Trial PaperMajor Depressive Disorder (MDD)Depressive DisordersNeuroimaging & Brain MeasuresPsilocybinPlacebo

Distinct brain responses to psilocybin and escitalopram in depression captured by the Fluctuation-Dissipation Theorem

This double-blind randomised controlled trial studied brain scans from people with major depressive disorder treated with psilocybin or escitalopram and found that the two treatments caused opposite changes in brain organisation. Baseline brain measures also helped distinguish who responded to each treatment.

Authors

  • Robin Carhart-Harris
  • David Nutt
  • David Erritzoe

Published

Biorxiv
individual Study

Abstract

In recent decades, the psychedelic psilocybin has been studied as a potential treatment for major depressive disorder (MDD), offering an alternative to traditional antidepressants. However, the brain changes underlying the clinical effects of different interventions remain unclear. Here, we investigated the effects of psilocybin and a conventional antidepressant, escitalopram, from the double-blind randomised controlled trial (DB-RCT) - NCT03429075 - on the brain's hierarchical organisation. Using pre- and post-treatment resting-state functional magnetic resonance imaging (fMRI) we built whole-brain models and obtained a generative effective connectivity (GEC) matrix for each patient. Based on the GEC, we measured the level of non-equilibrium brain dynamics by quantifying the deviation from the fluctuation-dissipation theorem (FDT) and performed complementary analysis on brain segregation and asymmetry. Our results showed opposite reconfigurations of the hierarchical non-equilibrium brain dynamics following each treatment. Additionally, baseline measures effectively distinguished responders from non-responders within each treatment. These findings suggest that the deviation of the FDT may serve as a marker for differentiating the effects of psilocybin and escitalopram in MDD treatment, overall, contributing to the understanding of therapeutic mechanisms of depression.

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Research Summary of 'Distinct brain responses to psilocybin and escitalopram in depression captured by the Fluctuation-Dissipation Theorem'

Editorial

βBlossom's Take

This secondary analysis is useful because it compares psilocybin with escitalopram at the level of post-treatment brain organisation, not just symptom change. The opposing FDT effects help explain why the two treatments may not be interchangeable even when both improve depression, and the baseline-response signals are a useful step towards stratification.

Introduction

Major depressive disorder is described as a highly burdensome and heterogeneous condition, and the authors note that existing antidepressants such as SSRIs, including escitalopram, often have only modest efficacy, limited adherence, relapse, and side effects. Against this backdrop, psilocybin has emerged as a candidate treatment, but the brain mechanisms underlying its effects, and how these compare with conventional antidepressants, remain incompletely understood. Previous fMRI research has mainly examined the acute psychedelic phase, often in healthy participants, leaving uncertainty about post-acute effects in depression and about how changes in brain organisation relate to different treatments. Dagnino and colleagues set out to compare psilocybin and escitalopram in patients with major depressive disorder by examining whole-brain hierarchy and non-equilibrium dynamics through a thermodynamic framework based on violations of the Fluctuation-Dissipation Theorem (FDT). They aimed to determine whether the two interventions produce distinct brain reconfigurations after treatment, whether these effects can be measured at whole-brain and regional levels, and whether baseline brain measures relate to clinical response. The paper is presented as an analysis of data from a double-blind randomised controlled trial.

Methods

The study analysed data from a double-blind randomised controlled trial, NCT03429075, in which participants with unipolar major depressive disorder were allocated to psilocybin or escitalopram. Eligibility required a clinician-confirmed diagnosis of unipolar MDD and a score of at least 16 on the 21-item Hamilton Depression Rating Scale. Exclusion criteria included personal or immediate family history of psychosis, serious suicide attempts, risky physical health conditions, pregnancy, MRI contraindications, SSRI contraindications, or prior escitalopram use. Treatment resistance was not used as an inclusion or exclusion criterion. Participants underwent screening by telephone and further medical assessment. A total of 59 patients were recruited, with 30 allocated to psilocybin and 29 to escitalopram. The final imaging sample comprised 22 participants in the psilocybin arm and 20 in the escitalopram arm. The main reasons for exclusion were missing post-treatment scans, excessive head motion, adverse reactions leading to discontinuation in the escitalopram arm, cannabis use, and COVID-19 lockdown-related loss to follow-up. Mean age was 41.9 years in the psilocybin group and 38.7 years in the escitalopram group; 8 participants were female in the psilocybin arm and 6 in the escitalopram arm. The treatment schedule included baseline resting-state fMRI with eyes closed, a first dosing day with either 25 mg psilocybin or 1 mg psilocybin in the escitalopram arm as a blinding procedure, a second dosing day three weeks later with the same respective dosing pattern, and six weeks plus one day of daily capsules after the first dosing day. The psilocybin arm received inert placebo capsules, whereas the escitalopram arm received 10 mg escitalopram capsules, starting with one capsule daily for three weeks and then two capsules daily thereafter. Participants were told they were receiving psilocybin but were not informed about dosage. Post-treatment resting-state fMRI was collected three weeks after the second dosing day. Clinical outcome assessment used the Beck Depression Inventory (BDI-1A) at baseline and at 2, 4 and 6 weeks after the first dosing day, although the paper states that the primary clinical outcome for the parent trial was the QIDS-SR-16. The imaging analysis focused on pre- and post-treatment resting-state fMRI. Data were parcellated into 80 regions using the DK80 atlas, and pre-processing used standard pipelines in FSL, AFNI, Freesurfer and ANTs, including motion correction, slice timing correction, registration, scrubbing, band-pass filtering and nuisance regression. For the main analysis, the authors built individual whole-brain models based on a supercritical Hopf bifurcation and derived a generative effective connectivity (GEC) matrix for each participant. They then quantified deviation from the FDT as a measure of non-equilibrium dynamics by perturbing each node and estimating how spontaneous fluctuations related to responses under small perturbations. They also computed a perturbability map, network-level summaries across the Yeo resting-state networks plus subcortical areas, segregation using Louvain modularity on both functional connectivity and GEC matrices, and asymmetry as the proportion of asymmetric interactions after thresholding the absolute difference between each matrix and its transpose. To explore treatment-response prediction, they applied support vector machine classifiers in the escitalopram group using several feature sets: global brain connectivity, GEC in-weight, GEC out-weight, GEC total weight, and the FDT-derived perturbability map. They used leave-one-out cross-validation shuffled 1,000 times, with feature ranking based on training-set separation. Finally, they tested associations between baseline brain measures and BDI change using Pearson correlation, and overall statistical testing relied on permutation-based t-tests with 1,000 permutations and false discovery rate correction for network analyses.

