressed the main research question of how pharmacological interventions affect brain dynamics by assessing hierarchical reconfiguration in the brain state in MMD patients enrolled in a double-blind phase II randomized controlled trial comparing two drugs (psilocybin and escitalopram)²³. In this study, as shown in Fig. 1a, neuroimaging resting-state data were acquired before and after the pharmacological intervention (details of the trial are provided in Methods). We used the data for these two sessions six weeks apart to quantify the effects on global directedness and regional trophic levels on the brain dynamics following either intervention.

Fig. 1: Pipeline for assessing hierarchy in brain states before and after pharmacological intervention for depression.

a, Neuroimaging resting-state data were acquired before and after a double-blind phase II randomized controlled trial (DB-RCT) comparing psilocybin therapy with escitalopram. b, The hierarchy was quantified using a new method measuring the directedness of a network based on trophic levels, inspired by previous work in ecology but extended to general directed networks. The top panel shows a flat hierarchy with low directedness (or trophic coherence), which reflects the low asymmetry of the network with the same trophic levels. In contrast, the bottom panel shows a strong hierarchy, associated with high directedness (and asymmetry), which emerges from the diversity of trophic levels reflecting the many layers in the network. c, Whole-brain modeling is then used on individual sessions of each patient of neuroimaging resting-state data in the DK80 parcellation. This estimates the underlying mechanisms captured by the GEC. d, The hierarchy of the brain state in each session can be quantified using the directedness method on the individual GEC. This produces the trophic levels for each brain region and a global measure of directedness (or trophic coherence). e, For each patient, we then estimate the difference in hierarchical organization by subtracting the before- from the after-intervention session. This is then used as the basis of machine-learning classification and for direct comparisons of the hierarchical reconfiguration.

Quantifying hierarchy in brain states

To reveal the spatiotemporal hierarchical organization of the brain dynamics for the two pharmacological interventions, we implemented a method measuring the directedness and trophic levels of a network based on previous work in ecology²⁹ and extended to general directed networks²⁴. This measure of hierarchy is very robust and has been used in many other fields; it has been described as ‘upstreamness’ in economics³⁰ and is a key ingredient in the construction of SinkRank, a measure of contribution to systemic risk³¹.

For a given directed network, this method provides both the hierarchical, node-level information (trophic level) and the global information (the directedness, or trophic coherence). In other words, the trophic level provides a measure of where a node sits in the hierarchy of a directed network. In ecology, low trophic levels would be assigned to plants, and high trophic level nodes would be assigned to carnivores, given that energy flows up the food web from low to high trophic levels. Our implementation of the hierarchy methods uses the recent extension from ref. ²⁴ to the standard definitions of trophic level, which allows the method to overcome the limitations of requiring a basal node (that is, a node with no incoming edges) and taking into account reverse flow. As a result, this optimized method is even more robust, as it captures aspects of related network measures of stability, cycles and normality.

We thus use a well-established method to measure the spatiotemporal hierarchical organization of brain dynamics. Figure 1b presents a cartoon illustrating the trophic levels and directedness measures for flat and hierarchical networks. As can be seen in the top panel, a flat hierarchy has approximately equal trophic levels, resulting in low directedness and reflecting the low asymmetry of the network. This is not the case for a strong hierarchy, which is associated with high directedness and consequently strong asymmetric connections. In the latter case, the diversity of trophic levels reflects that the network contains many hierarchical layers and an overall direction pointing from the lowest to the highest.

To estimate the functional hierarchy of a given brain state, we applied this method to the network produced by whole-brain modeling of a patient’s individual resting state in the DK80 parcellation²⁸. This network captures the underlying mechanisms generating the resting-state dynamics³². In brief, whole-brain modeling combines the anatomical connectivity with local dynamics to fit the dynamics of empirical neuroimaging data^32,33,34. The local dynamics can be simulated using, for example, spiking, dynamical mean field and Hopf local regional models to fit many different empirical observables. Overall, the best fit is obtained with the Hopf model, so we chose to fit this model to the model-free observable of non-reversibility of the neuroimaging data^26,35,36,37. More specifically, Fig. 1c shows the procedure for fitting a whole-brain model, initially using the anatomical connectivity and then iteratively adjusting a GEC, which is given as asymmetric weights of the existing anatomical connections²⁶. This is an extension of the concept of effective connectivity²⁷, but where GEC is generative because it uses the whole-brain model to adapt the strength of existing anatomical connectivity (that is, the effective conductive values of each fiber). In contrast to normal symmetrical measures of effective connectivity (typically using FC), here we use the asymmetrical optimization obtained from using the non-reversibility INSIDEOUT method²⁶. Recent advances in the analysis of brain-imaging data have shown that the thermodynamic concept of the arrow of time (or non-reversibility) is a very sensitive and robust measure of the underlying asymmetric information flow^{26,35,36,37,38,39,40,41,42,43}. This body of research has demonstrated that creating a whole-brain model of the arrow of time in empirical neuroimaging data can provide access to the generative mechanisms underlying hierarchy—which in turn can provide a direct measure of the hierarchical reconfiguration over time (Methods).

Figure 1d shows how the hierarchy of the brain state in each session can be quantified using the directedness method on the individual GEC. This produces the trophic levels for each brain region, that is, where in the hierarchy each is placed, as well as the global measure of directedness (or trophic coherence) based on the trophic levels.

Finally, Fig. 1e illustrates the procedure for estimating the difference in hierarchical organization, which is obtained by subtracting the sessions before the pharmacological intervention from after. As shown in the following, this is used as the basis of machine learning to compare pattern separation based on regional trophic levels and for the direct comparison of the hierarchical reconfiguration of directedness.

Machine learning of hierarchical reconfigurations

We used machine learning to establish the significant hierarchical reorganization between before and after treatment. To do this, we first computed the GEC for both sessions in each patient receiving either psilocybin or escitalopram, independent of treatment response. This allowed us to compute the trophic levels and directedness before and after intervention in each patient. The before and after scan sessions for each of the two types of intervention were classified using machine learning (Fig. 2a). For classification we used the hierarchical trophic levels for each region (for each patient and condition) as input features. We sorted the regions according to each region’s statistical significant hierarchical trophic level across patients, region by region, using Wilcoxon 10,000-permutation tests. To estimate with the highest possible accuracy, we selected sequentially the minimum numbers of regions from the sorted list of statistically significant trophic levels with the minimum number of inputs that yielded the largest accuracy. We found that the highest accuracy was obtained using 69 regions for the psilocybin treatment arm and six regions for the escitalopram treatment arm. Importantly, we trained the support vector machine (SVM) with the leave-one-out cross-validation procedure; that is, we randomly chose one patient for generalization and the rest for training, repeated, and shuffled 1,000 times. Furthermore, we made sure that the training set was balanced in terms of number of examples for each class label, and randomly selected the patients in each class for each shuffling iteration (Methods). The results show significant effects above chance levels with an accuracy of 0.89 ± 0.03 (mean ± s.d.) for psilocybin and 0.89 ± 0.02 for escitalopram. In addition, we also carried out machine learning for all 80 regions for both treatments to show that the preselection of regions does not affect the results (Supplementary Fig. 5).

