K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures.

For the most popular method of scan formation in Optical Coherence Tomography (OCT) based on plane-parallel scanning of the illuminating beam, we present a compact but rigorous K-space description in which the spectral representation is used to describe both the axial and lateral structure of the illuminating/received OCT signals. Along with the majority of descriptions of OCT-image formation, the discussed approach relies on the basic principle of OCT operation, in which ballistic backscattering of the illuminating light is assumed. This single-scattering assumption is the main limitation, whereas in other aspects, the presented approach is rather general. In particular, it is applicable to arbitrary beam shapes without the need for paraxial approximation or the assumption of Gaussian beams. The main result of this study is the use of the proposed K-space description to analytically derive a filtering function that allows one to digitally transform the initial 3D set of complex-valued OCT data into a desired (target) dataset of a rather general form. An essential feature of the proposed filtering procedures is the utilization of both phase and amplitude transformations, unlike conventionally discussed phase-only transformations. To illustrate the efficiency and generality of the proposed filtering function, the latter is applied to the mutual transformation of non-Gaussian beams and to the digital elimination of arbitrary aberrations at the illuminating/receiving aperture. As another example, in addition to the conventionally discussed digital refocusing enabling depth-independent lateral resolution the same as in the physical focus, we use the derived filtering function to perform digital "super-refocusing." The latter does not yet overcome the diffraction limit but readily enables lateral resolution several times better than in the initial physical focus.

Optical coherence elastography with osmotically induced strains: Preliminary demonstration for express detection of cartilage degradation.

Optical coherence elastography (OCE) demonstrated impressive abilities for diagnosing tissue types/states using differences in their biomechanics. Usually, OCE visualizes tissue deformation induced by some additional stimulus (e.g., contact compression or auxiliary elastic-wave excitation). We propose a new variant of OCE with osmotically induced straining (OIS-OCE) and demonstrate its application to assess various stages of proteoglycan content degradation in cartilage. The information-bearing signatures in OIS-OCE are the magnitude and rate of strains caused by the application of osmotically active solutions onto the sample surface. OCE examination of the induced strains does not require special tissue preparation, the osmotic stimulation is highly reproducible, and strains are observed in noncontact mode. Several minutes suffice to obtain a conclusion. These features are promising for intraoperative method usage when express assessment of tissue state is required during surgical operations. The "waterfall" images demonstrate the development of cumulative osmotic strains in control and degraded cartilage samples.

Compression OCT-elastography combined with speckle-contrast analysis as an approach to the morphological assessment of breast cancer tissue.

Currently, optical biopsy technologies are being developed for rapid and label-free visualization of biological tissue with micrometer-level resolution. They can play an important role in breast-conserving surgery guidance, detection of residual cancer cells, and targeted histological analysis. For solving these problems, compression optical coherence elastography (C-OCE) demonstrated impressive results based on differences in the elasticity of different tissue constituents. However, sometimes straightforward C-OCE-based differentiation is insufficient because of the similar stiffness of certain tissue components. We present a new automated approach to the rapid morphological assessment of human breast cancer based on the combined usage of C-OCE and speckle-contrast (SC) analysis. Using the SC analysis of structural OCT images, the threshold value of the SC coefficient was established to enable the separation of areas of adipose cells from necrotic cancer cells, even if they are highly similar in elastic properties. Consequently, the boundaries of the tumor bed can be reliably identified. The joint analysis of structural and elastographic images enables automated morphological segmentation based on the characteristic ranges of stiffness (Young's modulus) and SC coefficient established for four morphological structures of breast-cancer samples from patients post neoadjuvant chemotherapy (residual cancer cells, cancer stroma, necrotic cancer cells, and mammary adipose cells). This enabled precise automated detection of residual cancer-cell zones within the tumor bed for grading cancer response to chemotherapy. The results of C-OCE/SC morphometry highly correlated with the histology-based results (r =0.96-0.98). The combined C-OCE/SC approach has the potential to be used intraoperatively for achieving clean resection margins in breast cancer surgery and for performing targeted histological analysis of samples, including the evaluation of the efficacy of cancer chemotherapy.