Results

At the whole-brain level, psilocybin and escitalopram produced opposite changes in FDT deviation. After psilocybin, global deviation from the FDT increased significantly, whereas after escitalopram it decreased significantly. The paper reports p<0.05 for psilocybin and p<0.01 for escitalopram in the global analysis, and Figure 2 is described as showing within-group before-versus-after differences of p=0.044 for psilocybin and p=0.004 for escitalopram. An ANOVA supported treatment as the main factor driving these differences, while responder status and BDI change did not explain them. Correlations between change in FDT deviation and change in BDI were not significant when examined within each treatment arm or across both arms together. Regional analyses showed that, in both pre- and post-treatment scans, the highest FDT deviations were mainly in somatomotor and ventral attention areas, together with some subcortical regions, whereas the lowest values were mainly in limbic areas and some default mode and subcortical regions. Changes after treatment generally followed the same global pattern: most areas increased in the psilocybin arm and decreased in the escitalopram arm. For psilocybin, the largest increases were mainly in somatomotor regions; for escitalopram, the largest decreases were in somatomotor, dorsal attention and ventral attention regions. At the resting-state network level, psilocybin showed a trend towards increased FDT deviation across all networks, with significant changes in somatomotor, dorsal attention, ventral attention and default mode networks, although these did not survive multiple-comparisons correction. Escitalopram produced significant decreases across all networks, with several effects surviving correction, especially in ventral attention and subcortical networks. Segregation analysis yielded no significant findings when applied to functional connectivity matrices alone, but the GEC matrices showed significant opposite changes: modularity decreased after psilocybin and increased after escitalopram, both with p<0.001. The authors describe this as more overlapping communities after psilocybin and greater segregation after escitalopram. Correlations between change in GEC modularity and change in BDI were not significant within either treatment arm, although a positive correlation appeared when both groups were pooled. The authors interpreted this pooled association as masking the opposite treatment-specific effects. Asymmetry analyses showed that global asymmetric interactions increased after psilocybin and decreased after escitalopram across thresholds, matching the pattern observed for FDT deviation. Intra-module and inter-module asymmetry followed the same direction in each arm. When examining responders versus non-responders, psilocybin responders generally showed increases in perturbability across most cortical regions, whereas non-responders had more mixed and heterogeneous patterns. In the escitalopram arm, both responders and non-responders generally showed decreases in perturbability, but the changes were larger in responders. Subcortically, some regions did not follow the overall treatment trend in either arm, including the globus pallidus internal segment and caudate in the psilocybin group, and the globus pallidus internal segment, hippocampus, subthalamic nucleus and nucleus accumbens in the escitalopram group. For treatment-response prediction in escitalopram, the support vector machine performed best when using the FDT-derived perturbability map, reaching a maximum accuracy of 85.50% with one feature. This outperformed the GBC and the different GEC-based classifiers, which achieved maximum accuracies of 35.55%, 52.95%, 58.25% and 56.85% depending on the feature set. The most informative regions across classifiers were mainly in limbic, default mode and subcortical areas, with additional contributions from visual, somatomotor and ventral attention regions. Finally, baseline asymmetry within the somatomotor network was significantly positively correlated with change in BDI in the psilocybin arm, meaning that lower baseline asymmetry was associated with greater clinical improvement. No significant relationship was found for escitalopram or when both treatment groups were combined.

Discussion

The authors argue that their thermodynamic framework captured distinct post-treatment reconfigurations of hierarchical brain dynamics in depression. They interpret psilocybin as increasing non-equilibrium dynamics, asymmetry and reduced segregation, whereas escitalopram produced the opposite pattern across the same measures. They present these opposing effects as evidence that the two interventions may reduce depressive symptoms through different brain-level mechanisms, extending previous analyses from the same trial cohort. They place their findings in the context of earlier psychedelic research, noting that acute psilocybin effects in healthy participants have often been associated with reduced temporal asymmetry, increased complexity and a loosening of hierarchical constraints, whereas their study examined post-acute effects in depressed patients. The authors suggest, cautiously, that the post-acute increase in non-equilibrium after psilocybin may reflect recalibration of hierarchical organisation relative to the depressive baseline state, rather than simply mirroring the acute psychedelic state. They also note that future work should examine healthy versus depressed states and compare onset, peak and post-acute phases more directly. At the regional level, the authors emphasise the prominence of somatomotor and ventral attention regions, with additional involvement of default mode and dorsal attention networks, and they link these systems to depression-related processes such as embodied symptoms, cognitive vulnerability, self-referential thought and rumination. They interpret the responder analyses as showing that psilocybin responders tended to move towards greater perturbability across most areas, whereas escitalopram responders and non-responders generally showed reductions. For modularity, they interpret the decrease after psilocybin and increase after escitalopram as consistent with increased integration versus greater segregation, respectively, and they note that the GEC-based approach differentiated the groups more clearly than classical functional connectivity. The authors also highlight the baseline predictor findings, particularly the relationship between lower baseline somatomotor asymmetry and greater clinical improvement under psilocybin, and the superior classification performance of the FDT-based measure for escitalopram response. They frame these results as relevant to precision psychiatry and biomarker development. They acknowledge several limitations. The analysis used an 80-region DK80 parcellation, which they describe as a compromise between computational cost and spatial resolution, and there is no single agreed standard for fMRI parcellation. They also relied on a structural connectivity template from a separate healthy cohort rather than individual connectomes. In addition, the sample size was relatively small, limiting generalisability and statistical power. The authors conclude that larger replication studies would improve robustness and help clarify the value of the approach for understanding and optimising depression treatment.

View full paper sections

-TRIAL

The design of the trial and the primary clinical outcomes has been previously published (clinicaltrials.gov: NCT03429075)

-PARTICIPANTS

Eligibility criteria consisted of practitioner-confirmed diagnosis of unipolar MDD, with a score of 16 or higher on the 21-item Hamilton Depression Rating scale. Individuals were asked if they had prior experience with psychedelics, with 31% and 24% of individuals reporting previous use for the psilocybin and escitalopram groups, respectively. Exclusion criteria were: immediate family or personal history of psychosis, physician-assessed of risky physical health condition, serious suicide attempts history, positive pregnancy test, conditions that prevent undergoing an MRI, contraindications for SSRIs, or previous escitalopram use. Treatment resistance was not an inclusion or exclusion criterion. Eligible individuals had screening interviews via telephone, comprehensive evaluations of mental and physical medical history.

