A dynamical systems framework for precision psychiatry – npj Digital Medicine

Brains are multiscale machines. Their neural circuits create electrical fields that span time and frequency—from slow, coordinated rhythms to fast, transient bursts. To read meaning from such complexity, researchers are moving beyond simple averages and spectral power, embracing dynamical systems tools that capture how brain activity evolves across scales. This shift could help uncover more precise EEG biomarkers for psychiatric diagnosis and treatment.

Why multiscale matters

Multiscale entropy (MSE) introduced a scale-dependent view of physiological complexity. First used in cardiology, its key insight was that complexity across multiple scales carries diagnostic signal absent in the raw waveform. In aging and disease, complexity typically decreases—though the pattern of loss varies across scales. The coarse-graining used in MSE corresponds to approximations from the Haar wavelet transform, aligning the “scales” with familiar EEG frequency bands (delta, theta, alpha, beta, gamma). In short, multiscale complexity and spectral bands are two views of the same structure.

Noise, filters, and what we might be losing

EEG is easily contaminated—by muscle activity, eye blinks, electrode motion, or power line interference. Analysts often use low-pass, high-pass, band-pass, and notch filters to clean signals. But filtering changes signal dynamics. Some nonlinear metrics (e.g., Kolmogorov–Sinai entropy) are highly noise-sensitive; others (e.g., approximate entropy) are more robust. A critical, underexplored question is how filtering alters the true nonlinear properties of neural signals—especially in clinical workflows.

From “quantitative EEG” to dynamical biomarkers

Traditionally, quantitative EEG focuses on transforming time series to highlight components or compute spectral power. A broader, dynamical view treats the neuroelectric field itself as a dynamical system. If psychiatric states leave signatures in system dynamics, they should be detectable as quantitative invariants computed from EEG. This hypothesis is testable by calculating dynamical measures and evaluating their predictive value with machine learning.

Entropy—and beyond

Entropy is a family, not a single metric. Sample entropy (popular in MSE) is related to Shannon’s information entropy, but dozens of variants now exist, including Approximate, Renyi, and Fuzzy entropies. In this context, entropy is best interpreted as one facet of signal dynamics, not a full definition of “complexity.” Other valuable measures include:

• Correlation dimension
• Hurst exponent
• Lyapunov exponents
• Detrended Fluctuation Analysis (DFA)

A grand challenge is identifying a minimal yet sufficient “basis set” of measures to characterize brain dynamics, acknowledging that many metrics are not independent.

Recurrence plots: a QR code for brain dynamics

Recurrence plots (RPs) visualize how a system revisits similar states, projecting a high-dimensional phase portrait onto a two-dimensional grid. They often remain informative for short, noisy, non-stationary data—a key advantage for EEG. Embedding theorems (e.g., Takens) justify reconstructing dynamics from time series; in practice, multiple simultaneous EEG channels can improve reconstructions when data are digitized or noisy. Crucially, the required embedding dimension depends on the attractor, not the enormous number of microscopic neural degrees of freedom—reflecting how neurons synchronize into functional ensembles.

Recurrence Quantification Analysis (RQA) extracts statistics from RP structures (e.g., line distributions) to summarize system properties. A complementary approach interprets the RP as a network adjacency matrix—Recurrence Networks (RN)—to probe attractor geometry via network metrics, including ε-clustering coefficient, ε-motif density, ε-betweenness, and ε-efficiency. Together, RQA and RN capture dynamical features missed by purely algorithmic time-series methods.

Can foundation models do EEG?

Large language and vision models thrive on structured dependencies; EEG is more irregular and rapidly varying. Early signals of promise exist for seizure detection, sleep staging, and BCI tasks, but robust discovery of psychiatric dynamics via attention-based architectures remains unproven.

Reservoir computing: neuromorphic dynamics meet EEG

Reservoir computing (RC) offers a dynamical alternative to deep learning. It uses a fixed, high-dimensional dynamical system—the reservoir—to transform inputs, requiring training only in a simple readout layer. That makes RC efficient, hardware-friendly (optical, electronic, and neuromorphic implementations), and well-suited to time series. Remarkably, reservoirs can learn dynamical properties not explicitly present in training examples, likely due to conjugacy between source and reservoir dynamics. This aligns naturally with a dynamical systems view of brain function.

Taming data volume with supervised tensor factorization

Real-world EEG pipelines produce thousands of features: for example, 19 sensors × 6 bands × 15 measures yields 1,710 values per recording; high-density arrays multiply that dramatically. Many features are correlated (nearby sensors share sources; adjacent bands overlap), and we don’t yet know the minimal set needed.

A practical solution is to organize features into a tensor: participants × sensors × frequency bands × measures. Supervised tensor decomposition—such as Canonical Polyadic (CP) regression (e.g., via Tensorly) or SupCP—can extract latent factors most aligned with diagnoses or behavioral targets and relevant covariates (e.g., environment, sex assigned at birth). This generalizes matrix SVD/PCA to higher dimensions and supervised settings, distilling thousands of inputs into a small, interpretable set (often 3–20) of condition-relevant factors. These latent variables act as dynamical biomarkers grounded in the neuroelectric field.

A practical workflow

• Decompose EEG into standard frequency bands (or MSE scales).
• Compute dynamical invariants (entropy variants, Lyapunov exponents, RQA/RN), optionally via time-delay embedding or reservoir computing.
• Reduce dimensionality with supervised tensor factorization (or alternative feature selection).
• Train and validate predictive models for diagnoses or behavioral measures.

Signals from psychiatry

Emerging evidence links EEG dynamics to psychiatric phenotypes. Reported findings include: altered complexity in early autism, childhood anxiety, and ADHD; improved epilepsy detection and drug monitoring; sleep disorder characterization. Reviews suggest higher entropy in schizophrenia; reduced fractal dimension and complexity in major depression; and Lyapunov exponent variations in bipolar disorder, consistent with more chaotic mood dynamics. Mood symptoms in neurological diseases (e.g., Parkinson’s) further highlight shared circuitry. High-resolution intracranial recordings may reveal network dysfunctions to guide principled circuit retuning. The next step is systematic testing of comprehensive dynamical feature sets to refine biomarkers and identify overlaps across diagnoses.

Outlook

Nonlinear EEG analysis is maturing from concept to clinic-ready pipeline. Whether computed via classic embeddings or learned through reservoirs, dynamical invariants can be fused through supervised tensor factorization to yield compact, interpretable biomarkers. The promise is precision psychiatry built on the physics of the brain’s own dynamics—provided we rigorously validate what these measures predict, and why.