Harmonic decomposition of spacetime (HADES) framework characterises the spacetime hierarchy of the DMT brain state

Vohryzek and colleagues frame the brain as a complex system whose activity is organised continuously across space and time, and argue that existing approaches emphasise either spatial gradients or temporal dynamics but do not jointly capture a multiscale spacetime hierarchy. Earlier work on cortical gradients, resting-state networks and dynamic functional connectivity has shown gradient-like organisation from unimodal to transmodal cortex and that brain activity fluctuates through time in identifiable patterns, yet the mechanisms that produce the expression and temporal evolution of these spatial patterns remain unclear. To address this gap the investigators introduce the Harmonic Decomposition of Spacetime (HADES) framework. HADES decomposes whole-brain fMRI activity into spatially defined functional harmonics derived from a dense functional connectome and then characterises how those harmonics are expressed over time via temporal weights and dynamic measures. As a proof-of-principle application, the study applies HADES to fMRI data collected during a serotonergic psychedelic challenge with N,N-dimethyltryptamine (DMT) in healthy participants, testing the hypothesis that the DMT state flattens the brain’s functional hierarchy and increases global integration in line with REBUS/anarchic brain predictions.

HADES is built on functional harmonics defined as eigenvectors of the graph Laplacian computed from a group dense functional connectome. The dense connectome was derived from the Human Connectome Project (HCP) S1200 release: an 812-subject subset reconstructed with an improved pipeline ('recon2') was used to produce a low-noise dense connectome after minimal preprocessing, ICA+FIX denoising, inter-subject registration and group-PCA on temporally demeaned and variance-normalised timeseries. The dense connectome was binarised into a sparse, symmetric adjacency matrix by connecting each vertex (n = 59 412 surface vertices) to its 300 most correlated vertices; the eigen-decomposition of the resulting graph Laplacian yielded the functional harmonics. The investigators focussed on the first 11 non-global harmonics plus the global (zeroth) harmonic, giving 12 harmonics in total. Functional harmonics were validated functionally by comparison to canonical resting-state networks (Yeo 7/17) and then projected onto fMRI timeseries in surface space to obtain time-varying weights (τk(t)) for each harmonic; these weights quantify the contribution of each harmonic at each fMRI time point. Non-dynamic measures were defined as the mean absolute contribution (time-average of |τk(t)|) and a condition-normalised absolute contribution (each harmonic's magnitude normalised by the sum of all harmonics for that participant and condition). Dynamic measures adopted a winner-takes-all rule at each timepoint, assigning the dominant harmonic (largest contribution) and then computing Fractional Occupancy (FO, the proportion of time a harmonic is dominant), Life Time (LT, the mean consecutive duration a harmonic remains dominant) and a first-order Markov Transition Probability Matrix (TPM) describing transitions between dominant harmonics. A latent-space embedding used the harmonic basis to represent temporal trajectories in N-dimensional space (N = number of FHs); latent dimension spread was defined as the average across harmonics of the standard deviation of τk(t) over time, quantifying trajectory expansion or contraction. DMT dataset and experimental design: the pharmacological dataset was a single-blind, placebo-controlled, counterbalanced design. Twenty-five participants were recruited; 20 completed the whole study (7 female, mean age 33.5 years, SD = 7.9). The extracted text reports that a further three subjects were excluded due to excessive motion during the 8-minute DMT recording (more than 15% volumes scrubbed with framewise displacement of 0.4 mm). The extracted text does not clearly report the final analysed sample size after exclusions. Each subject underwent two scanning days, two weeks apart, each with two scanning sessions. On each session a 28-minute resting-state fMRI run was acquired with an intravenous injection (DMT or saline placebo) at the 8th minute; participants lay with eyes closed and wore an eye-mask. Simultaneous EEG was recorded. Imaging was performed on a 3T Siemens Magnetom Verio; parameters for the T2*-weighted EPI were TR/TE = 2000 ms/30 ms, voxel size 3x3x3 mm3, acquisition time 28.06 minutes. Structural T1 scans were also acquired. fMRI preprocessing followed a previously developed pipeline (used in an LSD study), including despiking, slice-timing correction, motion correction and scrubbing, brain extraction, registration to structural and to 2 mm MNI space, spatial smoothing (6 mm FWHM), bandpass filtering 0.01–0.08 Hz, linear and quadratic detrending and regression of nine nuisance regressors (three translations, three rotations, three anatomical signals). Timeseries were finally projected to the HCP surface vertex space for harmonic projection. Statistical analysis: comparisons across conditions used paired t-tests with Bonferroni correction where stated (e.g. corrected p < 0.05 notation). The investigators report both Bonferroni-corrected and uncorrected p-values for various contrasts; specific effect sizes and confidence intervals are not clearly provided in the extracted text.

