Elastography techniques, such as ultrasound elastography (USE) and optical coherence elastography (OCE), hold great promise in providing clinically actionable information by detecting altered tissue mechanical properties. In particular, recent OCE applications in oncology [1], dermatology [2], and ophthalmology [3] demonstrated the functionality of the technique for quantitative estimation of local tissue stiffness at microscale resolution [4,5]. The unique resolution advantage of OCE is related to the inherent feature of optical coherence tomography (OCT), which is the integral component of all OCE variants, i.e., static and dynamic OCE. These two variants of OCE differ in the temporal characteristics of the excitation method employed to induce tissue deformation; dynamic OCE utilizes transient or harmonic mechanical loading, while the time-dependent effects are negligible in static OCE. In typical dynamic OCE, tissue mechanical properties are commonly estimated by quantifying the speed of the propagating shear waves induced by the transient/harmonic loading. However, the inherent inhomogeneity of tissues and the existence of organ boundaries can cause multiple internal reflections, resulting in biased estimates of shear wave speeds. To overcome this limitation as well as achieve better tissue penetration and elasticity contrast, reverberant shear wave elastography (RevSWE), which assumes the existence of complex three-dimensional shear wave fields within the tissue, has been recently introduced [6]. Reverberant shear wave fields are naturally produced by the interaction of multiple shear waves propagating in random directions and can be experimentally reinforced by using multiple external sources. To this end, different excitation approaches were proposed, including an array of actuators (mechanical shakers) [6], a custom-made portable trifold futon with embedded quad resonators [7], and a multi-pronged ring actuated by a piezoelectric bender [8]. Such mechanical vibration sources can effectively generate reverberant shear waves with good penetration, enabling the assessment of deep tissues even at relatively high frequencies. However, the excitation of small and delicate structures/tissues (e.g., ocular tissues and embryos) using direct contact mechanical vibrators could pose a challenge, and thus, non-contact methods, e.g., acoustic radiation force (ARF), are preferable. Multiple ARF sources arranged in a desired configuration can generate reverberant shear wave fields in some applications, although the use of multiple transducers could result in unfavorable size and cost scaling [9].

Acoustic manipulation techniques, such as acoustic focusing and beam steering, have been widely used in biomedical applications of ultrasound to achieve desirable distribution and focal properties (e.g., focal intensity or focal spot size) within tissues [10,11]. A typical acoustic focusing method involves the alignment of a planar transducer with an acoustic lens, which can be fabricated from plastic, epoxy, rubber, or liquid. It refracts sound using the same basic law as optical lenses [12]. In this study, we developed a multifocal acoustic radiation force source using a combination of a single-element transducer and a 3D-printed acoustic lens array. Then, we experimentally demonstrated the functionality of this transducer-lens system in inducing reverberant shear wave fields using OCE imaging of a layered tissue-mimicking phantom.

An ∼38-mm-diameter single-element, 1-MHz immersion ultrasound transducer (A392S-SU, Olympus Co., Japan) was used to produce an unfocused acoustic beam. An acoustic lens array, comprising seven elements, was produced using TangoGray rubber-like material (TangoGray FLX950, Stratasys, Israel) with a 3D printer (Stratasys Objet Eden 260 v, Stratasys, Israel) of layer resolution 16 µm. The lens was attached to the transducer using a waterproof clear silicone (Loctite, USA) to produce seven different focal spots with a spatial separation of ∼12 mm on the focal plane, as shown in the left of Fig. 1(a). The middle of Fig. 1(a) shows the lens design in Creo software (Creo Parametric 6.0, PTC). Using a desired focal length, $f = 17.8\; \textrm{mm},$ the radius of curvature, r, of each lens was determined based on the lens formula as [13]

 

