1.1.

Elastography

Elastography is an experimental method and a noninvasive medical imaging technique that conveys new information about internal tissue structure and behavior under load and ultimately generates images called elastograms.¹ Examples include elastograms of axial strains, lateral strains, and elastic moduli. Different degrees of stiffness are demonstrated as different shades of light and dark in an elastogram.² Ideally, this elastography technique can extract the elastic modulus, which is a property of the constituent material describing the stiffness of an isotropic elastic material.³ There are several types of elastic moduli, where the main moduli used currently in elastography are the Young's modulus (the ratio of the uniaxial stress over the uniaxial strain) and shear modulus (the ratio of shear stress to the shear strain). Given any two of the six elastic moduli, the remaining modulus can be determined. Thus two elastic moduli can fully describe the elastic properties of a homogeneous and isotropic material.

The motivation underlying elastography stems from the fact that elastic properties of tissues are directly related to the underlying structure of the tissue and are strongly affected by pathological changes. For example, edema, fibrosis, and calcification alter the elastic modulus of the extracellular tissue matrix;⁴ different tissues within atherosclerotic plaque have distinctive elastic properties;⁵ and cancerous tumors are often stiffer than benign and normal tissue.⁶ Elastography images contain information of local variations of the stiffness inside a region of interest and may provide additional clinical information to aid the identification of suspicious lesions and diagnosis of various disease states.^{7, 8, 9} Currently, there are several potential applications of elastography, which include assessing breast or brain tissue for malignancy^{10, 11} and atherosclerotic arteries for vulnerability to myocardial infarction.¹²

1.2.

Optical Coherence Elastography

Optical coherence tomography (OCT)–based elastography, which is termed optical coherence elastography (OCE),¹³ was first introduced by Schmitt¹⁴ in 1998. OCE shows great potential for micron and submicron imaging applications because it benefits from the high resolution of OCT,¹⁵ while additionally providing the elastic properties of the sample. OCT provides structural images approaching histology, where the microstructures of biological tissues can be quantified based on the optical backscattering properties within the imaging region of interest. This beneficial high-resolution, noninvasive imaging modality allows OCE to evaluate the mechanics of intact tissue on a scale that cannot be offered by elastographies produced by the competing imaging modalities of ultrasound^{3, 16, 17, 18} or MRI (magnetic resonance imaging).^{19, 20} Recent advances of these technologies are pushing the resolution to higher values where high-frequency ultrasound²¹ can reach 30–70 μm and magnetic resonance microscopy²² has improved imaging resolution to ∼120 um. However, OCT has inherently high resolution, 1–10 μm in vivo; therefore, OCE has the potential to link microstructural data with biomechanical and functional information. In the last decade, several studies have demonstrated the ability of OCE to provide valuable information about the micromechanical properties of tissue. OCE has been used to investigate the microscopic deformation of gelatin tissue phantoms, porcine muscle, and human skin as a function of depth under compressive loads;²³ define the properties of collagen organization in musculoskeletal tissue;²⁴ provide the material properties of the cornea;²⁵ develop strain maps of engineered tissue and a Xenopus tadpole at different stages of embryonic development;¹³ and define tumor and normal adipose human breast tissue borders.²⁶ Finally, one of the current research directions in OCE imaging has been to develop intravascular OCE for rupture-prone (vulnerable) plaque detection.²⁷

1.3.

Intravascular Elastography for Atherosclerotic Plaque Detection

The main components of atherosclerotic plaque include a large extracellular necrotic core with a thin fibrous cap infiltrated by macrophages, all of which have varying biomechanical properties.^{28, 29} Rupture of the cap induces the formation of a thrombus, which may obstruct the coronary artery, causing an acute heart attack and frequently results in patient death.^{30, 31} Detailed characterization of the arterial wall biomechanics may provide complementary information to quantify lesion stability. Both in vitro and in vivo studies have revealed that strain is higher in fatty tissue components than in fibrous plaques.³² The presence of a high-strain area that is surrounded by a low-strain region has a high predictive power to identify the vulnerable plaque with high sensitivity and specificity.³³ Thus, changes in the mechanical properties of the tissue can be detected, quantified, and correlated with clinical symptoms and inflammation markers.

