2026-09-20
SINDy fits 24-D equations to mouse absence Ecog: held-out error 0.19 beats inter-mouse 0.24; a 6-fold coupling cut abolishes seizures.
Absence seizures cut consciousness for seconds without convulsions. The EEG signature is a bilaterally symmetric spike-and-wave discharge (SWD). In mice the fundamental sits near 7.5 Hz, one cycle every 133 ms.
The textbook story is a somatosensory cortical focus that rapidly recruits thalamocortical loops. Recent multielectrode and fMRI work finds little somatosensory hyperexcitability around onset. If there is no focus, what coordinates the multi-region synchrony?
Hull, Denomme, Ganguli and Huguenard at Stanford close that gap with interpretable machine learning: dynamical equations fit directly to seizure electrocorticograms, then tested with Neuropixels and optogenetics.
The animal model is Scn8a haploinsufficiency (Nav1.6), a standard mouse absence line. Recordings come in three layers: 16-site Ecog over motor, somatosensory and visual cortex; three simultaneous Neuropixels probes; multisite optogenetics in posterior thalamus (PO), premotor layer 5 and somatosensory layer 5.
The fit is restricted to the four earliest-onset exemplars: left/right motor (premotor Ecog) and left/right somatosensory (face Ecog). Each signal is split into three harmonic bands near 7.5, 15 and 22.5 Hz. Hilbert real and imaginary parts give a 24-dimensional state.
Sparse Identification of Nonlinear Dynamics (SINDy) regresses the state derivative against a polynomial library of up to 1,134 functions and 27,216 coefficients. Model selection does not follow one-step prediction error. It uses 60 state-space metrics: 12 amplitude trajectories, 24 within-region phase and coherence terms, 24 between-region terms. Elastic net (λ=0.04, α=0.9) is trained on 25 seizures per mouse from 5 mice, from 400 ms before onset to 800 ms after. Held-out tests start from 25 unseen pre-seizure states and integrate for 3 s.
The surviving terms collapse into amplitude-phase form. Isolated oscillators rotate at an intrinsic frequency and decay to zero amplitude through a cubic damper. Large oscillations require within-region cross-frequency coupling and linear between-region, within-band coupling. The latter reduces to a Kuramoto-like interaction with amplitude: a source drives the target's amplitude up fastest at a preferred phase lag, and down at the opposite lag.
Different seizures from the same region of the same mouse barely correlate in time (premotor left 0.09, face left 0.05). Relations between regions stay tight: 0.89 within motor, 0.85 within somatosensory, 0.58 between the two systems. Seizures live in a stereotyped phase-amplitude geometry, not on a repeatable voltage-versus-time curve.
SWD spikes lock more tightly to the trough of the 15 Hz band than to the 7.5 Hz fundamental; circular phase SD is 34% to 43% larger on band 1. Motor left spikes lag somatosensory left by 8.2 ms on average, matching a band-2 phase lag near −π/4.
Train and held-out total error are both 0.19, below the 0.24 error obtained by swapping one mouse's future for another's. Random initial conditions still fall into the same region of state space within about 2 s (error 0.23). The first six principal components explain 90.1% of experimental variance and 91.3% of the model's. A 1,200 s simulation never settles to a simple limit cycle. Largest Lyapunov exponent 0.25/s, sum of exponents −26.43/s, Kaplan–Yorke dimension 5.48: a low-dimensional chaotic attractor.
| Setting | Number |
| Train / held-out error | 0.19 / 0.19 |
| Inter-mouse swap as "prediction" | 0.24 |
| Random initial conditions | 0.23 |
| Attractor dimension | 5.48 |
| Between-region coupling ×1/6 | seizures gone |
Zeroing term classes one at a time, only between-region within-band coupling abolishes seizures. A six-fold downweight of that coupling does the same. Spreading intrinsic frequencies also kills synchrony, but the frequency scatter seen outside seizures is more than four-fold smaller than the detuning the model needs. The non-seizure to seizure switch is closer to a gain in effective coupling than to a sudden homogenization of intrinsic frequencies.
At the single-neuron level, Som:L5, PreMot:L5 and PO lock to 7.5 Hz first. Where the model predicts amplitude growth, layer 5 prefers bursts; where it predicts decay, isolated spikes dominate. Burst rate rises 4.4-fold in Som:L5 (0.22 to 0.97 /s) and 6.2-fold in PreMot:L5 (0.12 to 0.74 /s), and the two burst rates anti-correlate in time. PO bursts on both trajectories and leads cortex by about 15 to 20 ms.
Two optogenetic tests close the loop. Stimulating PO 15 ms before PreMot:L5 drives Som:L5 and a transient oscillation near the endogenous fundamental; PO alone, PreMot alone, or delays of 0 ms or 60 ms do not. Dual stimulation of PreMot:L5 and Som:L5 at lags near −17 to 0 ms (the predicted growth window) produces self-sustaining seizures; half-period lags (±67 ms) do not. The cross-region contribution to spike amplitude oscillates at about 12 to 13 Hz with a correlation of −0.77 between the two cortices.
For people who fit dynamical systems, this is SINDy on seconds-long, multi-region neural data, with geometry metrics in place of one-step MSE. Cross-validated one-step error barely ranks libraries; the 60 metrics do. The retained terms rewrite as amplitude-aware Kuramoto coupling, which a raw polynomial dump would not.
For epilepsy, the claim sits against a focal origin. Seizures grow when many between-region couplings push amplitude at preferred phase lags, then amplitude-phase feedback walks the system onto a low-dimensional chaotic attractor. No single region, cell type or fixed firing pattern is sufficient. Ethosuximide, the first-line anti-absence drug, blocks T-type calcium channels that support bursting. Under this account it attacks the drive into the attractor, not a cortical focus.
If the practical question is whether the model can be trained off the shelf, the main text does not ship a public repo. The reusable pieces are the three-band Hilbert embedding, the 60 geometric metrics, and iterative library expansion plus pruning.
The authors list several. The model covers seizure generation, not termination. Coefficients are a snapshot of slower parameters (arousal, attention, sensory drive, neuromodulation). LFP mixes spikes, synapses and subthreshold voltage, so biological labels on individual bands should stay tentative. Training hugs onset; a 3 s match does not imply a longer or a stopping model.
All data are Scn8a mice. Human absence is an extrapolation. Optogenetic n is small: 4 mice and 5 recordings for PO, 4 mice for dual cortical stimulation. The 0.19 versus 0.24 edge over inter-mouse variability is real, but there is no bake-off against neural ODEs or textbook sequentially thresholded least squares SINDy. Interpretable ML wins here because the equations can be read and then poked with light, not because it beat a leaderboard of black boxes.