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. 2022 Jan;4(1):012007.
doi: 10.1088/2516-1091/ac4512. Epub 2022 Jan 14.

Wave-based optical coherence elastography: The 10-year perspective

Fernando Zvietcovich  1 , Kirill V Larin  1
Affiliations

Wave-based optical coherence elastography: The 10-year perspective

Fernando Zvietcovich et al. Prog Biomed Eng (Bristol). 2022 Jan.

Abstract

After 10 years of progress and innovation, optical coherence elastography (OCE) based on the propagation of mechanical waves has become one of the major and the most studied OCE branches, producing a fundamental impact in the quantitative and nondestructive biomechanical characterization of tissues. Preceding previous progress made in ultrasound and magnetic resonance elastography; wave-based OCE has pushed to the limit the advance of three major pillars: (1) implementation of novel wave excitation methods in tissues, (2) understanding new types of mechanical waves in complex boundary conditions by proposing advance analytical and numerical models, and (3) the development of novel estimators capable of retrieving quantitative 2D/3D biomechanical information of tissues. This remarkable progress promoted a major advance in answering basic science questions and the improvement of medical disease diagnosis and treatment monitoring in several types of tissues leading, ultimately, to the first attempts of clinical trials and translational research aiming to have wave-based OCE working in clinical environments. This paper summarizes the fundamental up-to-date principles and categories of wave-based OCE, revises the timeline and the state-of-the-art techniques and applications lying in those categories, and concludes with a discussion on the current challenges and future directions, including clinical translation research.

