STRC Piezo Frequency Response Bundle Mechanics
The strain model dominates the piezo-prestin coupling by orders of magnitude. Beam-model stereocilia-shaft deposition fails at clinical SPLs (V_wall = 0.69 mV @ 1 kHz 60 dB). Wall-curvature deposition on the OHC apical membrane (R = 100 nm) passes the 10 mV prestin threshold across the full clinical audiogram at ≥ 50 dB (≥ 40 dB at 4-8 kHz). The hypothesis is physics-viable under one specific delivery geometry only.
Strain model matters — by orders of magnitude
PVDF-TrFE terpolymer, 100 nm thick, at 60 dB SPL:
| Strain model | Geometry assumed | V_wall @ 1 kHz | Audiogram pass |
|---|---|---|---|
| Beam | Euler-Bernoulli cantilever — film conforms to stereocilium shaft | 0.69 mV | 0 / 6 freqs ✗ |
| Hinge | Rigid stereocilium rotates, strain concentrated at rootlet | 7.63 mV | ~half freqs |
| Wall-curvature | Conformal on OHC apical membrane, R = 100 nm | 57.2 mV | 6 / 6 freqs ✓ |
Stereocilia are too stiff (EI of actin bundle) to generate enough bending strain at clinical SPLs — shaft strain is too low for PVDF-TrFE to produce 10 mV across the cell membrane. The physics works only if the film is on the OHC apical membrane itself, not on the stereocilia shafts.
System transfer function: H(ω) = jωR_mem·C_film / (1 + jωR_mem·(C_film + C_mem))
- -3 dB corner: 12.7 kHz — system reaches max transfer efficiency η∞ = C_film/(C_mem+C_film) at high freq
- Below corner: membrane resistance R_mem shunts signal (high-pass behaviour)
- Clinical speech band 200 Hz – 8 kHz: attenuated but still useful for wall-curvature / hinge geometries
- Ultra-high-frequency loss (>8 kHz): boosted where system transfer approaches max
Audiogram viability (wall-curvature, PVDF-TrFE terpolymer 100 nm)
| Freq (Hz) | 40 dB | 50 dB | 60 dB | 70 dB | 80 dB |
|---|---|---|---|---|---|
| 250 | 2.2 mV | 6.8 | 21.6 ✓ | 68 ✓ | 216 ✓ |
| 500 | 3.7 | 11.6 ✓ | 36.6 ✓ | 116 ✓ | 366 ✓ |
| 1000 | 6.0 | 19.0 ✓ | 60.1 ✓ | 190 ✓ | 601 ✓ |
| 2000 | 8.9 | 28.3 ✓ | 89.4 ✓ | 283 ✓ | 894 ✓ |
| 4000 | 11.5 ✓ | 36.4 ✓ | 115 ✓ | 364 ✓ | 1151 ✓ |
| 8000 | 10.2 ✓ | 32.3 ✓ | 102 ✓ | 323 ✓ | 1021 ✓ |
Wall-curvature geometry passes the 10 mV prestin threshold across the full clinical audiogram at ≥ 50 dB (≥ 40 dB at 4-8 kHz). Matches Misha’s loss spectrum.
Material comparison at 1 kHz 60 dB (beam model — hardest test)
| Material | d (pC/N) | ε_r | E_film (GPa) | V_wall (mV) | Pass? |
|---|---|---|---|---|---|
| PVDF-TrFE (baseline) | 25 | 10 | 3.0 | 1.13 | ✗ |
| PVDF-TrFE (thin) | 25 | 10 | 3.0 | 1.13 | ✗ |
| PVDF-TrFE terpolymer | 40 | 40 | 1.2 | 0.72 | ✗ |
| PLLA | 10 | 4 | 3.5 | 0.53 | ✗ |
| ZnO | 5 | 8 | 140 | 10.54 | ✓ |
Only ZnO passes the beam model — high Young’s modulus (140 GPa vs 3 GPa for PVDF) multiplies tiny bundle-shaft strain into enough stress for voltage. Trade-off: ZnO biocompatibility is concerning for chronic cochlear exposure (ionic dissolution at endolymphatic K⁺ concentrations).
Delivery engineering — what must be true
- Film deposits conformally on OHC apical membrane, NOT on stereocilia shafts. Apical membrane is partially covered by cuticular plate and surrounded by stereocilia — non-trivial target.
- Practical approaches:
- Nanoparticle carrier + sonoporation at the stria (cf. Liu 2026 mechanoluminescent sono-optogenetics)
- In-situ polymerisation from delivered monomers across the OHC apical domain
- Retrograde delivery from endolymph through apical ion channels (if small-enough monomer)
- Film thickness 50-200 nm — optimum ~100 nm
- Coverage fraction > 60% on OHC apical membrane for V_wall ≥ 10 mV at speech band
Verdict
Hypothesis VIABLE under one specific delivery geometry only: film conformally on the OHC apical membrane with effective curvature R ≤ 100 nm. Under beam-model stereocilia-shaft deposition (the “just coat the bundle” naive approach), it FAILS. The alien’s “build a better piezo coupler” hypothesis survives physics; what it stakes its life on is delivery to the right cellular surface.
Phase 3 next steps
- 2D axisymmetric FEM (FEniCS) of the OHC apical domain with patch-film deposition — validate H(ω) approximation
- Test ZnO+PVDF hybrid: high-modulus core with PVDF shell for biocompatibility
- Textured PVDF surfaces: micro-pillars amplify strain at biological deflections
- Piezo-composite hydrogel — cross-link with STRC Synthetic Peptide Hydrogel HTC
Files / Models
~/STRC/models/piezo_phase2_frequency_bundle.py— script with three strain models + H(ω)~/STRC/models/piezo_phase2_results.json— full frequency × SPL × material table~/STRC/models/piezo_phase2_frequency_bundle.png— 6-panel figure
Connections
[part-of]STRC Piezoelectric TM Bioelectronic Amplifier — parent hypothesis[see-also]STRC Piezo Voltage Budget PVDF-TrFE — Phase 1 per-unit-area voltage budget this Phase 2 extends[see-also]Prestin and OHC Electromotility — 10 mV activation threshold is the design constraint[see-also]STRC Synthetic Peptide Hydrogel HTC — piezo-composite hydrogel variant[applies]Misha — therapy target; audiogram matches his loss spectrum