Broadband Guided-Wave OCE
- Broadband guided-wave OCE is an optical elastography technique that actively excites elastic waves and analyzes frequency-dependent dispersion to infer tissue mechanical parameters.
- It employs phase-sensitive OCT with broadband sweeps and varied excitation methods to resolve layer-specific properties in tissues like the cornea, skin, lens, and arteries.
- Inverse reconstruction using full dispersion curves enables quantification of prestress, anisotropy, viscosity, and layered stiffness in soft tissues.
Broadband guided-wave optical coherence elastography (OCE) is a dynamic, phase-sensitive extension of optical coherence tomography (OCT) in which elastic waves are actively excited and optically tracked over a wide frequency band so that mechanical parameters are inferred from wave dispersion rather than from static deformation alone. Across recent implementations, the interrogated waves include shear-like antisymmetric -mode Lamb waves above in the cornea, simultaneous and modes from $2$ to , leaky Rayleigh surface waves from $0.1$ to in skin and from to in ultra-wideband systems, and guided waves from 0 to 1 in the lens and arterial wall (Li et al., 2023, Li et al., 2023, Feng et al., 2022, Feng et al., 2022, Feng et al., 2024, Jiang et al., 27 Jul 2025). In bounded and layered tissues, the central observable is the frequency-dependent phase velocity, typically written as 2, and its dependence on thickness, prestress, anisotropy, viscosity, and layer architecture.
1. Physical basis in bounded and layered media
Broadband guided-wave OCE is fundamentally a mechanics-of-waveguides problem. In cornea-like geometries, the tissue is modeled as a plate bounded by air on one side and fluid on the other, so the measured motion is governed by Lamb-wave dispersion rather than by bulk shear-wave propagation. Li et al. modeled the cornea as a prestressed, transversely isotropic elastic plate of thickness 3, with small-amplitude guided waves satisfying the acoustoelastic wave equation
4
and, under the plane-wave ansatz 5, the Lamb-mode dispersion relation follows from
6
whose real-root branches yield the 7 and 8 modes (Li et al., 2023).
For skin-oriented Rayleigh-wave OCE, the guiding principle is different but closely related: surface-confined elastic waves sample material to a depth of roughly one half of their wavelength, so frequency acts as a depth-selection parameter. In the 9–0 implementation for skin, high frequencies 1–2 probe the thin epidermis, whereas low frequencies 3–4 probe dermis and hypodermis (Feng et al., 2022). In the lens, the relevant geometry is a pre-stressed bilayer consisting of a capsule of thickness 5, modulus 6, and in-plane stress 7 over a cortical substrate with modulus 8 and stress 9, with dispersion determined by a 0 secular system 1 (Feng et al., 2024).
A recurring consequence of this bounded-medium setting is that wave speed is not a direct single-parameter proxy for stiffness. In prestressed corneal plates, the low-frequency 2 phase velocity approximately satisfies
3
so tension effectively stiffens the shear response (Li et al., 2023). In arterial walls, broadband guided-wave OCE was explicitly formulated within viscoelasto-acoustic theory, where the complex dynamic modulus
4
determines both dispersion and attenuation, allowing storage and loss behavior to be estimated under prestress (Jiang et al., 27 Jul 2025). A plausible implication is that broadband guided-wave OCE should be viewed less as a single “wave-speed measurement” than as a family of inverse problems whose conditioning depends on geometry, constitutive assumptions, and frequency coverage.
2. Instrumentation, excitation, and acquisition
Most reported broadband guided-wave OCE systems use swept-source OCT near 5 with phase-sensitive readout. In the simultaneous 6/7 corneal implementation, the OCT engine used a swept-source laser at central wavelength 8 with 9 sweep bandwidth and $2$0 A-line rate, giving axial resolution $2$1 in tissue; lateral scanning covered $2$2 transverse positions over $2$3, with beam spot $2$4, and illumination power on cornea was $2$5 (Li et al., 2023). In the lens system, the swept-source OCT was centered at $2$6, operated at $2$7, and used balanced detection with phase noise $2$8 to resolve nanometer-scale displacements (Feng et al., 2024).
