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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.

We report the first application of compression optical coherence elastography (C-OCE) to evaluate both linear and nonlinear elastic properties of lymph nodes (LNs) for assessing their status, which is an important factor for detecting metastasis and staging breast cancer. The reported study involved 27 excised sentinel and axillary LNs from 24 patients with breast cancer, including normal LNs (n = 6), reactive LNs with follicular hyperplasia (n = 7) and sinus histiocytosis (n = 8), and metastatic LNs (n = 6). C-OCE data were compared with co-registered gold-standard histopathology and demonstrated a significantly higher contrast in differentiation of LNs as compared to structural optical coherence tomography imaging. Normal LNs are characterized by low stiffness values in the areas of LN cortex (600 kPa). Since in terms of the tangent Young’s modulus there remained an appreciable overlap among these types of LNs, we also evaluated their elastic nonlinearity parameters. Complementary usage of both linear and nonlinear elastic parameters enabled very clear differentiation of all four main states of LNs. Thus, C-OCE imaging demonstrates high potential for future intraoperative usage to rapidly determine the LN status during breast-conserving surgery and to assess the extent of the cancer cells propagation in regional lymphatic collectors for preserving benign LNs. This is important for reducing the associated risks and complications (such as lymphedema) from excessive surgical removal of lymphoid structures.

Soft biological tissues, breast cancer tissues in particular, often manifest pronounced nonlinear elasticity, i.e., strong dependence of their Young’s modulus on the applied stress. We showed that compression optical coherence elastography (C-OCE) is a promising tool enabling the evaluation of nonlinear properties in addition to the conventionally discussed Young’s modulus in order to improve diagnostic accuracy of elastographic examination of tumorous tissues. The aim of this study was to reveal and quantify variations in stiffness for various breast tissue components depending on the applied pressure. We discussed nonlinear elastic properties of different breast cancer samples excised from 50 patients during breast-conserving surgery. Significant differences were found among various subtypes of tumorous and nontumorous breast tissues in terms of the initial Young’s modulus (estimated for stress < 1 kPa) and the nonlinearity parameter determining the rate of stiffness increase with increasing stress. However, Young’s modulus alone or the nonlinearity parameter alone may be insufficient to differentiate some malignant breast tissue subtypes from benign. For instance, benign fibrous stroma and fibrous stroma with isolated individual cancer cells or small agglomerates of cancer cells do not yet exhibit significant difference in the Young’s modulus. Nevertheless, they can be clearly singled out by their nonlinearity parameter, which is the main novelty of the proposed OCE-based discrimination of various breast tissue subtypes. This ability of OCE is very important for finding a clean resection boundary. Overall, morphological segmentation of OCE images accounting for both linear and nonlinear elastic parameters strongly enhances the correspondence with the histological slices and radically improves the diagnostic possibilities of C-OCE for a reliable clinical outcome.

Fracture geometry, density, and distribution control fluid and thermal transport in low porosity rocks, as well as their seismic attributes. The creation of cracks throughout the matrix can result ...

Linear elastic moduli of solids with similar chemical compositions usually vary fairly insignificantly. However, for a broad class of apparently similar materials, their higher-order (nonlinear) moduli may differ by many times or even by orders of magnitude. Besides their large magnitude, nonlinear effects often demonstrate qualitative/functional features inconsistent with predictions of the classical theory of nonlinear elasticity based on consideration of weak lattice (atomic) nonlinearity. The latter is mostly applicable to ideal crystals and flawless amorphous solids, whereas the presence of structural heterogeneities can drastically modify the acoustic nonlinearity of materials without appreciable variation in the linear elastic properties. Despite often rather nontrivial/nonstraightforward relationships between microstructural features of the material and the resultant “nonclassical” acoustic nonlinearity, the extremely high structural sensitivity makes utilization of nonlinear acoustic effects attractive for a broad range of diagnostic applications that have been emerging in recent years in various areas—from seismic sounding and nondestructive testing to materials characterization down to the nanoscale.

We present a computationally efficient full-wave spectral model of OCT-scan formation with the following capabilities/features: (i) the illuminating beam may have arbitrary phase-amplitude profile with allowance of a sharp diaphragm; (ii) paraxial approximation that limits the degree of focusing/divergence is not used; (iii) the broadly used approximation of ballistic (single) scattering by discrete scatterers is assumed without additional limitations on the density of scatterers, their distribution in space and scattering strengths with possible frequency-dependence; (iv) besides rigorous accounting for the influence of focusing/divergence of the waves, factors describing the wave decay can readily be introduced by analogy with Monte-Carlo approaches; (v) arbitrary measurement noises can easily be added to simulate required signal-to-noise ratios. The model also allows one to account for arbitrary (e.g., random or flow/deformation-induced) displacements of scatterers between subsequently generated scans. Thus, in view of the above-listed features the model can be characterized as comprehensive in the framework of ballistic scattering by discrete scatterers. The model is computationally efficient due to the use of only rapid summations and fast Fourier transforms. Main model features are illustrated, including simulations of OCT scans for a nearly non-diverging Bessel beam and a focused Gaussian beam, with the possibility to introduce at the tissue boundary arbitrary aberrations represented via Zernike polynomials often utilized for describing aberrations in ophthalmology. The unprecedented flexibility and high computational efficacy of the model open a broad range of possibilities for studying OCT-scan properties and developing new methods of their processing for biomedical diagnostics.

