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Abstract
Optical coherence elastography (OCE) has seen rapid growth since its introduction in 1998. The past few decades have seen tremendous advancements in the development of OCE technology and a wide range of applications, including the first clinical applications. This tutorial introduces the basics of solid mechanics, which form the foundation of all elastography methods. We then describe how OCE measurements of tissue motion can be used to quantify tissue biomechanical parameters. We also detail various types of excitation methods, imaging systems, acquisition schemes, and data processing algorithms and how various parameters associated with each step of OCE imaging can affect the final quantitation of biomechanical properties. Finally, we discuss the future of OCE, its potential, and the next steps required for OCE to become an established medical imaging technology.
© 2022 Optica Publishing Group
1. INTRODUCTION
This tutorial aims to provide readers with an introduction to optical coherence elastography (OCE) [1] and enable others to set up their own elastography imaging systems and research. Elastography, in general, has grown rapidly since its formal introduction in the 1990s [2,3] and has become a powerful technique with specific clinical applications in areas such as chronic liver disease [4]. Expanding upon the remarkable progress reported by major reviews in the last few years [5–8], this tutorial will be focused on the fundamental areas of elastography: (1) an introduction to solid mechanics, (2) tissue excitation methods, (3) system setup and imaging paradigms, and (4) signal processing methods.
Elastography, in general, entails inducing a perturbation in tissues, measuring the subsequent motion, and linking the motion to biomechanical parameters with an appropriate mechanical model. Just like ultrasound elastography (USE) and magnetic resonance elastography (MRE), OCE relies on its parent imaging modality, optical coherence tomography (OCT) [9], to detect motion, albeit with much greater (nm-scale) displacement sensitivity. OCE adopted many methods from USE and MRE, such as static/quasi-static compression [2] and elastic wave imaging [3,10].
Schmitt first implemented OCE in 1998, where OCT images were taken before and after compression [1]. The compression-induced displacement was quantified by a correlation-based algorithm that relied on the OCT structural image. Since then, OCE has drastically improved its displacement/motion sensitivity and imaging speed, and a wide variety of implementations have been demonstrated. Most recently, OCE has transitioned from a focus on the development of novel techniques and analysis methods to feasibility and validation studies in humans in vivo as OCE moves from the bench to the clinic.
2. BIOMECHANICAL THEORY
This section will describe the mechanical models of tissues used in OCE and how different models are applied to OCE measurements to obtain biomechanical parameters, such as Young’s modulus.
A. Purely Elastic Models
The relationship between stress, ${\sigma _{\textit{ij}}}$, and strain tensors, ${\varepsilon _{\textit{ij}}}$, in the case of a linear isotropic displacement can be defined as [7]
Young’s modulus, $E$, and the shear modulus, $\mu$, are related by
which in the case of tissues, reduces to because the Poisson’s ratio of tissues is generally very close to 0.5 under the assumption of low compressibility. In wave-based elastography methods, the shear modulus can be closely estimated by the bulk shear wave speed, ${c_s}$, with certain assumptions about sample geometry and boundary conditions, by where $\rho$ is the tissue density (${\sim}{{1000}}\;{\rm{kg/}}{{\rm{m}}^3}$). Figure 1 shows how shear wave speed can be used to detect diseased tissue. We will further explore special cases of this equation and where it is and is not applicable in later sections. Beyond using mechanical waves to extract the shear or Young’s modulus, we can also utilize longitudinal compression by applying uniaxial stress, ${\sigma _{11}}$, where ${\sigma _{22}} = {\sigma _{33}} = 0$, ${\varepsilon _{22}} = \;{\varepsilon _{33}} = - \nu {\varepsilon _{11}}$, and again assuming $\nu \cong 0.5$, we arrive at
Fig. 1. Left, excitation of a mechanical shear wave in a tissue with a healthy soft region and diseased stiff region. Right, propagation of the shear wave is faster in the diseased stiff region as compared to the soft healthy region.
Since we are only applying uniaxial stress, Eq. (2) simplifies to
Going forward, ${x_1}$ will be referred to as $z$, as it is the axial direction in OCT imaging.
Critically, this means that only the axial displacement, ${u_1}$, and its spatial derivative need to be calculated to obtain the axial strain, ${\varepsilon _{11}}$, and if the stress, ${\sigma _{11}}$, is known, Young’s or shear modulus. This principle forms the foundation of the majority of static/quasi-static OCE techniques that are based on uniaxial compression (Fig. 2) [7], which includes the seminal USE [2] and OCE papers [1] and the field of compressional elastography, as we will discuss shortly.
Fig. 2. Uniaxial compression of tissue with a stiff diseased region. The tissue can be modeled as a series of springs [1,2], and the axial displacement, ${u_1}$, and its spatial derivative, strain, ${\varepsilon _{11}}$, can be used to localize the stiffer diseased region.
One issue to note is the presence of elastic non-linearity, even in purely elastic models. During elastography measurements, a common assumption about tissues is linearity during the small strains. However, tissues can exhibit non-linearity even in relatively small strains (${\lt}{{5}}\%$) encountered during OCE [11]. We will further address the impact of tissue non-linearity on OCE measurements in a later section.
B. Viscoelasticity and Anisotropy
We have only considered the simplistic case where the shear modulus is purely elastic, i.e., $\mu$ is a real number and greater than 0. Most tissues are viscoelastic [12–15], meaning that $\mu$ has a frequency dependence and is complex, $\tilde\mu(\omega)$, which can be written as
where ${\mu _s}(\omega)$ and ${\mu _l}(\omega)$ are the storage and loss moduli, respectively, and $\omega$ is the angular frequency ($\omega = 2\pi\! f$). To interpret the meaning of a complex shear modulus, a rheological model must be applied, and a handful of models has been proposed for viscoelastic tissues [16]. The Kelvin–Voigt model is most commonly used and models the elastic part of tissue as a purely elastic spring (${E_0}$ parameter) and viscous part of tissue as a purely viscous damper ($\eta$ parameter) in parallel [16]. Then, $\tilde\mu(\omega)$ is represented asWe need to point out that there are numerous other models [6,16–25], such as the Voigt, Maxwell, Kelvin–Voigt fractional derivative, and standard linear solid, discussion of which are beyond the scope of this tutorial.
So far, we have assumed that tissues are homogeneous and isotropic. However, there are obvious cases where this is not true, such as skeletal muscles, which have a preferential orientation of the muscle fibers. This means that, in addition to the frequency dependence of biomechanical parameters, there is an angular or orientation dependence [26], which has been studied in OCE on muscular tissue [27–30] and the cornea [31,32].
3. OCE METHODS
There are two major categories of OCE methods: static/quasi-static methods and dynamic methods. The dynamic methods can be further separated into vibrometry and wave-based methods. Here, we will briefly describe the fundamentals of each technique and the various types of OCE measurements for each method.
A. Static/Quasi-Static OCE
Static/quasi-static OCE methods are predominantly based on uniaxial compression with a mechanical actuator and have been reviewed extensively in [7]. Here, OCT data are taken before and after loading, which is usually performed with a ring-shaped mechanical actuator affixed to a transparent compression plate (Fig. 3). Then, the displacement between the unloaded and loaded states is quantified by an appropriate algorithm, and then axial strain, ${\varepsilon _{11}}$, is calculated. Figure 4 shows the wrapped phase difference between the unloaded and loaded states and axial microstrain of a stiff inclusion within a soft bulk material [33]. Application of a stress sensor [34] with a known elasticity enables conversion of the measured axial strain, ${\varepsilon _{11}}$, to Young’s modulus by Eq. (6). Beyond measuring only the axial displacement, the lateral displacement of the sample can also be calculated [35], which can result in significantly more accurate mapping of sample elasticity [36]. Since its introduction in the seminal OCE publication [1], compression OCE has seen drastic improvements in instrumentation, speed, and sensitivity and has recently been shown to improve cancer detection [37,38]. A thorough analysis of the mechanical contrast and elasticity sensitivity in compression OCE has shown that the mechanical resolution is an order of magnitude greater than the OCT structural resolution (${\sim}{{150}}\;{\rm{\unicode{x00B5}{\rm m}}}$ versus ${\sim}{{10}}\;{\rm{\unicode{x00B5}{\rm m}}}$) [39].
Fig. 3. Schematic of static/quasi-static compression OCE. An OCT image is taken when the sample is unloaded, then the actuator applies a force, which compresses the sample, and another OCT image is taken. The stress sensor enables quantitative mapping of Young’s modulus.
Fig. 4. (a) Wrapped phase difference between the unloaded and loaded states and (b) axial microstrain of a stiff inclusion in a soft bulk material as imaged by compression OCE. Adapted from [33].
Compression OCE techniques are not the only type of static/quasi-static OCE. Other techniques have been introduced that utilize other phenomena to introduce a perturbation in tissues. For example, Nair et al. have shown that the heartbeat-induced ocular pulse can be used to measure axial strain in vivo [40], resulting in a truly passive OCE method for assessing corneal biomechanical properties. The main benefit of this passive method is that virtually any current phase-sensitive OCT system could use it without introducing any additional hardware. Similarly, Kling modulated the ambient pressure to induce displacement in corneas to measure stress distribution [41].
