Phase-sensitive Optical Coherence Elastography Research Articles

Computationally efficient adaptive optimization of vector-method parameters for phase-sensitive strain estimation in optical coherence elastography

A new method for automatic adaptive optimization of strain estimation in phase-sensitive optical coherence tomography (OCT) is introduced. More specifically, this paper focuses on optimizing the estimation of strain using the vector method, in which OCT signals are treated as vectors in the complex plane. In phase-sensitive optical coherence elastography, the tissue strain is extracted from the interframe phase variation between the complex-valued scans acquired for the initial and deformed tissue. This phase variation is proportional to interframe displacements of scatterers and corresponds to the argument of the pixel-by-pixel product of the initial OCT scan and complex-conjugate deformed scan. Measurement noises and the so-called ‘speckle noise’ that are intrinsic to OCT scans cause degradation of the derived scan obtained by such multiplication. To mitigate the noise influence, complex-valued pixel amplitudes in the derived scan are usually averaged over a certain window. The interframe strain is found by estimating the gradient of the interframe phase difference. The noise influence on the strain estimation can also be reduced by increasing the scale over which the phase-variation gradient is estimated. However, choosing a too large window for preliminary averaging may significantly distort the reconstructed strain distribution. Similarly, a too large scale for gradient estimation may also cause errors in the estimated-strain magnitude and even its sign (because of possible phase wrapping). Therefore, appropriately performed adaptive choice of the strain-estimation parameters can greatly improve the quality of strain estimation. Here, we present a unified approach for adaptive choice of both the averaging-window size and gradient-estimation scale that were initially considered separately. The new method is computationally simplified but enables approximately the same strain-estimation quality, as demonstrated using both simulated and experimental OCT data.

Phase unwrapping for MHz optical coherence elastography and application to brain tumor tissue.

During neuro-oncologic surgery, phase-sensitive optical coherence elastography (OCE) can be valuable for distinguishing between healthy and diseased tissue. However, the phase unwrapping process required to retrieve the original phase signal is a challenging and critical task. To address this issue, we demonstrate a one-dimensional unwrapping algorithm that recovers the phase signal from a 3.2 MHz OCE system. With a processing time of approximately 0.11 s per frame on the GPU, multiple 2π wraps are detected and corrected. By utilizing this approach, exact and reproducible information on tissue deformation can be obtained with pixel accuracy over the entire acquisition time. Measurements of brain tumor-mimicking phantoms and human ex vivo brain tumor samples verified the algorithm's reliability. The tissue samples were subjected to a 200 ms short air pulse. A correlation with histological findings confirmed the algorithm's dependability.

Dual-convolutional neural network-enhanced strain estimation method for optical coherence elastography.

Strain estimation is vital in phase-sensitive optical coherence elastography (PhS-OCE). In this Letter, we introduce a novel, to the best of our knowledge, method to improve strain estimation by using a dual-convolutional neural network (Dual-CNN). This approach requires two sets of PhS-OCE systems: a high-resolution system for high-quality training data and a cost-effective standard-resolution system for practical measurements. During training, high-resolution strain results acquired from the former system and the pre-existing strain estimation CNN serve as label data, while the narrowed light source-acquired standard-resolution phase results act as input data. By training a new network with this data, high-quality strain results can be estimated from standard-resolution PhS-OCE phase results. Comparison experiments show that the proposed Dual-CNN can preserve the strain quality even when the light source bandwidth is reduced by over 80%.

Optimization of Preliminary Vector Averaging for Improving Strain-Estimation Accuracy in Phase-Sensitive Optical Coherence Elastography

Optimization of Preliminary Vector Averaging for Improving Strain-Estimation Accuracy in Phase-Sensitive Optical Coherence Elastography

Vector method of strain estimation in OCT-elastography with adaptive choice of scale for estimating interframe phase-variation gradients