Excitation strategies vary with target geometry. Corneal studies used contact piezoelectric transducers (PZT), including a $2$9 radius sapphire tip with gentle preload 0 for high-frequency 1-wave work, and a flat probe tip of contact length 2 at tilt angle 3 for simultaneous 4/5 excitation (Li et al., 2023, Li et al., 2023). Lens measurements used a home-built contact probe capped by a 6D-printed, 7-diameter plastic tip with contact force 8, while the porcine aorta system used a custom PZT actuator with a 9 contact length to drive harmonic surface displacements from $0.1$0 to $0.1$1 (Feng et al., 2024, Jiang et al., 27 Jul 2025).
Broadband excitation has been realized in more than one sense. One approach uses discrete pure-tone stepping across a wide band, as in cornea ($0.1$2–$0.1$3), lens ($0.1$4–$0.1$5), and artery ($0.1$6–$0.1$7) (Li et al., 2023, Feng et al., 2024, Jiang et al., 27 Jul 2025). Another uses physically broadband transient pushes. In bounded-media resolution studies, a line-focused “acoustic micro-tapping” transducer delivered a transient radiation-force push with $0.1$8, generating an ultra-broad spectrum $0.1$9–0, whereas quasi-harmonic pushes were centered around 1–2 (2206.13402). At still higher frequencies, ultra-wideband OCE used anti-aliasing demodulation and time-jitter correction to preserve sensitivity from 3 to 4, with a 5 swept-source interferometer, 6 A-line rate, 7 beam waist, and sub-nanometer displacement sensitivity (Feng et al., 2022).
Acquisition is commonly organized as repeated M-scans over a lateral raster. Representative protocols include 8 A-lines over time at each of 9 lateral positions in cornea and lens, 0 A-lines per position for corneal spatial mapping, and 1 M-scans at 2 lateral positions in acoustic micro-tapping OCE (Li et al., 2023, Feng et al., 2024, Li et al., 2023, 2206.13402). These designs are optimized to estimate phase ramps, wavenumber spectra, and local dispersion with phase-sensitive OCT.
3. Constitutive modeling and inverse reconstruction
The inverse problem in broadband guided-wave OCE is the recovery of material parameters from measured dispersion curves. In the in vivo corneal anisotropy study and in the simultaneous 3/4 corneal study, the constitutive model was Holzapfel–Gasser–Ogden (HGO). One reported strain-energy density was
5
where 6 is the intrinsic zero-stress shear modulus, 7, 8, and 9 are fiber-stiffness and nonlinearity parameters. Under equi-biaxial stretch 0, acoustoelastic parameters were written as
1
linking prestress and constitutive behavior to guided-wave dispersion (Li et al., 2023). In the simultaneous 2/3 formulation, the corneal biaxial tension was related to intraocular pressure by
4
and 5 and 6 were estimated by nonlinear least-squares fitting of measured 7 and 8 (Li et al., 2023).
Broadband inversion in bounded isotropic layers has often been formulated in the 9–00 domain. In the spatial-resolution study, the windowed spatio-temporal field 01 was Fourier transformed to 02, and a goodness-of-fit functional accumulated spectral energy along the theoretical 03 and 04 ridges,
05
with the best-fit modulus 06 maximizing 07 (2206.13402). Li et al. also described pointwise corneal inversion by sweeping 08 from 09 to 10, extracting 11 and 12, and minimizing
13
to estimate 14 (Li et al., 2023).
Layered tissues require more specialized parameterizations. In skin, broadband Rayleigh-wave OCE used a dual-bilayer inverse model: a dermis–hypodermis bilayer for 15–16 and an epidermis–dermis bilayer for 17–18, with single-parameter fits for each band and iterative refinement through an equivalent dermal thickness 19 (Feng et al., 2022). In the lens, inversion proceeded by first extracting 20 from the low-frequency plateau using
21
then fitting the full stress-free dispersion to estimate 22, and finally refitting under preload to estimate 23 and 24; capsule tension was reported as 25 and often directly as 26 because 27 was known (Feng et al., 2024). In arteries, inverse modeling compared single-layer elastic, single-layer viscoelastic, and two-layer viscoelastic models over 28–29, with a genetic algorithm minimizing 30 to recover layer-specific shear moduli, tensile moduli, viscosity parameters, and fractional order (Jiang et al., 27 Jul 2025).
At the opposite end of the spectrum, ultra-wideband Rayleigh-wave OCE also admitted continuous depth-profile inversion. For a continuous 31, the local modulus at depth 32 was estimated by
33
with 34 fitting guided-wave penetration in soft tissues (Feng et al., 2022). This suggests that “broadband guided-wave OCE” encompasses both discrete layered inversions and continuum depth-profile recovery, depending on geometry and bandwidth.