Intravascular elastography is particularly used to correlate elastograms with histological characteristics of the blood vessel wall. The ultrasound community has made significant progress in developing intravascular ultrasound (IVUS) elastography,³⁴ which has been successfully used to extract arterial radial strains with a spatial resolution of 200 μm. Schmitt ³⁵ have used ultrasound elastography within carotid walls induced by the natural cardiac pulsation, and coupled to a simple inverse problem, to recover the wall elastic modulus at the blood pulsatility frequency (1 Hz). This was the first in vivo axial strain and shear distributions of atherosclerotic carotid arteries measurement. In 2008, Schmitt ³⁶ made further progress by adapting the dynamic microelastography method and formulating an inverse problem to study the radial viscoelasticity of the vessel wall. Although this has provided some success in plaque identification, there exist several limitations because vulnerable atherosclerotic plaques have structural components (e.g., fibrous caps) on the order of 50–200 μm, which lie below the resolvable limit of the IVUS imaging system. OCT is a potential technical solution to overcome these hurdles because it is not limited, in this regard, due to its inherent high resolution and provides noninvasive near-cellular-level imaging for plaque quantification.

An important application of intravascular OCT^{37, 38} is the detection of thin-cap fibroatheroma (TCFA), the most important type of vulnerable plaques. Xu ³⁹ have addressed fundamental issues that underlie the tissue characterization of OCT images obtained from coronary arteries. With high spatial resolution and, thus, the ability to visualize structures on the size scale of thin fibrous caps, intravascular OCE has the potential to provide high-resolution characterization of strains in tissue lying within 1.0–1.5 mm of the lumen interface, the region most susceptible to plaque disruption.²⁷ Chau ³² have used OCT as a basis for finite element analysis and obtained results comparable to histology methods for stress and strain analysis of atherosclerosis. Their results suggest that OCT-based finite element analysis may be a powerful tool for investigating coronary atherosclerosis and detecting vulnerable plaque. The capability of OCE to resolve TCFA is advantageous when compared to competing technologies, such as IVUS. Chan ²⁷ and Khalil ^{40, 41} have performed several studies highlighting the benefits of intravascular OCE, which may play an important role in the elasticity estimation of vulnerable plaques and provide patient risk stratification for appropriate treatment or vascular targeted therapies.

1.4.

Technique Development of Optical Coherence Elastography

When considering OCE as a diagnostic tool, two important issues must be considered. The first is the mechanical design of a loading system because an external load is usually required to excite tissues for a certain deformation. Therefore, a loading system must be able to apply a known and reproducible stress to avoid artifacts from nonuniform stress distributions, be easy to use, and be compatible with the existing time-domain (TD) or frequency-domain (FD) OCT systems. The second issue relates to data analysis for reconstruction of tissue elastograms, which is a process of combining imaging, elastography, and computational modeling to build maps of soft-tissue mechanical properties. In general, soft tissues are viscoelastic, anisotropic, and incompressible. No biological soft tissue exhibits a truly elastic response, but under some conditions, the assumption of linear elasticity is both reasonable and useful.⁴² For example, when the deformation is small (<0.1%), the nonlinearity of the elastic constants of soft tissues can be neglected.²⁵ Under the assumption that the tissue is linear elastic, isotropic, and subjected to a constant stress field, the strain field could be interpreted as a relative measure of elasticity distribution, where the strain is large in a compliant (soft) tissue, and small in a rigid (hard) tissue.⁴³ However, for anisotropic materials, such as arteries with asymmetric geometries and the presence of plaques leading to a nonhomogeneous arterial wall stress field, the material property identification is much more complicated than for isotropic materials.

Inverse problem-solving^{43, 44} methods are usually developed to solve for unknown material properties from measured displacements in anisotropic materials. Prior to solving the inverse problem, constitutive relations need to be defined to describe the behavior of individual tissues depending on the conditions of interest, including the parameters of the loading profile, material properties, geometric feature of the structure, boundary conditions, and/or a combination of these behaviors. Then, if a set of experimentally measured data (displacement, velocity, strain, natural frequency, etc., obtained by OCE) are available for the structure of interest, the material property can be characterized by minimizing the sum of the squares of the errors or discrepancy between the experimental and computed structure behavior data.^{45, 46} Elastograms of strain or modulus can then be reconstructed. Although hurdles to widespread clinical acceptance exist, short-term engineering solutions are being investigated, such that OCE may play a very important role as a diagnostic tool in the near future.

This review summarizes recent advances in OCE, including technical issues involved in the design of loading schemes associated with OCT platforms along with theoretical analysis for displacement, strain, and elastic moduli elastogram reconstruction. Clinical applications including intravascular OCE are presented, followed by a discussion of the future role of OCE in terms of technical development and clinical utility.

3.1.