Fig. 2: Hierarchical reconfiguration following the administration of psilocybin and escitalopram.

Throughout, the full results are shown for psilocybin in the left column and for escitalopram in the right column for both responders and non-responders. a, Machine learning of the hierarchical organization reflected in the trophic levels was used to classify the scan sessions, that is, the brain dynamics before and after the intervention. The confusion matrices show the percentage results of the 22 patients treated with psilocybin and the 20 patients treated with escitalopram. This gives an accuracy of 0.89 ± 0.03 (mean ± s.d.) for psilocybin and 0.89 ± 0.02 for escitalopram, revealing a significant level of hierarchical reconfiguration. b, The hierarchical reorganization is shown by comparing the directedness (or trophic coherence) as a global measure of the hierarchical reconfiguration. This shows significant differences between the before and after (paired Wilxocon rank test 10,000 permutations, two-sided and Cohen’s d for the effect size; psilocybin, ***P = 0.002, d = 1.1; escitalopram, ***P = 0.001, d = 1.4). Importantly, the change in directedness goes in opposite directions, reflecting the differential hierarchical reconfiguration for the two pharmacological interventions. c, The average regional trophic levels are rendered on the brain before and after the intervention. The subcortical regions are rendered on four coronal slices in Montreal Neurological Institute (MNI) space (y = [−26, −14, −2, −10] mm). d, The rendering shows the differences in trophic levels between before and after treatment. As can be seen, the effects of the two interventions are very different, reflecting the fact that psilocybin mostly increases the hierarchical organization, whereas escitalopram causes a general decrease in hierarchical organization.

Directedness of hierarchical reconfiguration

The overall global hierarchical reconfiguration can be directly quantified using the measure of directedness, which is a global measure of hierarchy based on regional trophic levels (Methods). Figure 2b shows the significant differences between before and after treatment (P < 0.001, paired Wilcoxon test using 10,000 permutations) for both the psilocybin and escitalopram treatment arms. Importantly, with psilocybin treatment, the directedness significantly decreases, but it increases for the escitalopram treatment, reflecting the differential hierarchical reconfiguration for the two pharmacological interventions. This demonstrates differential, opposite statistical effect responses, whereby the directedness decreases for the psilocybin treatment but increases for the escitalopram treatment.

Importantly, the finding of a differential treatment-dependent hierarchical reconfiguration was confirmed by additional analyses. First, we computed the correlations between changes in Beck Depression Inventory (BDI)/treatment response (post–pre) for hierarchy (changes in directedness post–pre) for the psilocybin and escitalopram groups. As shown in Supplementary Fig. 6, this yielded no significance for psilocybin (corr: −0.023, P = 0.91 (not significant (NS)), red line) and for escitalopram (corr: 0.16, P = 0.50 (NS), blue line). Yet, as expected when we combine the two groups, this yields a significant correlation of 0.3 (P = 0.049, black line). The results mean that the change in BDI score is not predictive for the change in hierarchy for either group, but only when combining them. Overall, this shows that treatment is the important variable.

Second, further validating this important result, we ran an analysis of variance (ANOVA) with three variables: (1) binary variable of whether a patient was classified as responder, (2) change in BDI score (post–pre) and (3) type of treatment (psilocybin or escitalopram). The results confirmed that only the treatment is significant: factor 1 (response): F-statistics 0.063, P = 0.81 (NS); factor 2 (BDI change): F-statistics 1.22, P = 0.35 (NS); factor 3 (treatment): F-statistics 16.086, P = 0.0013.

We also investigated possible self-reported sex effects using multi-way ANOVA of the differences in directedness before and after intervention. This showed non-significant effects of sex (P > 0.05) on the mean of the differences in directedness (F(1,39) = 3.08, P = 0.087), whereas the intervention effect was highly significant (F(1,39) = 33.28, P < 0.001).

It is also important to remark that although the interventions had different remission rates (based on the BDI: 64% for psilocybin and 30% for escitalopram), the main finding of different reconfigurations between the treatment arms is independent of remission rates, but based on the significant differential, opposite statistical effect responses in the changes in hierarchy after intervention. In the case of patients given psilocybin, the mean directedness of the hierarchy is decreasing, whereas it increases for patients given escitalopram. Furthermore, this reconfiguration in hierarchy is also found at the node level, as shown in the new analysis presented in Supplementary Fig. 1, which shows the statistical significance of the differential reconfiguration with differential, opposite statistical effect responses (one is positive and the other negative).

We also carried out a rigorous analysis matching patients with a similar baseline and change in depression score and tested for differential, opposite statistical effect responses. Supplementary Fig. 2 shows the changes in directedness for patients with similar initial BDI baseline scores (>23) and changes in BDI after and before (<−10). The results shows that the mean directedness hierarchy decreases for the psilocybin arm (P < 0.05, paired Wilcoxon test using 10,000 permutations), but increases for the escitalopram arm (P < 0.05, paired Wilcoxon test using 10,000 permutations).

More detailed information was obtained from running four different linear mixed-effect models. Supplementary Table 4 provides the details of a linear mixed-effect model for paired repeated measures analysis with a random effect and matching (grouping) patients according to (1) their BDI baseline, (2) their BDI change (post–pre) and (3) their treatment type (psilocybin or escitalopram) to predict hierarchy change (directedness change post–pre). For this procedure, we first used k-means clustering to find the optimal silhouette and used n = 5 clusters to define the grouping. We thus matched five similar groups of participants across the whole group of participants and ran the linear mixed-effect model in MATLAB (2022b). The results showed an intercept (bias) t-statistic = −0.394 (P = 0.695 (NS)), BDI baseline t-statistic = 0.431 (P = 0.668 (NS)), BDI change t-statistic = 0.399 (P = 0.692 (NS)) and treatment t-statistic = −5.152 (P < 0.001). This highly significant result demonstrates that only the treatment is important, without any confounding factors.

Supplementary Table 5 provides the details of a linear mixed model of directedness using BDI change as a fixed effect grouped by treatment as the random effect. The results showed an intercept (bias) t-statistic = −0.051 (P = 0.96 (NS)) and BDI change t-statistic = 0.409 (P = 0.68 (NS)). The lack of significance for intercept and BDI change when using treatment as the random effect shows that treatment is the important factor.

Supplementary Table 6 provides the details of a linear mixed model of directedness change using BDI change, BDI baseline, QIDS baseline, QIDS change, age, sex, illness duration, medication withdrawal and medication as a fixed effect grouped by treatment as the random effect. As can be seen in the table, none of the results are significant and are therefore not confounding factors.