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Figures

Figure 1.
Figure 1.
Characteristics of wave propagation produced by the same localized excitation device in homogeneous tissues with different mechanical properties: (a,d) elastic and isotropic, (b,e) viscoelastic and isotropic, and (c,f) elastic and anisotropic. In (d), phase speed corresponding to (a) is not dispersive and is the same for any radial direction with respect to the excitation origin. In (e), phase speed is frequency-dependent, which produces spatio-temporal distortion and attenuation of wave propagation in (b). Nevertheless, the propagation in (e) is still isotropic with respect to the excitation origin. Finally, in (f), phase speed is non-dispersive but highly anisotropic with respect to the orientation of fibers in (c).
Figure 2.
Figure 2.
Tissue spatial distribution and boundary conditions with respect to the characteristic wavelength λc of the mechanical wave propagating in the tissue. In the horizontal axis, three categories of homogeneity are shown: homogeneous (with thickness d), layered (with different thickness for each layer), and heterogeneous (with softer and/or stiffer inclusions compared to the background) materials. In the vertical axis, two categories of boundary conditions are shown: semi-infinite, when d > λc; and thin-plate type media, when d < λc. In all cases, we assume the tissues are low-viscosity media and extend infinitely along the lateral directions.
Figure 3.
Figure 3.
Mechanical waves in OCE. In (a), axial motion at the surface of a tissue sample is produced by an excitation source for the generation of mechanical wave propagation. (b) Numerically simulated diagram depicting different mechanical wave branches generated when an axial harmonic load is applied at the surface of a semi-infinite elastic medium. Four waves are identified: surface acoustic wave (traveling along the surface), shear wave, compressional wave and longitudinal shear wave (both traveling towards depth). Colormap represent normalized displacement magnitude in arbitrary units.
Figure 4.
Figure 4.
Generation of surface acoustic waves in a semi-infinite type tissue when the surface of the tissue is interfacing (a) air, and (a) liquid fluid. The excitation source is producing localized axial displacement at the tissue surface in both cases. After excitation, (a) Rayleigh, and (b) Scholte waves propagate guided by the tissue surface.
Figure 5.
Figure 5.
Propagation of Lamb waves in tissues. (a) Thin-plate type tissue (interfacing air at the top and liquid fluid at the bottom) being locally excited with axial motion at the top surface. (b) Lamb waves are generated and guided by the thin-plate in the quasi-symmetric (S0) and quasi-antisymmetric (A0) zero-order modes. Red and blue fields represent positive and negative displacement, respectively. (c) A0 mode solution of Equation 3.6 showing frequency-dependent Lamb wave speed for different thin-plate thicknesses H. For all cases, cp = cF = 1500 m/s, ρ = ρF =1000 kg/m3, μ = 10 kPa, which produces a cs ≈ 3.07 m/s. The asymptotic Scholte wave speed (cSc) was calculated using Equation 3.5.
Figure 6.
Figure 6.
Diagram showing different types of active and passive excitation sources used in wave-based OCE divided into two groups according to their coupling nature: contact and non-contact.
Figure 7.
Figure 7.
The impact of the excitation spatial extend (A, defined as the area diameter) in the characteristic wavelength of transient mechanical waves in tissue. In (a), localized sources (smaller A) can produce smaller excitation wavelengths in tissues. In (b), extended sources (larger A) can produce stronger waves with less attenuation by the cost of larger wavelengths.
Figure 8.
Figure 8.
Types of temporal excitation signals in wave-based OCE (a, c, e) with their respective frequency responses (b, d, f). In (a), the temporal displacement uz(t) in two elastic materials with different relaxation times (stiff: τR = 1 ms, and soft: τR = 4 ms) is produced by a transient pulse with a duration TPulse. In (b), the frequency response of the pulses in (a) is shown with the calculation of the average frequency (fAvg) for each case. The quasi-harmonic displacement in the stiffer (τR = 1 ms) and softer (τR = 4 ms) elastic media is shown in (c) when produced by a train of 4 pulses (periodicity 2TPulse). (d) Frequency response of the quasi-harmonic displacement signals of (c). Finally, multifrequency signals used for the excitation of tissues are shown in (e) including its frequency response in (f) for two cases: a chirp signal covering [100 - 900] Hz range, and a sum of five harmonic signals with random phases covering [100 - 900] Hz with steps of 200 Hz.
Figure 9.
Figure 9.
Schematic of wave-based OCE experimental setups including the excitation method, the target sample, and the optical system based on two OCT implementations: (a) SD-OCT, and (b) SS-OCT. FC: fiber coupler, L1: collimation lens, L2: telecentric scan lens, C1, C2: circulators.
Figure 10.
Figure 10.
M-mode acquisition protocol. In (a), A-lines (M repetitions) are acquired at the fixed lateral position x0 along depth and time. The mechanical excitation produces longitudinal shear waves propagating towards the z-axis. In (b), the spatio-temporal propagation of the wave in (a) is temporally sampled at the step time Ts which enables the tracking of the wave at the smallest travel distance Δz along the z-axis. The slope m of the line plot represents the inverse of the wave speed. Colormap in (a) and (b) represents particle velocity (motion) along the z-axis.