B. Wave-Based OCE
Another most common OCE technique is based on exciting and measuring the propagation of mechanical waves in tissues. A mechanical wave is created when a brief and locally applied force creates a disturbance spreading in the medium. Basic properties of this wave, such as its speed, can be used to estimate the mechanical properties of the medium, as shown by Eq. (5) and in Fig. 1. However, it should be noted that many different waves can be created, so Eq. (5) is not always directly applicable. In OCE, four different types of waves are generally created: (1) body waves, (2) longitudinal waves, (3) Rayleigh/Scholte waves, and (4) Lamb waves.
Body waves, or bulk waves, are independent of boundary conditions, and the relationship between their speed and biomechanical parameters is straightforward. The transversely propagating body wave is a shear wave (S-wave), and its speed, ${c_{\!s}}\!$, can be converted to the shear modulus by Eq. (5) when assuming isotropy. Here, the particle motion is orthogonal to the propagation direction. The longitudinally propagating body wave is the pressure wave (P-wave), where the particle motion is parallel to the direction of propagation. Its speed, ${c_{\!p}}$, is related to the P-wave modulus, or longitudinal modulus, $M$, by
The longitudinal modulus is composed of both the shear modulus, $\mu$, and the bulk modulus, $K$ by [42]
Since tissues are mostly water-based, $K$ is a few GPa, and $\mu$ ranges from a few Pa to tens of MPa [43]. Thus, the P-wave speed in tissues is almost entirely determined by $K$, with P-wave speeds near the speed of sound in water (${\sim}{{1500}}\;{\rm{m/s}}$). Hence, OCE is not focused on measuring P-waves since they are weakly sensitive to the Young’s or shear modulus and travel faster than current OCT systems can detect reliably. Although Brillouin microscopy is highly sensitive to $K$ (and $M$), current spectrometers have sufficient sensitivity to obtain a relationship between the Young’s (and shear) modulus with the Brillouin measurements [44–46]. However, the link between the Brillouin shift and elastic moduli appears to be sample-dependent, and multimodal elastography may offer a solution to the semi-quantitative nature of Brillouin microscopy by combining it with OCE [44].
Recently, there has been a demonstration of “longitudinal shear waves” detected by OCE [47–50]. These waves result from the superposition of coherent crossed shear waves and have longitudinal and transversal components of motion, and they are not pure transversal as in shear waves [50]. Unlike P-waves, these waves travel at the shear wave speed of ${\sim}{0.1}$ to ${\sim}{{50}}\;{\rm{m/s}}$ in tissues and are easily detectable by OCT systems [50–52]. Since the waves propagate longitudinally, they are less affected by tissue boundary conditions, simplifying their interpretation. However, the angle of the original shear waves combining to form the longitudinal wave determines its speed and must be accounted for to estimate biomechanical parameters correctly.
Depending on the interface between the tissue, Rayleigh or Scholte waves can be excited. These waves propagate following the surface geometry. The depth of field of these waves is proportional to their wavelength (e.g., a Rayleigh wave of ${\sim}{0.5}\;{\rm{mm}}$ wavelength could be detected within ${\sim}{0.5}\;{\rm{mm}}$ depth from the surface), and their speed depends on the coupling medium at the surface. Assuming a semi-infinite medium and low compressibility ($\nu \cong 0.5$), we can relate the Rayleigh or Scholte wave speed to the shear modulus depending on the boundary conditions. When the tissue interfaces with vacuum or air, e.g., skin, a Rayleigh wave is excited, and its speed, ${c_{\!R}}$, is
When the tissue is coupled with a fluid, e.g., the crystalline lens or retina in the eye, a Scholte wave propagates, and its speed, ${c_{\rm{Sc}}}$, is
Many waves measured in OCE are Rayleigh waves, and so the measured speed should be adjusted accordingly, albeit only slightly.
Lamb waves propagate in structures where the thickness of the medium is the same order as the wavelength as shown in Fig. 5. Lamb waves are guided by the sample geometry and are generally dispersive. In contrast to the previously mentioned waves, Lamb waves depend not only on the shear (or Young’s) modulus of the tissue but also its coupling medium, boundary interface, thickness, and propagation mode. The Lamb wave solution is not explicit like the previously mentioned waves, but numerical methods can be used to obtain Young’s modulus. Lamb wave models have been demonstrated for various boundary conditions in OCE [17,54]. Multiple types of waves can be generated in heterogeneous tissues (shear, pressure, longitudinal, and surface waves) when an incident mechanical wave collapses with inclusions of different stiffnesses, boundaries, and fluid interfaces that do not support mechanical shearing [42]. In such cases, proper modeling is required to convert wave speed into mechanical properties.
Fig. 5. Propagation of a Lamb wave in a porcine cornea for different cross-linking (CXL) treatment localizations. The propagation of the wave can be clearly seen from the red/blue regions moving through the imaged region. (a) B-mode structural OCT images of untreated (virgin), half CXL-treated, and full CXL treated corneas. (b) Axial particle velocity snapshots extracted at 1.5 ms. (c) 2D speed maps calculated from corneas in (b). (d) Space-time map (averaged along depth) extracted along the wave propagation path in half treated CXL cornea. (e) Comparison of average speed values calculated from all cases in (c) along the right and left sides of corneas. Adapted from [53].
C. Vibrometry OCE
The other major branch of dynamic OCE is focused on the localized oscillations of tissues in response to transient forces [55]. Here, the tissue is often modeled as a spring-mass damper system to obtain biomechanical parameters that can then be linked to the elastic modulus or shear viscosity. Most commonly, this parameter is the natural frequency, ${f_n}$, of the tissue response, which can be represented as [56,57]
in the single degree of freedom mass-damper system with a damping ratio, $\epsilon$, ofThen, the localized temporal displacement, $d(t)$, can be written as
Fig. 6. (a) Damping model of tissue and (b) corresponding signal and its single degree of freedom equation for the displacement. Reprinted from [59].
Fig. 7. (a) Experimentally measured by OCE and (b) analytical solution of ARF-induced localized damping in young and mature rabbit lenses in situ. Adapted from [57].
4. TISSUE EXCITATION
In static/quasi-static compression OCE, tissue excitation is quite straightforward, as shown in earlier sections, but special care must be taken to avoid biases caused by friction and misalignment. For example, friction can cause a noticeable decrease in elastography sensitivity and underestimation of sample elasticity [62]. This could potentially be ameliorated by non-contact methods such as widefield acoustic radiation force (ARF) excitation [63,64] with the added benefit of enabling spectroscopic analysis, e.g., for viscoelasticity. However, with dynamic techniques, the excitation can have a significant impact on the resulting measurements.
Different excitation methods are detailed in recent OCE reviews [5–8]. Here, we will briefly cover some of the important parameters to consider when choosing an excitation modality. As shown by Kirby et al. for wave-based OCE [65] and Leartprapun et al. for vibrometry-based OCE [66], the spatiotemporal characteristics of tissue motion predominantly determine the resulting mechanical resolution. Therefore, one should consider what scale of mechanical resolution is desired in addition to physical limitations associated with the tissue (e.g., non-contact versus contact excitation or safety limits). For example, a tightly controlled excitation spot can result in high-frequency elastic waves that are less susceptible to boundary conditions and can improve the mechanical resolution. However, high-frequency waves generally attenuate more rapidly as shown in Fig. 8 and usually require more energy to produce a similar amplitude of motion as compared to lower frequency waves, which should be considered for tissue safety limits for live imaging.
Fig. 8. (a) Wave propagation, (b) axial motion at the excitation, and (c) power spectra in a tissue-mimicking phantom at the indicated frequencies. Reprinted from [53].
One of the most straightforward techniques to induce dynamic motion is directly contacting the tissue, such as with a small, blunted wire tip. However, in some cases, direct contact with the tissue is not desired, so methods such as focused micro air-pulse stimulation [67], ARF [68], photothermal stimulation [69], or air-coupled ARF [70] can be utilized. Air-pulse stimulation can be easily implemented and is a more focused version of clinically approved non-contact tonometers. However, it has limited bandwidth and, thus, can only excite relatively low-frequency elastic waves. Nevertheless, it was able to distinguish diseased skin from healthy skin in patients, as an example [71].
Although non-contact in nature, magnetomotive OCE requires impregnating the tissue with magnetic particles, which are then moved by a magnetic field to induce vibrations [72] or even elastic waves [73]. The Lorentz force can also be used to induce elastic waves in the presence of a magnetic field by contacting a conductive tissue and applying a transient electric field [74]. Other exotic techniques have also been demonstrated, such as exploding nanoparticles to generate localized, targeted, and high-frequency elastic waves [75]. One of the most interesting excitation methods is to use physiological processes to induce dynamic motion [76]. These methods have been used in static/quasi-static OCE [40] and have the added benefit of requiring no modifications to OCT system hardware to perform elastography.
