Ghaffari et al. 2007 — Longitudinally propagating traveling waves of the mammalian tectorial membrane
Ghaffari, Aranyosi and Freeman showed that the isolated mouse TM, when driven at audio frequencies, supports its own intrinsic traveling waves propagating longitudinally. This was unexpected — prior models treated TM as a stiff plate. The wave velocities matched basilar membrane traveling wave velocities near the characteristic-frequency place, suggesting TM waves enhance cochlear sensitivity through resonant coupling. Dynamic shear modulus (G′) and shear viscosity (η) were extracted from wave propagation measurements.
TL;DR. Isolated TM segments at 2–20 kHz produce longitudinally propagating waves with velocities similar to BM waves; G′ ranges from 16 kPa (apical) to 40 kPa (basal); shear viscosity 0.18–0.33 Pa·s; basal TM is approximately 2.5× stiffer than apical.
Key finding. TM is not a rigid structure — it is a viscoelastic medium with frequency-dependent stiffness. The G′ = 16–40 kPa range is orders of magnitude softer than PVDF-TrFE (3 GPa), quantifying the mechanical mismatch at the core of the h02 hypothesis concern.
Numbers that matter
| Parameter | Value | Units | Source location | Conditions |
|---|---|---|---|---|
| Shear storage modulus G′ (apical) | 16 | kPa | Abstract/Results | Isolated mouse TM, 2–20 kHz |
| Shear storage modulus G′ (basal) | 40 | kPa | Abstract/Results | Isolated mouse TM |
| Representative G′ (basal example fit) | 30 | kPa | Results | One basal segment fit |
| Shear viscosity η (apical) | 0.18 | Pa·s | Results | Apical TM segments |
| Shear viscosity η (basal) | 0.33 | Pa·s | Results | Basal TM segments |
| Wave frequency range measured | 2–20 | kHz | Methods | Ex vivo, isolated segments |
| Apical phase lag vs basal | apical > basal | — | Results | ”Apical segments accumulated more phase lag” |
Relevance to h02 mechanical mismatch. PVDF-TrFE E_mod ≈ 3 GPa vs. TM G′ ≈ 16–40 kPa. Young’s modulus is approximately 3× shear modulus for incompressible materials, so TM E ≈ 48–120 kPa. Ratio PVDF/TM ≈ 25,000–60,000×. This directly quantifies the substrate mismatch flagged in the h02 audit. The film is ~10⁴–10⁵× stiffer than the substrate across the cochlear tonotopic range.
Limitations
- Ex vivo isolated TM; in-vivo constraints (attachment to spiral limbus and hair bundles) may alter stiffness.
- Frequency range 2–20 kHz; sub-2 kHz behavior extrapolated.
- Mouse TM only; human TM is larger and may differ.
Connections
[source]tectorial-membrane — primary source for TM shear modulus G′ parameter[see-also]2026-04-25-masaki-2009-tm-col11a2-anisotropy — companion paper on TM collagen structure and anisotropy[see-also]2026-04-25-gueta-2008-tm-anisotropy-stereocilia-deflection — TM anisotropy and stereocilia deflection[applies]STRC Piezoelectric TM Bioelectronic Amplifier[supports]mechanical mismatch concern in STRC h02 Parameter Provenance Audit 2026-04-23