Supplementary Table 7 provides the details of a linear mixed model of directedness change using treatment as a fixed effect and using other variables as random effects: BDI baseline, QIDS baseline, QIDS change, age, sex, illness duration, medication withdrawal and medication. The results showed an intercept (bias) t-statistic = 0.526 (P = 0.60 (NS)) and treatment t-statistic = −4.08 (P < 0.001). This highly significant result demonstrates that only the treatment is important, without any confounding factors.

Overall, all these investigations (Fig. 2b, Supplementary Figs. 3, 4 and 6 and Supplementary Tables 4–7) converge on the fact that the differential, opposite statistical effect responses in hierarchy are consistently changed in opposite directions for the psilocybin and escitalopram arms. This strongly supports the main finding of a differential reconfiguration of hierarchy.

In addition to this hierarchy analysis, we also tested this claim using more traditional methods based on FC. We first tested the ability of FC (Supplementary Fig. 3a) to distinguish the effects of psilocybin and escitalopram before and after intervention. We compared the mean across all elements in FC matrices and did not find any significant differences between before and after intervention. Second, we tested the ability of time-shifted FC (with a shift of 1 repetition time (TR); Supplementary Fig. 3b) using a measure of asymmetry of these matrices before and after intervention. In particular, we computed asymmetry as the mean of the absolute difference between the respective time-shifted FC matrix and the transposed matrix. We found a significant difference for the psilocybin session (P < 0.05, paired Wilcoxon test using 10,000 permutations) but not for the escitalopram session. Still, the effect for psilocybin is less statistically significant than what we found using the hierarchy measure.

This lack of sensitivity of both alternate measurements is not surprising given that these methods are focused on grand average static, spatial correlation and lack sensitivity to temporal dynamics. Even more importantly, in the case of FC, this measure is symmetric, meaning that FC does not capture the asymmetry intrinsic to hierarchical organization. On the other hand, the time-shifted FC is a simple but effective measure to capture asymmetry. Yet, it only captures static spatial correlations across the entire time window. In contrast, the hierarchy measure captures the hierarchical organization of spatiotemporal dynamics generated from a whole-brain model. It is therefore more sensitive to changes for both interventions and, more importantly, reveals the differential, opposite statistical effect responses.

Additionally, we tested the power of using our measure of hierarchical organization to distinguish treatment effects in a relatively small sample of patients and repeated these procedures using another measure of global brain connectivity (GBC; Methods), which captures the functional coupling of each region with the rest of the brain. Supplementary Fig. 4 shows that this measure performs significantly worse using GBC than when using hierarchical levels. This poorer performance can be seen in the differences in the scatterplots in Supplementary Fig. 4a for GBC and hierarchical levels before and after both psilocybin and escitalopram. To further quantify this difference, we directly tested the inability of FC for distinguishing treatment effects by comparing the individual correlations after versus before treatment: psilocybin (P < 0.001, paired Wilcoxon test with 10,000 permutations) and escitalopram (P < 0.04, paired Wilcoxon test with 10,000 permutations) (see the violin plots in Supplementary Fig. 4b).

Regional differences in hierarchical reconfiguration

To achieve a better understanding of the regional changes underlying the differential hierarchical reconfiguration for each treatment arm, Fig. 2c shows cortical and subcortical renderings of the average trophic regional levels (across patients) for before and after treatment with psilocybin (left column) and escitalopram (right column). Figure 2d shows renderings of the differential trophic levels, demonstrating the hierarchical reconfiguration and how the differential effects of the two interventions result in strikingly different patterns of regional trophic levels. Although the small sample size makes statistical testing at the regional level more difficult due to the multiple comparisons, Supplementary Table 1 presents quantitative information reporting on the top 20% of regions involved in the hierarchical reorganization overall in each intervention arm (irrespective of whether responders or non-responders). As can be seen, the psilocybin treatment changes the hierarchy for a large number of mainly cortical regions, many of which have been shown to be part of the global workspace²⁸. The top regions include both cortical (left posterior cingulate and left rostral anterior cingulate cortices) and subcortical (right hippocampus and right amygdala) regions. In contrast, the overall response to escitalopram treatment does not change the hierarchy of cortical regions, but only subcortical regions (of which the amygdala, left putamen and right hippocampus are found in the global workspace).

In spite of the small sample size, we also carried out rigorous statistical testing. Supplementary Table 2 shows the results for the full psilocybin treatment arm (22 patients), where 61 of 80 regions survive statistical testing (P < 0.05, paired Wilcoxon test using 10,000 permutations and false discovery rate (FDR)-corrected for multiple comparisons). In contrast, only 4 of 80 regions survive similar statistical testing for the escitalopram treatment arm (20 patients, P < 0.05, paired Wilcoxon test using 10,000 permutations and FDR-corrected for multiple comparisons). Please note that this difference in number of significant regions between the two treatment arms is also found in the classification.

Reconfiguration in responders and non-responders

Importantly, we also found significant differences between responders and non-responders in the hierarchical reconfigurations of brain dynamics following psilocybin and escitalopram treatment. Given the potential limitations of statistical testing in the small sample, we used machine learning (again with cross-validation; Methods) to quantify the significant hierarchical reorganization related to treatment response. We used the efficacy of treatment using the amended (revised) Beck Depression Inventory (BDI-1A), which captures a broad range of symptoms and places emphasis on the cognitive features of depression⁴⁴. For further justification for the use of this measure here, see ref. ⁴⁵. Here we used the classification from Daws and colleagues²², where a patient is classified as a responder if they show a significant reduction in BDI-1A after treatment (details in ref. ²²).

Figure 3a shows the results of using machine learning for testing significantly above chance level accuracies of pattern separation between responders versus non-responders for each treatment arm (0.67 ± 0.05 for psilocybin and 0.69 ± 0.04 for escitalopram, using the methods described above). The highest accuracy was obtained using five regions for psilocybin and six regions for escitalopram treatment.

Fig. 3: Significant differential hierarchical reconfiguration between responders and non-responders.

Psilocybin results are shown in the left column and escitalopram results in the right column. a, The changes in hierarchical reorganization were used for machine-learning classification of responders versus non-responders. The confusion matrices show the percentage results of the 22 patients treated with psilocybin (of which there were 18 responders) and the 20 patients treated with escitalopram (of which there were eight responders). The results showed significantly above chance levels in hierarchical reconfigurations for responders and non-responders in both interventions (0.67 ± 0.05 (mean ± s.d.) for psilocybin and 0.69 ± 0.04 for escitalopram). b, The renderings show the differences between before and after for responders and non-responders. The subcortical regions are rendered on four coronal slices in MNI space (y = [−26, −14, −2, −10] mm). As can be seen, there are significant differences in the hierarchical reconfiguration between these two groups, both between and within psilocybin and escitalopram. The renderings show lower precuneus and prefrontal hierarchical levels after treatment in the psilocybin responders compared to non-responders, and there is an intriguing increase in hierarchical levels of the inferior frontal gyrus for the non-responders. Similarly, the brains of the escitalopram responders compare to the full group in that regions of the cingulate and regions of the prefrontal cortex have stronger hierarchical levels in the responders than in non-responders.

