Recording and CNAP

Recording & CNAP

Beyond stimulation, golgi can predict what a cuff records: the compound nerve action potential (CNAP) evoked on the fiber population, using a reciprocity-based forward model. This closes the loop for studies of evoked CNAP / ECAP biomarkers.

Source: golgi/pipeline/recording.py, with FEM lead fields from golgi/compute/solve_nerve.py. Unit-tested in tests/test_recording_cable.py (no solver stack required).

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The forward model

The recorded potential at a contact is computed by reciprocity: the contribution of each fiber is its transmembrane current weighted by the contact's lead field along the fiber, integrated over the fiber and summed over the population.

1. Lead fields. The FEM solver emits a per-contact unit-current lead field Vₑᴿ(s) sampled on the fiber nodes (one V_e_rec_<id>.npz per recording contact). Enable with GOLGI_EMIT_RECORDING=1.

2. Transmembrane current. From each fiber's membrane potential Vₘ(s,t) (from the activation simulation), golgi computes the cable transmembrane current

   $$I_m(n,t) = \frac{\pi d^2}{4,\rho_a,\Delta x},\big(V_m(n{+}1) - 2V_m(n) + V_m(n{-}1)\big)$$

   with axoplasmic resistivity ρ_a ≈ 0.7 Ω·m.

3. Single-fiber contribution. Interpolate the lead field onto the fiber's nodes and sum φ(t) = Σ_n I_m(n,t) · (Vₑᴿ⁺ − Vₑᴿ⁻)(n) for a bipolar recording montage (plus/minus contacts).

4. Population CNAP. Sum over all fibers (optionally decomposed by fiber type), giving the compound response.

A recording montage (RecordingMontage) names the plus/minus contacts; any bipolar/multipolar montage is a linear combination of the cached single-contact lead fields, so montages are cheap to evaluate once the basis is solved.

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What's verified

The cable-current and summation math is covered by pure-numpy unit tests:

• zero current for a spatially uniform Vₘ,
• constant second difference for a quadratic Vₘ,
• current conservation along the fiber,
• correct lead-field subtraction for a bipolar montage,
• population sum / type decomposition, and shape validation.

Run them with pytest tests/test_recording_cable.py -q (no FEniCSx needed).

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References

• McIntyre CC, Richardson AG, Grill WM (2002). Modeling the excitability of mammalian nerve fibers: influence of afterpotentials on the recovery cycle. J Neurophysiol 87:995. — the cable model supplying the transmembrane currents.
• Lubba CH, et al. (2019). PyPNS: multiscale simulation of a peripheral nerve in Python. Neuroinformatics. — related compound-action-potential modeling.

The reciprocity (lead-field) approach is a standard volume-conductor result for recording; see the Finite-Element Solver page for how the per-contact lead fields are computed.

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See also

Finite-Element Solver · Fiber Models & Activation · Electrodes & Cuff Designer · Validation