The investigators first derived functional harmonics from the HCP dense connectome and verified their functional relevance by comparison with Yeo resting-state networks. Empirical fMRI timeseries could be reconstructed from a subset of harmonics, supporting that the harmonics capture meaningful spatial patterns. Absolute contributions: When they computed mean absolute contributions of each harmonic across conditions, a widespread decrease in absolute contribution was observed in the DMT-induced state relative to pre-injection and placebo conditions across most of the first 11 functional harmonics; the global (zeroth) harmonic was not decreased. In contrast, analysis of condition-normalised absolute contributions revealed a relative increase in the global harmonic together with a decrease specifically in the second functional harmonic (ψ2) after DMT injection versus pre-injection and placebo. Statistical significance is reported with paired t-tests, with markers indicating both Bonferroni-corrected and uncorrected p < 0.05 in the figures. Dynamic measures: Using the winner-takes-all assignment to identify the dominant harmonic at each timepoint, Fractional Occupancy and Life Time metrics were computed for the 11 non-global FHs. The strongest and most consistent statistical effects for both FO and LT were observed for ψ2, which showed reductions in occupancy and lifetime in the DMT state; significance is reported both uncorrected and corrected for multiple harmonics. The authors also computed a first-order Markov Transition Probability Matrix describing transitions between dominant harmonics and report statistics for two DMT conditions, although specific transition probabilities or numerical TPM results are not detailed in the extracted text. Latent space and temporal trajectory: Embedding the temporal trajectory in the 12-dimensional functional-harmonic space, the investigators quantified latent dimension spread (average standard deviation of τk(t) across harmonics) as a measure of trajectory expansion/contraction. The DMT-induced state showed a significant contraction of the temporal trajectory spread compared with DMT_pre and PCB_post (reported as Bonferroni-corrected p < 0.05). This contraction was described as a global reduction in the contributions of functional harmonics across the board in the DMT post-injection condition. Additional notes: The authors note that ψ2 resembles the previously described principal gradient (a unimodal-to-transmodal axis) and that its suppression under DMT mirrors prior reports of collapse or flattening of functional hierarchy and increased global integration in psychedelic states. Exact numerical effect sizes, confidence intervals and the final sample size used for statistical tests are not clearly reported in the extracted text.

Vohryzek and colleagues present HADES as a novel, multiscale framework that links spatial functional harmonics—derived from a group dense functional connectome—to their temporal expression in fMRI recordings, arguing that this offers a sensitive and interpretable characterisation of spatio-temporal brain dynamics. Applied to the DMT-induced state, HADES revealed a broad decrease in absolute harmonic contributions alongside a relative increase in the global harmonic and a specific decrease in the second functional harmonic (ψ2), which the authors interpret as a flattening of the unimodal-to-transmodal functional hierarchy. Dynamic reductions in ψ2’s fractional occupancy and life time, together with a contracted latent temporal trajectory, further support a collapse of hierarchical organisation and a shift towards greater global integration in the psychedelic state. The discussion situates these findings within prior work on cortical gradients, connectome harmonics and psychedelic neuroimaging. The authors note that their results are consistent with the REBUS/anarchic brain model and previous reports of increased global functional connectivity and desegregation of functional networks under psychedelics. They also argue that functional harmonics provide a multiscale, frequency-ordered representation that complements other gradient and network-based descriptions and that embedding dynamics in a latent harmonic space helps capture temporally evolving multivariate structure. The investigators acknowledge several limitations. They concede that the winner-takes-all scheme is reductionist because it assigns only a single dominant harmonic per timepoint and may ignore concurrent multi-harmonic contributions; they recommend future implementations that use weighted contributions at each timepoint. They also point out conceptual limits: structural connectivity alone does not fully explain spontaneous activity, cortical cytoarchitectonic heterogeneity and neuromodulatory influences matter, and fMRI’s temporal resolution constrains direct links between spatial and temporal frequencies — hence the authors suggest follow-up work using modalities such as EEG or MEG. Finally, practical limitations in the presented analysis include reliance on a harmonic basis derived from group-level HCP data and some ambiguity in the extracted text about the final DMT sample size after motion exclusions; numerical effect sizes and full TPM details are not clearly reported in the provided extraction. The authors propose that HADES can be applied broadly to neuroimaging data to study spacetime hierarchies and their perturbation in different brain states, while noting that further methodological development (e.g. weighted temporal contributions and multimodal validation) is needed to capture the full multidimensionality of spatio-temporal brain dynamics.

The study introduces Harmonic Decomposition of Spacetime (HADES) as a method to describe brain spatio-temporal dynamics via functional harmonics derived from the brain’s communication structure and their time-varying contributions. The investigators validated the functional relevance of these harmonics against resting-state networks and demonstrated that empirical timeseries can be reconstructed from a subset of harmonics. Applying HADES to the DMT-induced state, they report suppression of a principal functional hierarchy (notably in the second functional harmonic) alongside a relative increase in a global harmonic and reduced fractional occupancy and lifetimes of that hierarchical harmonic. These results are presented as corroborating the REBUS/anarchic brain model by showing dynamic perturbation of functional hierarchies and enhanced whole-brain integration under DMT.