We systematically investigated the regional changes underlying these different responses. Figure 3b shows renderings of the differences in trophic levels after and before treatment for psilocybin (left column) and escitalopram (right column) for non-responders (left) and responders (right). Confirming the significant machine-learning pattern separation results, within each treatment the responders and non-responders show differences in the regional trophic levels for responders versus non-responders. Supplementary Table 3 presents quantitative information reporting on the top 20% of regions involved in the overall hierarchical reorganization in each intervention arm. These results offer some added insights into the treatment mechanisms. In the case of the escitalopram treatment, the results show that patients improve if the treatment also affects the hierarchical reorganization of cortical regions that could be said to be part of the global workspace. Specifically, the following cortical regions of the global workspace moved up in hierarchy following treatment: left and right posterior cingulate, left rostral anterior cingulate and right rostral anterior cingulate cortices. In addition, the subcortical regions (left putamen, left nucleus accumbens and right amygdala) of the global workspace also moved back up the hierarchy. However, this will need to be confirmed in future larger studies.

In the case of the psilocybin, most of the patients responded and so show hierarchical changes similar to the general treatment response, which is both cortical and subcortical regions of the global workspace moving back up the hierarchy. As expected, non-responders do have a slightly different response to responders, with prefrontal regions more likely to move up the hierarchy.

We note that, due to the small sample size, statistical testing at the regional level is difficult due to multiple comparisons. Still, for psilocybin responders (18/22), we found 41 regions that were significantly different before and after successful treatment (P < 0.05, paired Wilcoxon test using 10,000 permutations and FDR-corrected for multiple comparisons). In escitalopram responders (8/20), there was only one surviving region (left STN), which is at the top of the changing hierarchy in Supplementary Table 3.

Treatment response can be differentiated and predicted by the hierarchical reorganization

Further investigating the treatment response, we show that when comparing the directedness of the hierarchical organization in treatment, the after session gives significant differences across patients (P < 0.001, paired Wilcoxon test with 10,000 permutations; Fig. 4a). In other words, the directedness reveals which intervention a given patient has received, confirming the significantly different hierarchical reorganization linked to the two pharmacological interventions. Furthermore, as shown in Fig. 4b, we can also classify the treatment response using the regional trophic levels with a high accuracy of 0.83 ± 0.03 for the pattern-separation machine learning with cross-validation (Methods). Please note that the training set was carefully balanced in terms of number of examples for each class label, and the patients in each class for each shuffling iteration were randomly selected. Finally, we were able to predict the treatment response using the baseline data (that is, the before escitalopram treatment data). This was only done for escitalopram, because this arm, unlike psilocybin, had the necessary power, with roughly equal numbers of responders and non-responders. Using machine learning with cross-validation, Fig. 4c shows a high accuracy of prediction (0.85 ± 0.04). This significant prediction is potentially interesting for future clinical applications.

Fig. 4: Treatment response can be differentiated and predicted by hierarchical organization.

a, The directedness of the hierarchical organization in the session after treatment shows significant differences across patients (***P < 0.001, paired Wilcoxon test with 10,000 permutations). b, The machine-learning classification of the treatment response (using the trophic levels) also found that difference between psilocybin versus escitalopram after sessions can be classified with 0.83 ± 0.03 (mean ± s.d.) accuracy. The confusion matrices show the percentage results of 22 patients treated with psilocybin and 20 patients treated with escitalopram. c, Equally, machine learning can be used to make a prediction of the treatment response for patients on escitalopram. We only do this for escitalopram, because the roughly equal numbers of responders (eight patients) and non-responders (12 patients) made this possible. The confusion matrices show the percentage results for the 20 patients treated with escitalopram. This resulted in a significant prediction above chance level and an accuracy of 0.85 ± 0.04 (mean ± s.d.).

Discussion

We have studied the effects of pharmacological interventions on the brain dynamics of MDD patients before and after treatment with either psilocybin or escitalopram. Directly addressing our main research question, we were able to show that—despite leading to equal improvements in depressive symptoms (as measured with BDI-1A)—the two drugs work in significantly different ways and show differential, opposite statistical effect responses, as indexed by how each reconfigures the global functional hierarchy of brain dynamics. In particular, we have demonstrated that hierarchical measures of both directedness and trophic levels associated with brain dynamics are significantly different before and after intervention, as well as different between responders and non-responders for both drug types. Our results complement previous research showing that there are shared and unique changes in brain connectivity following different types of intervention for depression⁴⁶. More generally, the framework presented here offers a principled route to evaluate the effects of any pharmacological intervention with before and after empirical brain dynamics data. To generalize the results, however, they should be replicated in larger populations and for other interventions, but there could be a path for fulfilling the great expectations of using neuroimaging for understanding the underlying mechanisms of neuropsychiatric disorders and successful treatments³².

Hierarchical reorganization for psilocybin and escitalopram

We found that psilocybin treatment leads to a decrease in the overall global measure of directedness of the hierarchy of brain dynamics when comparing brain dynamics after versus before treatment (Fig. 2b). In contrast, escitalopram leads to an increase in the overall global measure of directedness of the hierarchy of brain dynamics.

These differential effects are in line with the known differential effects of the pharmacology of the two drugs. Psilocybin is the prodrug of psilocin (4-OH-dimethyltryptamine) and has been shown to act mainly through the serotonin 2A receptor (5-HT_2AR)^18,19,47, thereby initiating a multi-level plasticity⁴⁸. Psychedelics works partly through 5-HT2A receptor agonism leading to an increase in the sensitivity of excitatory neurons expressing the receptor, which in turn causes dysregulation of spontaneous population-level activity and spike-wave decoupling⁴⁹. Attesting to this, dynamic sensitivity analysis of the systematic perturbation of whole-brain models has been used to identify brain networks that are part of the transition away from a depressive brain state following administration of psilocybin⁵⁰.

In contrast, escitalopram is a member of the most frequently prescribed antidepressant drug class, the so-called selective serotonin reuptake inhibitors (SSRIs). Unlike psilocybin, which has no appreciable affinity or action of the serotonin transporter (5-HTT), SSRIs are thought to rely on reuptake blockade at the 5-HTT.

