neurojax-anesthesia-dynamics

name	neurojax_anesthesia_dynamics
description	Detect Loss of Consciousness (LOC) using SINDy-based bifurcation analysis on EEG.

Skill: Anesthesia Dynamics & Bifurcation Analysis

Context

You are an expert in nonlinear dynamics and EEG processing. Your goal is to detect the transition from wakefulness to unconsciousness (LOC) in the PhysioNet GABAergic Anesthesia dataset using neurojax.

Strategy

We model the brain state as a dynamical system $\dot{z} = f(z; \mu)$. As the drug concentration ($\mu$) increases, the system undergoes a Hopf Bifurcation (stable limit cycle $\to$ stable fixed point). We track the eigenvalues of the Jacobian $J = \partial f / \partial z$.

Pipeline steps

1. Data Ingestion

• Use neurojax.io.load_physionet (if available) or standard mne loader for EDF files.
• Filter: Bandpass 0.1-40 Hz to align with slow-wave dynamics.
• Reference: Use average reference or Laplacian if HD-EEG.

2. Dimensionality Reduction

• Spectrogram: Compute power in standard bands ($\delta, \theta, \alpha, \beta, \gamma$).
• Embedding: Use sklearn.decomposition.PCA or neurojax.preprocessing.pca to reduce the high-dim spectrogram/channel space to a latent trajectory $z(t) \in \mathbb{R}^3$.

3. Continuous Dynamics (The Core)

• Windowing: Iterate over sliding windows (e.g., 30s window, 5s step).
• SINDy Fit: For each window $W_t$, use neurojax.dynamics.SINDyOptimizer:

  from neurojax.dynamics import SINDyOptimizer, polynomial_library
  opt = SINDyOptimizer(threshold=0.01)
  Xi = opt.fit(z, dz, polynomial_library)
  

• Stability Analysis:
  • Construct the Jacobian $J$ from coefficients Xi.
  • Compute eigenvalues $\lambda = \text{eig}(J)$.
  • Metric: Track $\max(\text{Re}(\lambda))$. A crossing from + (unstable/oscillatory) to - (stable) usually indicates LOC (suppression of alpha/beta).

4. Verification Check

• Plot: Time vs $\max(\text{Re}(\lambda))$.
• Overlay: Expert annotations of LOC boundaries.
• Success: The metric shifts significantly at the annotated LOC time.

Critical Instructions

• Do not interpolate: Use the raw irregular data if possible, but SINDy usually needs a grid. If needed, resample to uniform dt.
• Noise Sensitivity: Derivatives dz are noisy. Use diffrax or a robust differentiator (Savitzky-Golay) before passing to SINDy.