Perturbing whole-brain models of brain hierarchy: An application for depression following pharmacological treatment

Understanding the scale at which the brain represents information—localised single neurons versus distributed hierarchical networks—remains a central challenge. Earlier research using fMRI, MEG and diffusion tractography has shown that functional connectivity (FC) and structural connectivity (SC) capture distributed network organisation, and graph-theoretical approaches have revealed features such as modularity and small-worldness. However, symmetric FC alone does not resolve the causal, hierarchical relationships between regions. To address this, the thermodynamics of mind framework links temporal irreversibility in neural time series to hierarchical, directional information flow; incorporating such asymmetry into generative whole-brain models produces generative effective connectivity (GEC) that aims to identify mechanistic drivers of functional hierarchy.

Socoró-Garrigosa and colleagues analysed resting-state fMRI from a double-blind Phase II randomised trial comparing psilocybin and escitalopram in unipolar major depressive disorder (ClinicalTrials.gov: NCT03429075). Inclusion required a confirmed unipolar MDD diagnosis and a Hamilton Depression Rating Scale score ≥16; exclusions included personal or immediate family history of psychosis, severe suicide attempts, pregnancy, MRI contraindications and prior escitalopram use. Of 59 recruited participants, attrition and motion-related exclusions left 22 patients in the psilocybin arm (mean age 41.9 years, SD 11.0; 8 female) and 20 in the escitalopram arm (mean age 38.7 years, SD 11.0; 6 female). Reported prior psychedelic experience was 31% in the psilocybin arm and 24% in the escitalopram arm. Participants received two dosing days three weeks apart: the psilocybin arm received 25 mg on dosing days and placebo capsules daily thereafter, whereas the escitalopram arm received 1 mg psilocybin (presumed negligible) on dosing days and escitalopram capsules (10 mg daily for first 3 weeks, then 20 mg) subsequently. The post-treatment fMRI session occurred shortly after completion of the capsule regimen. The extracted MRI acquisition description for the trial was truncated; the authors therefore used an external healthy target constructed from 100 unrelated Human Connectome Project (HCP) Young Adult subjects (first rs-fMRI session, DK80 parcellation). A standard SC template derived from prior HCP diffusion tractography was used because the trial did not include diffusion scans.

Whole-brain models were constructed per subject using 80-region DK80 parcellation nodes, with local dynamics modelled by Stuart–Landau oscillators (a normal form of a supercritical Hopf bifurcation). Intrinsic frequencies were estimated from patient-averaged narrowband BOLD peaks, and the models were linearised near a slightly negative bifurcation parameter (a = -0.02) to permit analytical solution of stationary covariances. Critically, model fitting optimised anatomical weights to match both static FC and estimates of pairwise temporal irreversibility (difference between forward and reversed time-shifted correlations), producing subject-specific generative effective connectivity (GEC) matrices that encode hierarchical causal influences. Optimization details reported include learning rates (α = 0.0004 and ζ = 0.0001) and use of a Lyapunov solver for stationary covariance, though some formula fragments in the extraction are truncated.

The study assessed in-silico perturbations by increasing the white-noise amplitude (β) at single sites and via a greedy multi-site algorithm, measuring two outcomes: susceptibility (S), defined as the dissimilarity between perturbed and unperturbed FC (Pearson correlation-based decorrelation), and perturbation effectivity for recovery (PER), defined as the similarity between perturbed FC and a healthy target, with nPER denoting PER normalized by baseline similarity (BSR). For single-site perturbations at β = 0.04, psilocybin-treated brain states showed a significant increase in average susceptibility after treatment (p<0.01, paired Wilcoxon with 5,000 permutations), whereas escitalopram-treated states showed a significant decrease (p<0.05, paired Wilcoxon with 5,000 permutations). The psilocybin versus escitalopram divergence in susceptibility was robust across intensities between β = 0.02 and 0.05. Region-wise analysis indicated that more regions increased susceptibility after psilocybin than after escitalopram (p<0.001, unpaired Wilcoxon with 5,000 permutations).

Perturbation analyses showed that tailored stimulations can meaningfully move simulated patient FC toward a healthy target: PER values for optimal perturbations were significantly higher than baseline similarity (p<0.001, paired Wilcoxon tests with 5,000 permutations), and nPER increased after pharmacological intervention for both drugs (p<0.05), indicating an enhanced capacity to benefit from optimal perturbations post-treatment. Multi-site (20-level greedy) perturbations yielded significantly larger nPER than single-site approaches (p<0.001). The most frequent optimal single-site targets across patients were the right amygdala (present in 50% of optimal single-site perturbations for both treatments) and the nucleus accumbens (the remaining 50%, split between left and right); multi-site solutions again prominently recruited bilateral nucleus accumbens, right amygdala and right medial orbitofrontal cortex. The authors interpret the increased susceptibility after psilocybin as consistent with a plasticity window and the REBUS account (flattening of hierarchical constraints), whereas escitalopram tended to constrain average malleability but still permitted specific perturbations to drive healthy transitions. Limitations noted include the modest sample size (n=42), absence of subject-specific diffusion data requiring an SC template, truncated reporting of some MRI acquisition details in the extraction, and the short post-treatment imaging window. Suggested future directions include larger samples, alternative perturbation protocols (e.g., perturbing the bifurcation parameter or using coloured noise), use of dynamic FC or hierarchy measures (metastability, temporal irreversibility) rather than static averages, and longer follow-up to capture delayed plasticity effects.