This suggests an overall flattening of the hierarchy for psilocybin after administration in MDD patients, which is consistent with the evidence from healthy participants on psilocybin and other classic psychedelics^51,52. Specifically, psychedelics have been shown to broaden the repertoire of connectivity states^{53,54,55,56,57}, increase the entropy of resting-state activity^58,59,60,61, and enhance the connectivity between central high-level networks and the rest of the brain^51,60,62,63. More generally, the results are consistent with the REBUS theory²¹ and the anarchic brain hypothesis, integrating Friston’s free-energy principle⁶⁴ with the entropic brain hypothesis of Carhart-Harris^58,65. Here, the main hypothesis is that psychedelics can bring about a relaxation of the precision of high-level priors or ‘beliefs’ (REBUS), allowing (anarchic) bottom–up information flow, consistent with ‘anarchic’ (that is, hierarchy-free) system dynamics. This theory is consistent with our results showing psilocybin treatment leading to a hierarchical reconfiguration and general flattening of the hierarchy. In contrast, the increase in directedness of the hierarchical reorganization after escitalopram treatment would imply that the responders show a more top–down hierarchical organization of their brain dynamics. It is tempting to speculate that this top–down organization may also be linked to dampened responsivity in stress circuitry under these drugs⁶⁶, allowing easier top–down control. However, to test this speculation would require a new, carefully designed study, for which some progress has already been made⁶⁷. Even so, further work is required to better scrutinize this hypothesis.

The results show that psilocybin and escitalopram work in very different ways when used for rebalancing the hierarchical organization of the brain dynamics in depression. Both interventions may lead to a significant reduction in depressive symptoms, but do so in significantly different ways. This was first hypothesized by Carhart-Harris and Nutt⁶⁶, and implied but not proven in the research of Daws and colleagues²², who used the same data analysed here but only found a change in integration–segregation for psilocybin but not for escitalopram, thus missing the differential, opposite statistical effect. Crucially, as we have demonstrated here, this differential, opposite statistical effect is not revealed using simple symmetric FC measures or even asymmetric time-shifted FC, which do not capture the relevant temporal dynamics. Fully revealing the hierarchical organization of the underlying spatiotemporal dynamics requires the sensitivity of our hierarchical method combined with a causal, generative whole-brain model.

The key argument for causality in connection with whole-brain modeling is that removing a ‘causal’ region from the model results in a significant inability to maintain the fit to empirical data. This is analogous to how lesions are used in animal models, but used now for ‘in silico’ models. Previously, Deco and colleagues lesioned the top and bottom of the hierarchy and showed that only the first lesioning significantly changed the fit of the model to the empirical data²⁸. Here, we first determine the GEC that allows the whole-brain model to generate the best fit to the empirical data. Hence, we know that the regions in this network are causally important for generating the functional dynamics.

Regional hierarchical reorganization for treatments

The regional results show that positive depression recovery is linked to when both cortical and subcortical regions of the global workspace are moving back up in the hierarchy following treatment. However, these changes differ in how psilocybin and escitalopram restore the orchestration of healthy brain function, and the main mechanisms underlying the treatment response for depression involve regional hierarchical reconfiguration.

In terms of hierarchical organization at the regional level, psilocybin treatment (Fig. 2c, left column brain rendering) leads to broad changes across the whole brain, with multiple regions in the cingulate cortex increasing their trophic level when comparing after with before the treatment. Similarly, subcortical regions such as the STN, hippocampus and amygdala are also moving up in the hierarchy and drive the orchestration to a higher degree than before. In contrast, large parts of the prefrontal and temporal cortices decrease their trophic level, suggesting that they are moving down the hierarchical organization.

These patterns of hierarchical reconfiguration are very different after escitalopram treatment for all patients (Fig. 2c, right column brain rendering); in all cortical regions the trophic levels decrease from after to before treatment for all patients, and many subcortical regions (such as amygdala, putamen, hippocampus, caudate and STN) show an increase in trophic levels. This drives the global increase in directedness from before to after treatment, irrespective of outcome. Importantly, comparing the regional trophic levels for responders with non-responders following escitalopram treatment (Fig. 3b, right column), the responders show a significantly different pattern, with increases of trophic level in parts of cortical as well as subcortical regions. These changes in the hierarchical position of brain regions are driving the treatment response. In fact, the patients that respond to either pharmacological intervention show an increase in the hierarchical position of both cortical and subcortical regions. Given that the trophic hierarchical levels are based on the GEC measure coming from a whole-brain model of the brain dynamics, this implicates these brain regions in the healthy transition away from treatment-resistant depression.

These findings fit well with previous literature, which has implicated major depression with disturbances in multiple resting-state networks, including the SN and DMN, which are known to regulate cognitive control and attention^68,69,70,71. In particular, the findings also fit well with the changes in large-scale FC between networks^72,73. Specifically in remitted depressed patients, increased FC has been observed between the DMN and the dorsal attention network, and also within and between networks such as the SN and executive control networks⁷⁴. There is also an emerging literature showing how an increase in activity in the DMN is associated with rumination and recurrence of depression^75,76.

Interestingly, many of the regions changing with treatment have been shown to be part of the global workspace²⁸, which orchestrates healthy brain function. This opens up the interesting hypothesis that depression is caused by a malfunctioning orchestration of brain dynamics, where there is a partial breakdown in one or more of the brain regions at the top of the hierarchy²⁸. This hypothesis may even hold for other neuropsychiatric disorders⁷⁰ and, as such, it would be of considerable interest to further test this hypothesis in other datasets.

Predicting outcome using machine learning

Even more relevant for treatment, we were able to demonstrate that the trophic hierarchical levels for an individual depressed patient at baseline before treatment can be used to predict the outcome of escitalopram treatment (Fig. 4c). However, there were too few non-responders for the psilocybin treatment arm to be able to use this for prediction. This finding for escitalopram is potentially exciting but will need replication in a much larger dataset to test the true predictive value of this finding. The importance of more data can be appreciated when comparing this predictive result with the lower accuracy results in Fig. 3a, where machine learning was used to measure the accuracy in separating the difference between responders and non-responders before and after treatment. This lower accuracy runs counter to the intuition that more information should lead to higher accuracy than the prediction accuracy. Still, in both cases, machine learning performs significantly better than chance, although the noise level is clearly having a major effect with the relatively low sample size. Hence, in future this problem should be further investigated in more appropriate large-scale studies with more non-responders.

Potential limitations

Importantly, it should be noted that there are several potential limitations to this study. First, the results here are based on neuroimaging using BOLD signals from fMRI and thus carry a number of potential limitations. These include the fact that BOLD signals are indirect measures of neural activity⁷⁷ at a coarse spatial scale of ~1–2 mm³, corresponding to ~5 million neurons with diverse properties and functions^78,79. This heterogeneity of neuronal populations is especially true in the higher-order brain regions often associated with neuropsychiatric disorders⁸⁰. Equally, another limitation of resting-state fMRI is the significant intra-individual rest–retest variability, which has been linked to variations in a number of different factors including diet, diurnal changes, blood pressure and even cognitive load⁸¹. Nevertheless, BOLD signals are still useful given that they are highly correlated with local field potentials and multi-unit activity and thus accurately reflect the activity in local cortical circuits^78,79. Second, the study has a relatively low sample size, which limits the statistical power used for regional analyses. As such, the regional results mentioned above are not conclusive but will require further study and replication in larger studies.