-TREATMENT PROTOCOL

The total number of patients with MDD recruited was 59, from which 30 individuals were allocated to the psilocybin group and 29 individuals were assigned to the escitalopram group using a random number generator. The final samples for this analysis were n=22 in the psilocybin arm (mean age= 41.9 years, s.d. = 11.0, 8 female) and n=20 for in the escitalopram arm (mean age= 38.7 years, s.d. = 11.0, 6 female). The excluded patients for the psilocybin arm consisted in: one patient for choosing not to take daily placebo capsules and COVID-19 UK lockdown, two patients for not attending post-treatment session, five patients from excessive fMRI head motion. The excluded patients for the escitalopram arm consisted in: four patients discontinued from escitalopram's adverse reactions, one patient with reported cannabis use, one patient lost due to COVID-19 UK lockdown, three patients excluded from excessive fMRI head motion. Before each treatment, patients had a baseline resting-state fMRI session with eyes closed. The first dosing day (DD1) consisted of either 25 mg of psilocybin, or a presumed negligible dose of 1 mg of psilocybin, for the psilocybin and escitalopram arms, respectively. Participants were informed they received psilocybin but to ensure blinding no information on dosage was provided. Three weeks later there was a second dosing day (DD2), consisting of the same dosage as in the first session for each arm, with no dosage crossover between the two arms. Starting from the first day after DD1, all patients took daily capsules during 6 weeks and 1 day. It consisted of 1 capsule per day during the first 3 weeks, and 2 capsules per day afterwards. In the psilocybin arm, the content of the capsules was inert placebo (microcrystalline cellulose). In the escitalopram arm, the content was 10 mg of escitalopram, resulting in a total of 1 x 10 mg during the first 3 weeks, and 2 x 10 mg afterwards. For blinding, all patients were informed to receive psilocybin but unaware of the dosage. Post-treatment resting-state fMRI with eyesclosed scans were performed for all patients 3 weeks after DD2.

-TREATMENT OUTCOME

The depression severity assessment used in this study is the Beck Depression Inventory (BDI) -BDI-1A. This measure is patient-rated and captures a wider range of symptoms than other kinds of scoring, with an emphasis in cognitive features of depression. The total score range is 0-63, where 0-13 is minimal range, 14-19 is mild, 20-28 is moderate and 29-63 is severe. Assessments were conducted at baseline (before the first dosing day DD1), and at 2, 4 and 6 weeks after DD1. As a note, the measure BDI is the secondary outcome for this study. The primary outcome measure is the Quick Inventory of Depressive Symptomatology (QIDS) -QIDS-SR-16. For justification on the use of BDI and not QIDS please refer to.

-MAGNETIC RESONANCE IMAGING ACQUISITION

Brain imaging was obtained using a 3T Siemens Tim Trio set-up at Invicro. Anatomical image acquisition was done using the recommended MPRAGE parameters from the Alzheimer's Disease Neuroimaging Initiative, Grand Opportunity (ADNI-GO56): 1-mm isotropic voxels; 2,300 ms repetition time (TR); 2.98 ms echo time (TE); 160 sagittal slices; 256 x 256 in-plane field of view; 9° flip angle; 240 Hz per pixel bandwidth; 2 generalised autocalibrating partially parallel acquisitions (GRAPPA) acceleration. Functional data (i.e., fMRI) was collected during resting-state for eyes closed, using T2*weighted echo-planar images and a 32-channel head coil. A total of 480 volumes in ~10 min were collected with the following parameters: 3-mm isotropic voxels; 1,250 ms TR; 30 ms TE; 44 axial slices; 70° flip angle; 2,232 Hz bandwidth per pixel; 2 GRAPPA acceleration.

-BRAIN PARCELLATION

Neuroimaging data was parcellated into 80 brain areas using DK80. This parcellation combines the Mindboggle-modified Desikan-Killiany parcellationof 62 cortical brain areas (31 areas in each hemisphere), with the following 18 subcortical areas (9 areas in each hemisphere): hippocampus, amygdala, subthalamic nucleus (STN), global pallidus internal segment (GPi), global pallidus external segment (GPe), putamen, caudate, nucleus accumbens (NA) and thalamus.

-BOLD FMRI PRE-PROCESSING

The fMRI data pre-processing was done with a custom in-house pipeline using FMRIB Software Library (FSL), Analysis of Functional NeuroImages (AFNI), Freesurferand Advanced Normalization Toolspackages. Details can be found in. The stages consisted in de-spiking, slice time correction, motion correction, brain extraction, rigid body registration to anatomical scans, nonlinear template registration, scrubbing, band-pass filtering, regression (with six realignment motion regressors, three tissue signal regressors, draining veins and local white matter). Bias from movement artifacts were ruled out by.

-THEORETICAL FRAMEWORK: VIOLATIONS OF THE FLUCTUATION-DISSIPATION THEOREM

Einstein's work on Brownian motion describes equilibrium systems using the Fluctuation-Dissipation Theorem (FDT), which establishes the balance between friction (i.e., dissipation, transfer of energy) and thermal noise (i.e., spontaneous fluctuations). Onsager proposed a derivation of the FDT using his regression principle. This principle states that when a system shifts from an initial equilibrium state towards a final equilibrium state, by a weak external perturbation, this shift can be considered as a spontaneous equilibrium fluctuation (i.e., the initial spontaneous fluctuations predict the dissipation after a perturbation). Conversely, in non-equilibrium systems the spontaneous fluctuations no longer determine the effects of a perturbation). Let's assume an observable 𝐵 at time 𝑡 = 0 has a weak external perturbation 𝜀 coupled. The expectation value of another observable 𝐴 in the unperturbed state is denoted as ⟨𝐴(𝑡)⟩ 0 , and the expectation value of 𝐴 after the perturbation is applied in 𝐵 is denoted as ⟨𝐴(𝑡)⟩ 𝜀 . The difference between ⟨𝐴(𝑡)⟩ 𝜀 and ⟨𝐴(𝑡)⟩ 0 is given by: where 𝛽 is the inverse temperature from equilibrium thermodynamics. Furthermore, the time-dependent susceptibility is as follows: When taking the limit 𝑡 → ∞, the static form of FDT is obtained: given correlations factorise for infinitely separated times. In equilibrium, we obtain the correspondence between the response of a system to perturbation (the left-hand side of the equation) and the system's unperturbed correlations (right-sand side of the equation). By first defining the initial unperturbed state such that the mean values of observables set to zero (i.e., ⟨𝐴⟩ 0 = 0 and ⟨𝐵⟩ 0 = 0), the level of non-equilibrium can be calculated as the system's normalised deviation from FDT: Here, 𝛽⟨𝐴𝐵⟩ 0 corresponds to the unperturbed fluctuations, and 𝜒 𝐴,𝐵 is the response to a small perturbation 𝜀. Finally, the total deviation 𝐷 is calculated by averaging 𝐷 𝐴,𝐵 over all observables 𝐴 and all perturbation sites 𝐵. In this way, D quantifies the degree of violation of the FDT, hence the distance of the system from equilibrium.