Beyond localized sources, distributed sources have unique properties that make them useful in many scenarios. In the case of interference of two sources at identical wavelengths, a standing wave can be induced [77,78], which can be easily imaged with slow OCT systems. Similarly, two sources with slightly mismatched frequencies can induce crawling waves, which, again, can be imaged by slower imaging paradigms [77,79]. Finally, when multiple sources are used, a reverberant or diffuse shear field can be created [80], which has been shown to have superior mechanical contrast for assessing layered tissues like the cornea [81].
Tissues can also be excited in various temporal paradigms. For example, a single-tone burst can be used for inciting mechanical waves or measuring the point-wise damping properties as in vibrometry. On the other hand, a long sequence of single frequency content can be used to incite harmonic motion at a given frequency, which can significantly boost the motion amplitude at that frequency and even excite motion beyond the natural frequency limitations of the tissue. However, this is limited to a single frequency, so the stimulation frequency must be swept to obtain spectroscopic measurements. Hence, most wave-based OCE methods utilize a single burst to enable rapid measurements of wave dispersion, e.g., Lamb waves. To overcome the limitations of single burst and harmonic motion, a small number of stimulations at a single frequency can be used as plotted in Fig. 8(b), which include the benefits of exciting strong motion, overcoming bandwidth limitations of tissue motion, and can include limited spectroscopic measurements centered around the stimulation frequency as shown in Fig. 8(c).
Finally, modulated excitation has been used to produce mechanical waves with broad and localized frequency content in tissues using ARF. Recent work has demonstrated the possibility of using pulse-compression (i.e., a form of modulated excitation) to spread the ultrasonic excitation amplitude over a long emission (to minimize exposure for delicate tissues) and still recover a high-energy localized excitation pulse [82]. Finally, modulated excitation has also been used in ARF with immersion and air-coupled transducers to produce quasi-harmonic excitation [53].
5. OCE IMAGING
The standard methodology in OCE (and elastography in general) is to perturb the sample and image the subsequent motion. In static/quasi-static OCE, the amplitude of the displacement is critical, so careful consideration should be taken when applying displacement retrieval algorithms to ensure the accuracy of the displacement. On the other hand, the amplitude of the motion is not always critical in dynamic measurements, such as in wave-based OCE, where the reconstruction of the temporal properties of the motion is far more important. In this section, we will cover the various OCE imaging paradigms and subsequent data processing steps commonly found in OCE and discuss their benefits and limitations.
A. Intensity-Based Imaging
The seminal publications in OCE and USE utilized an intensity-based correlation algorithm to detect displacement in the sample caused by uniaxial compression [1,2]. Intensity-based methods have been commonly used in OCE due to their simplicity and sub-pixel accuracy [83]. However, these techniques require the speckle field to remain mostly constant during displacement, which is only true for a very small distances (${\lt}{{1}}\%$ of the sample thickness), after which speckle decorrelation leads to ambiguous results [84–86]. In the case of very large displacements (10 s of µm to mm-scale), the entire sample can be tracked [87–89] like non-contact tonometers used in ophthalmology.
B. Phase-Sensitive OCE
The vast majority of current OCE techniques rely on phase-sensitive imaging to detect small displacements in tissues. Phase-sensitive techniques have far greater displacement sensitivity (µm or even sub-µm) [90] and can retrieve the true axial displacement amplitude and temporal shape. The tissue motion can be directly obtained from the phase term of the complex OCT signal, requiring little to no computational processing like Doppler OCT techniques. However, more robust techniques for obtaining the tissue displacement or axial particle velocity can be utilized, such as Loupas’s algorithm [91] or the vector method [92], which greatly benefit in cases of low OCT SNR, such as a dark speckle or poorly scattering tissues. Recent work has shown that speckle greatly reduces the displacement sensitivity of OCE (up to ${{3}} \times$), but averaging locally in areas with different speckle patterns can overcome this limitation and even surpass standard methods [93]. Like intensity-based techniques, speckle decorrelation can lead to significant errors.
C. Hybrid Methods
To overcome the limitations of either intensity- or phase-based methods, hybrid methods may be able to provide sensitive measurements even in the case of pixel-scale motion [84,86,94]. These methods correct for large scale motion and remove the necessity for error-prone unwrapping techniques, enabling measurements of larger strains without compromising displacement sensitivity.
D. Imaging Paradigms
1. M-B-Mode
In dynamic OCE, M-B-mode imaging is typically used because it enables effective framerates equal to the OCT system A-scan rate (typically tens of kHz) [8]. This form of imaging can be easily performed in 3D (x,z,t) or 4D (x,y,z,t), and is accomplished by acquiring several M-mode scans, which is when the OCT probe beam is held stationary for a period of time (generally tens of ms). Multiple M-mode scans are taken across the sample in the desired sampling pattern, and each M-mode scan can be synchronized with the excitation for wave-based OCE [8,95]. One major issue with M-B-mode imaging is that safety issues must be addressed since the OCT beam is held stationary and multiple mechanical excitations are performed on the sample, often at the same location. The spatial sampling during imaging can be greatly reduced to minimize safety concerns because the mechanical resolution is an order of magnitude coarser than the OCT resolution [65], thus reducing the number of excitations. Finally, only the necessary data can be acquired to limit the tissue exposure to the laser radiation even though OCT imaging, even in M-mode, is generally safe for many tissues.
2. B-M-Mode
B-M-mode imaging is the preferred method in static/quasi-static OCE [7,96]. Here, the inter-frame displacement is of interest and is at the Hz scale to adhere to the assumptions of static displacement (in contrast to the kHz scale of motion in dynamic OCE) [8]. In compression-based techniques, a pair of OCT scans are taken at the same location, with one scan acquiring data while the sample is unloaded and the next scan is acquired while the sample is loaded, as shown in Fig. 3. B-M-mode imaging can also be performed in dynamic OCE, particularly vibrometry [97,98]. Recently, B-M-mode imaging has also been demonstrated for wave-based OCE by utilizing an ultra-fast swept-source laser [99,100]. Instead of holding the beam stationary as in M-B-mode imaging, the beam is rapidly scanned across the sample while the wave propagates across the field of view. By ensuring proper synchronization between the scanner, laser, and data acquisition, this technique can achieve displacement sensitivity on par with traditional OCE methods [101]. Moreover, since the OCT beam is never stationary and only one excitation is required for a single line measurement, safety issues are minimized as compared to M-B-mode imaging. However, the requirement to use ultra-fast lasers is costlier than standard OCT sources, and the number of spatial pixels available for wave propagation analysis is quite limited, restricting the accuracy and robustness of subsequent calculations. Recently, ultra-fast OCE has also been demonstrated based on a parallel spectral-domain OCT (SD-OCT) system [102]. This system utilized line-field illumination rather than scanning a point across the sample and, therefore, had no moving parts but utilized a costly high-speed 2D camera.
E. Signal Processing
1. Noise Removal
As with any imaging technique, noise reduction or removal techniques are critical to enhancing its capabilities. One of the easiest ways to reduce noise in OCE is to improve the OCT image SNR because the displacement stability is related to the OCT image SNR by [103]
Static/quasi-static techniques often use averaging to reduce displacement noise and reduce the influence of speckles [62,93]. Dynamic techniques commonly utilize spatiotemporal filtering techniques to remove motion unrelated to the exciting motion, e.g., temporal filtering for harmonic/quasi-harmonic excitation and directional filtering to remove mechanical wave reflections [104]. Correlation-based methods, such as Loupas’s algorithm mentioned earlier, can also reduce noise in OCE. Beyond digital techniques, the imaging setup can be optimized as well. For example, common-path imaging is routinely used in compression-based OCE because it effectively eliminates environmental noise, which is the slow and large amplitude oscillations in Fig. 3. In common-path imaging, the sample and reference light travel through the same set of optical components, greatly reducing any stray motion that may occur in a traditional dual-arm setup. It can also be implemented in dynamic OCE [59,105–109], as shown in Fig. 9, but is not commonly used because of the physical presence of the optical window as a reference arm, which can interfere with tissue stimulation methods.
Fig. 9. Comparison of the displacement stability in (a) conventional dual-arm OCT and (b) common-path OCT by comparison of the environmental noise. Each profile shows a different measurement with an artificial offset given for clarity. Note the difference in scale of amplitudes of the noise, which is greatly reduced in (b). Adapted from [109].