Conclusion

Overall, the hierarchy of brain dynamics is clearly a very sensitive measure of change. This is made possible by recent advances in whole-brain modeling using a novel thermodynamics-inspired framework²⁶, providing the level of non-reversibility (or arrow of time) in brain signals^35,37,43. This provides the observable for a model-based, direct quantification of the asymmetric interactions, which is then quantified using the trophic framework. The thermodynamic framework provides measures of the non-reversibility of brain states and the identification of brain regions involved in breaking the balance as well as the net fluxes between underlying brain networks before and after interventions. In other words, the arrow of time of brain signals can provide a powerful new way to identify the cause and effect when the brain is reorganized. Here we have used this framework to identify how different pharmacological interventions reorganize brain dynamics differently. This has provided insights into the underlying mechanisms of depression and may in time lead to even better interventions. The results also confirm the hypothesis that problems with the main regions of the global workspace orchestrating brain dynamics could be the main cause of neuropsychiatric disorders—consistent with previous findings and hypotheses^70,82. Future larger studies should further investigate this hypothesis. We also note that the present whole-brain modeling framework could be used for treatment studies using any kind of effective intervention, whether pharmacological, electrical or behavioral.

Methods

Empirical data

The trial’s design (Fig. 1a) and primary clinical outcomes (clinicaltrials.gov: NCT03429075) have been documented previously^22,23. The clinical trial took place at the National Institute for Health Research Imperial Clinical Research Facility and received sponsorship from Imperial College London. It obtained ethical approval (ID 17/LO/0389) from the NHS Research and Imperial College Joint Research and Compliance Office, as well as approval from the Health Research Authority and Medicines and Healthcare Products Regulatory Agency. This study was carried out under a Schedule 1 Drug Licence granted by the UK Home Office. Written informed consent was provided by all participants who did not receive any financial compensation.

Participants

To be eligible for participation, individuals needed a confirmed diagnosis of unipolar MDD from a general practitioner, scoring 16 or higher on the 21-item Hamilton Depression Rating scale. Patients were also queried about any prior use of psychedelics. Within this trial, 31% of patients in the psilocybin group and 24% in the escitalopram group reported previous experience with psychedelics. Individuals were excluded from the trial if they had an immediate family or personal history of psychosis, a physician-assessed risky physical health condition, a history of serious suicide attempts, a positive pregnancy test or contraindications for undergoing an MRI. In addition, individuals with contraindications for selective serotonin reuptake inhibitors (SSRIs) or previous use of escitalopram were also excluded. It is important to note that treatment resistance was not considered as an inclusion or exclusion criterion. All eligible patients underwent telephone screening interviews, provided written informed consent, and underwent comprehensive evaluations of their mental and physical medical histories. Supplementary Table 8 provides the self-reported demographics for all patients.

Interventions

Of the 59 recruited patients with MDD, a random number generator was used to assign 30 patients to the psilocybin arm and 29 patients to the escitalopram arm. Similar to Daws and colleagues²², we excluded some of the patients in each arm. Specifically, for the psilocybin arm, one patient was excluded for choosing not to take the daily (placebo) capsules, and due to the COVID-19 UK lockdown, two patients did not attend the post-treatment session; finally, five patients were excluded due to excessive fMRI head motion. The remaining 22 patients (mean age, 41.9 years, s.d. = 11.0, 14 men and 8 women) were included in the psilocybin imaging sample. For the escitalopram arm, four patients discontinued due to adverse reactions to escitalopram, one patient reported cannabis use, one patient was lost due to the COVID-19 UK lockdown, and a further three patients were excluded due to excessive fMRI head motion. The remaining 20 patients (mean age, 38.7 years, s.d. = 11.0, 14 men and 6 women) were included in the escitalopram imaging sample. Before treatment, all patients underwent a baseline resting-state fMRI session with their eyes closed. On the first dosing day (DD1), patients received either 25 mg of psilocybin (psilocybin arm) or a presumed negligible dose of 1 mg of psilocybin (escitalopram arm). Although all patients were informed that they would receive psilocybin, they were unaware of the specific dosage to ensure blinding. A second dosing day (DD2) took place three weeks after DD1, where patients received the same dosage as in the first session. There was no crossover in dosages between the two arms. Starting from the day after DD1, patients took daily capsules for a total of six weeks and one day. In both conditions, patients ingested one capsule per day during the initial three weeks, and increased the dosage to two capsules per day afterward. The capsule content was either an inert placebo (microcrystalline cellulose in the psilocybin arm) or escitalopram in the escitalopram arm. In the escitalopram arm, patients received 10 mg of escitalopram for the first three weeks and a total of 2 × 10 mg (20 mg) thereafter. Blinding was not done in the clinical trial upon which the data were based. However, there are recent data showing that psychedelic therapy may be less vulnerable to expectancy biases than previously suspected⁸³. In this study, the authors analyzed the clinical data with mixed linear models to investigate the association between both escitalopram and psilocybin and pre-treatment efficacy-related expectations, baseline trait suggestibility and absorption and therapeutic response. The results showed that patients overall had significantly higher expectancy for psilocybin relative to escitalopram. Yet, expectancy for escitalopram was associated with improved therapeutic outcomes to escitalopram, and expectancy for psilocybin was not predictive of the response to psilocybin. The BDI remission rates were 64% for the psilocybin arm and 30% for the escitalopram arm.

Measuring depression severity

The severity of depression was evaluated using BDI (BDI-1A) scores in this study. BDI-1A is a patient-rated assessment tool that encompasses a wider range of symptoms and places particular emphasis on the cognitive aspects of depression⁴⁴. Baseline BDI assessments were conducted before the first dosing day (DD1), and subsequent evaluations took place at two, four and six weeks after DD1. It is important to note that BDI was considered a secondary outcome measure for this study, as indicated by its registration on ClinicalTrials.gov (NCT03429075). The primary outcome measure (QIDS-SR-16) was found not to be different between the two intervention arms²³.

MRI acquisition

Imaging of the brain was carried out with a 3T Siemens Tim Trio set-up at Invicro. For the acquisition of brain anatomy, we used the recommended MPRAGE parameters from Alzheimer’s Disease Neuroimaging Initiative, Grand Opportunity (ADNI-GO56): 1-mm isotropic voxels; 160 sagittal slices; 256 × 256 in-plane field of view; echo time (TE), 2.98 ms; TR, 2,300 ms; generalized autocalibrating partially parallel acquisitions (GRAPPA) acceleration, 2; flip angle, 9°; bandwidth, 240 Hz per pixel.

