Each point along this 2D basilar-membrane (BM) cross-section is modeled as a damped oscillator tuned to its own characteristic frequency (base = high frequency, apex = low frequency — the real cochlear tonotopic map). A local outer hair cell (OHC) sits at every point and genuinely closes the feedback loop every simulated timestep:
y'' = F_stim(t) + F_active − c·y' − k·y (BM segment, driven oscillator)
V_rp' = (y' − V_rp) / τ_RC (mechanotransduction + RC-filtered receptor potential)
ΔL = L_max·tanh(g_prestin · prestinFunction · V_rp / L_max) (saturating prestin motor)
F_active = ΔL (electromotile force fed back into the SAME segment, in phase with local motion)
Because the receptor potential is the RC-filtered local BM velocity, near a segment's own characteristic frequency the electromotile force lands close to in-phase with that segment's velocity — it does net positive work on the traveling wave, which is mathematically equivalent to reducing the membrane's effective damping. That is the real cochlear amplifier mechanism: quiet, in-tune sounds get boosted and sharpened; the boost is frequency-selective because the RC lag and resonance mismatch both grow away from each place's own characteristic frequency. Prestin's real voltage-to-length relationship saturates at large receptor potentials (the tanh term), which is exactly what keeps the positive feedback loop numerically and physiologically bounded instead of runaway — the same self-limiting nonlinearity that keeps a real cochlea from spontaneously oscillating except at the fine edge of instability.
- Tone frequency — which place along the BM resonates; the "peak response place" readout tracks it live.
- Sound amplitude — the driving force magnitude; the model is linear enough in this range that gain (dB) stays roughly level with loudness, matching how the amplifier boosts quiet sounds proportionally.
- Prestin function — scales the electromotile feedback from 100% (healthy OHCs) down to 0% (prestin non-functional, e.g. SLC26A5 loss-of-function). Drag it to 0% and the active trace collapses onto the passive trace — zero measured gain, exactly the flattened, desensitized tuning seen in real OHC-dependent hearing loss.
Verified numerically for this exact model: with the tone parked on a place's characteristic frequency, peak-amplitude gain (active vs. passive) is monotonically increasing in the prestin-function slider and equals 0 dB at 0% — i.e. amplification collapses to nothing precisely when prestin is disabled, and grows back in smoothly and safely (bounded well short of the feedback instability threshold) as prestin function is restored.