Fig. 1. (a) 3D view of the acoustic lens and transducer system showing multi-foci beam formation (left), a 3D model of the geometrical lens array (middle), and the cross-sectional view of the individual lenses (right). d: diameter of the individual acoustic lens, f: focal length of the lens, FB: focused acoustic beam, L: acoustic lens, r: radius of curvature, S: sample, t: the maximum thickness of the individual acoustic lens, UB: unfocused acoustic beam, US: single element ultrasound transducer. (b) Schematic representation of the experimental setup used to measure the focal pressure field of the multi-foci system using a needle hydrophone mounted on a computer-controlled translational stage. For this study, 2D scanning was performed in the focal plane (x-y) to characterize the spatial distribution of the focused acoustic fields. (c) Schematic of the Rev-OCE system based on a PhS-SDOCT system for imaging elastic wave propagation induced by the multi-foci lens and transducer system. C: collimator, CCD: charge-coupled device, FG: function generator, G: grating, GS: 2D galvo scanner, L: lens, M: mirror, P: pinhole, SL: scan lens, SLD: superluminescent diode, WB: water bucket. The inset at the bottom is a schematic of the ROI (5.7 × 4.6 × 0.9 mm³) of a layered gelatin phantom (4% and 8%, both w/w) with both horizontal and vertical layer distributions. L = 2.55 mm and Δh = 0.68 mm.

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Figure 1(b) shows a schematic of the experimental setup used to measure the spatial profile of the acoustic field at the focal plane using a needle hydrophone with a 0.2 mm sensor diameter (NH0200, Precision Acoustics Ltd, UK). The transducer driving signal, a square pulse of 0.5 ms duration, was generated with an arbitrary function generator (DG4162, RIGOL Tech, China) and amplified by a radio-frequency (RF) power amplifier (1040 L, Electronics & Innovation, Ltd., USA). A 3-axis stage driven by a motion controller (ESP301, Newport Co., USA) was used to scan the acoustic pressure field in the focal plane (40 × 40 mm²). The detected pressure intensity was pre-amplified and transferred to a computer via a digital oscilloscope (DS4000, RIGOL Tech, China). Data were processed using MATLAB 2021 (The MathWorks, Inc., USA) to produce the pressure field map at the focal plane. Measurements were compared with numerical simulations, carried out using the k-wave MATLAB toolbox, of the acoustic beam profile formed by the lens (density = 1255 kg m⁻³) with a continuous 1 MHz transducer input signal.

To assess the capability of the lens–transducer system to generate a reverberant shear wave field, we conducted OCE imaging in a layered gelatin phantom (4% and 8%, both w/w). Figure 1(c) shows a schematic of the OCE system, including the multifocal lens–transducer system and a phase-sensitive spectral domain optical coherence tomography system (PhS-SDOCT). The PhS-SDOCT used a broadband superluminescent diode (S480-B-I-20; Superlum Diodes Ltd., Ireland) operating with a center wavelength ${\lambda _\textrm{o}} = \; $ 840 nm and a full width at half maximum (FWHM) bandwidth of 50 nm as the light source. The PhS-SDOCT system was characterized by a displacement stability and axial (in the air) and transverse resolutions of 0.28 nm, ∼9 µm, and ∼8 µm, respectively. Experiments were conducted at an A-line rate of 25 kHz. For excitation, a sinusoidal signal (the resonance frequency of the transducer was 1 MHz) was amplitude modulated by a 2 kHz rectangular pulse train (ten cycles, 50% duty cycle) and input to the power amplifier to drive the transducer. The excitation frequency was selected based on the desired wavelength for the layered phantom imaging while avoiding significant wave attenuation. Three-dimensional M-C mode scanning was performed as described in Ref. [15], with each M-mode scan consisting of 400 A-lines, and a total of 151 × 151 points were acquired over a transverse ROI of 5.7 mm x 4.6 mm in ∼6 minutes. The 4D data (3D spatial, 1D temporal) were processed using MATLAB, where the phase shift, $\Delta \emptyset $, between successive A-lines was exploited to compute the axial particle velocity, ${v_z}$, using the equation ${v_z} = {\lambda _o}\Delta \emptyset /({4\pi n\Delta \tau } )$, where the refractive index $n = 1.36$ for gelatin [16] and $\Delta \tau = 40\; {\mathrm{\mu} \mathrm{s}}.$ To minimize noise, a 2D spatial bandpass filter, a donut-shaped ring with Gaussian edges in k-space, was applied to the particle velocity volumes. The typical wave speed ranges (i.e., 0.2 m/s to 10 m/s) observed in previous studies of soft tissues were taken into account to determine the cutoff frequencies of the wavenumber filter [8]. Then, the local shear wave speed was estimated using the relation ${v_s} = 2\pi F/k$, where $F$ = 2 kHz was the excitation frequency and k was the local wavenumber calculated using the 2D autocorrelation (window size = 0.4 × 0.4 mm²) of the particle velocity volume and by fitting the autocorrelation profiles to the analytical solutions of the reverberant shear wave field model [6,15,17]. Finally, the elastography resolution was estimated using the speed transitions in the layered phantom. As depicted in the inset of Fig. 1(c), the imaged phantom region (5.7 × 4.6 × 0.9 mm³) exhibits horizontal and vertical layer distributions, and hence, the lateral and axial resolutions can be assessed using wave speed profiles at the respective transition regions. For both lateral and axial layers, the average shear wave speed profiles near the transitions from the softer (4%) to the stiffer (8%) regions were computed from the shear wave speed maps. Then, the speed profiles were fitted to the basic Boltzmann sigmoid function, $c(R ),$ described as

