Skill: Pharmacodynamics & Dose-Response Recovery

Context

You are analyzing drug effects (e.g., Anticonvulsants, Psychedelics) on neural activity. Your goal is to reverse-engineer the "Effect Function" $E(C)$ from the dynamical changes observed in the EEG.

Strategy

We assume the brain dynamics obey $\dot{x} = A x + B(u) x$, where $u$ is the Drug Concentration (proxy) or Dose. We use SINDy with control inputs to identify the structure of $B(u)$.

Pipeline steps

1. Data Setup

• Dataset: Mendeley Pharmaco-EEG (Rat) or PsiConnect.
• Input:

- $x(t)$: Neural features (e.g., Total Power, Complexity/Entropy). - $u(t)$: Drug concentration curve (often modeled as a simple decay $u(t) = D_0 e^{-kt}$ if blood samples unavailable).

2. SINDy with Control

• Model: $\dot{x} \approx \Theta(x, u) \Xi$.
• Library: Include interaction terms between state and drug: $x$, $u$, $x \cdot u$, $x \cdot \frac{u}{K+u}$ (Michaelis-Menten).
• Execution:

``python # Custom library required for Michaelis-Menten terms def drug_library(x, u): linear = jnp.concatenate([x, u], axis=1) interaction = x u saturation = x (u / (1.0 + u)) # Test Emax hypothesis return jnp.concatenate([linear, interaction, saturation], axis=1) ``

• Use neurojax.dynamics.SINDyOptimizer with this custom library.

3. Verification

• Coefficient Analysis:

- If the term $x \cdot u$ is sparse/zero but $x \cdot \frac{u}{K+u}$ is active, we have "discovered" a saturating receptor occupancy model. - If $x \cdot u$ is active, it's a linear effect (low dose range).

• Simulation: forward simulate the discovered ODE with a new dose protocol and verify prediction against a held-out subject/dose.

Critical Instructions

• Proxy Concentration: If blood concentration is unknown, explicitly state the assumed Pharmacokinetics (PK) model (e.g., 1-compartment bolus).
• Group Level: Ideally fit a "Mixed Effects" SINDy where coefficients are shared across subjects, but this is advanced. Start with subject-level fits.