In this paper we present a method which significantly improves strain-estimation quality in phase-sensitive optical coherence elastography (OCE). Specifically, we consider the realization of phase-sensitive OCE termed ‘vector method’, among main advantages of which are its high computational efficiency and high robustness with respect to measurement noises. The method does not require any search operations, but the quality of local strain estimation heavily depends on the quality of numerical spatial differentiation of inter-frame phase variations. This differentiation does not require phase unwrapping even for supra-wavelength displacements of scatterers, but the differentiation results depend on the chosen scale for phase-gradient estimation. Either too small or too large scale may strongly degrade the results of elastographic visualization, especially in the presence of pronounced spatio-temporal strain inhomogeneity. The proposed adaptive automatic choice of the differentiation scale complements earlier proposed vector averaging and significantly improves strain-mapping quality in OCE. The method efficiency is demonstrated using both numerically simulated and real OCT scans.

The lens capsule significantly affects the viscoelastic properties of the lens as quantified by optical coherence elastography.

The crystalline lens is a transparent, biconvex structure that has its curvature and refractive power modulated to focus light onto the retina. This intrinsic morphological adjustment of the lens to fulfill changing visual demands is achieved by the coordinated interaction between the lens and its suspension system, which includes the lens capsule. Thus, characterizing the influence of the lens capsule on the whole lens's biomechanical properties is important for understanding the physiological process of accommodation and early diagnosis and treatment of lenticular diseases. In this study, we assessed the viscoelastic properties of the lens using phase-sensitive optical coherence elastography (PhS-OCE) coupled with acoustic radiation force (ARF) excitation. The elastic wave propagation induced by ARF excitation, which was focused on the surface of the lens, was tracked with phase-sensitive optical coherence tomography. Experiments were conducted on eight freshly excised porcine lenses before and after the capsular bag was dissected away. Results showed that the group velocity of the surface elastic wave, , in the lens with the capsule intact ( ) was significantly higher (p < 0.001) than after the capsule was removed ( ). Similarly, the viscoelastic assessment using a model that utilizes the dispersion of a surface wave showed that both Young's modulus, E, and shear viscosity coefficient, η, of the encapsulated lens ( ) were significantly higher than that of the decapsulated lens ( ). These findings, together with the geometrical change upon removal of the capsule, indicate that the capsule plays a critical role in determining the viscoelastic properties of the crystalline lens.

Simultaneously measurement of strain field and Poisson’s ratio by using an off-axis phase-sensitive optical coherence elastography

Phase-sensitive optical coherence elastography (PhS-OCE) is a novel functional imaging modality capable of mapping strain fields inside semi-transparent materials. In this work, an off-axis PhS-OCE was further developed to measure strain field and Poisson’s ratio simultaneously. Based on the intrinsic equations of continuum mechanics, the relationship between the elastic parameters of the measured material and the physical quantity (i.e. optical path difference) of PhS-OCE was first established. For validation, the depth-resolved strain field and Poisson’s ratio of a silicone rubber film were quantitatively measured during tensile tests. The experimental results, such as the estimates for Poisson’s ratio, agreed with the reference values. Moreover, phase difference maps of bilayer composites were discussed, indicating the effectiveness and potential of the proposed off-axis measurement method.

Analysis of strain estimation methods in phase-sensitive compression optical coherence elastography.

In compression optical coherence elastography (OCE), deformation is quantified as the local strain at each pixel in the OCT field-of-view. A range of strain estimation methods have been demonstrated, yet it is unclear which method provides the best performance. Here, we analyze the two most prevalent strain estimation methods used in phase-sensitive compression OCE, i.e., weighted least squares (WLS) and the vector method. We introduce a framework to compare strain imaging metrics, incorporating strain sensitivity, strain signal-to-noise ratio (SNR), strain resolution, and strain accuracy. In addition, we propose a new phase unwrapping algorithm in OCE, fast phase unwrapping (FPU), and combine it with WLS, termed WLSFPU. Using the framework, we compare this new strain estimation method with both a current implementation of WLS that incorporates weighted phase unwrapping (WPU), termed WLSWPU, and the vector method. Our analysis reveals that the three methods provide similar strain sensitivity, strain SNR, and strain resolution, but that WLSFPU extends the dynamic range of accurate, measurable local strain, e.g., measuring a strain of 2.5 mɛ with ∼4% error, that is ×11 and ×15 smaller than the error measured using WLSWPU and the vector method, respectively. We also demonstrate, for the first time, the capability to detect sub-resolution contrast in compression OCE, i.e., changes in strain occurring within the strain axial resolution, and how this contrast varies between the different strain estimation methods. Lastly, we compare the performance of the three strain estimation methods on mouse skeletal muscle and human breast tissue and demonstrate that WLSFPU avoids strain imaging artifacts resulting from phase unwrapping errors in WLSWPU and provides improved contrast over the other two methods.