Figure 2(a) shows the 2D spatial acoustic pressure distribution measured using the needle hydrophone on the focal plane. The results clearly demonstrate the 3D-printed lens system’s effectiveness in forming multiple beams and focusing them at multiple spots in the focal plane. Qualitatively, the mean 3D intensity map shown in Fig. 2(b) illustrates the axis-symmetrical pressure distribution produced by the seven lenses with minimal side lobes. The axial pressure profile shown in Fig. 2(c) was simulated using the designed lens geometry and material parameters for comparison with the measured results. The extended depth of focus could be a useful characteristic in OCE measurements as it minimizes the need to precisely position the focal spot during excitation. However, this comes at the expense of an increase in the focal spot size. The spot size, described as the FWHM, of the normalized pressure intensity at the focal plane was found to be 1.96 mm, which is in good agreement with the simulation results, as plotted in Fig. 2(d).

 

Fig. 2. (a) Normalized acoustic pressure distributions produced by the lens array of seven foci in the focal plane. (b) Normalized focal 3D intensity map averaged over the seven lenses. (c) Simulated acoustic beam profile along the propagation axis produced using the lens–transducer acoustic characteristics. The profile of only a single lens is shown, as all seven lenses are identical. Color bar refers to the normalized intensity for (a), (b), and (c). (d) Measured and simulated acoustic pressure profiles at the focal plane. The measured acoustic pressure profile represents the average of the profiles for all the focal spot profiles produced by the seven lenses.

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Figure 3(a) shows the 3D structural 5.7 × 4.6 × 0.9 mm³ volume of the gelatin phantom that forms layers distributed in both lateral and axial orientations. The softer region [4% (w/w) gelatin concentration] forms the left and top thin layers in the horizontally and vertically distributed two-layer phantom, with a partially sandwiched stiffer region [8% (w/w) gelatin concentration] shown by a light gray color. Instantaneous motion frames in the x-y plane extracted from a particle velocity motion volume of the phantom showing wave propagation at a depth location of z = 0.42 mm are depicted in Fig. 3(b). In Fig. 3(c), a representative en face image (z = 0.45 mm) showing the softer and stiffer regions is demonstrated, and, notably, the shear waves propagating in the two regions exhibit a difference in wavelength [Fig. 3(d)], with a longer wavelength seen in the stiffer region. Overall, it is evident that the multifocal ARF system can effectively induce a reverberant shear wave field in samples, enabling a non-contact excitation alternative for Rev-OCE.