For the acquisition of functional data, we collected eyes-closed resting-state fMRI data using T2*-weighted echo-planar images. We used a 32-channel head coil to acquire 480 volumes in ~10 min: 3-mm isotropic voxels; 44 axial slices; TE, 30 ms; TR, 1,250 ms; GRAPPA acceleration, 2; flip angle, 70°; bandwidth, 2,232 Hz per pixel.

Parcellations

All neuroimaging data were processed using the DK80 cortical parcellation²⁸, which is a combination of the Mindboggle-modified Desikan–Killiany parcellation⁸⁴ with a total of 62 cortical regions (31 regions per hemisphere)⁸⁵ and 18 subcortical regions, that is, nine regions per hemisphere: hippocampus, amygdala, subthalamic nucleus (STN), globus pallidus internal segment (GPi), globus pallidus external segment (GPe), putamen, caudate, nucleus accumbens and thalamus. We chose this parcellation given our previous work showing that this is the best compromise between spatial accuracy and computational load for whole-brain modeling when measuring brain hierarchy in neuropsychiatric disorders²⁸. However, we note that there is no current consensus about what is the best spatial parcellation scheme, as shown by the paper by Eickhoff and colleagues reviewing the literature on the topographic organization of the brain⁸⁶.

fMRI data preprocessing

The imaging data were preprocessed using an in-house pipeline using the FMRIB Software Library (FSL)⁸⁷, Analysis of Functional NeuroImages (AFNI)⁸⁸, Freesurfer⁸⁹ and Advanced Normalization Tools⁹⁰ packages, as described in detail in a previous publication²². Briefly, this pipeline consists of de-spiking, slice time correction, motion correction, brain extraction, rigid body registration to anatomical scans, nonlinear template registration, scrubbing, bandpass filtering, regression with six realignment motion regressors, three tissue signal regressors, draining veins and local white matter. Daws and colleagues were careful to rule out any systematic bias from akathisia or similar movement artifacts, as also shown in their supplementary materials and in particular their supplementary table 1 showing the head motion descriptive statistics²². The DK80 parcellated timeseries used here for hierarchical analysis was extracted from this preprocessed data.

Hopf whole-brain model

In this study we utilized a Stuart–Landau oscillator model to represent the local dynamics of each brain region. This model, which corresponds to the normal form of a supercritical Hopf bifurcation, is widely used for investigating the transition from noisy to oscillatory dynamics⁹¹. Previous research has successfully employed whole-brain Hopf models to replicate important characteristics of brain dynamics observed in electrophysiology^92,93, magnetoencephalography⁹⁴ and fMRI⁹⁵. The full mathematical description of the Hopf model and the linearization of this model are available in Supplementary Information.

Model optimization—GEC

To fit the model to the empirical data (BOLD fMRI of each participant in each brain state), we used a pseudo-gradient procedure to optimize the coupling connectivity matrix C, where the starting point was the standard structural connectivity matrix computed from the diffusion MRI data from a specially optimized state-of-the-art Human Connectome Project (HCP) protocol²⁸. The final optimized matrix comprises the effective conductivity values for each anatomical existing pair connections instead of just the diffusion MRI (dMRI)-based density of fibers. Specifically, we iteratively compared the output of the model with the empirical measures of the functional correlation matrix (FC^empirical), that is, the normalized covariance matrix of the functional neuroimaging data.

Additionally, to fit the whole-brain level of non-reversibility, we define the forward and reversal matrices of time-shifted correlations for the forward version and respective reversed backward version of a multidimensional timeseries for the different brain regions. This allows us to compute the forward and reversal matrices, expressing the functional causal dependencies between the different variables for the forward and artificially generated reversed backward version of a multidimensional system. We compared the output of the model with the forward normalized τ time-shifted covariances (${{{FS}}}_{{\rm{forward}}}^{{\rm{empirical}}}{\left(\tau \right)}$). These normalized time-shifted covariances were derived by shifting the empirical covariance matrix ${{{KS}}}_{{\rm{forward}}}^{{\rm{empirical}}}{(\tau )}$ and dividing each pair (i, j) by ${\sqrt{{{KS}}_{{\rm{forward}},\,{ii}}^{{\rm{empirical}}}{\left(0\right){KS}}_{{\rm{forward}},\,{jj}}^{{\rm{empirical}}}(0)}}$. It is worth noting that these normalized time-shifted covariances break the symmetry of the couplings, resulting in an enhanced fitting quality⁹⁶. To fully capture the asymmetry, we fit the non-reversibility by performing the same procedure on the reversed normalized τ time-shifted covariances (${{{FS}}}_{{\rm{reversal}}}^{{\rm{empirical}}}{(\tau )}$).

Using a heuristic pseudo-gradient algorithm, we set α = ς = 0.00001 and updated C until achieving a fully optimized fit. More specifically, the updating uses the following form:

$$\begin{array}{l}{C}_{{ij}}={C}_{{ij}}+\alpha \left({{FC}}_{{ij}}^{{\rm{empirical}}}-{{FC}}_{{ij}}^{{\rm{model}}}\right)\\\qquad\qquad+\varsigma \left(\left({{FS}}_{{\rm{forward}},\,{ij}}^{{\rm{empirical}}}\left({\tau}\right)-{{FS}}_{{\rm{reversal}},\,{ij}}^{{\rm{empirical}}}\left({\tau}\right)\right)\right.\\\left.\qquad\qquad-\left({{FS}}_{{\rm{forward}},\,{ij}}^{{\rm{model}}}\left({\tau}\right)-{{FS}}_{{\rm{reversal}},\,{ij}}^{{\rm{model}}}\left({\tau}\right)\right)\right)\end{array}$$

(1)

where ${{FS}}_{{\rm{forward}},\,{ij}}^{{\rm{model}}}{(\tau )}$ is defined similarly for forward ${{FS}}_{{\rm{forward}},\,{ij}}^{{\rm{empirical}}}{\left(\tau \right)}$ and ${{FS}}_{{\rm{reversal}},\,{ij}}^{{\rm{model}}}{(\tau )}$ is defined for reversal ${{FS}}_{{\rm{reversal}},\,{ij}}^{{\rm{empirical}}}{\left(\tau \right)}$. In other words, for the forward version, it is given by the first N rows and columns of the simulated τ time-shifted covariances ${{{KS}}}_{{\rm{forward}}}^{{\rm{model}}}{(\tau )}$ normalized by dividing each pair (i, j) by ${\sqrt{{{KS}}_{{\rm{forward}},\,{ii}}^{{\rm{model}}}{\left(0\right){KS}}_{{\rm{forward}},\,{jj}}^{{\rm{model}}}(0)}}$, where ${{{KS}}}_{{\rm{forward}}}^{{\rm{model}}}{(\tau )}$ is the shifted simulated covariance matrix computed as

$${{{KS}}}_{{\rm{forward}}}^{{\rm{model}}}{(\tau )}={\exp \left(\tau {{J}\,}\right){{K}}}$$