-MODEL-BASED FDT OF WHOLE-BRAIN DATA

Following, we computed the deviation from the FDT of each participant to evaluate the non-equilibrium dynamics in the brain resulting from asymmetries in information flow (Figure). To do so, we built a whole-brain model of each individual fitted to the corresponding functional empirical data (Figure). This allowed us to derive analytical expressions for the correlation between brain areas from the spontaneous fluctuations, and the perturbation effects in each brain region on the average activity across the rest of the brain areas. In other words, we systematically perturb all brain areas B and observe the corresponding responses on all brain areas A.

WHOLE-BRAIN MODEL

The whole-brain model consists of describing the local dynamics of each brain area as the normal form of a supercritical Hopf bifurcation, capable of describing transitions from asynchronous noise to oscillations. From each whole-brain model we created a generative effective connectivity (GEC) matrix. Full mathematical description of the Hopf model, its linearization and optimisation is described in detail in Supplementary Information.

FDT COMPUTATION

After obtaining a GEC for each participant in each group, we derived an analytical expression for the deviation from the FDT (Equation). To do so, the expectation values of the state variables ⟨𝛿𝑢⟩ 𝜀𝑗 are calculated when a perturbation 𝜀 is applied to a node 𝑗. From Supplementary Information Equation, we have the relationship 𝑑 𝑑𝑡 ⟨𝛿𝑢⟩ 𝜀𝑗 = 𝐽⟨𝛿𝑢⟩ 𝜀𝑗 + ℎ 𝑗 = 0, in which ℎ 𝑗 is a 2𝑁 vector composed by zeros except component 𝑗 corresponding to the perturbation 𝜀. By solving this for the desired expectation value, the result is ⟨𝛿𝑢⟩ 𝜀𝑗 = -𝐽 -1 ℎ 𝑗 . By considering the real part of ⟨𝛿𝑢⟩ 𝜀𝑗 , the following is defined: ⟨𝛿𝑥⟩ 𝑗 = ⟨𝛿𝑥⟩ 𝜀𝑗 /𝜀. This way, the deviation from the FDT for area 𝑖 when a perturbation is applied to area 𝑗 can be derived as: (5) In this equation, the term 2/𝜎 2 corresponds to the inverse of temperature 𝛽 and the covariance ⟨𝛿𝑥 𝑖 𝛿𝑥⟩ 0 is derived from 𝐾𝑆 𝑠𝑖𝑚 . Due to numerical motives, the global effect of perturbing node 𝑗 is obtained averaging the numerator and denominator over brain regions: Overall, we obtained for each participant the vector 𝑃 𝑗 , defined as the perturbability map over all brain areas (size 1xN), corresponding to the effect of perturbing each brain area across the rest of the areas (averaged). In other words, the position of the vector is a perturbed brain area, and the value in the corresponding position is the effect on each of the remaining brain areas at an individual level and then averaged. We finally calculated the level of non-equilibrium 𝐷 ̂ by averaging the deviation from the FDT over all perturbations (i.e., 𝐷 ̂= 1

𝑁 ∑ 𝑃 𝑗 𝑗

). We also reduced the perturbability map from 80 brain areas to 8 networks: the 7 well-known Yeo networks (Visual, Somatomotor, Dorsal Attention, Ventral Attention, Limbic, Frontoparietal and Default Mode networks), plus the subcortical areas. We used a map of size areas * networks which is computed by counting the number of voxels of each brain area in each network and dividing by the total number of voxels of the corresponding brain area. Thus, each cell contains the probability values of each brain area in each network. For each network, firstly, we multiplied the probability of each area belonging to that network by the area's perturbability value. Then, we summed the resulting values across all areas and divided by the total sum of probabilities for that network. In other sections of this study, we determine the resting-state network of each brain area by looking at the network with highest associated probability.

-SEGREGATION

To quantify brain segregation (i.e., breakdown of a system into subcomponents), we implemented the Louvain community detection algorithm that assesses the quality of a partition by the modularity index Q. This method looks for the maximum extent of separation of non-overlapping modules in a network) (Figure). We implemented the function community_louvain from the Brain Connectivity Toolbox in MATLAB, which iteratively moves nodes between communities, aggregates the network, and quantifies the modularity index Q. This process is repeated until convergence, calculating the modularity score (i.e., Q) 100 times and choosing the highest value as the final result. This output Q (i.e., modularity) corresponds to the optimal division of the network into distinct modules (i.e., quality of the network partition) and is considered the measure of segregation. Higher values correspond to a more clearly defined modular organisation. Modularity is a cost-function that maximises edges within modules and minimises edges across modules. We used Newman as cost-function adapted for weighted networks. Followingwe first computed the modularity on the FC matrices. Since the modularity algorithm requires positive weights, we applied the absolute value of the FC matrices to retain information from negative correlations. We excluded self-connections by setting the diagonal of the input network to 0, which could otherwise bias the true segregation estimation. For undirected matrices (i.e., FC), Q is defined as: where 𝑚 = 1 2 ∑ (𝐴 𝑖𝑗 ) .

𝑖𝑗

The matrix 𝐴 𝑖𝑗 corresponds to the weight between node 𝑖 and node 𝑗 of the network and 𝜆 is the structural resolution free parameter (set to 1 by default). The term 2𝑚 is the expected null network, defined by the total sum of the network across all connections with node 𝑖 as 𝑘 𝑖 = ∑ 𝐴 𝑖𝑗 𝑗 . In addition, 𝑐 𝑖 is the community to which a node is assigned to. And, 𝛿(𝑐 𝑖 , 𝑐 𝑗 ) is the Kronecker 𝛿 function with a value of 1 if nodes 𝑖 and 𝑗 belong to a same community and a value of 0 if they belong to different communities. Subsequently, we computed the modularity in the GEC matrices derived from our models. Given the GEC is stored as in vs. out flow of information, we transpose the matrices before computing the modularity in accordance with the computation convention. For directed matrices (i.e., GEC), Q is defined as: where 𝑚 = 1 2 ∑ (𝐴 𝑖𝑗 ) ).

𝑖𝑗

In the implementation, 𝑘 𝑖 𝑜𝑢𝑡 and 𝑘 𝑗 𝑖𝑛 correspond to the outgoing and incoming weights for nodes i and j. Lastly, in order to obtain partitions (i.e., modules) representative of each group whilst preserving individual variability, we followed a three-step process from. First, we built a nodal association matrix T by looking at the number of times each pair of nodes are assigned to a same module in each individual. Then, we divided by the total number of individuals, thus Tij indicates the probability of nodes i and j assigned to the same community. Then, we built a null-model T r by permutating randomly the initial partitions of each participant whilst preserving the number of modules and module size of the original computation. We set to 0 values of T less than the maximum value of T r to remove noise. Finally, we computed the modularity of the association matrix T following the same procedure as described initially (i.e., Louvain algorithm, Newman cost-function, 100 iterations).