4. Resolution, bandwidth, and failure modes
A central result in bounded-media OCE is that elastographic resolution is not generally OCT-limited. Numerical simulations and acoustic micro-tapping experiments showed that, for guided-wave propagation in bounded media such as cornea, the lateral resolution of the reconstructed modulus map is mainly defined by the thickness of the bounded tissue layer rather than by OCT resolution (2206.13402). For broadband excitation with a 35 push, the reported transition width obeyed
36
independent of 37. For 38, 39, and 40, the optimum window sizes were 41, 42, and 43, respectively, and 44, 45, and 46; experiments in a two-part PVA phantom with 47 confirmed 48 and 49 (2206.13402).
This bounded-media limitation coexists with high axial OCT precision. In the same study, axial resolution remained governed by the OCT coherence gate 50 and was not limiting for shear-wave inversion (2206.13402). Corneal mapping nevertheless achieved sub-millimetric mechanical localization: the reported spatial resolution of the final shear-modulus map was 51, with window size 52, for example 53 at 54 (Li et al., 2023). Ultra-wideband OCE reported axial resolution 55, lateral resolution 56, and effective elastographic resolution 57 in each wave regime, such as 58–59 at MHz frequencies (Feng et al., 2022).
Broadband excitation is also a stability strategy. In bounded layers, broadband inversion over a continuum of frequencies was reported to suppress interference from other modes and minimize interface artifacts, whereas quasi-harmonic pushes produced strong mode conversion, phase jitter, unstable local phase or 60-extraction, and spurious “islands” of modulus error (2206.13402). A common misconception is therefore that any narrowband guided-wave measurement with high OCT signal-to-noise ratio will automatically yield stable modulus maps. The reported evidence indicates otherwise for bounded media: robustness depends strongly on spectral breadth and on fitting the full dispersion rather than on local single-frequency phase alone.
Bandwidth also controls what can be resolved mechanically. In skin, the high-frequency range 61–62 was described as critical to resolve the thin epidermis, whereas lower frequencies alone would not recover its 63MPa-scale modulus (Feng et al., 2022). In lens measurements, sensitivity to kPa-scale 64 and Pa-scale 65 was attributed to rich dispersion between 66–67 and 68, even though practical measurements in that study were limited to 69–70 (Feng et al., 2024).
5. Representative tissue implementations and quantitative findings
The experimental literature spans ophthalmic, dermatologic, musculoskeletal, and vascular tissues, with each implementation choosing a frequency band and guided-wave model suited to tissue thickness, prestress, and heterogeneity.
| System | Wave regime and band | Reported outputs |
|---|---|---|
| Human cornea in vivo (Li et al., 2023) | Shear-like antisymmetric 71-mode Lamb waves, 72; sweep 73–74 | Central cornea 75, periphery 76, limbus 77; precision 78; spatial resolution 79 |
| Human cornea in vivo (Li et al., 2023) | Simultaneous 80 and 81, 82–83 | Mean tensile modulus 84; mean shear modulus 85; estimated errors 86 |
| Porcine lens and capsule (Feng et al., 2024) | Guided leaky Rayleigh-like surface waves, 87–88 | Anterior capsular tensions 89–90; posterior capsular tensions 91–92; 93 anterior capsule, 94 posterior capsule; cortical tissue 95 |
| Porcine aorta (Jiang et al., 27 Jul 2025) | Guided Lamb waves, 96–97 | Stretch-dependent reduction in viscosity; adventitia becomes significantly stiffer than media under loading; layer and directional mapping with 98–99 precision |
| Human forearm skin in vivo (Feng et al., 2022) | Broadband Rayleigh waves, 00–01 | Epidermis 02 at 03–04; dermis 05; hypodermis 06 at 07–08 |
| Cartilage and skin, ultra-wideband (Feng et al., 2022) | Rayleigh surface waves, 09–10 | Shear modulus range 11 to 12 in depth profiling; cartilage sublayers 13, 14, and 15 |
In the cornea, the high-frequency 16-mode implementation provided the first reported in vivo observation of significant spatial variation in the shear modulus of healthy corneal stroma, with central cornea 17, peripheral cornea 18, and limbus exceeding 19; the displacement profiles were described as consistent with highly anisotropic corneal tissues, and the ratio 20–21 indicated strong fiber orientation effects (Li et al., 2023). The related simultaneous 22/23 method extracted both tensile and shear properties in vivo, reporting 24 shear and 25 plane-strain tensile modulus in one healthy subject, and 26 shear with 27 tensile modulus in another, corresponding to anisotropy of approximately 28 and 29 (Li et al., 2023).