Real-Time Strain and Elasticity Imaging in Phase-Sensitive Optical Coherence Elastography Using a Computationally Efficient Realization of the Vector Method

We present a real-time realization of OCT-based elastographic mapping local strains and distribution of the Young’s modulus in biological tissues, which is in high demand for biomedical usage. The described variant exploits the principle of Compression Optical Coherence Elastography (C-OCE) and uses processing of phase-sensitive OCT signals. The strain is estimated by finding local axial gradients of interframe phase variations. Instead of the popular least-squares method for finding these gradients, we use the vector approach, one of its advantages being increased computational efficiency. Here, we present a modified, especially fast variant of this approach. In contrast to conventional correlation-based methods and previously used phase-resolved methods, the described method does not use any search operations or local calculations over a sliding window. Rather, it obtains local strain maps (and then elasticity maps) using several transformations represented as matrix operations applied to entire complex-valued OCT scans. We first elucidate the difference of the proposed method from the previously used correlational and phase-resolved methods and then describe the proposed method realization in a medical OCT device, in which for real-time processing, a “typical” central processor (e.g., Intel Core i7-8850H) is sufficient. Representative examples of on-flight obtained elastographic images are given. These results open prospects for broad use of affordable OCT devices for high-resolution elastographic vitalization in numerous biomedical applications, including the use in clinic.

Deep-learning-based approach for strain estimation in phase-sensitive optical coherence elastography.

In this Letter, a deep-learning-based approach is proposed for estimating the strain field distributions in phase-sensitive optical coherence elastography. The method first uses the simulated wrapped phase maps and corresponding phase-gradient maps to train the strain estimation convolution neural network (CNN) and then employs the trained CNN to calculate the strain fields from measured phase-difference maps. Two specimens with different deformations, one with homogeneous and the other with heterogeneous, were measured for validation. The strain field distributions of the specimens estimated by different approaches were compared. The results indicate that the proposed deep-learning-based approach features much better performance than the popular vector method, enhancing the SNR of the strain results by 21.6 dB.

Adaptive incremental method for strain estimation in phase-sensitive optical coherence elastography.

We proposed an adaptive incremental method for the cumulative strain estimation in phase-sensitive optical coherence elastography. The method firstly counts the amount of phase noise points by mapping a binary noise map. After the noise threshold value is preset, the interframe interval is adaptively adjusted in terms of the phase noise ratio. Finally, the efficient estimation of cumulative strain is implemented by reducing the cumulative number. Since the level of phase noise is related to the different strain rates in accordance with the speckle decorrelation, the proposed method can estimate the large strains with high computation efficiency as well as signal-to-noise ratio (SNR) enhancement in nonlinear change of sample deformations. Real experiments of visualizing polymerization shrinkage with nonlinear change of deformations were performed to prove the superiority of adaptive incremental method in estimating the large strains. The proposed method expands the practicability of the incremental method in more complex scenes.

Analysis of spatial resolution in phase-sensitive compression optical coherence elastography.

Optical coherence elastography (OCE) is emerging as a method to image the mechanical properties of tissue on the microscale. However, the spatial resolution, a main advantage of OCE, has not been investigated and is not trivial to evaluate. To address this, we present a framework to analyze resolution in phase-sensitive compression OCE that incorporates the three main determinants of resolution: mechanical deformation of the sample, detection of this deformation using optical coherence tomography (OCT), and signal processing to estimate local axial strain. We demonstrate for the first time, through close correspondence between experiment and simulation of structured phantoms, that resolution in compression OCE is both spatially varying and sample dependent, which we link to the discrepancies between the model of elasticity and the mechanical deformation of the sample. We demonstrate that resolution is dependent on factors such as feature size and mechanical contrast. We believe that the analysis of image formation provided by our framework can expedite the development of compression OCE.