-ASYMMETRY

We assessed the asymmetry in terms of the proportion of asymmetric interactions in a given matrix (global GEC, intra-module GEC and inter-module GEC) (Figure). First, we calculated the absolute difference between a matrix and its transpose. Then, we binarised the resulting matrix A by converting to zero the cells below a threshold cut-off value 𝛾 as follows: Here, 𝑎 𝑖𝑗 corresponds to the value of each cell in A, and the threshold 𝛾 is computed as a percentage of the mean of A. Finally, we computed the asymmetry as the proportion of remaining cells (i.e., different to zero) divided by the total number of existing cells.

-SUPPORT VECTOR MACHINE

We used a support vector machine (SVM) to classify the escitalopram group at baseline into responders and non-responders. The classifier was implemented with the fitcecoc function and a Gaussian kernel in MATLAB. We trained the SVM with the leave-one-out cross-validation procedure shuffled 1,000 times, each time randomly excluding one individual and using the rest, with their corresponding class labels, for training. In each iteration, the fully trained two-class model was used to assign a class label to the excluded individual. The final accuracy was the average across all iterations. We computed a total of 5 classifications using the following different data as inputs: global brain connectivity (GBC), GEC in-weight (GEC in ), GEC out-weight (GEC out ), GEC total weight (GEC total ) and the perturbability map obtained in the main analysis using the FDT framework. The GBC is given by the following equation: Furthermore, the other calculations on the GEC are as follows: 𝐺𝐸𝐶 𝑡𝑜𝑡𝑎𝑙 = 𝐺𝐸𝐶 𝑖𝑛 +𝐺𝐸𝐶 𝑜𝑢𝑡 . (13) Each input has a size of 1 x N (i..e, brain areas). In each of the 5 classifications, we computed the SVM for a number of features F (i.e., brain areas) of the input, spanning from 1 to N (i.e., 80). Particularly, in each classification (i.e., 5) and number of features F, for each k-fold (i.e., 1, 2, 3, …, 1000), we computed the standard error of the mean (SSND) of each brain area between the groups being compared (i.e., responders vs. non-responders) in the training set. Then, we ordered the brain areas in descending order of SSND, and chose the top F brain areas. Then, we selected those same brain areas for the testing set. As a note, the inputs provided by the models (GEC in , GEC out GEC total ) were calculated for each individual using the DTI as a starting point in the GEC optimisation, not the GEC of the group as for the previous analysis. This way, the goal of the SVM is still to separate underlying patterns between responders and non-responders while lessening the influence of the initial group optimisation.

-CORRELATION

We studied the relation between baseline brain measures and the level of improvement of the patients by calculating the Pearson correlation between the brain asymmetry within the SOM network at baseline and the change in BDI scores.

-STATISTICAL ANALYSIS

Statistical analysis was performed using permutation-based t-tests with 1000 permutations and a significance threshold of 0.05, paired and non-paired when applicable. For the resting-state network analysis, we applied a False Discovery Rate (FDR) method to correct for multiple comparisons..

RESULTS

In this study, we investigated the hierarchical non-equilibrium brain dynamics in a double-blind phase II randomised control trial comparing intervention with psilocybin and escitalopram for MDD patients. Specifically, the fMRI resting-state data at baseline and after treatment (Figure). We used a thermodynamic inspired framework, namely the Fluctuation-Dissipation Theorem (FDT), to uncover the changes in non-equilibrium dynamics which are driven by asymmetries between brain areas and that reveal the hierarchical organisation of the whole-brain (Figure). To quantify the FDT in the brain, we created whole-brain models for each participant, fitted to their empirical neuroimaging data. We obtained generative effective connectivity (GEC) matrices, which link anatomical with functional connections through an optimisation process, adjusting anatomical connections with asymmetric weights in an iterative manner. We computed the FDT from the GEC matrices and analysed group differences. Specifically, we perturbed one brain area at a time (e.g., node B) and observed the deviation from the FDT in another area (e.g., node A) (see Materials and Methods for detailed explanation). We repeated this for all nodes A after perturbing all nodes B. From this, we constructed a perturbability map in which, for each perturbed area, the deviation of the FDT was averaged over all other areas. We also averaged the perturbability map to obtain the global FDT violation (i.e., deviation from equilibrium) (Figure). In addition, we analysed the GEC by quantifying functional segregation and the proportion of asymmetric interactions (global, intra-and inter-modular) (Figure). Lastly, we evaluated the relation between the brain measures and clinical changes.

-QUANTIFYING THE WHOLE-BRAIN FDT DEVIATION IN EACH TREATMENT

At a global level, we found a significant increase of the FDT deviation after psilocybin treatment (p < 0.05), and a significant decrease of the FDT deviation after escitalopram treatment (p < 0.01) (Figure). This reveals a statistically differential treatment-dependent deviation of the FDT. We supported the effect of treatment as the principal factor for the different direction of change using an analysis of variance (ANOVA). The ANOVA analysis showed a significant effect in treatment, and not in the binary classification of responders and non-responders, nor depression scores using the Beck Depression Inventory (BDI) change (after-before) (Supplementary Information Table). Patients were classified as responders if they had a decrease in BDI score of 50% from baseline. Furthermore, the Pearson correlation between the change in FDT deviation and the change in BDI scores for each group separately, and together, were not significant (Supplementary Information Figure).

FIGURE 2: FDT DEVIATION VALUES ACROSS THE WHOLE-BRAIN FOLLOWING ADMINISTRATION OF PSILOCYBIN AND ESCITALOPRAM. PSILOCYBIN AND ESCITALOPRAM TREATMENTS CAN BE OBSERVED IN THE LEFT AND RIGHT COLUMNS, RESPECTIVELY. A. REPEATED MEASURES PLOT FOR THE FDT DEVIATION ACROSS INDIVIDUALS FOR EACH CONDITION. GREY LINES REPRESENT THE TRAJECTORY OF EACH INDIVIDUAL WHEREAS THE COLOURED LINE REPRESENTS THEIR AVERAGED TRAJECTORY WITHIN EACH INTERVENTION ARM (RED FOR PSILOCYBIN AND BLUE FOR ESCITALOPRAM).