 

Fig. 3. (a) 3D OCT image of a layered phantom (5.7 × 4.6 × 0.9 mm³) with horizontal and vertical distributions of a softer layer (gelatin concentration of 4%) and a stiffer layer (gelatin concentration of 8%). (b) Wave propagation snapshots at different instants of time in the displayed plane n (z = 0.42 mm) shown in (a). (c) En face image of the two-sided gelatin phantom (z = 0.45 mm) and (d) corresponding representative shear wave propagation exhibiting the differences in wavelength between the two regions. Color bar refers to the axial particle velocity (a.u.) for (b) and (d).

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To characterize the elastic contrast achievable using this technique, we produced a volumetric speed map and assessed the speed transitions at the boundaries of the layers. Figure 4(a) illustrates typical sub-volumes of speed maps extracted to produce spatial speed profiles in the lateral (bottom) and axial (top) directions at the transition regions. The mean elastic wave speeds near the transition between the softer and stiffer regions (shown by the black dashed lines) were 2.02 ± 0.48 m/s and 2.94 ± 0.39 m/s, respectively. For measurements conducted on three different gelatin phantoms with a similar layer distribution, the estimated lateral and depth elastography resolutions were 92.5 ± 27 μm and 35.1 ± 9.1 μm, respectively, as shown in Fig. 4(b) and Fig. 4(c). Note that the obtained lateral resolution could decrease with an increase in the 2D autocorrelation window size applied to the reverberant particle velocity volume and vice versa, though an increased window size could yield a better estimate of the shear wave speeds [15].

 

Fig. 4. Characterizing the resolution of multifocal ARF-based Rev-OCE imaging using the two-sided gelatin phantom shown in Fig. 3(a). (a) Spatial wave speed map in the composite phantom: volumetric segments showing axial (top) and en face (bottom) cross sections of the elastogram. The dashed-line rectangles illustrate the ROIs selected to produce lateral and axial shear wave speed profiles. (b) Lateral (x-y plane) and (c) axial (x-z plane) wave speed profiles and sigmoid curve fitting at the transition from the softer to the stiffer regions of the phantom. The elasticity resolution was obtained using the derivative of the sigmoid function. SE stands for the standard error of the wave speed.

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This preliminary study has demonstrated a promising excitation technique for high-resolution elasticity imaging with Rev-OCE. The results show that a simple 3D-printed acoustic lens can manipulate a collimated acoustic beam to produce multifocal ARF at a desired focal plane. Also, experimental results characterizing the focal beam profile were consistent with simulations, validating the robustness of the lens design. However, the focal distance of the individual beams can also be independently varied by simply changing the geometry of the lenses. As such, this could enable the focusing of the excitation at desired positions on samples of irregular sizes and shapes (e.g., tumor tissue). Furthermore, the characteristic ability of ARF to penetrate deep into tissues makes it an ideal candidate for probing the biomechanical properties of deeper tissues without dissection.

The Rev-OCE results for the layered gelatin phantom indicate that the multifocal ARF system can effectively generate reverberant shear wave fields, which can be used to probe the mechanical properties of tissues non-invasively. Compared to piezoelectric actuators, which are commonly used in reverberant OCE, such a simple multifocal system would be beneficial as a non-contact excitation source to assess the mechanical properties of delicate tissues. One noticeable shortcoming of the system demonstrated in this study is the large lateral focal spot size (∼1.96 mm), which may make it unsuitable for the excitation of small samples (e.g., mouse embryos). However, this can be improved by increasing the numerical aperture of the lens and/or by using a transducer with a higher resonance frequency. For example, our preliminary assessments indicate that a 7.5 MHz transducer can produce a diffraction-limited focal spot size of ∼0.29 mm when coupled with an acoustic lens of 12 mm aperture diameter and 17 mm focal distance. Further research may also consider reducing the separation between focal spots (i.e., a narrow excitation field of view) using an array of tilted or decentered acoustic lenses to enable the excitation of small ROIs. Also, the setup could be reconfigured so that the acoustic transducer–lens and OCT systems can be on the same side of the sample for some applications.