Enhancing the dynamic range of phase-sensitive optical coherence elastography by overcoming speckle decorrelation.

Phase-sensitive optical coherence elastography (PhS-OCE) is a high-sensitivity method for measuring internal displacement fields of semi-transparent materials. Although the displacement measurement sensitivity of PhS-OCE reaches sub-nanometer level, the dynamic range of the measured displacements is limited to micrometers due to displacement-induced speckle decorrelation. In this Letter, a displacement tracking method is developed to overcome this limitation. The method uses a subset-based match approach and takes the noise number of the phase difference map as the match quality, which can effectively track both axial and lateral displacements. For validation, the phase changes inside the polymer samples due to the displacements produced by the temperature/mechanical load changing were measured. The results show that many previously undetectable mechanical behaviors can be quantitatively detected after applying the proposed method.

Assessing the biomechanical properties of the porcine crystalline lens as a function of intraocular pressure with optical coherence elastography.

In this study, we investigated the relationship between the biomechanical properties of the crystalline lens and intraocular pressure (IOP) using a confocal acoustic radiation force (ARF) and phase-sensitive optical coherence elastography (OCE) system. ARF induced a small displacement at the apex of porcine lenses in situ at various artificially controlled IOPs. Maximum displacement, relaxation rate, and Young's modulus were utilized to assess the stiffness of the crystalline lens. The results showed that the stiffness of the crystalline increased as IOP increased, but the lens stiffening was not as significant as the stiffening of other ocular tissues such as the cornea and the sclera. A mechanical hysteresis in the lens was also observed while cycling IOP, indicating that the viscoelastic response of the lens is crucial to fully understanding its biomechanical properties.

Vector method for strain estimation in phase-sensitive optical coherence elastography

A noise-tolerant approach to strain estimation in phase-sensitive optical coherence elastography, robust to decorrelation distortions, is discussed. The method is based on evaluation of interframe phase-variation gradient, but its main feature is that the phase is singled out at the very last step of the gradient estimation. All intermediate steps operate with complex-valued optical coherence tomography (OCT) signals represented as vectors in the complex plane (hence, we call this approach the ‘vector’ method). In comparison with such a popular method as least-square fitting of the phase-difference slope over a selected region (even in the improved variant with amplitude weighting for suppressing small-amplitude noisy pixels), the vector approach demonstrates superior tolerance to both additive noise in the receiving system and speckle-decorrelation caused by tissue straining. Another advantage of the vector approach is that it obviates the usual necessity of error-prone phase unwrapping. Here, special attention is paid to modifications of the vector method that make it especially suitable for processing deformations with significant lateral inhomogeneity, which often occur in real situations. The method’s advantages are demonstrated using both simulated and real OCT scans obtained during reshaping of a collagenous tissue sample irradiated by an IR laser beam producing complex spatially inhomogeneous deformations.

Common-path phase-sensitive optical coherence tomography provides enhanced phase stability and detection sensitivity for dynamic elastography.

Phase-sensitive optical coherence elastography (PhS-OCE) is an emerging optical technique to quantify soft-tissue biomechanical properties. We implemented a common-path OCT design to enhance displacement sensitivity and optical phase stability for dynamic elastography imaging. The background phase stability was greater in common-path PhS-OCE (0.24 ± 0.07nm) than conventional PhS-OCE (1.60 ± 0.11μm). The coefficient of variation for surface displacement measurements using conventional PhS-OCE averaged 11% versus 2% for common-path PhS-OCE. Young's modulus estimates showed good precision (95% CIs) for tissue phantoms: 24.96 ± 2.18kPa (1% agar), 49.69 ± 4.87kPa (1.5% agar), and 116.08 ± 12.14kPa (2% agar), respectively. Common-path PhS-OCE effectively reduced the amplitude of background dynamic optical phase instability to a sub-nanometer level, which provided a larger dynamic detection range and higher detection sensitivity for surface displacement measurements than conventional PhS-OCE.