2. Strain Estimation
In static/quasi-static OCE, the inter-frame displacement can be utilized to obtain the axial strain, ${\varepsilon _{11}}$. Due to measurement ambiguity, such as system noise, displacement sensitivity, and speckle, the true axial strain cannot be obtained directly. Hence, methods have been developed that utilize spatial averaging or fitting [96]. Thus, the axial strain can be estimated by
where ${{\Delta}}{u_1}$ is the change in axial displacement over depth range ${{\Delta}}z$. In comparison to Eq. (7), here ${\varepsilon _{11}}$ is most often obtained from spatially fitting the displacement over some depth $z$, and various methods have been proposed to improve the fitting and find the optimal balance between spatial resolution and fit quality [39,62,96]. Most simply, this can be calculated by least squares linear regression fitting of the compression-induced displacement over a given axial range, as shown in Fig. 2. By weighting the fitting with the OCT image intensity, the fitting quality can be improved by minimizing the influence of data from dark areas, which have poor phase data, as seen in Eq. (17) [33]. The longer the fitting distance, the more robust the strain calculation, but this comes at the cost of a loss in resolution or the ability to detect sharp changes in stiffness. Again, averaging can be employed here to improve the fitting quality over a shorter window to improve resolution and fidelity, including averaging laterally to remove the influence of speckles [62]. Another technique, the vector method [7], incorporates the displacement of multiple scatterers in the complex plane to obtain the local phase variation gradient, which can provide an accurate estimate of displacement that is more resistant to large displacements and speckle noise. This method has been further expanded to include supra-pixel displacements, enabling more accurate displacement estimations for the larger amplitude of displacement that often require smaller processing kernels compared to least squares style fitting [7,11,86].Beyond the axial displacement, the 2D displacement in static/quasi-static OCE can also be measured [35] to obtain more accurate estimates of tissue elasticity by accounting for the lateral displacement caused by stiffness heterogeneity and incompressibility [36,110].
Strain is very useful for elucidating mechanical contrast in tissues, but Young’s modulus can provide even greater elastic contrast [111]. This can be accomplished by applying a stress sensor to calculate the applied stress on the sample [34], which can be used to convert strain to Young’s modulus by Eq. (6). Here, the stress sensor is calibrated, i.e., its stress-strain curve is measured before the OCE measurements. Then, the sensor strain is obtained during OCE imaging and is correlated back to the stress-strain calibration to obtain the stress that was applied to the sample surface. The OCE measurements can also be combined with iterative numerical methods [112] or numerical simulations [113] to obtain high-resolution maps of stiffness in tissue with greater fidelity and accuracy than the aforementioned algebraic methods. Moreover, these methods do not rely on first-order and linear approximations, so they may be able to provide greater mechanical resolution, but thorough investigations are still needed to confirm this hypothesis.
As mentioned earlier, there can be noticeable non-linearity in tissues even at the small strain encountered during OCE imaging [11,37,114]. Moreover, the utilization of stress sensors can compound the non-linearity if calibration is not performed correctly. Nevertheless, measuring the sensor stress during imaging enables more robust and repeatable measurements of sample elasticity since the stress on the sample can be selected before OCE imaging [114], ensuring that multiple OCE measurements are performed in the same region of tissue non-linear stress-strain curves.
3. Wave Propagation Analysis
We have discussed the relationship between the various wave propagation parameters, e.g., speed and dispersion, biomechanical parameters, and sample geometry. Here we will briefly detail the various methods to calculate the wave propagation parameters.
The most common method to obtain the wave speed is to calculate the time of flight. Various methods can be used to obtain the wave propagation lags, such as peak tracking or correlation-based methods. The wave propagation lags are then fitted to the corresponding wave propagation distances to obtain the wave speed. However, we previously described how mechanical waves are generally dispersive in tissues due to their viscoelastic nature or geometry. Therefore, frequency-domain methods are commonly utilized to obtain wave speed dispersion. Application of a 2D Fourier transform, ${\cal F}$, to the spatiotemporal map of a wave traveling along the $x$ direction in time, ${u_1}({x,t})$, results in a frequency wavenumber map,
where $k$ is the wavenumber and $\omega$ is the angular frequency. Then the peak at every angular frequency can be tracked and converted to phase velocity, ${c_{\rm{ph}}}(\omega),$ byAnother technique to calculate the wave propagation speed utilizes the phase-derivative of the local wave propagation. Here, the phase of the wave propagation calculated after the Fourier transform can be fitted over a small region to obtain the wave propagation speed. This method can be used to rapidly generate elastograms, or elasticity maps, with great fidelity and can incorporate or isolate wave propagation in several directions [53].
In cases of multiple excitation sources, such as diffuse shear wave OCE or reverberant OCE, the autocorrelation of the particle velocity or displacement field can be used to estimate local biomechanical properties. In reverberant OCE, the autocorrelation is fitted to the analytical solution of the interference of multiple shear waves, i.e., the diffuse shear wave field. The resulting fitting can obtain the local wavenumber, which can then be converted to wave speed if the excitation frequency is known. In passive wave-based OCE, or diffuse shear wave imaging, the local wavenumber can be obtained by the autocorrelation of the noise-like displacement caused by multiple shear waves interfering with the local strain to obtain the wavenumber of the diffuse shear field [76]. However, unlike reverberant OCE, the excitation frequency might be challenging to obtain since it is not actively stimulated.
6. OCE SYSTEM CONSIDERATIONS
Here we will discuss some of the practical aspects of setting up, configuring, and optimizing an OCE system, including the OCT system itself and incorporation of a tissue excitation technique. Several parameters such as penetration depth and physical access to the tissue must be considered before deciding on an OCE setup, and we discuss the benefits and limitations of commonly used OCE imaging paradigms.
A. Spectral-Domain OCT
SD-OCT systems are the most common type of OCT system used in OCE due to their relative simplicity and cost-effectiveness. SD-OCT systems are phase stable by nature of the light source used and, therefore, can be readily used for OCE imaging. Most SD-OCT systems operate in the near-infrared region (${\sim}{{850}}\;{\rm{nm}}$) and utilize silicon-based detectors (generally a line-scan camera) to capture the raw OCT data. However, SD-OCT systems can suffer from significant sensitivity roll-off due to the limited spatio-spectral bandwidth of the spectrometer, and imaging in the near-infrared results in poorer depth penetration as a trade-off of superior spatial resolution. Longer wavelengths can be used (${\sim}{{1000}}$ to ${\sim}{{1300}}\;{\rm{nm}}$) with specialized InGaAs cameras to improve depth penetration, but sensitivity roll-off is still an issue. SD-OCT systems generally operate in the tens of kHz range but can approach a few hundred kHz. At such high speeds, more powerful sources, such as supercontinuum lasers, are required to regain sensitivities achieved at lower speeds with traditional SD-OCT sources, e.g., superluminescent diodes. However, ultra-fast OCE has been recently demonstrated at an effective A-line rate of 11.5 MHz with a line-field parallel SD-OCT system [102].
B. Swept-Source OCT
The other major type of OCT in use is swept-source OCT (SS-OCT). Here, the spectral information is encoded in time as compared to space in SD-OCT systems. Therefore, high bandwidth detectors can be used, resulting in noticeable improvements in sensitivity roll-off to the point that modern SS-OCT systems can have effectively no sensitivity roll-off for much of their imaging range, which can approach or surpass 10 mm. Moreover, SS-OCT systems can operate at longer wavelengths (${\sim}{{1000}}\;{\rm{nm}}$ to ${\sim}{{1300}}$) for greater depth penetration with the trade-off of poorer spatial resolution. However, SS-OCT systems are typically not phase stable by nature and, thus, require specialized hardware [115] or precise triggering schemes [116] in order to achieve displacement stabilities required for sensitive OCE imaging. As mentioned earlier, SS-OCT sources are now available with A-scan rates in the MHz regime [100], enabling a new regime of ultra-fast dynamic OCE imaging [99]. Moreover, these ultra-fast lasers are phase stable but still require precise synchronization to obtain displacement stabilities on par with SD-OCT systems [101], and they remain costly compared to traditional swept-source lasers.
C. Excitation Alignment
One of the most practical aspects of OCE is the alignment of excitation modality with the OCT system. Figure 10 shows some of the most used OCE setups. The off-axis excitation shown in Fig. 10(a) is one of the simplest and earliest techniques for inducing motion in tissues in OCE. The excitation is angled such that it does not interfere with the OCT scan lens. In cases of wave propagation, the tissue stimulation hardware can be orthogonally aligned with the tissue surface and placed away from the OCT scan lens. However, when the localized damping, as in some vibrometry methods, is measured, the excitation needs to be co-focused with the excitation so off-axis stimulation can be used. If the tissue is thin enough, the motion in the sample can be excited from underneath the sample. For example, with ARF excitation, tissue can be placed in a water bath for acoustic coupling with the ARF transducer located at the bottom of the water bath. This may not be applicable in many cases, such as in live imaging. The excitation hardware can be shaped like a ring or have an imaging window [53], as shown in Fig. 10(b), enabling confocal excitation, which is especially useful for live imaging. Like confocal excitation, coaxial excitation can also be performed using photothermal excitation where the OCT beam and pulsed excitation laser beam are combined [75,98]. However, this method cannot measure transversely propagating waves because the beams are usually combined before the scanners. In this case, off-axis excitation can be used.
Fig. 10. Commonly used OCE excitation setups. (a) Off-axis and opposing stimulation paradigms. (b) Confocal tissue stimulation with ring-shaped excitation hardware. (c) Off-axis excitation in a common-path setup with a reference glass window. (d) Orthogonal stimulation.