Spatio-Temporal Dynamics of Diffusion-Associated Deformations of Biological Tissues and Polyacrylamide Gels Observed with Optical Coherence Elastography.

In this work, we use the method of optical coherence elastography (OCE) to enable quantitative, spatially resolved visualization of diffusion-associated deformations in the areas of maximum concentration gradients during diffusion of hyperosmotic substances in cartilaginous tissue and polyacrylamide gels. At high concentration gradients, alternating sign, near-surface deformations in porous moisture-saturated materials are observed in the first minutes of diffusion. For cartilage, the kinetics of osmotic deformations visualized by OCE, as well as the optical transmittance variations caused by the diffusion, were comparatively analyzed for several substances that are often used as optical clearing agents, i.e., glycerol, polypropylene, PEG-400 and iohexol, for which the effective diffusion coefficients were found to be 7.4 ± 1.8, 5.0 ± 0.8, 4.4 ± 0.8 and 4.6 ± 0.9 × 10-6 cm2/s, respectively. For the osmotically induced shrinkage amplitude, the influence of the organic alcohol concentration appears to be more significant than the influence of its molecular weight. The rate and amplitude of osmotically induced shrinkage and dilatation in polyacrylamide gels is found to clearly depend on the degree of their crosslinking. The obtained results show that observation of osmotic strains with the developed OCE technique can be applied for structural characterization of a wide range of porous materials, including biopolymers. In addition, it may be promising for revealing alterations in the diffusivity/permeability of biological tissues that are potentially associated with various diseases.

Application of compression optical coherence elastography for characterization of human pericardium: A pilot study.

The recent impressive progress in Compression Optical Coherence Elastography (C-OCE) demonstrated diverse biomedical applications, comprising ophthalmology, oncology, etc. High resolution of C-OCE enables spatially resolved characterization of elasticity of rather thin (thickness < 1 mm) samples, which previously was impossible. Besides Young's modulus, C-OCE enables obtaining of nonlinear stress-strain dependences for various tissues. Here, we report the first application of C-OCE to nondestructively characterize biomechanics of human pericardium, for which data of conventional tensile tests are very limited and controversial. C-OCE revealed pronounced differences among differently prepared pericardium samples. Ample understanding of the influence of chemo-mechanical treatment on pericardium biomechanics is very important because of rapidly growing usage of own patients' pericardium for replacement of aortic valve leaflets in cardio-surgery. The figure demonstrates differences in the tangent Young's modulus after glutaraldehyde-induced cross-linking for two pericardium samples. One sample was over-stretched during the preparation, which caused some damage to the tissue.

Simulating scan formation in multimodal optical coherence tomography: angular-spectrum formulation based on ballistic scattering of arbitrary-form beams.

We present a computationally highly efficient full-wave spectral model of OCT-scan formation with the following features: allowance of arbitrary phase-amplitude profile of illuminating beams; absence of paraxial approximation; utilization of broadly used approximation of ballistic scattering by discrete scatterers without limitations on their density/location and scattering strength. The model can easily incorporate the wave decay, dispersion, measurement noises with given signal-to-noise ratios and arbitrary inter-scan displacements of scatterers. We illustrate several of such abilities, including comparative simulations of OCT-scans for Bessel versus Gaussian beams, presence of arbitrary aberrations at the tissue boundary and various scatterer motions. The model flexibility and computational efficiency allow one to accurately study various properties of OCT-scans for developing new methods of their processing in various biomedical applications.

Strain and elasticity imaging in compression optical coherence elastography: The two-decade perspective and recent advances.