In the lens, broadband guided-wave OCE separated intrinsic modulus from in-plane tension. For intact porcine lenses, the anterior capsule had 30, 31, and 32, while the posterior capsule had 33, 34, and 35. Under 36 radial zonular stretch, the anterior side reached 37, with 38 and 39 (Feng et al., 2024).
In arteries, broadband guided-wave OCE characterized not only stiffness but nonlinear viscoelasticity. In axial single-layer elastic fits over 40, the arterial shear parameter 41 rose from 42 to 43, while 44 rose from 45 to 46. In two-layer fits, media shear 47 grew from 48 to 49, whereas adventitia shear 50 grew from 51 to 52; the adventitia/media tensile-modulus ratio climbed from 53 at rest to 54 at physiological tension, reflecting collagen engagement (Jiang et al., 27 Jul 2025).
In skin and cartilage, bandwidth primarily enabled depth selectivity. Broadband Rayleigh-wave OCE measured epidermis including stratum corneum at 55, dermis at 56, and hypodermis at 57 in vivo (Feng et al., 2022). Ultra-wideband OCE extended this logic to 58–59, recovering three cartilage layers with moduli 60, 61, and 62, and showing in fingertip skin that water hydration increased stratum corneum thickness from 63 to 64, reduced high-frequency phase velocity, and lowered the inverted surface modulus to 65 (Feng et al., 2022).
6. Clinical and methodological significance
The established clinical rationale is tissue-specific but methodologically consistent: broadband guided-wave OCE provides in situ mechanical information under physiologic or controlled preload. In corneal biomechanics, reported applications include refractive surgery planning, degenerative disorder diagnosis, intraocular pressure assessment, preoperative screening for keratoconus, monitoring corneal cross-linking efficacy, and tonometry correction (Li et al., 2023, Li et al., 2023). The ability to distinguish tensile from shear response is especially relevant because corneal deformation depends on both in-plane collagen-dominated tension and out-of-plane shear resistance.
In lens biomechanics, the principal advance is simultaneous access to elastic modulus and mechanical tension. Reported clinical promise includes optimizing capsulorhexis in cataract surgery and future translation to assessment of presbyopia, accommodative capacity, and post-implant lens mechanics, potentially through non-contact ultrasound excitation combined with wide-band OCE (Feng et al., 2024). In vascular biomechanics, the method was positioned as a route to noninvasive assessment of stiffness biomarkers such as collagen engagement and viscoelastic damping, with translation pathways including intravascular catheter probes combining OCT/OCE and extracorporeal shear-wave excitation for carotid monitoring (Jiang et al., 27 Jul 2025).
Methodologically, broadband guided-wave OCE has also clarified several limits. In bounded layers, elastographic lateral resolution cannot generally reach OCT resolution and is fundamentally linked to layer thickness (2206.13402). Many formulations assume incompressibility, uniform thickness, and local homogeneity within the analysis window; corneal implementations additionally noted practical limits from direct contact, PZT bandwidth, and OCT phase stability, with higher IOP or stiffer tissues potentially requiring 66 (Li et al., 2023). Lens measurements reported that fitting accuracy at 67 was limited by signal-to-noise ratio as wave amplitude decayed (Feng et al., 2024).
At the same time, the cross-organ studies indicate a coherent trajectory. Broadband guided-wave OCE now supports anisotropic and acoustoelastic corneal mapping, dual-mode tensile/shear estimation, bilayer tension-modulus inversion in the lens, dual-bilayer skin analysis, layer-specific viscoelastic fitting in arteries, and ultra-wideband depth profiling in cartilage and skin (Li et al., 2023, Li et al., 2023, Feng et al., 2024, Feng et al., 2022, Jiang et al., 27 Jul 2025, Feng et al., 2022). A plausible implication is that the field is converging toward a general framework in which broadband dispersion, rather than any single wave regime, serves as the common observable for reconstructing prestress, anisotropy, viscosity, and depth dependence in layered soft tissues.