As mentioned earlier, a common-path OCT setup can be used to perform ultra-sensitive OCE measurements, which can be useful in some cases, e.g., safety regulations limit the amplitude of motion that can be excited. Here, a reference glass is placed between the tissue and OCT scan lens to function as the reference mirror as illustrated in Fig. 10(c). However, the reference glass can interfere with tissue stimulation, so an off-axis excitation or tissue stimulation at the edge of the imaging field of view can overcome the physical limitations of multiple pieces of hardware in a relatively small space. As mentioned earlier, common-path OCE is the preferred method in many static/quasi-static techniques, particularly compression-based OCE as shown in Fig. 3. However, this setup can also be used to excite longitudinal shear waves and detect them with superior displacement sensitivity and mechanical contrast [52].
Another method of exciting tissue is to stimulate shear waves by orthogonal excitation [68] as presented in Fig. 10(d). Here, motion is excited from the side of the sample as opposed to from the tissue surface in most OCE applications. However, orthogonal excitation requires access to the side of the tissue but can be used readily with long focal length excitation techniques, such as ARF. Finally, OCE can be performed in a probe-based setup for minimally invasive imaging. Recent probe-based OCE demonstrations have used ARF excitation combined with fiber-based OCT probes for mechanical wave imaging [117] and vibrometry [118]. An OCT fiber can also be inserted into a needle and pushed through the tissue for compression-based OCE measurements [119].
7. LOOKING FORWARD
Since its introduction, OCE has seen rapid growth, with recent demonstrations of its clinical applicability using both static/quasi-static and dynamic techniques. Rigorous studies have shown that the mechanical contrast with OCE is about an order of magnitude greater than the OCT structural image resolution. Two of the most exciting directions OCE has taken are focused on passive elastography techniques where physiological processes [76] such as the heartbeat-induced motion and multimodal optical elastography techniques [44]. Passive approaches may be particularly beneficial because they can be implemented with standard OCT instruments, which are ubiquitous in ophthalmology, enabling rapid and widespread implementations of OCE without additional hardware. Multimodal approaches would provide crucial information at different scales or functional targets, as seen in medical imaging, e.g., SPECT$+$CT. Another direction for OCE improvement is focused on speed for single-shot measurements that are safe for patients. Another area that is experiencing rapid growth is computational approaches based on multiphysics inversion methods and artificial intelligence, as seen in other imaging fields. Although OCE has shown its usefulness in the clinic with breast cancer biopsy samples [38] and in vivo skin imaging for systemic sclerosis [71], large scale prospective clinical trials featuring OCE are the next major step for OCE to become a clinically viable modality, such as its predecessors, MRE and USE.
Funding
National Institutes of Health (R01EY022362, R01EY030063, R01HD095520, R01HD096335, R21CA231561, R61AR078078).
Acknowledgment
The authors would like to extend their gratitude to Dr. Salavat R. Aglyamov at the University of Houston for his insightful discussions about solid mechanics.
Disclosures
The authors have a financial interest in ElastEye LLC, which is not directly related to this work.
Data availability
Data presented in this work can be obtained from the respective authors.
REFERENCES
1. J. Schmitt, “OCT elastography: imaging microscopic deformation and strain of tissue,” Opt. Express 3, 199–211 (1998). [CrossRef]
2. J. Ophir, I. Cespedes, H. Ponnekanti, Y. Yazdi, and X. Li, “Elastography: a quantitative method for imaging the elasticity of biological tissues,” Ultrason. Imaging 13, 111–134 (1991). [CrossRef]
3. R. Muthupillai, D. J. Lomas, P. J. Rossman, J. F. Greenleaf, A. Manduca, and R. L. Ehman, “Magnetic resonance elastography by direct visualization of propagating acoustic strain waves,” Science 269, 1854–1857 (1995). [CrossRef]
4. A. Srinivasa Babu, M. L. Wells, O. M. Teytelboym, J. E. Mackey, F. H. Miller, B. M. Yeh, R. L. Ehman, and S. K. Venkatesh, “Elastography in chronic liver disease: modalities, techniques, limitations, and future directions,” Radiographics 36, 1987–2006 (2016). [CrossRef]
5. K. V. Larin and D. D. Sampson, “Optical coherence elastography–OCT at work in tissue biomechanics [Invited],” Biomed. Opt. Express 8, 1172–1202 (2017). [CrossRef]
6. M. A. Kirby, I. Pelivanov, S. Song, L. Ambrozinski, S. J. Yoon, L. Gao, D. Li, T. T. Shen, R. K. Wang, and M. O’Donnell, “Optical coherence elastography in ophthalmology,” J. Biomed. Opt. 22, 1–28 (2017). [CrossRef]
7. V. Y. Zaitsev, A. L. Matveyev, L. A. Matveev, A. A. Sovetsky, M. S. Hepburn, A. Mowla, and B. F. Kennedy, “Strain and elasticity imaging in compression optical coherence elastography: the two-decade perspective and recent advances,” J. Biophoton. 14, e202000257 (2021). [CrossRef]
8. F. Zvietcovich and K. V. Larin, “Wave-based optical coherence elastography: the 10-year perspective,” Prog. Biomed. Eng. 4, 012007 (2021). [CrossRef]
9. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991). [CrossRef]
10. J. Bercoff, M. Tanter, and M. Fink, “Supersonic shear imaging: a new technique for soft tissue elasticity mapping,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 396–409 (2004). [CrossRef]
11. V. Y. Zaitsev, A. L. Matveyev, L. A. Matveev, E. V. Gubarkova, A. A. Sovetsky, M. A. Sirotkina, G. V. Gelikonov, E. V. Zagaynova, N. D. Gladkova, and A. Vitkin, “Practical obstacles and their mitigation strategies in compressional optical coherence elastography of biological tissues,” J. Innovative Opt. Health Sci. 10, 1742006 (2017). [CrossRef]
12. M. W. Urban, S. Chen, and M. Fatemi, “A review of shearwave dispersion ultrasound vibrometry (SDUV) and its applications,” Curr. Med. Imaging Rev. 8, 27–36 (2012). [CrossRef]
13. C. F. Guimarães, L. Gasperini, A. P. Marques, and R. L. Reis, “The stiffness of living tissues and its implications for tissue engineering,” Nat. Rev. Mater. 5, 351–370 (2020). [CrossRef]
14. S. Cheng, E. C. Clarke, and L. E. Bilston, “Rheological properties of the tissues of the central nervous system: a review,” Med. Eng. Phys. 30, 1318–1337 (2008). [CrossRef]
15. B. J. Wilhelmi, S. J. Blackwell, J. S. Mancoll, and L. G. Phillips, “Creep vs. stretch: a review of the viscoelastic properties of skin,” Ann. Plast. Surg. 41, 215–219 (1998). [CrossRef]
16. E. L. Carstensen and K. J. Parker, “Physical models of tissue in shear fields,” Ultrasound Med. Biol. 40, 655–674 (2014). [CrossRef]
17. Z. Han, J. Li, M. Singh, C. Wu, C. H. Liu, R. Raghunathan, S. R. Aglyamov, S. Vantipalli, M. D. Twa, and K. V. Larin, “Optical coherence elastography assessment of corneal viscoelasticity with a modified Rayleigh-Lamb wave model,” J. Mech. Behav. Biomed. Mater. 66, 87–94 (2017). [CrossRef]
18. N. Leartprapun, R. Iyer, and S. G. Adie, “Model-independent quantification of soft tissue viscoelasticity with dynamic optical coherence elastography,” Proc. SPIE 10053, 1005322 (2017). [CrossRef]
19. A. Ramier, B. Tavakol, and S. H. Yun, “Measuring mechanical wave speed, dispersion, and viscoelastic modulus of the cornea using optical coherence elastography,” Opt. Express 27, 16635–16649 (2019). [CrossRef]
20. X. Zhang, “Identification of the Rayleigh surface waves for estimation of viscoelasticity using the surface wave elastography technique,” J. Acoust. Soc. Am. 140, 3619–3622 (2016). [CrossRef]
21. Y. Wang, N. D. Shemonski, S. G. Adie, S. A. Boppart, and M. F. Insana, “Dynamic method of optical coherence elastography in determining viscoelasticity of polymers and tissues,” in 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (IEEE, 2013), pp. 117–120.