Quantitative mapping of deformation and elasticity in optical coherence tomography has attracted much attention of researchers during the last two decades. However, despite intense effort it took ~15 years to demonstrate optical coherence elastography (OCE) as a practically useful technique. Similarly to medical ultrasound, where elastography was first realized using the quasi-static compression principle and later shear-wave-based systems were developed, in OCE these two approaches also developed in parallel. However, although the compression OCE (C-OCE) was proposed historically earlier in the seminal paper by J. Schmitt in 1998, breakthroughs in quantitative mapping of genuine local strains and the Young's modulus in C-OCE have been reported only recently and have not yet obtained sufficient attention in reviews. In this overview, we focus on underlying principles of C-OCE; discuss various practical challenges in its realization and present examples of biomedical applications of C-OCE. The figure demonstrates OCE-visualization of complex transient strains in a corneal sample heated by an infrared laser beam.

Histological validation of in vivo assessment of cancer tissue inhomogeneity and automated morphological segmentation enabled by Optical Coherence Elastography.

We present a non-invasive (albeit contact) method based on Optical Coherence Elastography (OCE) enabling the in vivo segmentation of morphological tissue constituents, in particular, monitoring of morphological alterations during both tumor development and its response to therapies. The method uses compressional OCE to reconstruct tissue stiffness map as the first step. Then the OCE-image is divided into regions, for which the Young's modulus (stiffness) falls in specific ranges corresponding to the morphological constituents to be discriminated. These stiffness ranges (characteristic "stiffness spectra") are initially determined by careful comparison of the "gold-standard" histological data and the OCE-based stiffness map for the corresponding tissue regions. After such pre-calibration, the results of morphological segmentation of OCE-images demonstrate a striking similarity with the histological results in terms of percentage of the segmented zones. To validate the sensitivity of the OCE-method and demonstrate its high correlation with conventional histological segmentation we present results obtained in vivo on a murine model of breast cancer in comparative experimental study of the efficacy of two antitumor chemotherapeutic drugs with different mechanisms of action. The new technique allowed in vivo monitoring and quantitative segmentation of (1) viable, (2) dystrophic, (3) necrotic tumor cells and (4) edema zones very similar to morphological segmentation of histological images. Numerous applications in other experimental/clinical areas requiring rapid, nearly real-time, quantitative assessment of tissue structure can be foreseen.

In vivo assessment of functional and morphological alterations in tumors under treatment using OCT-angiography combined with OCT-elastography.

Emerging methods of anti-tumor therapies require new approaches to tumor response evaluation, especially enabling label-free diagnostics and in vivo utilization. Here, to assess the tumor early reaction and predict its long-term response, for the first time we apply in combination the recently developed OCT extensions - optical coherence angiography (OCA) and compressional optical coherence elastography (OCE), thus enabling complementary functional/microstructural tumor characterization. We study two vascular-targeted therapies of different types, (1) anti-angiogenic chemotherapy (ChT) and (2) photodynamic therapy (PDT), aimed to indirectly kill tumor cells through blood supply injury. Despite different mechanisms of anti-angiogenic action for ChT and PDT, in both cases OCA demonstrated high sensitivity to blood perfusion cessation. The new method of OCE-based morphological segmentation revealed very similar histological structure alterations. The OCE results showed high correlation with conventional histology in evaluating percentages of necrotic and viable tumor zones. Such possibilities make OCE an attractive tool enabling previously inaccessible in vivo monitoring of individual tumor response to therapies without taking multiple biopsies.

Interplay of temperature, thermal-stresses and strains in laser-assisted modification of collagenous tissues: Speckle-contrast and OCT-based studies.

Moderate heating of collagenous tissues such as cartilage and cornea by infrared laser irradiation can produce biologically nondestructive structural rearrangements and relaxation of internal stresses resulting in the tissue reshaping. The reshaping results and eventual changes in optical and biological properties of the tissue strongly depend on the laser-irradiation regime. Here, a speckle-contrast technique based on monochromatic illumination of the tissue in combination with strain mapping by means of optical coherence elastography (OCE) is applied to reveal the interplay between the temperature and thermal stress fields producing tissue modifications. The speckle-based technique ensured en face visualization of cross correlation and contrast of speckle images, with evolving proportions between contributions of temperature increase and thermal-stresses determined by temperature gradients. The speckle-technique findings are corroborated by quantitative OCE-based depth-resolved imaging of irradiation-induced strain-evolution. The revealed relationships can be used for real-time control of the reshaping procedures (e.g., for laser shaping of cartilaginous implants in otolaryngology and maxillofacial surgery) and optimization of the laser-irradiation regimes to ensure the desired reshaping using lower and biologically safer temperatures. The figure of waterfall OCE-image demonstrates how the strain-rate maximum arising in the heating-beam center gradually splits and drifts towards the zones of maximal thermal stresses located at the temperature-profile slopes.