Figure 11.
Figure 11.
Spatio-temporal 2D/3D acquisition protocols in wave-based OCE. (a) Ideal simultaneous acquisition of motion produced by wave propagation in tissues along the xz-plane. (b) Motion snapshot obtained at the instant t0 from (a). (c) Spatio-temporal analysis of wave propagation along the lateral axis in (b). (d) Timing diagram of the MB-acquisition protocol using M=200 temporal repetitions and 250 lateral location. The OCT A-line is 1/Ts. (e) Redistribution of zt-frames from (d) into a 3D matrix for the calculation of spatial xz-frames with fs∗=1/Ts apparent frame rate. (f) Timing diagram of the BM-acquisition protocol using 100 lateral location and M temporal repetitions. A single xz-frame is acquired in Δt = 100Ts. (g) Stack of motion xz-frames along time with a resultant frame rate of fs = 1/Δt.
Figure 12.
Figure 12.
Classification of mechanical waves and interferences typically found in wave-based OCE according to the spatio-temporal properties of the excitation method, and boundary conditions of tissues.
Figure 13.
Figure 13.
Elastography resolution characterization in wave-based OCE. In (a)-top Wave propagation generated at the center of a two-sided phantom (softer-to-stiffer transition) tissue-mimicking phantom. In (a)-bottom, the elastogram (i.e. wave speed map) was calculated based using a wavelength estimator (Section 6.4.1). Average wave speeds in both regions show a differentiated elasticity between both phantom halves. (b) Lateral-dependent speed transition plot obtained from the elastogram in (a) fitted to the Sigmoid function (Equation 6.10). The spatial derivate of the Sigmoid plot was obtained in order to calculate the FWHM spreading of the pulse. (Figure reproduced from Ref. [119]).
Figure 14.
Figure 14.
3D elastography of a heterogeneous tissue-mimicking phantom using transient excitation. (a) B-mode structural en face images of a half-sided phantom with soft (3% gelatin) and stiff (8% gelatin) regions. Wave propagation was initiated using a transient ARF excitation (0.5 ms pulse) exited at the center of the stiff region (black dot). (b) 3D elastogram representing group velocity in m/s. (c) 3D elastogram of phase velocity calculated at f0 = 375 Hz. The near-field effect of wave propagation can be observed in the excitation area of both (b) and (c) cases. (Figure adapted from Ref. [161])
Figure 15.
Figure 15.
Elastography of layers in ex vivo porcine cornea using reverberant shear wave fields (Section 4.2.2). (a) B-mode structural (left) and motion (right) volumes of a cornea. Motion represents particle velocity produced by 8 localized contact displacement sources vibrating at 2 kHz. (b) The en face motion frame (left) extracted from the top layer in (a) is auto-correlated within a smaller region (discontinuous-line square) and fitted to Equation 4.5 (right) for the estimation of local wavelength and local shear wave speed, (c) Depth-dependent shear wave speed obtained after applying (b) to every single corneal depth is compared against the physiological description of corneal layers (left) and the structural OCT image of the cornea (center), (d) Shear wave elastogram (in m/s) of the cornea superimposed with its B-mode structural image. (Figure reproduced from Ref. [65])
Figure 16.
Figure 16.
Wave-based OCE of ex vivo porcine cornea under localized UV-CXL treatment, (a) B-mode structural images of untreated (left), half-CXL-treated, and full-CXL-treated corneas, (b) Particle velocity snapshots (extracted at t0 = 1.5 ms instant) showing Lamb wave propagation in corneas under the cases in (a) produced using an AC-ARF excitation method (quasi-harmonic vibration at 2 kHz) focused at the corneal apex, (c) Lamb wave speed elastogram of the corneas in (b) obtained using a wavelength estimator (Equation 6.8). (d) Space-time map showing average propagation of Lamb waves in the half-CXL-treated cornea case, (e) Comparison of average Lamb wave speeds obtained in the left and right side of each corneal case obtained from (c). (Figure reproduced from Ref. [119]).
Figure 17.
Figure 17.
Wave-based OCE of the ex vivo porcine anterior segment of the eye. (a) Experimental schematic showing the eyeball being cannulated for the IOP control using a closed-loop system. The FOV indicates the region being scanned using an SS-OCT system. (b) Schematic showing a contact displacement method (based on a piezoelectric actuator generating quasi-harmonic excitation at 800 Hz) producing Lamb waves propagation from the sclera all the way to the cornea passing through the limbal connecting tissue. (c) Lamb wave speed elastograms (in m/s) of the anterior segment of the eye when IOP is subject to 10, 20, and 40 mmHg. (d) Comparison of average Lamb wave speed in cornea, limbus, and sclera tissues for different IOP levels. Error bars represent inter-sample standard error (n = 8 eyeballs). (Figure adapted from Ref. [22]).
Figure 18.
Figure 18.
In vivo elastography of human corneas using wave-based OCE. (a) Schematic of the contact probe, including the OCT system and the vibration contact displacement tip touching the corneal epithelium, (b) Displacement snapshots showing Lamb wave propagation at [6, 8, 12] kHz harmonic frequencies, (c) Depth-dependent phase speed (left) and attenuation (right) extracted in the cornea of one of the human subjects over a range of 6 – 16 kHz frequencies. Gray box plots were left out from the analysis due to insufficient wave amplitude. (Figure adapted from Ref. [12]).
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