22. S. R. Aglyamov, S. Wang, A. B. Karpiouk, J. Li, M. Twa, S. Y. Emelianov, and K. V. Larin, “The dynamic deformation of a layered viscoelastic medium under surface excitation,” Phys. Med. Biol. 60, 4295–4312 (2015). [CrossRef]
23. F. Zvietcovich, J. P. Rolland, and K. J. Parker, “An approach to viscoelastic characterization of dispersive media by inversion of a general wave propagation model,” J. Innovative Opt. Health Sci. 10, 1742008 (2017). [CrossRef]
24. M. Zhang, P. Nigwekar, B. Castaneda, K. Hoyt, J. V. Joseph, A. di Sant’Agnese, E. M. Messing, J. G. Strang, D. J. Rubens, and K. J. Parker, “Quantitative characterization of viscoelastic properties of human prostate correlated with histology,” Ultrasound Med. Biol. 34, 1033–1042 (2008). [CrossRef]
25. H. Zhang, Q. Zhang, L. Ruan, J. Duan, M. Wan, M. F. Insana, H. Zhang, Q. Zhang, L. Ruan, J. Duan, M. Wan, and M. F. Insana, “Modeling ramp-hold indentation measurements based on Kelvin–Voigt fractional derivative model,” Meas. Sci. Technol. 29, 035701 (2018). [CrossRef]
26. D. Royer, J. L. Gennisson, T. Deffieux, and M. Tanter, “On the elasticity of transverse isotropic soft tissues (L),” J. Acoust. Soc. Am. 129, 2757–2760 (2011). [CrossRef]
27. F. Zvietcovich, M. Singh, Y. S. Ambekar, S. R. Aglyamov, M. D. Twa, and K. V. Larin, “Micro air-pulse spatial deformation spreading characterizes degree of anisotropy in tissues,” IEEE J. Sel. Top. Quantum Electron. 27, 6800810 (2021). [CrossRef]
28. S. Wang, M. Singh, T. T. Tran, J. Leach, S. R. Aglyamov, I. V. Larina, J. F. Martin, and K. V. Larin, “Biomechanical assessment of myocardial infarction using optical coherence elastography,” Biomed. Opt. Express 9, 728–742 (2018). [CrossRef]
29. L. A. Aleman-Castaneda, F. Zvietcovich, and K. J. Parker, “Reverberant elastography for the elastic characterization of anisotropic tissues,” IEEE J. Sel. Top. Quantum Electron. 27, 7201312 (2021). [CrossRef]
30. J. R. Rippy, M. Singh, S. R. Aglyamov, and K. V. Larin, “Ultrasound shear wave elastography and transient optical coherence elastography: side-by-side comparison of repeatability and accuracy,” IEEE Open J. Eng. Med. Biol. 2, 179–186 (2021). [CrossRef]
31. M. Singh, J. Li, Z. Han, R. Raghunathan, A. Nair, C. Wu, C. H. Liu, S. Aglyamov, M. D. Twa, and K. V. Larin, “Assessing the effects of riboflavin/UV-A crosslinking on porcine corneal mechanical anisotropy with optical coherence elastography,” Biomed. Opt. Express 8, 349–366 (2017). [CrossRef]
32. J. J. Pitre Jr., M. A. Kirby, D. S. Li, T. T. Shen, R. K. Wang, M. O’Donnell, and I. Pelivanov, “Nearly-incompressible transverse isotropy (NITI) of cornea elasticity: model and experiments with acoustic micro-tapping OCE,” Sci. Rep. 10, 12983 (2020). [CrossRef]
33. B. F. Kennedy, R. A. McLaughlin, K. M. Kennedy, L. Chin, A. Curatolo, A. Tien, B. Latham, C. M. Saunders, and D. D. Sampson, “Optical coherence micro-elastography: mechanical-contrast imaging of tissue microstructure,” Biomed. Opt. Express 5, 2113–2124 (2014). [CrossRef]
34. K. M. Kennedy, S. Es’haghian, L. Chin, R. A. McLaughlin, D. D. Sampson, and B. F. Kennedy, “Optical palpation: optical coherence tomography-based tactile imaging using a compliant sensor,” Opt. Lett. 39, 3014–3017 (2014). [CrossRef]
35. K. Kurokawa, S. Makita, Y. J. Hong, and Y. Yasuno, “Two-dimensional micro-displacement measurement for laser coagulation using optical coherence tomography,” Biomed. Opt. Express 6, 170–190 (2015). [CrossRef]
36. P. Wijesinghe, L. Chin, and B. F. Kennedy, “Strain tensor imaging in compression optical coherence elastography,” IEEE J. Sel. Top. Quantum Electron. 25, 5100212 (2018). [CrossRef]
37. A. A. Plekhanov, M. A. Sirotkina, A. A. Sovetsky, E. V. Gubarkova, S. S. Kuznetsov, A. L. Matveyev, L. A. Matveev, E. V. Zagaynova, N. D. Gladkova, and V. Y. Zaitsev, “Histological validation of in vivo assessment of cancer tissue inhomogeneity and automated morphological segmentation enabled by optical coherence elastography,” Sci. Rep. 10, 11781 (2020). [CrossRef]
38. K. M. Kennedy, R. Zilkens, W. M. Allen, K. Y. Foo, Q. Fang, L. Chin, R. W. Sanderson, J. Anstie, P. Wijesinghe, A. Curatolo, H. E. I. Tan, N. Morin, B. Kunjuraman, C. Yeomans, S. L. Chin, H. DeJong, K. Giles, B. F. Dessauvagie, B. Latham, C. M. Saunders, and B. F. Kennedy, “Diagnostic accuracy of quantitative micro-elastography for margin assessment in breast-conserving surgery,” Cancer Res. 80, 1773–1783 (2020). [CrossRef]
39. M. S. Hepburn, P. Wijesinghe, L. Chin, and B. F. Kennedy, “Analysis of spatial resolution in phase-sensitive compression optical coherence elastography,” Biomed. Opt. Express 10, 1496–1513 (2019). [CrossRef]
40. A. Nair, M. Singh, S. Aglyamov, and K. V. Larin, “Heartbeat optical coherence elastography: corneal biomechanics in vivo,” J. Biomed. Opt. 26, 020502 (2021). [CrossRef]
41. S. Kling, “Optical coherence elastography by ambient pressure modulation for high-resolution strain mapping applied to patterned cross-linking,” J. R. Soc. Interface 17, 20190786 (2020). [CrossRef]
42. K. F. Graff, Wave Motion in Elastic Solids (Dover, 2012).
43. Y. Fung, Biomechanics: Mechanical Properties of Living Tissues (Springer, 2013).
44. Y. S. Ambekar, M. Singh, J. Zhang, A. Nair, S. R. Aglyamov, G. Scarcelli, and K. V. Larin, “Multimodal quantitative optical elastography of the crystalline lens with optical coherence elastography and Brillouin microscopy,” Biomed. Opt. Express 11, 2041–2051 (2020). [CrossRef]
45. G. Scarcelli and S. H. Yun, “Reply to ‘Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,’” Nat. Methods 15, 562–563 (2018). [CrossRef]
46. P. J. Wu, I. V. Kabakova, J. W. Ruberti, J. M. Sherwood, I. E. Dunlop, C. Paterson, P. Török, and D. R. Overby, “Water content, not stiffness, dominates Brillouin spectroscopy measurements in hydrated materials,” Nat. Methods 15, 561–562 (2018). [CrossRef]
47. S. Catheline and N. Benech, “Longitudinal shear wave and transverse dilatational wave in solids,” J. Acoust. Soc. Am. 137, 200–205 (2015). [CrossRef]
48. E. L. Carstensen and K. J. Parker, “Oestreicher and elastography,” J. Acoust. Soc. Am. 138, 2317–2325 (2015). [CrossRef]
49. E. L. Carstensen and K. J. Parker, “Erratum: Oestreicher and elastography [J. Acoust. Soc. Am. 138, 2317–2325 (2015)],” J. Acoust. Soc. Am. 143, 180 (2018). [CrossRef]
50. J. Zhu, Y. Miao, L. Qi, Y. Qu, Y. He, Q. Yang, and Z. Chen, “Longitudinal shear wave imaging for elasticity mapping using optical coherence elastography,” Appl. Phys. Lett. 110, 201101 (2017). [CrossRef]
51. C. H. Liu, D. Nevozhay, H. Zhang, S. Das, A. Schill, M. Singh, S. Aglyamov, K. V. Sokolov, and K. V. Larin, “Longitudinal elastic wave imaging using nanobomb optical coherence elastography,” Opt. Lett. 44, 3162–3165 (2019). [CrossRef]
52. F. Zvietcovich, G. R. Ge, H. Mestre, M. Giannetto, M. Nedergaard, J. P. Rolland, and K. J. Parker, “Longitudinal shear waves for elastic characterization of tissues in optical coherence elastography,” Biomed. Opt. Express 10, 3699–3718 (2019). [CrossRef]
53. F. Zvietcovich, A. Nair, Y. S. Ambekar, M. Singh, S. R. Aglyamov, M. D. Twa, and K. V. Larin, “Confocal air-coupled ultrasonic optical coherence elastography probe for quantitative biomechanics,” Opt. Lett. 45, 6567–6570 (2020). [CrossRef]
54. Z. Han, J. Li, M. Singh, C. Wu, C. H. Liu, S. Wang, R. Idugboe, R. Raghunathan, N. Sudheendran, S. R. Aglyamov, M. D. Twa, and K. V. Larin, “Quantitative methods for reconstructing tissue biomechanical properties in optical coherence elastography: a comparison study,” Phys. Med. Biol. 60, 3531–3547 (2015). [CrossRef]
55. V. Crecea, A. L. Oldenburg, X. Liang, T. S. Ralston, and S. A. Boppart, “Magnetomotive nanoparticle transducers for optical rheology of viscoelastic materials,” Opt. Express 17, 23114–23122 (2009). [CrossRef]
56. M. Singh, J. Li, S. Vantipalli, Z. Han, K. V. Larin, and M. D. Twa, “Optical coherence elastography for evaluating customized riboflavin/UV-A corneal collagen crosslinking,” J. Biomed. Opt. 22, 091504 (2017). [CrossRef]
57. C. Wu, Z. Han, S. Wang, J. Li, M. Singh, C. H. Liu, S. Aglyamov, S. Emelianov, F. Manns, and K. V. Larin, “Assessing age-related changes in the biomechanical properties of rabbit lens using a coaligned ultrasound and optical coherence elastography system,” Invest. Ophthalmol. Visual Sci. 56, 1292–1300 (2015). [CrossRef]
58. A. L. Oldenburg and S. A. Boppart, “Resonant acoustic spectroscopy of soft tissues using embedded magnetomotive nanotransducers and optical coherence tomography,” Phys. Med. Biol. 55, 1189–1201 (2010). [CrossRef]
