LSD-induced increase of Ising temperature and algorithmic complexity of brain dynamics

Ruffini and colleagues situate this study within a tradition of applying statistical physics to brain activity, arguing that large-scale neural dynamics can be meaningfully described in terms of phase transitions and critical phenomena. Previous work has suggested that healthy brains may operate near critical points where a balance of order and disorder affords rich, multiscale correlations and computational advantages, and that pharmacological perturbations—such as psychedelics—alter the repertoire and entropy of spontaneous brain activity. The authors note that LSD in particular has been associated in prior functional neuroimaging studies with increased signal diversity, weakened canonical functional configurations, and greater global integration and flexibility. Building on these ideas, the study aims to characterise how LSD affects whole-brain dynamics using pairwise maximum-entropy (Ising) models and measures of algorithmic complexity. Specifically, the investigators construct a group-level "archetype" Ising model from resting-state fMRI BOLD data, then personalise that archetype for each subject and condition by fitting a single temperature parameter that controls randomness and distance from the model's critical point. They also estimate signal complexity using Lempel–Ziv–Welch (LZW) compression and the Block Decomposition Method (BDM) on both empirical and model-generated (synthetic) binary time series, testing the hypothesis that complexity metrics will correlate with fitted Ising temperature and distinguish LSD from placebo.

The dataset comprised resting-state fMRI BOLD recordings from 15 participants, each contributing two scans under LSD and two under placebo; one music-containing scan was excluded so that four scans per participant (two LSD, two placebo) were analysed, yielding 60 scans total. The extracted text reports the administered dose as "75 mg of LSD via a 10ml solution" and describes scanning approximately 70 minutes after administration for a one-hour session; the text does not comment on potential ambiguities in this dosing wording. BOLD data were parcellated to 90 non‑cerebellar regions using the AAL atlas; preprocessing used FSL tools as described in the original dataset source. For Ising-model construction, each parcel's BOLD time series was binarised by thresholding at the parcel median so that each time point was mapped to +1 or −1, maximising the binary series' entropy. The authors concatenated data across subjects and conditions to estimate an archetype pairwise maximum-entropy (Ising) model, fitting coupling matrix J and local fields h via an approximate maximum-likelihood approach using the pseudo-likelihood (a tractable mean-field approximation) and gradient ascent. Personalisation was achieved by keeping J and h fixed and fitting a single inverse-temperature β (equivalently temperature T = 1/β) per subject and condition so that the model's expected Hamiltonian matched the empirical one. Synthetic data were generated from personalised models using the Metropolis algorithm to sample configurations at the fitted temperatures; model observables (magnetisation, energy, susceptibility, heat capacity) were estimated from steady-state samples. Signal complexity was quantified two ways: Lempel–Ziv–Welch (LZW) compression was applied to spatially flattened, binarised strings; an "archetype dictionary" built from concatenated data was used as an initial dictionary when compressing per-subject data and when compressing synthetic series. The LZW-derived normalised description length ρ0 = l_LZ/n was used as a complexity proxy. The Block Decomposition Method (BDM), employing precomputed Coding Theorem Method tables for small blocks, was used as a complementary algorithmic-complexity measure sensitive to both statistical and algorithmic regularities. Statistical comparisons used within-subject tests: paired Wilcoxon tests (one‑tailed where stated) to compare LSD versus placebo for temperatures and complexity metrics, and permutation tests (n = 1000) that shuffled ROI labels to assess whether temperature changes were specific to the archetype architecture (h and J). Pearson correlations were computed to relate temperatures and complexity measures, and questionnaire scores (VAS and the 11‑factor ASC) were correlated with the extracted features.