Static or Quasi-Static OCE Method

OCE takes advantage of the short coherence lengths of broadband light sources to image micron-level displacement and strain distributions of individual tissue elements as they are stretched, compressed, or vibrated by an external force.⁴⁸ When static or quasi-static compression is applied to tissue, the majority of OCE techniques reported to date rely on speckle tracking⁴⁹ to estimate the relative motion of subsurface structures imaged under different applied forces. The following sections present and discuss these OCE techniques in detail.

3.1.2.

Phase-Sensitive Optical Coherence Elastography

Phase-sensitive OCE (PSOCE) is based on the measurement of phase changes induced by tissue motions in complex OCT images. Kirkpatrick ⁵⁰ and Wang ⁵⁴ developed a tissue Doppler OCE (tDOCE) approach to obtain large movement of speckles from Doppler frequency shift induced by instantaneous tissue motion. Theoretical basis of tDOCE is similar with Doppler OCT.^{55, 56} In the spectral domain, the spectral density of combined reference and sample beams is⁵⁰

Eq. 2

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{eqnarray} I_d (\upsilon) &=& S(\upsilon)\left[ 1 + \int R(\tau)d\tau + 2R_{{\rm self}}\right.\nonumber\\ &&\left. +\, 2\int {\sqrt {R(\tau)} \cos (2\pi \upsilon \tau + \phi _0)d\tau } \right], \end{eqnarray}\end{document} $$\begin{array}{ccc}\hfill I_d\left(\upsilon \right)& =& S\left(\upsilon \right)\left[1+\int R\left(\tau \right)d\tau +2R_{\mathrm{self}}\right.\hfill \\ & & \left.+2\int \sqrt{R\left(\tau \right)}\cos (2\pi \upsilon \tau +{\phi }_0)d\tau \right],\hfill \end{array}$$

where υ is the frequency of the light source, R(τ) is the normalized intensity backscattered from the scatter at time τ, ϕ₀ is the initial phase value at τ = 0, and S(υ) is the spectral density of the light source. The fourth term in the brackets represents the spectral interference between the sample and the reference and is the term that contributes to the OCT signal. Discard the first three terms and perform Fourier transform; the depth information regarding the local scatters in the sample is obtained:

Eq. 3

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} I(z) = A(z)\exp [ - i\Phi (z)]. \end{equation}\end{document} $$I\left(z\right)=A\left(z\right)\exp [-i\Phi (z\left)\right].$$

If the scatterer at position z is translated by a distance Δd(z) during the time interval Δt between two successive A-scans, then the induced phase change will be

Eq. 4

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} \Delta \Phi (z,t) = 2nk\Delta d(z), \end{equation}\end{document} $$\Delta \Phi (z,t)=2nk\Delta d\left(z\right),$$

where k is the wavenumber of the light source and n is the refractive index of the sample. The depth-resolved tissue velocity v(z,t) in the beam direction could then be obtained from the phase change, ΔΦ(z,t) by

Eq. 5

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} v(z,t) = \frac{{\Delta d}}{{\Delta t}} = \frac{{\Delta \Phi (z,t)\lambda }}{{4\pi n\Delta t}},\end{equation}\end{document} $$v(z,t)=\frac{\Delta d}{\Delta t}=\frac{\Delta \Phi (z,t)\lambda }{4\pi n\Delta t},$$

where λ is the wavelength. The strain rate [TeX:] $\dot \varepsilon (z,t)$ $\dot{\varepsilon }(z,t)$ can be obtained by

Eq. 6

[TeX:] \documentclass[12pt]{minimal}\begin{document}\begin{equation} \dot \varepsilon (z,t) = \frac{{v(z,t)}}{{z_0 }} = \frac{{\Delta \Phi (z,t)\lambda }}{{4\pi nz_0 \Delta t}},\end{equation}\end{document} $$\dot{\varepsilon }(z,t)=\frac{v(z,t)}{z_0}=\frac{\Delta \Phi (z,t)\lambda }{4\pi n{z}_0\Delta t},$$

where z ₀ is the initial depth of the sample before the tissue movement. The instantaneous tissue deformation and strain rate could then be imaged in real time, and the total displacement and strain over a time period can be obtained by integration of the instantaneous displacement and strain over the elapsed time. This approach was expanded to detecting phase change between successive OCT-B scans so that small deformation can also be measured.⁵⁷ tDOCE is faster than cross-correlation-based OCE methods, but the sensitivity is fundamentally limited by the phase sensitivity of the OCT system. Example images of velocity, displacement, strain rate, and cumulative strain maps of a phantom are illustrated in Fig. 2,⁵⁷ where the phantom was compressed repeatedly by a triangular wave.