59. G. Lan, K. V. Larin, S. Aglyamov, and M. D. Twa, “Characterization of natural frequencies from nanoscale tissue oscillations using dynamic optical coherence elastography,” Biomed. Opt. Express 11, 3301–3318 (2020). [CrossRef]
60. N. Leartprapun, Y. Lin, and S. G. Adie, “Microrheological quantification of viscoelastic properties with photonic force optical coherence elastography,” Opt. Express 27, 22615–22630 (2019). [CrossRef]
61. Y. Lin, N. Leartprapun, and S. G. Adie, “Spectroscopic photonic force optical coherence elastography,” Opt. Lett. 44, 4897–4900 (2019). [CrossRef]
62. J. Li, M. S. Hepburn, L. Chin, A. Mowla, and B. F. Kennedy, “Analysis of sensitivity in quantitative micro-elastography,” Biomed. Opt. Express 12, 1725–1745 (2021). [CrossRef]
63. G. Guan, C. Li, Y. Ling, Y. Yang, J. B. Vorstius, R. P. Keatch, R. K. Wang, and Z. Huang, “Quantitative evaluation of degenerated tendon model using combined optical coherence elastography and acoustic radiation force method,” J. Biomed. Opt. 18, 111417 (2013). [CrossRef]
64. C. Li, G. Guan, Y. Ling, Y. T. Hsu, S. Song, J. T. Huang, S. Lang, R. K. Wang, Z. Huang, and G. Nabi, “Detection and characterisation of biopsy tissue using quantitative optical coherence elastography (OCE) in men with suspected prostate cancer,” Cancer Lett. 357, 121–128 (2015). [CrossRef]
65. M. A. Kirby, K. Zhou, J. J. Pitre, L. Gao, D. Li, I. Pelivanov, S. Song, C. Li, Z. Huang, T. Shen, R. Wang, and M. O’Donnell, “Spatial resolution in dynamic optical coherence elastography,” J. Biomed. Opt. 24, 096006 (2019). [CrossRef]
66. N. Leartprapun, R. R. Iyer, C. D. Mackey, and S. G. Adie, “Spatial localization of mechanical excitation affects spatial resolution, contrast, and contrast-to-noise ratio in acoustic radiation force optical coherence elastography,” Biomed. Opt. Express 10, 5877–5904 (2019). [CrossRef]
67. S. Wang, K. V. Larin, J. Li, S. Vantipalli, R. K. Manapuram, S. Aglyamov, S. Emelianov, and M. D. Twa, “A focused air-pulse system for optical-coherence-tomography-based measurements of tissue elasticity,” Laser Phys. Lett. 10, 075605 (2013). [CrossRef]
68. J. Zhu, Y. Qu, T. Ma, R. Li, Y. Du, S. Huang, K. K. Shung, Q. Zhou, and Z. Chen, “Imaging and characterizing shear wave and shear modulus under orthogonal acoustic radiation force excitation using OCT Doppler variance method,” Opt. Lett. 40, 2099–2102 (2015). [CrossRef]
69. C. Li, G. Guan, Z. Huang, M. Johnstone, and R. K. Wang, “Noncontact all-optical measurement of corneal elasticity,” Opt. Lett. 37, 1625–1627 (2012). [CrossRef]
70. L. Ambrozinski, I. Pelivanov, S. Song, S. J. Yoon, D. Li, L. Gao, T. T. Shen, R. K. Wang, and M. O’Donnell, “Air-coupled acoustic radiation force for non-contact generation of broadband mechanical waves in soft media,” Appl. Phys. Lett. 109, 043701 (2016). [CrossRef]
71. C. H. Liu, S. Assassi, S. Theodore, C. Smith, A. Schill, M. Singh, S. Aglyamov, C. Mohan, and K. V. Larin, “Translational optical coherence elastography for assessment of systemic sclerosis,” J. Biophoton. 12, e201900236 (2019). [CrossRef]
72. A. Oldenburg, F. Toublan, K. Suslick, A. Wei, and S. Boppart, “Magnetomotive contrast for in vivo optical coherence tomography,” Opt. Express 13, 6597–6614 (2005). [CrossRef]
73. A. Ahmad, J. Kim, N. A. Sobh, N. D. Shemonski, and S. A. Boppart, “Magnetomotive optical coherence elastography using magnetic particles to induce mechanical waves,” Biomed. Opt. Express 5, 2349–2361 (2014). [CrossRef]
74. C. Wu, M. Singh, Z. Han, R. Raghunathan, C. H. Liu, J. Li, A. Schill, and K. V. Larin, “Lorentz force optical coherence elastography,” J. Biomed. Opt. 21, 090502 (2016). [CrossRef]
75. C. H. Liu, D. Nevozhay, A. Schill, M. Singh, S. Das, A. Nair, Z. Han, S. Aglyamov, K. V. Larin, and K. V. Sokolov, “Nanobomb optical coherence elastography,” Opt. Lett. 43, 2006–2009 (2018). [CrossRef]
76. T. M. Nguyen, A. Zorgani, M. Lescanne, C. Boccara, M. Fink, and S. Catheline, “Diffuse shear wave imaging: toward passive elastography using low-frame rate spectral-domain optical coherence tomography,” J. Biomed. Opt. 21, 126013 (2016). [CrossRef]
77. F. Zvietcovich, J. P. Rolland, J. Yao, P. Meemon, and K. J. Parker, “Comparative study of shear wave-based elastography techniques in optical coherence tomography,” J. Biomed. Opt. 22, 035010 (2017). [CrossRef]
78. H. C. Liu, P. Kijanka, and M. W. Urban, “Two-dimensional (2D) dynamic vibration optical coherence elastography (DV-OCE) for evaluating mechanical properties: a potential application in tissue engineering,” Biomed. Opt. Express 12, 1217–1235 (2021). [CrossRef]
79. P. Meemon, J. Yao, Y. J. Chu, F. Zvietcovich, K. J. Parker, and J. P. Rolland, “Crawling wave optical coherence elastography,” Opt. Lett. 41, 847–850 (2016). [CrossRef]
80. K. J. Parker, J. Ormachea, F. Zvietcovich, and B. Castaneda, “Reverberant shear wave fields and estimation of tissue properties,” Phys. Med. Biol. 62, 1046–1061 (2017). [CrossRef]
81. F. Zvietcovich, P. Pongchalee, P. Meemon, J. P. Rolland, and K. J. Parker, “Reverberant 3D optical coherence elastography maps the elasticity of individual corneal layers,” Nat. Commun. 10, 4895 (2019). [CrossRef]
82. T. M. Nguyen, B. Arnal, S. Song, Z. Huang, R. K. Wang, and M. O’Donnell, “Shear wave elastography using amplitude-modulated acoustic radiation force and phase-sensitive optical coherence tomography,” J. Biomed. Opt. 20, 016001 (2015). [CrossRef]
83. C. Sun, B. Standish, B. Vuong, X. Y. Wen, and V. Yang, “Digital image correlation-based optical coherence elastography,” J. Biomed. Opt. 18, 121515 (2013). [CrossRef]
84. V. Y. Zaitsev, A. L. Matveyev, L. A. Matveev, G. V. Gelikonov, E. V. Gubarkova, N. D. Gladkova, and A. Vitkin, “Hybrid method of strain estimation in optical coherence elastography using combined sub-wavelength phase measurements and supra-pixel displacement tracking,” J. Biophoton. 9, 499–509 (2016). [CrossRef]
85. V. Y. Zaitsev, A. L. Matveyev, L. A. Matveev, G. V. Gelikonov, V. M. Gelikonov, and A. Vitkin, “Deformation-induced speckle-pattern evolution and feasibility of correlational speckle tracking in optical coherence elastography,” J. Biomed. Opt. 20, 075006 (2015). [CrossRef]
86. V. Y. Zaitsev, A. L. Matveyev, L. A. Matveev, G. V. Gelikonov, A. A. Sovetsky, and A. Vitkin, “Optimized phase gradient measurements and phase-amplitude interplay in optical coherence elastography,” J. Biomed. Opt. 21, 116005 (2016). [CrossRef]
87. D. Alonso-Caneiro, K. Karnowski, B. J. Kaluzny, A. Kowalczyk, and M. Wojtkowski, “Assessment of corneal dynamics with high-speed swept source optical coherence tomography combined with an air puff system,” Opt. Express 19, 14188–14199 (2011). [CrossRef]
88. C. Dorronsoro, D. Pascual, P. Perez-Merino, S. Kling, and S. Marcos, “Dynamic OCT measurement of corneal deformation by an air puff in normal and cross-linked corneas,” Biomed. Opt. Express 3, 473–487 (2012). [CrossRef]
89. E. Maczynska, K. Karnowski, K. Szulzycki, M. Malinowska, H. Dolezyczek, A. Cichanski, M. Wojtkowski, B. Kaluzny, and I. Grulkowski, “Assessment of the influence of viscoelasticity of cornea in animal ex vivo model using air-puff optical coherence tomography and corneal hysteresis,” J. Biophoton. 12, e201800154 (2019). [CrossRef]
90. M. Sticker, C. K. Hitzenberger, R. Leitgeb, and A. F. Fercher, “Quantitative differential phase measurement and imaging in transparent and turbid media by optical coherence tomography,” Opt. Lett. 26, 518–520 (2001). [CrossRef]
91. T. Loupas, J. T. Powers, and R. W. Gill, “An axial velocity estimator for ultrasound blood flow imaging, based on a full evaluation of the Doppler equation by means of a two-dimensional autocorrelation approach,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 672–688 (1995). [CrossRef]
92. A. L. Matveyev, L. A. Matveev, A. A. Sovetsky, G. V. Gelikonov, A. A. Moiseev, and V. Y. Zaitsev, “Vector method for strain estimation in phase-sensitive optical coherence elastography,” Laser Phys. Lett. 15, 065603 (2018). [CrossRef]
93. M. S. Hepburn, K. Y. Foo, P. Wijesinghe, P. R. T. Munro, L. Chin, and B. F. Kennedy, “Speckle-dependent accuracy in phase-sensitive optical coherence tomography,” Opt. Express 29, 16950–16968 (2021). [CrossRef]
94. H. Khodadadi, O. Goksel, and S. Kling, “Motion estimation for optical coherence elastography using signal phase and intensity,” arXiv:2103.10784 (2021).