Archetype parameters and phase behaviour: The archetype coupling matrix J and fields h were estimated from the concatenated dataset. Comparing archetypes estimated separately on LSD and placebo data, the LSD archetype showed a modest reduction in mean coupling (mean change −3.4%) and a reduction in coupling variance (−6.7%), while the mean of the local field array h decreased markedly (−96.3%) with a smaller reduction in its standard deviation (−14.5%), indicating a substantially weaker external drive in the LSD archetype. Exploration of the archetype's phase space revealed that peaks of susceptibility, heat capacity and LZW variance occur at approximately the same temperature, whereas BDM variance peaks at a somewhat higher temperature; at the nominal archetype temperature T = 1, all nodes were reported to be above the model's critical temperature. Individualised temperature shifts: Personalised Ising temperatures fitted per subject and condition were consistently higher under LSD than placebo. On average the LSD temperature exceeded placebo by 6.7% ± 5.1% (mean ± SD). A two‑tailed t-test yielded p = 6.1 × 10^-5 and Cohen's d = 1.35. Given non-normality of temperature estimates, a rank-based one‑tailed Wilcoxon test gave p = 9 × 10^-5, and the permutation test that shuffled ROI labels in the archetype produced p = 1 × 10^-3, supporting the robustness of the LSD-related temperature increase. Complexity measures — empirical and model-derived: LZW complexity computed directly from binarised experimental data showed a weak but statistically significant relationship with condition (paired one‑tailed Wilcoxon p = 0.04), with LSD increasing LZW for roughly two‑thirds of subjects; however, LZW from empirical data did not correlate significantly with individual Ising temperature (r(13) = 0.13, p = 0.65). In contrast, LZW computed on synthetic data sampled from personalised Ising models correlated strongly with fitted temperature (p = 2.7 × 10^-6) and distinguished conditions (one‑tailed Wilcoxon p = 9 × 10^-5); the model-derived LZW difference correlated with delta Ising temperature (r(13) = 0.91, p = 2.7 × 10^-6). BDM produced complementary results. BDM complexity computed from empirical data displayed a moderate correlation with Ising temperature (r(13) = 0.56, p = 0.03) and a weak but significant relationship with condition (one‑tailed Wilcoxon p = 0.04). BDM values computed on synthetic data were highly correlated with temperature (r(13) = 0.97, p = 8.9 × 10^-10) and with condition (one‑tailed Wilcoxon p = 2 × 10^-4). When comparing complexity increases under LSD using synthetic data, both LZW and BDM showed statistically significant increases (one‑tailed Wilcoxon p = 3.5 × 10^-5 and p = 2.1 × 10^-4, respectively). The change in model-derived complexity metrics tracked closely the change in fitted temperature across subjects. Questionnaire correlations: Subjective reports (VAS and 11‑factor ASC) showed no strong, statistically robust relationships with Ising temperature or the complexity metrics. The authors note trend-level correlations: complex imagery with Ising temperature (r = 0.42), elementary imagery with LZW (r = 0.48), and VAS emotional arousal showed trend-level associations with all three features (positive with Ising temperature and BDM, negative with LZW). The extracted text reports these as non‑strong trends rather than conclusive associations.

Ruffini and colleagues interpret their findings as consistent with an overall LSD-induced loosening of large-scale network structure and an increase in the disorder and algorithmic complexity of BOLD dynamics. They found that building a single archetype Ising model from the pooled dataset was useful both because fMRI provides relatively limited data per participant and because it yields a common reference against which personalised temperatures can be compared. The archetype exhibits a clear critical point and, unlike translationally symmetric nearest‑neighbour Ising models, shows parcel-dependent sensitivity because its parameters J and h vary across regions; the authors suggest parcels with high susceptibility may be informative targets for stimulation studies. The principal empirical observation is a robust, within-subject increase in fitted Ising temperature under LSD, with the personalised temperatures and archetype temperature both lying above the model's critical point, placing the system in the paramagnetic (disordered) phase. Complexity analyses support this picture: algorithmic-complexity proxies (LZW and BDM) rose with temperature in synthetic data and, to a weaker degree, in empirical data—BDM from empirical data displayed a significant correlation with temperature whereas empirical LZW was only weakly associated. The authors relate these outcomes to theoretical accounts such as REBUS and the entropic‑brain hypothesis, which posit that 5‑HT2A receptor stimulation increases neuronal excitability and reduces the precision of high‑level priors, thereby expanding the repertoire and entropy of spontaneous activity; their results are presented as broadly consistent with those frameworks. Methodological caveats acknowledged by the authors include reliance on binary‑thresholded data (making results dependent on binarisation choices), the limited data length per participant affecting empirical complexity estimates, and the computational cost and scale‑dependence of BDM (which tends towards an entropy-like measure as block size grows and precomputed CTM tables are used). They also emphasise that the Ising approach implemented is a simple, one‑parameter personalisation (temperature) on top of a group archetype, and that alternative methods and metrics of criticality can yield different conclusions. Indeed, the authors note that other studies have reported effects that might be interpreted as shifting dynamics closer to criticality, and that reconciling such differences will require further work examining modelling choices, criticality definitions (statistical vs dynamical), and metric sensitivity. Finally, the investigators report only weak, trend‑level associations between their model-derived features and subjective self-reports, and they attribute this to limited sample size, heterogeneity of subjective reports and the post-hoc timing of some ratings rather than a definitive absence of relation.

The study concludes that, within the Ising-model framework applied here, LSD increases fitted system temperature and algorithmic complexity of binarised BOLD dynamics relative to placebo, consistent with a shift into a more disordered (paramagnetic) regime. Personalised Ising temperatures were robustly higher under LSD, and synthetic-data complexity measures derived from the personalised models correlated strongly with those temperature changes. The authors caution that these findings reflect a specific, simple modelling approach and that other methods and criticality metrics may yield different inferences; they call for further research to reconcile divergent results and to refine models linking pharmacology, whole‑brain dynamics, complexity metrics, and subjective experience.