Fig. 2

Characterization of the tissue mechanical properties of a bilayer phantom at the time instant of t = 5 s when it was subjected to a slow dynamic compression: (a) OCT structural image (in decibels), (b) wrapped phase map determined by the PSOCE system (radians), (c) instant tissue deformation (in microns) map calculated from (b) after the application of unwrapping algorithm, (d) localized velocity map (in microns per second), (e) instant strain rate map (in percent per second), and (f) instant strain map (in percent) (Ref. 57). Reproduced with permission from The American Institute of Physics.

The techniques mentioned above can obtain deformation or strain elastograms, which may be enough to show the stiffness difference between healthy and diseased tissues in scenarios such as cancer diagnosis. However, for the case of atherosclerotic plaque characterization, the absolute value of modulus of elasticity needs to be known. Moreover, as intrinsic mechanical properties of materials, the elastic moduli are thought to be more advantageous for wider clinical applications.¹ Inverse problem approaches can be applied to aid the reconstruction of distributed elastic moduli elastograms.

3.2.

Dynamic Optical Coherence Elastography Method

In dynamic excitation, samples are excited by various mechanical wave forms, where the distributions of dynamic displacements (time or space) within a small region of the samples are imaged to capture dynamic OCE signals. These OCE systems have high resolution in both axial and transverse directions with the major advantage of not requiring a cross-correlation algorithm.

Liang ^{26, 63, 65} and Xing and Boppart⁶⁴ proposed a dynamic optical coherence elastography method in which tissue was excited by optomechanical waves, such as a step or sinusoidal wave form or acoustic pressure, coaxially with the optical beam, with a piezoelectric rod actuator operating in a frequency range from a 100 Hz to kilohertz. The Young's moduli were then extracted from the detected phase-resolved signals. In detail, the sample and mechanical wave driver were modeled as a Voigt body, via the following equation:⁶³

Fig. 3

Phase-resolved OCE map of human breast tissue elasticity. (a) B-mode OCT image of breast tissue. The left side of (a) represents the adipose tissue while the right side of (a) represents the tumor tissue. (b) Histology image corresponding to (a), (c) map of elasticity by sinusoidally driven phase-resolved OCE, and (d) error map of elasticity by sinusoidally driven phase-resolved OCE. Unit for color bar is kPa (Ref. 26). Reproduced with permission from OSA. (Color online only.)

Acoustic radiation force are currently popularly used to generate an internal load noninvasively.⁶⁶ Liang ⁶⁷ presented an internal mechanical excitation method using acoustic radiation forces and developed an acoustomotive OCE based on the similar mechanical model introduced above. The acoustomotive OCE has the potential for imaging biomechanical properties in vivo. However, using these dynamic methodologies, every pixel in the OCE image or biomechanical map requires wave-equation fitting and, as a result, the processing time is too long for real-time applications. In addition, the feasibility of accurately detecting vibration amplitude in the presence of lateral scatterer motion, such as when shear waves are excited, needs to be investigated further for applicability in this model.

Adie ⁶⁸ proposed an OCE technique based on analysis of the dynamic interferometry caused by sample excitation at audio frequencies. This approach is suitable for quantitative measurement of tissue elastic properties in the 100 Hz to kilohertz frequency range, which matches the typical frequency response range of many biological tissues. The theoretical basis of this method is to expand the detected photocurrent signal of interest as a series of Bessel functions resulting in

Because dynamic OCE is an active area of research, several additional techniques are in the beginning stages of feasibility demonstration. Huang ⁶⁹ used a pressure-controlled air jet as an indenter to compress the soft tissue from the same side of imaging, in a noncontact manner and utilize the OCT signals to extract the deformation. Kennedy ⁷⁰ have designed an appropriate sample arm based on a ring actuator and also enabled excitation and imaging to be achieved from the same side of the sample. Oldenburg and Boppart⁷¹ have proposed a method using embedded magnetomotive nanotransducers to excite soft tissues. However, experimental and computational techniques are still needed to further improve all of these techniques. Because of acquisition speed and the need for coaxial optical beam and vibration excitation, the in vivo application of dynamic OCE are limited to exposed skin, such as human hands.

As previously mentioned, OCE shows great advantage over ultrasound elastography on vascular disease diagnosis. However, for applications of OCE to vascular tissue characterization, special processing methodologies are usually required.