95. S. Wang and K. V. Larin, “Shear wave imaging optical coherence tomography (SWI-OCT) for ocular tissue biomechanics,” Opt. Lett. 39, 41–44 (2014). [CrossRef]
96. B. F. Kennedy, S. H. Koh, R. A. McLaughlin, K. M. Kennedy, P. R. Munro, and D. D. Sampson, “Strain estimation in phase-sensitive optical coherence elastography,” Biomed. Opt. Express 3, 1865–1879 (2012). [CrossRef]
97. R. K. Wang, Z. Ma, and S. J. Kirkpatrick, “Tissue Doppler optical coherence elastography for real time strain rate and strain mapping of soft tissue,” Appl. Phys. Lett. 89, 144103 (2006). [CrossRef]
98. N. Leartprapun, R. R. Iyer, G. R. Untracht, J. A. Mulligan, and S. G. Adie, “Photonic force optical coherence elastography for three-dimensional mechanical microscopy,” Nat. Commun. 9, 2079 (2018). [CrossRef]
99. M. Singh, C. Wu, C. H. Liu, J. Li, A. Schill, A. Nair, and K. V. Larin, “Phase-sensitive optical coherence elastography at 1.5 million A-Lines per second,” Opt. Lett. 40, 2588–2591 (2015). [CrossRef]
100. T. Klein and R. Huber, “High-speed OCT light sources and systems [Invited],” Biomed. Opt. Express 8, 828–859 (2017). [CrossRef]
101. S. Song, W. Wei, B. Y. Hsieh, I. Pelivanov, T. T. Shen, M. O’Donnell, and R. K. Wang, “Strategies to improve phase-stability of ultrafast swept source optical coherence tomography for single shot imaging of transient mechanical waves at 16 kHz frame rate,” Appl. Phys. Lett. 108, 191104 (2016). [CrossRef]
102. M. Singh, A. W. Schill, A. Nair, S. R. Aglyamov, I. V. Larina, and K. V. Larin, “Ultra-fast dynamic line-field optical coherence elastography,” Opt. Lett. 46, 4742–4744 (2021). [CrossRef]
103. B. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13, 3931–3944 (2005). [CrossRef]
104. S. Song, N. M. Le, Z. Huang, T. Shen, and R. K. Wang, “Quantitative shear-wave optical coherence elastography with a programmable phased array ultrasound as the wave source,” Opt. Lett. 40, 5007–5010 (2015). [CrossRef]
105. Y. Li, S. Moon, J. J. Chen, Z. Zhu, and Z. Chen, “Ultrahigh-sensitive optical coherence elastography,” Light Sci. Appl. 9, 58 (2020). [CrossRef]
106. G. Lan, B. Gu, K. V. Larin, and M. D. Twa, “Clinical corneal optical coherence elastography measurement precision: effect of heartbeat and respiration,” Transl. Vis. Sci. Technol. 9, 3 (2020). [CrossRef]
107. G. Lan, S. Aglyamov, K. V. Larin, and M. D. Twa, “In vivo human corneal natural frequency quantification using dynamic optical coherence elastography: repeatability and reproducibility,” J. Biomech. 121, 110427 (2021). [CrossRef]
108. G. Lan, S. R. Aglyamov, K. V. Larin, and M. D. Twa, “In vivo human corneal shear-wave optical coherence elastography,” Optom. Vis. Sci. 98, 58–63 (2021). [CrossRef]
109. G. Lan, M. Singh, K. V. Larin, and M. D. Twa, “Common-path phase-sensitive optical coherence tomography provides enhanced phase stability and detection sensitivity for dynamic elastography,” Biomed. Opt. Express 8, 5253–5266 (2017). [CrossRef]
110. E. Li, S. Makita, S. Azuma, A. Miyazawa, and Y. Yasuno, “Compression optical coherence elastography with two-dimensional displacement measurement and local deformation visualization,” Opt. Lett. 44, 787–790 (2019). [CrossRef]
111. K. M. Kennedy, L. Chin, R. A. McLaughlin, B. Latham, C. M. Saunders, D. D. Sampson, and B. F. Kennedy, “Quantitative micro-elastography: imaging of tissue elasticity using compression optical coherence elastography,” Sci. Rep. 5, 15538 (2015). [CrossRef]
112. L. Dong, P. Wijesinghe, D. D. Sampson, B. F. Kennedy, P. R. T. Munro, and A. A. Oberai, “Volumetric quantitative optical coherence elastography with an iterative inversion method,” Biomed. Opt. Express 10, 384–398 (2019). [CrossRef]
113. P. Wijesinghe, D. D. Sampson, and B. F. Kennedy, “Computational optical palpation: a finite-element approach to micro-scale tactile imaging using a compliant sensor,” J. R. Soc. Interface 14, 20160878 (2017). [CrossRef]
114. A. A. Sovetsky, A. L. Matveyev, L. A. Matveev, E. V. Gubarkova, A. A. Plekhanov, M. A. Sirotkina, N. D. Gladkova, and V. Y. Zaitsev, “Full-optical method of local stress standardization to exclude nonlinearity-related ambiguity of elasticity estimation in compressional optical coherence elastography,” Laser Phys. Lett. 17, 065601 (2020). [CrossRef]
115. R. K. Manapuram, V. G. R. Manne, and K. V. Larin, “Development of phase-stabilized swept-source OCT for the ultrasensitive quantification of microbubbles,” Laser Phys. 18, 1080–1086 (2008). [CrossRef]
116. S. Moon and Z. Chen, “Phase-stability optimization of swept-source optical coherence tomography,” Biomed. Opt. Express 9, 5280–5295 (2018). [CrossRef]
117. A. B. Karpiouk, D. J. VanderLaan, K. V. Larin, and S. Y. Emelianov, “Integrated optical coherence tomography and multielement ultrasound transducer probe for shear wave elasticity imaging of moving tissues,” J. Biomed. Opt. 23, 105006 (2018). [CrossRef]
118. Y. Qu, T. Ma, Y. He, M. Yu, J. Zhu, Y. Miao, C. Dai, P. Patel, K. K. Shung, Q. Zhou, and Z. Chen, “Miniature probe for mapping mechanical properties of vascular lesions using acoustic radiation force optical coherence elastography,” Sci. Rep. 7, 4731 (2017). [CrossRef]
119. K. M. Kennedy, R. A. McLaughlin, B. F. Kennedy, A. Tien, B. Latham, C. M. Saunders, and D. D. Sampson, “Needle optical coherence elastography for the measurement of microscale mechanical contrast deep within human breast tissues,” J. Biomed. Opt. 18, 121510 (2013). [CrossRef]