Analysis of low-scattering regions in optical coherence tomography: applications to neurography and lymphangiography.

Analysis of semi-transparent low scattering biological structures in optical coherence tomography (OCT) has been actively pursued in the context of lymphatic imaging, with most approaches relying on the relative absence of signal as a means of detection. Here we present an alternate methodology based on spatial speckle statistics, utilizing the similarity of a distribution of given voxel intensities to the power distribution function of pure noise, to visualize the low-scattering biological structures of interest. In a human tumor xenograft murine model, we show that these correspond to lymphatic vessels and nerves; extensive histopathologic validation studies are reported to unequivocally establish this correspondence. The emerging possibility of OCT lymphangiography and neurography is novel and potentially impactful (especially the latter), although further methodology refinement is needed to distinguish between the visualized lymphatics and nerves.

OCT-elastography-based optical biopsy for breast cancer delineation and express assessment of morphological/molecular subtypes.

Application of compressional optical coherence elastography (OCE) for delineation of tumor and peri-tumoral tissue with simultaneous assessment of morphological/molecular subtypes of breast cancer is reported. The approach is based on the ability of OCE to quantitatively visualize stiffness of studied samples and then to perform a kind of OCE-based biopsy by analyzing elastographic B-scans that have sizes ~several millimeters similarly to bioptates used for "gold-standard" histological examinations. The method relies on identification of several main tissue constituents differing in their stiffness in the OCE scans. Initially the specific stiffness ranges for the analyzed tissue components (adipose tissue, fibrous and hyalinized tumor stroma, lymphocytic infiltrate and agglomerates of tumor cells) are determined via comparison of OCE and morphological/molecular data. Then assessment of non-tumor/tumor regions and tumor subtypes is made based on percentage of pixels with different characteristic stiffness ("stiffness spectrum") in the OCE image, also taking into account spatial localization of different-stiffness regions. Examples of high contrast among benign (or non-invasive) and several subtypes of invasive breast tumors in terms of their stiffness spectra are given.

Revealing structural modifications in thermomechanical reshaping of collagenous tissues using optical coherence elastography.

Moderate heating of such collagenous tissues as cornea and cartilages by infra-red laser (IR laser) irradiation is an emerging technology for nondestructive modification of the tissue shape and microstructure for a variety of applications in ophthalmology, otolaryngology and so on. Postirradiation high-resolution microscopic examination indicates the appearance of microscopic either spheroidal or crack-like narrow pores depending on the tissue type and irradiation regime. Such examinations usually require special tissue preparation (eg, staining, drying that affect microstructure themselves) and are mostly suitable for studying individual pores, whereas evaluation of their averaged parameters, especially in situ, is challenging. Here, we demonstrate the ability of optical coherence tomography (OCT) to visualize areas of pore initiation and evaluate their averaged properties by combining visualization of residual irradiation-induced tissue dilatation and evaluation of the accompanying Young-modulus reduction by OCT-based compressional elastography. We show that the averaged OCT-based data obtained in situ fairly well agree with the microscopic examination results. The results obtained develop the basis for effective and safe applications of novel nondestructive laser technologies of tissue modification in clinical practice. PICTURE: Elastographic OCT-based images of an excised rabbit eye cornea subjected to thermomechanical laser-assisted reshaping. Central panel shows resultant cumulative dilatation in cornea after moderate (~45-50°C) pulse-periodic heating by an IR laser together with distribution of the inverse Young modulus 1/E before (left) and after (right) IR irradiation. Significant modulus decrease in the center of irradiated region is caused by initiated micropores. Their parameters can be extracted by analyzing the elastographic images.