There are significant differences between the before and after (* represents p < 0.05; ** represents p < 0.01) for both psilocybin (p = 0.044) and escitalopram (p = 0.004). The change in FDT goes in opposite directions for each treatment, with an increase in psilocybin and a decrease in escitalopram. B. Brain renders show the FDT deviation across brain areas (i.e., perturbability map) for the sessions (before and after) of each intervention. Subcortical areas are shown on slices in Montreal Neurological Institute (MNI) space (coronal axis y= -10 and 12 mm). C. Brain renders with the difference in FDT deviation (after-before treatment) in each intervention across brain areas. The differential opposite effect for each treatment can be observed.

-REGIONAL DIFFERENCES IN FDT DEVIATION

We then carried out an analysis on the FDT deviation at a regional level (Figure). This way, we could evaluate similarities and differences in the patterns of hierarchical reconfiguration between the intervention groups. In both acquisition times (before and after) and treatments (psilocybin and escitalopram), the areas with highest FDT deviation belonged mainly to the somatomotor (SOM) and ventral attention (VAN) networks, as well as some subcortical areas (SCN). Furthermore, the areas with lowest FDT deviation were mainly from the limbic network (LIM), and some areas from the defaultmode network (DMN) and SCN (Supplementary Information Tableand). With respect to the differences in FDT deviation changes (after-before) within each treatment (Figure), almost all brain areas increased following psilocybin and decreased following escitalopram, in line with their corresponding changes in global FDT deviation. In other words, changes in global FDT deviations are caused by most brain areas within each treatment arm. Under psilocybin treatment, the highest increase was found in areas mainly from the SOM,In escitalopram, the largest decrease was found in areas mainly from the SOM, dorsal attention network (DAN), and VAN (Supplementary Information Table). Statistics comparing before and after FDT deviation within each treatment revealed less significant brain areas for psilocybin compared to escitalopram (approximately 30 and 50, respectively, with 2 and 37 surviving corrections for multiple comparisons, respectively) (Supplementary Information Table). We also computed the weighted average of FDT deviation across the well-established Yeo resting-state networks (RSN)to evaluate the changes across different spatial scales (global level, regional level, and now RSN level). Psilocybin had an increasing trend of FDT deviation for all networks with significant differences in the SOM, DAN, VAN and DMN (all p < 0.05, non-surviving correction by multiple comparisons) (Supplementary Information Figure). The escitalopram group presented a significant decrease of FDT deviation in all networks: visual network (VIS) and LIM (p < 0.05); SOM, DAN, frontoparietal network (FPN) and DMN (p < 0.01); VAN and SCN (p < 0.001), all surviving correction for multiple comparisons. In both treatments, the SOM and VAN were the networks with highest absolute changes (Supplementary Information Figure). Although the change in these networks was positive for psilocybin and negative for escitalopram, they still had the highest FDT deviation before and after treatment within each group (Supplementary Information Figure).

-BRAIN SEGREGATION

We examined community organisation in the brain network by measuring segregation, the breakdown of a system into subcomponents. We quantified segregation by estimating the modularity, a metric that looks for the highest degree of separation of distinct modules in a network. In particular, we employed the Louvain algorithm with Newman's cost function. Firstly, to evaluate concordance with the findings of, we calculated the segregation of functional connectivity (FC) matrices, finding no significance for either group (Supplementary Information Figure). We extended the analysis to the GEC matrices. We found a significant difference in modularity after treatment compared to baseline, decreasing for psilocybin (p < 0.001) and increasing for escitalopram (p < 0.001) (Figure). This shows the increased power of the GEC compared to the classical FC to differentiate groups and supports the differential opposite statistical effects of psilocybin and escitalopram. B. Modularity of the association matrices of each group (i.e., matrix with the probability of two nodes belonging to a same module) followingin order to show representative communities whilst preserving inter-subject variability. The first row shows the association matrices with each module in a new colour. Module colours are not comparable between treatments nor before and after within each group. The second row shows the modules coloured according to community affiliation of the baseline within each treatment group. The third row shows the group-level GEC matrices with the modules detected outlined in red. C. Intra-and inter-module asymmetry using 90% of the mean of each matrix as threshold, which was the threshold revealing maximum significance in all cases. In all plots, * represents p < 0.05; ** represents p < 0.01 and *** represents p < 0.001. Lastly, grey lines represent the trajectory of each individual whereas the coloured line represents their averaged trajectory within each intervention arm (red for psilocybin and blue for escitalopram). The correlation between the change in GEC modularity and the change in BDI scores did not give any significance for either treatment arm. When combining both groups (psilocybin and escitalopram), the correlation was significantly positive (Supplementary Information Figure). This significant effect after aggregating the groups is masking the fact that treatments show opposite changes in brain organisation (psilocybin leads to a decrease in modularity and escitalopram to an increase in modularity). Therefore, brain modularity changes with treatment, and treatment-specific brain modularity changes are not directly related to BDI changes. We also obtained representative communities (i.e., modules) of each group by calculating the modularity on the group association matrices (i.e., matrix with the probability of two nodes belonging to a same module) following. This method reveals robust modules and preserves variability of individuals. Results in Figureshow graphs for the association matrix of each group (psilocybin and escitalopram) and session (before and after treatment) with each module in a different colour. After treatment with psilocybin communities are more overlapped, whereas the opposite occurs for escitalopram (i.e., there is more segregation). Furthermore, the reconfiguration of modules from before to after treatment within each group reveals some communities are fully preserved and others are reorganised. Lastly, the number of modules schematised on the average GEC across individuals go in line with the subject-level segregation analysis, decreasing for psilocybin and increasing for escitalopram.

-BRAIN ASYMMETRY

We then studied the asymmetries in the information flow underlying the deviations from the FDT. We obtained the asymmetry of the GEC matrix by quantifying the proportion of remaining cells after thresholding the absolute difference between the matrix and its transposed (spanning the cut-off value across 10-100% of the mean of the resulting matrix) (Supplementary Information Figure). The global asymmetry significantly increased for psilocybin and decreased for escitalopram, both across all thresholds, in line with the changes in FDT deviation. Moreover, we calculated the asymmetry in the GEC modules previously found. The intra-and intermodular asymmetry significantly increased and decreased for psilocybin and escitalopram, respectively (Figureand Supplementary Figure). Therefore, within each arm, the change in FDT deviation (and global asymmetric interactions) is driven by both internal and external processing of modules. -Differences between responders and non-responders