Lorentz force optical coherence elastography.

Quantifying tissue biomechanical properties can assist in detection of abnormalities and monitoring disease progression and/or response to a therapy. Optical coherence elastography (OCE) has emerged as a promising technique for noninvasively characterizing tissue biomechanical properties. Several mechanical loading techniques have been proposed to induce static or transient deformations in tissues, but each has its own areas of applications and limitations. This study demonstrates the combination of Lorentz force excitation and phase-sensitive OCE at ?1.5??million A-lines per second to quantify the elasticity of tissue by directly imaging Lorentz force-induced elastic waves. This method of tissue excitation opens the possibility of a wide range of investigations using tissue biocurrents and conductivity for biomechanical analysis.

Phase-sensitive optical coherence elastography at 1.5 million A-Lines per second.

Shear-wave imaging optical coherence elastography (SWI-OCE) is an emerging method for 3D quantitative assessment of tissue local mechanical properties based on imaging and analysis of elastic wave propagation. Current methods for SWI-OCE involve multiple temporal optical coherence tomography scans (M-mode) at different spatial locations across tissue surface (B- and C-modes). This requires an excitation for each measurement position leading to clinically unacceptable long acquisition times up to tens of minutes. In this Letter, we demonstrate, for the first time, noncontact true kilohertz frame-rate OCE by combining a Fourier domain mode-locked swept source laser with an A-scan rate of ∼1.5 MHz and a focused air-pulse as an elastic wave excitation source. The propagation of the elastic wave in the sample was imaged at a frame rate of ∼7.3 kHz. Therefore, to quantify the elastic wave propagation velocity in a single direction, only a single excitation was needed. This method was validated by quantifying the elasticity of tissue-mimicking agar phantoms as well as of a porcine cornea ex vivo at different intraocular pressures. The results demonstrate that this method can reduce the acquisition time of an elastogram to milliseconds.

Assessing age-related changes in the biomechanical properties of rabbit lens using a coaligned ultrasound and optical coherence elastography system.

To evaluate the capability of a novel, coaligned focused ultrasound and phase-sensitive optical coherence elastography (US-OCE) system to assess age-related changes in biomechanical properties of the crystalline lens in situ. Low-amplitude elastic deformations in young and mature rabbit lenses were measured by an US-OCE system consisting of a spectral-domain optical coherence tomography (OCT) system coaligned with a focused ultrasound system used to produce a transient force on the lens surface. Uniaxial compressional tests were used to validate the OCE data. The OCE measurements showed that the maximum displacements of the young rabbit lenses were significantly larger than those of the mature lenses, indicating a gradual increase of the lens stiffness with age. Temporal analyses of the displacements also demonstrate a similar trend of elastic properties in these lenses. The stress-strain measurements using uniaxial mechanical tests confirmed the results obtained by the US-OCE system. The results demonstrate that the US-OCE system can be used for noninvasive analysis and quantification of lens biomechanical properties in situ and possibly in vivo.

Analysis of image formation in optical coherence elastography using a multiphysics approach.

IMAGE FORMATION IN OPTICAL COHERENCE ELASTOGRAPHY (OCE) RESULTS FROM A COMBINATION OF TWO PROCESSES: the mechanical deformation imparted to the sample and the detection of the resulting displacement using optical coherence tomography (OCT). We present a multiphysics model of these processes, validated by simulating strain elastograms acquired using phase-sensitive compression OCE, and demonstrating close correspondence with experimental results. Using the model, we present evidence that the approximation commonly used to infer sample displacement in phase-sensitive OCE is invalidated for smaller deformations than has been previously considered, significantly affecting the measurement precision, as quantified by the displacement sensitivity and the elastogram signal-to-noise ratio. We show how the precision of OCE is affected not only by OCT shot-noise, as is usually considered, but additionally by phase decorrelation due to the sample deformation. This multiphysics model provides a general framework that could be used to compare and contrast different OCE techniques.