An approach to viscoelastic characterization of dispersive media by inversion of a general wave propagation model

Abstract

In the characterization of elastic properties of tissue using dynamic optical coherence elastography, shear/surface waves are propagated and tracked in order to estimate speed and Young's modulus. However, for dispersive tissues, the displacement pulse is highly damped and distorted during propagation, diminishing the e®ectiveness of peak tracking approaches, and leading to biased estimates of wave speed. Further, plane wave propagation is sometimes assumed, which contributes to estimation errors. Therefore, we invert a wave propagation model that incorporates propagation, decay, and distortion of pulses in a dispersive media in order to accurately estimate its elastic and viscous components. The model uses a general¯rst-order approximation of dispersion, avoiding the use of any particular rheological model of tissue. Experiments are conducted in elastic and viscoelastic tissue-mimicking phantoms by producing a Gaussian push using acoustic radiation force excitation and measuring the wave propagation using a Fourier domain optical coherence tomography system. Results con¯rmed the e®ectiveness of the inversion method in estimating viscoelastic parameters in both the viscoelastic and elastic phantoms when compared to mechanical measurements. Finally, the viscoelastic characterization of a fresh porcine cornea was conducted. Preliminary results validate this approach when compared to other methods.

Relaxation time constant based optical coherence elastography

“…Stress field distribution highly depends on excitation frequency, which has been reported by Adie et al. [27] as well as our previous work [28]. OCE can also be utilized for viscoelasticity estimation, most publications related to tissue viscosity evaluation are wave-based methods.…”

Reverberant 3D optical coherence elastography maps the elasticity of individual corneal layers

“…For instance, it does not require prior knowledge of the direction of wave propagation for the estimation of local shear wave speed, which is a fundamental requirement for most of dynamic OCE techniques. In particular, the properties and boundary conditions of cornea such as (1) the top and bottom surfaces, (2) the heterogeneity in layer distribution along depth, and (3) the significant change in elastic properties in the cornea-sclera junction, produce multiple reflection and aberration of shear waves, which diminishes the effectivity of peak tracking techniques 51–53 . However, Rev3D-OCE does not require knowledge of a single direction of wave propagation (due to the nature of the auto-correlation in Eqs.…”

“…This method for non-contact excitation of the cornea was successfully demonstrated by Ambrozinski et al 42 . Subsequently, the acquisition scheme presented here can be expanded to acquire reverberant volumes in a faster fashion (time scales in the sub-second order) by upgrading the current OCT system to a faster camera with an A-line rate of 5 μs, resulting in a total acquisition time of 0.5 s. Finally, the characterization of viscoelastic parameters in cornea is of great importance 46,51,57 . Therefore, the excitation scheme of the current Rev3D-OCE method can be modified to send multi-harmonic vibrations all sent and captured simultaneously in order to calculate depth-dependent shear wave dispersion plots for the estimation of viscoelastic parameters.…”

“…The MB-mode acquisition approach 51 , is used in the quasi-synchronized (for Rev3D-OCE) and fully-synchronized (for Lamb wave method) versions. For the Lamb wave method, the acquisition consists of triggering the excitation (1 ms tone) and acquiring M = 100 A-lines during M × T s = 4 ms at a single ( x 0 , y 0 ) position in cornea along depth.…”

Dynamic Optical Coherence Elastography of the Anterior Eye: Understanding the Biomechanics of the Limbus

“…The M-B-mode protocol was used for the acquisition of motion in samples in 2D along the xz -plane, where the x -axis and z -axis correspond to lateral and axial (depth) directions, respectively. 24 This protocol consists of the OCT acquisition of M = 601 A-line repetitions (∼ 20 ms) for a given lateral position, whereas the excitation system is triggered to produce mechanical waves in the sample. Subsequently, the steering mirror controlled by a galvanometer (GVS002; Thorlabs Inc., Newton, NJ, USA) moves the OCT beam to the next consecutive lateral position for the next acquisition of M A-lines.…”