REGIONAL DIFFERENCES IN FDT DEVIATION

To gain a better understanding of the regional changes underlying the differential hierarchical reconfigurations following response to each treatment, we studied the changes (after-before) in FDT deviation for responders and non-responders (Figureand Supplementary Information Tableand). Regarding cortical areas, for psilocybin, responders had positive increases in FDT deviations in almost all brain regions, with the largest positive FDT deviation found mainly in areas associated with the SOM, VAN and DMN. As expected, these changes go in line to the general treatment response, given that most of the patients responded. On the other hand, non-responders had more heterogeneous directions of change in FDT deviation, with half of brain areas changing mainly in the VAN, and the other half negatively, mainly in the VIS and some belonging mainly to the SOM and LIM. For escitalopram, both responder and non-responder groups presented the same direction of change (i.e., negative) in the deviation of FDT, in almost all areas. The responder group showed stronger absolute values in most regions compared to the non-responder group, except some areas from the SCN, as well as VAN and LIM. The highest differences in FDT deviation between before versus after treatment were found for responders in areas mainly from the SOM, VAN and DAN as with the general treatment response, and in non-responders mainly in the VAN. When focusing on subcortical areas for the responder groups of each treatment, the changes showed different patterns between the intervention arms (Supplementary Figure). Firstly, in both treatments, some areas did not follow the respective global trend (i.e., decrease in FDT deviation instead of increase for psilocybin, and increase in FDT deviation instead of decrease for escitalopram). In the psilocybin group, these were the left and right global pallidus internal segment (GPi) and caudate. In the escitalopram group, these were left and right GPi, right hippocampus and left subthalamic nucleus (STN) and nucleus accumbens (NA). Furthermore, with respect to the areas with highest FDT deviation, before treatment these corresponded to the left and right putamen, caudate and thalamus in both psilocybin and escitalopram arms. After treatment, cortical areas replaced these higher positions for psilocybin but not with escitalopram. Regarding the areas with lowest FDT deviations, before treatment these were the left and right amygdala, GPi, STN and NA, both in psilocybin and escitalopram arms. After treatment, cortical areas replaced these lower positions for escitalopram and not in psilocybin. The left and right hippocampus and global pallidus externus (GPe) were maintained in the middle of the FDT deviation distribution across time and treatment, changing in deviation of FDT with the global trend within each group. A support vector machine (SVM) was used to predict the treatment response for patients in the escitalopram arm. The analysis could be done given that there are similar number of responders and non-responders for this group, contrarily to psilocybin. We evaluated the performance of the SVM trained with GBC, GEC, and FDT with different number of features (i.e., brain areas) across 1000 k-folds. In the left, confusion matrices show the accuracy as percentages represented in the colour scale, for the maximum accuracy (averaged across 1000 k-folds) reached in each case for a given number of features. TP stands for true positive, TN for true negative, PN for predicted negative and PP for predicted positive. In the right, barplots display the accuracy of each aforementioned SVM, by averaging groups of 10 folds from the total k-folds. The asterisks indicate the significant differences (*, p < 0.05; ***, p < 0.001). The green asterisks correspond to the differences that remain significant after correction by multiple comparisons with FDR. C. Correlation of baseline asymmetry within the SOM with the change of BDI scores (after-before). For psilocybin, a significant positive correlation is found, showing that the lower the baseline asymmetry, the higher the improvement in clinical score.

SUPPORT VECTOR MACHINE FOR PREDICTION OF TREATMENT RESPONSE IN ESCITALOPRAM

We used a support vector machine (SVM) to distinguish the underlying patterns of escitalopram treatment response by classifying responders and non-responders at baseline. For the psilocybin group we could not implement a classification given the limited number of non-responder individuals. In particular, we trained five classifiers using as input the following (all with same dimensionality): global brain connectivity (GBC), in-weights of the GEC (GEC in ), out-weights of the GEC (GEC out ), total weights of the GEC (GEC total ) and the perturbability map of brain regions from the FDT analysis. In each classifier, we computed one SVM for each number of features F in an accumulated manner (i.e., brain areas 1-N). In each SVM of a given number of features, for each k-fold (i.e., 1, 2, 3, …, 1000), we calculated the standard error of the mean (SSND) of brain areas between responders and non-responders in the training set, ranked them in descending order, and used the top F brain areas for training. We selected those same areas for the testing set. The maximum accuracy reached in each classifier was 35.55% with 31 features for GBC, 52.95% with 5 features for GEC in , 58.25% with 3 features for GEC out , 56.85% with 69 features for GEC total , and 85.50% with 1 feature for FDT. Results in Figureshow the corresponding confusion matrices and statistics between classifiers. The GEC measures had higher robustness than the FC to classify subgroups of individuals. Furthermore, the deviation of the FDT presented even higher accuracy. The most relevant brain areas for all classifications were mainly from the LIM, DMN, SCN, and others from VIS, SOM and VAN (Supplementary Table). The evolution of the accuracy for each number of features F in each classification can be found in Supplementary Information Figure.

HIERARCHICAL RECONFIGURATION AS A PREDICTOR OF DEPRESSION SCORE IN PSILOCYBIN

We then looked for a relation between baseline brain measures and the level of clinical improvement of the patients. We calculated the correlation between the asymmetry within the SOM, at baseline, and the change (after-before) in BDI scores (i.e., clinical depression symptoms). For psilocybin, the correlation was significantly positive, whereas for escitalopram, or when combining both groups, it was nonsignificant (Figureand Supplementary Information Figure). In other words, for the psilocybin arm, lower baseline asymmetry within the SOM is related to higher clinical improvements after treatment. The SOM network was chosen given it showed higher FDT deviation across time (before and after treatment) and treatment (psilocybin and escitalopram) (Figure), highest absolute changes between before and after treatment (Figure), and areas in the top differences between responders and non-responders for both treatment groups (Figure).