(2)

where the J matrix is the Jacobian of the linearized Hopf model evaluated at the fixed point (Supplementary Information). It is important to note that ${{{KS}}}_{{\rm{forward}}}^{{\rm{model}}}{\left(0\right)={{K}}}$. The same procedure was applied to the reversal version of ${{FS}}_{{\rm{reversal}},\,{ij}}^{{\rm{model}}}{\left(\tau \right)}$. The model is executed iteratively with the updated C until a stable and convergent fit is achieved. We use this method in two stages: (1) at the group level (for the before and after for each of the two treatment types); (2) this is then used as the starting point for individual optimization. At the group level, we initialize C as the anatomical connectivity data obtained through probabilistic tractography from dMRI (Methods). The update process only modifies the known existing connections from this matrix within each hemisphere, following the anatomical connections. However, an exception is made for homolog connections between corresponding regions in both hemispheres, as tractography tends to be less accurate in capturing this type of connectivity. For the Stuart–Landau model, as mentioned above, we set α = ς = 0.00001 and continue the algorithm until convergence is attained. In each iteration, we compute the model results by averaging over multiple simulations corresponding to the number of participants. In summary, we refer to the optimized matrix C as the GEC²⁶.

Briefly, the main difference between the GEC and other examples of effective connectivity such as dynamic causal modeling (DCM)²⁷, Granger causality⁹⁷ and transfer entropy^{28,98,99,100,101,102} is the anatomically constrained nature of GEC. In most implementations of DCM, Granger and transfer entropy, the underlying brain anatomy is not constraining the results. Furthermore, both methods measure some form of causality from the timeseries but do not use a generative form of causality. In our GEC, this generative aspect is explicitly given by brain anatomical constraints and whole-brain modeling. Importantly, this modeling typically allows for an estimation across the whole brain rather than only for the limited amount of regions given by DCM (up to ten regions in recent implementations), although recent work has applied the framework to the whole brain^103,104,105.

Defining GBC

For each session in each patient, we computed the GBC, given by

$${\rm{GBC}}_{i}={\frac{1}{N}\mathop{\sum }\limits_{j=1}^{N}{{FC}}_{{ij}}}$$

(3)

Functional hierarchy metrics

To investigate functional hierarchical organization following pharmacological treatments in MDD patients, we adapted the hierarchy measures of directedness and trophic levels in directed networks²⁴. This provides both the hierarchical node-level information (trophic level) and the global information (directedness, or trophic coherence), and here we apply this to the directed graph obtained from the GEC matrix, the individualized optimized matrix C given by equation (1).

Trophic levels

The GEC matrix defines a graph of N nodes connected by weighted edges determined by the elements of C. For each node n in the graph, we introduce the concepts of in-weight (${d}_{n}^{\,{\rm{in}}}$), by summing the m columns of C, and out-weight (${d}_{n}^{\,{\rm{out}}}$), by summing the m rows of C, defined as follows:

$${d}_{n}^{\,{\rm{in}}}={\sum _{m}{C}_{{nm}}}$$

(4)

$${d}_{n}^{\,{\rm{out}}}={\sum _{m}{C}_{{mn}}}$$

(5)

We define the total weight of node n as u_n by

$${u}_{n}={d}_{n}^{\,{\rm{in}}}+{d}_{n}^{\,{\rm{out}}}$$

(6)

Furthermore, we define the imbalance for node n as v_n, representing the difference between the flow into and out of the node by

$${v}_{n}={d}_{n}^{\,{\rm{in}}}-{d}_{n}^{\,{\rm{out}}}$$

(7)

The (weighted) graph-Laplacian operator Λ on vector h is given by

$${{\Lambda }}={\rm{diag}}{\left(u\right)}-{{C}}-{{{C}}}^{{\bf{T}}}$$

(8)

Consequently, the enhanced concept of trophic level corresponds to the solution h of the linear system of equations

$${{\Lambda }}{\bf{h}}={\bf{v}}$$

(9)

Here each component of the vector h corresponds to the trophic level in a given brain region. Importantly, while the operator Λ is symmetric, the asymmetry of the network is evident in the imbalance vector v.

Directedness (trophic coherence) of a network

Once the hierarchy level h has been established, we can assess the network’s global directionality by computing its directedness (or trophic coherence) using the equation

$${F}_{0}={1-\frac{\sum _{{mn}}{C}_{{mn}}\,{({h}_{n}-{h}_{m}-1)}^{2}}{\sum _{{mn}}{C}_{{mn}}}}$$

(10)

A network is considered maximally coherent when F₀ = 1, whereas it is regarded as incoherent when F₀ = 0. The trophic coherence is a graph theoretical measure of hierarchical organization. Elevated values of trophic coherence indicate a greater degree of hierarchical organization. Using the GEC obtained through the whole-brain model-based framework, we computed hierarchical levels for each region in our parcellation and trophic coherence characterizing the global level of hierarchical organization.

SVM for pattern separation and classification

Both pattern separation and classification were conducted using a support vector machine (SVM) with Gaussian kernels as implemented by the function fitcecoc in MATLAB (2022b), returning a full, trained, two-class, error-correcting output codes model with the predictors in the input with class labels. We used the one-versus-one coding design with K = 2 as the number of unique class labels in K(K − 1)/2 binary SVM models.

The output of the SVM was two classes, which correspond to (1) after versus before, (2) responder versus non-responder or (3) psilocybin versus escitalopram treatment. The input features used for classification were hierarchical trophic levels (for each patient and condition). We used a selection of inputs by statistically comparing hierarchical trophic levels across patients, region by region, using a Wilcoxon 10,000 permutation tests and sorting these. We selected the minimum number of inputs that yielded the largest accuracy. The SVM was trained using the leave-one-out cross-validation procedure; that is, we randomly chose one patient for generalization and used the rest for training. This was repeated and shuffled 1,000 times. Furthermore, the training set was balanced in terms of number of examples for each class label, while randomly selecting the patients in each class for each shuffling iteration.

To estimate the highest possible accuracy, we systematically computed the accuracy by sequentially selecting different numbers of regions from the sorted list of statistically significant trophic levels mentioned above. In terms of the minimum number of regions used for the pattern separation in Fig. 2a, the highest accuracy was obtained for 69 regions for psilocybin and six regions for escitalopram treatment before versus after. In Fig. 3a, for the pattern separation between responders versus non-responders, the highest accuracy was obtained using five regions for psilocybin and six regions for escitalopram treatment. In Fig. 4b, the highest accuracy comparing treatment was obtained using 33 regions. In Fig. 4c, the highest accuracy was obtained using five regions for the prediction of treatment response.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.