Optical coherence elastography for strain dynamics measurements in laser correction of cornea shape.

We describe the use of elastographic processing in phase-sensitive optical coherence tomography (OCT) for visualizing dynamics of strain and tissue-shape changes during laser-induced photothermal corneal reshaping, for applications in the emerging field of non-destructive and non-ablative (non-LASIK) laser vision correction. The proposed phase-processing approach based on fairly sparse data acquisition enabled rapid data processing and near-real-time visualization of dynamic strains. The approach avoids conventional phase unwrapping, yet allows for mapping strains even for significantly supra-wavelength inter-frame displacements of scatterers accompanied by multiple phase-wrapping. These developments bode well for real-time feedback systems for controlling the dynamics of corneal deformation with 10-100 ms temporal resolution, and for suitably long-term monitoring of resultant reshaping of the cornea. In ex-vivo experiments with excised rabbit eyes, we demonstrate temporal plastification of cornea that allows shape changes relevant for vision-correction applications without affecting its transparency. We demonstrate OCT's ability to detect achieving of threshold temperatures required for tissue plastification and simultaneously characterize transient and cumulative strain distributions, surface displacements, and scattering tissue properties. Comparison with previously used methods for studying laser-induced reshaping of cartilaginous tissues and numerical simulations is performed.

Optimized phase gradient measurements and phase-amplitude interplay in optical coherence elastography.

In compressional optical coherence elastography, phase-variation gradients are used for estimating quasistatic strains created in tissue. Using reference and deformed optical coherence tomography (OCT) scans, one typically compares phases from pixels with the same coordinates in both scans. Usually, this limits the allowable strains to fairly small values <10?4 to 10?3, with the caveat that such weak phase gradients may become corrupted by stronger measurement noises. Here, we extend the OCT phase-resolved elastographic methodology by (1) showing that an order of magnitude greater strains can significantly increase the accuracy of derived phase-gradient differences, while also avoiding error-phone phase-unwrapping procedures and minimizing the influence of decorrelation noise caused by suprapixel displacements, (2) discussing the appearance of artifactual stiff inclusions in resultant OCT elastograms in the vicinity of bright scatterers due to the amplitude-phase interplay in phase-variation measurements, and (3) deriving/evaluating methods of phase-gradient estimation that can outperform conventionally used least-square gradient fitting. We present analytical arguments, numerical simulations, and experimental examples to demonstrate the advantages of the proposed optimized phase-variation methodology.

Hybrid method of strain estimation in optical coherence elastography using combined sub-wavelength phase measurements and supra-pixel displacement tracking.

A novel hybrid method which combines sub-wavelength-scale phase measurements and pixel-scale displacement tracking for robust strain mapping in compressional optical coherence elastography is proposed. Unlike majority of OCE methods it does not rely on initial reconstruction of displacements and does not suffer from the phase-wrapping problem for super-wavelength displacements. Its robustness is enabled by direct fitting of local phase gradients obviating the necessity of phase unwrapping and error-prone numerical differentiation. Furthermore, axial displacements significantly exceeding not only the optical wavelength, but pixel scales (i.e., multiple wavelengths) can be efficiently tracked and compensated. This feature strongly reduces errors in phase-gradient estimation and ensures high robustness with respect to both additive and decorrelation noises. Illustration of exceptionally high tolerance of the proposed method to noises: contrast of only 25% in the stiffness of the layers is clearly seen in the strain map even for equal intensities of the OCT signal and additive noise (SNR = 0 dB).

Nonlinear scattering of acoustic waves by natural and artificially generated subsurface bubble layers in sea.

The paper describes nonlinear effects due to a biharmonic acoustic signal scattering from air bubbles in the sea. The results of field experiments in a shallow sea are presented. Two waves radiated at frequencies 30 and 31-37 kHz generated backscattered signals at sum and difference frequencies in a bubble layer. A motorboat propeller was used to generate bubbles with different concentrations at different times, up to the return to the natural subsurface layer. Theoretical consideration is given for these effects. The experimental data are in a reasonably good agreement with theoretical predictions.