DISCUSSION

We successfully implemented a thermodynamic-inspired framework for analysing the hierarchy of nonequilibrium brain dynamics in patients with major depressive disorder before and after treatment with psilocybin or escitalopram (Figure). This framework, developed by, proposes that asymmetrical interactions between brain areas can lead to deviations from the Fluctuation-Dissipation Theorem (FDT), characteristic of non-equilibriums systems. Our analysis revealed differential effects for each drug. Psilocybin significantly increased the FDT deviation after treatment compared to baseline. Furthermore, brain segregation significantly decreased, and the global, intra-and inter-module proportion of asymmetric interactions significantly increased. In other words, increased desegregation and asymmetry were found following psilocybin. We found opposite and significant results in all measures (i.e., FDT deviation, segregation and asymmetry) for the escitalopram group. These findings support and extend previous analyses in the same cohort, which suggested and showed that while both interventions reduce depressive symptoms, they do so through distinct mechanisms. Overall, by applying a thermodynamic perspective on brain function, our study offers new insights into the underlying non-equilibrium brain dynamics of depression in the post-acute effects of treatment with psilocybin and escitalopram. The changes in FDT deviation at a whole-brain level indicate changes in the brain's functional hierarchical organisation and distance from equilibrium dynamics in terms of the breaking of the detailed balance. Our results showed that the level of hierarchical non-equilibrium brain dynamics increased for psilocybin and decreased for escitalopram (Figure). Furthermore, they reflected the same trend within each therapy in the proportion of global asymmetric interactions (Supplementary Figure). We move a step further from the study showing global directedness decreases after psilocybin and increases after escitalopram in the same dataset. During the acute stage of psychedelic action in healthy participants, brain dynamics appear to move closer to equilibrium -based on reduced temporal asymmetry in the directionality of information flow -and higher complexity. This is interpreted as a relaxation of hierarchical constraints alongside a broadened repertoire of brain substates, enabling novel and unpredictable trajectories consistent with the 'entropic brain' model of conscious states. In contrast, our results showed post-acute departures from equilibrium, which we suggest, with caution, may reflect a recalibration of hierarchical organisation relative to condition-specific baseline brain dynamics in depression, compatible with clinical improvement. To further understand the different results, a future step would be to quantify these measures at the condition level (healthy versus depressed), and during the onset and peak of psychedelic action versus post-acute effects. It would also be important to carefully contextualise the underlying assumptions and nuances in the characterisation of hierarchy in each method (Nartalio-Kaluarachchi, 2025). At a regional level, our results revealed distinct post-treatment reconfigurations in perturbability (i.e., regional FDT deviation) between psilocybin and escitalopram (Figure). For both treatment groups, the perturbability of almost all areas followed their respective global trends in FDT deviation (i.e., positive for psilocybin and negative for escitalopram). The areas with highest changes in perturbability were primarily located in the SOM and VAN networks, which were also the ones orchestrating the hierarchy (i.e., highest perturbability) across sessions. Other brain regions with largest absolute differences in perturbability were located mainly in the DMN for psilocybin and DAN for escitalopram. The relevance of these networks in depression has been highlighted in several studies. In the case of the SOM, it has been associated with the severity of depression given the physical component of the disorder arising from how the body interacts with the environment (i.e., embodied phenomenon). Furthermore, the salience network has been linked with cognitive vulnerability in depression. In addition, the DMN has been hypothesised to be implicated in depressiongiven its association with mind-wandering, internal thoughts, self-referential thinking and rumination. Lastly, the DAN has shown group connection differences between MDD and healthy controls after escitalopram treatment. We also analysed regional differences between responders and non-responders in each intervention arm. Brain area perturbability changes showed differences for each treatment associated with clinical improvements (Figure). Regarding cortical brain areas, psilocybin responders presented increases in perturbability after treatment across almost all areas, while non-responders exhibited more heterogeneous changes with only half of the areas increasing in perturbability. On the other hand, escitalopram responders and non-responders both showed reductions in perturbability after treatment for almost all areas, with more pronounced changes for responders overall. The segregation analysis provides insights into the global network reorganisation following each treatment. Results for the psilocybin arm showed a significant lower modularity in the GEC matrices (Figure). Interestingly, this goes in line with the acute phase of psilocybin in healthy participants characterised by global integration and communication, increased/decreased connectivity between/within networks, and reduced functional differentiation at the extremes of the principal gradient of cortical organisation. Furthermore, increased global functional integration has been related with the peak (i.e., 'mystical') experience during psychedelic action, which is in turn associated with positive effects in mental health. The impact of psychedelics on modularity is further discussed in. On the other hand, our analysis in the escitalopram arm presented a significant increase in modularity, supporting the opposite effects of the treatments. In the same cohort and timeframe as our study (i.e., MDD patients, 3 weeks and 1 day after DD2),found a significant decrease in FC modularity after psilocybin therapy, which correlated with antidepressant efficacy, and no significance in neither analysis (i.e., FC modularity change and correlation with clinical scores) for the escitalopram arm. Our work extends on these previous results two-fold, revealing the opposite neural changes of psilocybin and escitalopram in a significant way, and the increased efficacy of the GEC compared to the FC to show brain changes. Lastly, using the modules obtained, we computed the within and between modular asymmetry (i.e., in terms of proportion of asymmetric interactions) and found that the global trends in FDT deviation and asymmetry are led by both inter and intra-module processing (Figureand Supplementary Information Figure). Furthermore, we successfully associated baseline brain measures with changes in clinical scores after treatment. For psilocybin, we found a significant positive correlation between baseline asymmetry (i.e., proportion of asymmetric interactions) within the SOM network and BDI score change (after -before) (Figure). In other words, lower baseline asymmetry within the SOM is related with higher clinical improvement after treatment. Interestingly, another study has already related the SOM with response to treatment of depression. For escitalopram, we performed a pattern separation of responders from non-responders using a SVM classifier which had as input the global brain connectivity (GBC), in-weights of the GEC (GEC in ), out-weights of the GEC (GEC out ), total weights of the GEC (GEC total ) and the FDT deviation across areas. The classifier reached a maximum accuracy with the FDT deviation (85.50%), performing significantly higher than the GEC measures and the GBC (Figure). Different fMRI-based biomarkers of depression have been already implemented in previous studies, and together with our results they are interesting for the growing field of individualised treatments and precision psychiatry. Our study has several limitations worth mentioning. It relies on a brain parcellation of 80 areas (i.e., DK80), which balances computational costs and spatial accuracy of the findings. There is no agreed-upon standard for fMRI parcellation, but we must acknowledge that our findings are constrained to the DK80 resolution. We also used a structural connectivity template from a separate healthy cohort given we did not have individualised connectomes of the analysed cohort. Nevertheless, studies in the past have successfully implemented templates, as they are a neutral starting point, with relevant links in the GEC optimisation process fitted to the patient's empirical data. Lastly, the relatively small sample size limits the generalisability of the findings. Some of the findings may not be representative of the broader population of individuals with MDD treated with psilocybin and escitalopram. Replicating the study with larger cohorts would enhance the statistical power and improve the robustness of the conclusions. Overall, our work shows that in the context of thermodynamics, the deviation from the Fluctuation-Dissipation Theorem is a powerful tool for uncovering the hierarchical reorganisation and nonequilibrium brain dynamics accompanying interventions for major depressive disorder. We found significant differential effects for the interventions of psilocybin and escitalopram. Psilocybin shifts the brain towards more non-equilibrium (i.e., greater deviation from the FDT) and proportion of asymmetric interactions, and less segregation, while escitalopram produces opposite effects in all measures. To conclude, the thermodynamics frameworkis paving the way for future research aimed at optimizing existing therapeutic interventions and developing more effective treatments for depression and potentially other brain disorders.

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