4.1.

Variational Method

Chan ⁷² proposed a variational method to improve deformation and strain estimation in OCE. The variational method takes a data-driven approach in which velocity filtering takes place during the correlation maximization process itself. In this manner, all the available correlation data are taken into consideration in the robust velocity estimation. Specifically, the variational method incorporates prior knowledge about velocity fields in the pulsating arterial wall, where the overall variational energy functional is

The velocity estimation of an intact aortic segment was obtained experimentally by mounting the specimen horizontally and applying mechanical load (lateral direction) with a one-dimensional translation micromanipulator to approximate circumferential stretching. This method produced improved results when compared to the traditional cross-correlation method, but a priori knowledge about arterial wall behavior was required for robust estimation of tissue motion and strain. These constraints may limit the overall usefulness of this technique in a clinical scenario based on the inhomogeneity of human tissue.

In 2005, Khalil ⁴⁰ improved their OCE technique with the introduction of the nonlinear least-squares method, which minimizes the difference between computed and measured mechanical responses of soft tissue to estimate elasticity fields of soft tissues. This was an important step toward gaining quantitative elasticity information from in vivo OCT imaging of coronary arteries.

In 2006, the inverse elasticity problem approach⁷³ was used comprising of FEM-derived mechanics directly within the image registration, which is the process of transforming the different sets of data into one coordinate system. Using a gradient-based search algorithm, tissue elasticity images were reconstructed given the internal tissue displacements based on subsequent imaging as the tissue is deformed. Results of in vitro OCE measurement of a porcine aorta injected with lipid are shown in Fig. 4. A fatty region was identified at the center of the arterial wall, showing a higher contrast in both the elastogram and the modulus image, further demonstrating the potential of OCE in vascular disease diagnosis by characterizing atherosclerotic plaque.

Fig. 4

(a) OCT image of porcine aorta temporally and spatially blurred with a Gaussian filter, (b) lateral strain while stretched laterally, (c) axial strain at the same state, and (d) relative modulus image (Ref. 73). Reproduced with permission from IEEE.

4.2.

Optical Coherence Tomography Alternating-Line Elastography

To measure the radial displacement of vascular tissue, van Soest ^{74, 75} developed a catheter-based OCT alternating-line elastography (OCTALE) technique. It employs the correlation between the overlapping point-spread functions of adjacent A-scans, instead of subsequent B-mode imaging. The B-mode data are then separated into the odd and even A-scans, where acoustic forces are applied synchronously with the A-scan rate of the OCT system. This alternated sequence of A-scans, correlating to a low- or high-pressure scenario, yields odd and even displacement fields. The OCE image can be calculated by optimizing a one-dimensional cross-correlation function⁷⁵

Fig. 5

(a) Displacement and (b) strain fields resulting from the ALE algorithm, and the value of (c) the correlation coefficient. The data in (a) and (b) may be compared to the simulated data (d) and (e) used for input. (f) The OCT image used for the simulation (Ref. 75). Reproduced with permission from IOP.

The OCTALE method is less sensitive to motion artifacts and nonuniform catheter rotation than the traditional cross-correlation-based method, but it is difficult to apply in practice. The applied localized force to the vascular wall at a rate of exactly half the OCT line-scan frequency must be applied, and the frequency of the applied pressure oscillation must be locked to the instrument's line rate, which brings many requirements for the load and control systems design. However, ALE expands the potential of OCT as a powerful tool for intracoronary vulnerable plaque detection.

There are still challenges faced in deployment of OCE for in vivo catheter-based imaging. The cross-correlation between frames is not suitable for cardiovascular applications because the displacement and strain patterns induced by a change in fluid pressure in a tubular geometry differ from those resulting from a mechanical force applied in a planar geometry. Additionally, when one operates an OCE probe inside a living patient, while imaging through a rotating catheter, the images and resulting stress/strain maps are more susceptible to artifacts due to motion and optical disturbances. Arteries are typically characterized by asymmetric geometries, which together with the presence of plaques with varying compositions lead to inhomogeneous stress fields in the arterial wall. Furthermore, arterial tissues exhibit a nonlinear behavior and experience high cyclic strain levels in each single cycle of a heart beat. These strain fields can vary up to 10% at the common carotid artery or carotid bifurcation.^{76, 77} Viscoelastic models might be needed for dynamic analysis, especially for the lipid pool component of the plaques to fully characterize tissue in an effort to predict which plaques are truly vulnerable to stratify appropriate treatments or targeted cardiovascular therapies.