Laser-assisted relaxation of internal stresses can be used to stabilize the new shape of cartilaginous implants. The ability of cartilage tissue to experience irreversible deformation under certain conditions, as well as to restore its original configuration after external mechanical stress, is studied in near real time using a new method of optical coherent elastography (OCE), developed to visualize slow deformation. The OCE technique allows one to monitor the efficiency of laser-induced stress relaxation at 1–2 minute intervals using 2D subsurface strain mapping. It has been shown that the redistribution of the interstitial fluid due to the applied load is an important factor for the mechanism of "shape memory" of the cartilage. Deviations in the behavior of cartilage from the usual elastic properties of homogeneous materials, such as subsurface dilatation opposing the applied load, are identified and analyzed.

This report presents an overview of recent progress in the development of novel OCE-based technologies enabling non-invasive morphological segmentation of tumor tissues during their natural development and response to therapies. The approach is based on preliminary quantitative assessment of characteristic elasticity ranges corresponding to the segmented morphological constituents (“quasistatic elasto-spectroscopy”). It has been found that such constituents are characterized by fairly well separated ranges of the Young’s modulus, which makes it possible to automatically segment up to 4-6 such zones in OCE-based elasticity maps. High consistency of such OCE-based procedure with conventional morphological segmentation of histological slides in terms of percentages of the segmented-zone areas has been demonstrated. Unlike invasive, time-consuming and laborious histological studies the developed OCE-based segmentation is non-invasive and can be performed even in vivo. High accuracy and sensitivity of the OCE-based-segmentation was demonstrated in vivo for two different types of model tumors (4T1 and Ct26) treated by PDT and chemotherapies. The OCE-based analysis can readily be combined with such OCT-based extensions as texture analysis and OCT-based angiography. The latter opens the possibility to combine morphological assessment with functional characterization of tumor response to therapies. OCE-based characterization of mechanical heterogeneity and elasticity spectra of tumors has also proven to be efficient for express assessment of patients’ breast-cancer subtypes. Overall, the developed OCE-based assessment in many applications suggests a rapid and in vivo feasible alternative to conventional histology and can be efficiently used in a wide range of biomedical problems.

An important factor in assessing tumor status for determining therapeutic and surgical tactics is the study of its morphological structure. In particular, preoperative differentiation/grading of colorectal adenocarcinomas is very important for the adjustment of neoadjuvant therapy, surgical technique choice and survival prediction. To achieve the maximum benefit and to avoid unnecessary side effects, the ability to distinguish high-grade from low-grade colorectal adenocarcinoma, as well as identification of patients with high recurrence risk before the possible initiation of treatment will increase the quality and duration of patients' life. Taking into account the peculiarities of the biology of intestinal cancer, optical coherence elastography, as a method of studying tissue structure at a shallow depth, may be promising in the study of colorectal adenocarcinoma. Possibilities of optical coherence elastography in differentiating low-grade and high-grade types of colorectal adenocarcinoma are demonstrated in this study. The reported results are based on revealed qualitative criteria for assessment of OCE images in combination with quantitative statistically significant differences in characteristic stiffness values for low-grade and high-grade colorectal adenocarcinomas.

An understanding of micro- and macrofracture behavior in low porosity rocks is pertinent to several areas of energy and environmental science such as petroleum production, carbon sequestration, and enhancement of technologies based on geothermal energy, etc. For example, the carbonate reservoirs in dolomitic or micritic formations with matrix porosities below 6% suggest the importance of fracture-augmented permeability in production. Similarly, hydrocarbons have been found on nearly every continent in tight basement rocks, all of which have little matrix porosity and their permeability therefore rely solely on hydraulic connectivity from fractures. For geothermal energy, various igneous and sedimentary rocks (granites, basalts, and limestones) are being exploited across the globe, with some of the lowest porosity and permeability. In all these cases, fractures are necessary to improve rock permeability and thermal exchange between the rock and working fluid, which can be enabled by hydraulic stimulation, as well as by secondary cracking due to extreme temperature gradients from the injection of cold water. The fracture geometry, density, and distribution all together control not only fluid and thermal transport in the rocks, but also their seismic attributes that can be used to extract information about the fractures. In order to accurately interpret the seismo-acoustic data (usually, the velocities of compression and shear waves) reliable rock physics models are required. Here, we report the results of interpretation of such experimental data for both as-cored rock samples and those subjected to thermo-hydro-chemo-mechanical damage (THCMD) in the laboratory. For interpretation, we use a convenient model of fractured rock in which fractures are represented as planar defects with decoupled shear and normal compliances. The application of such an approach makes it possible to assess and compare the elastic properties of fractures in the rocks before and after application of THCMD procedures. For the analyzed samples of granites, basalts, and limestones it has been found that for a significant portion of rocks, the ratio of normal-to-shear compliances of cracks significantly differ from the value typical of conventionally assumed penny-shape cracks. Furthermore, for some samples, this ratio appears to be noticeably different for fractures existing in the as-cored rock and arising in the same rock after THCMD procedures. These results indicate that damage to a rock typically changes its compliance ratio since the old and new cracks are likely to have different elastic properties. Our results are also consistent with the notion that a specific damage process occurring for a given microstructure will consistently create cracks with a particular set of elastic properties. The proposed methodology for assessment of elastic properties of cracks in rock samples subjected to thermo-hydro-chemo-mechanical damage has given previously inaccessible useful information about the elastic properties of fractures and can be extended to interpretation of seismic attributes of rocks for a broad range of other applications.

We present a novel method, which by analogy with the term "mass-spectroscopy" can be called "quasistatic elasto-spectoscopy" based on quantitative compressional Optical Coherence Elastogrphy (C-OCE). The method relies on initial determining of characteristic stiffness ranges for various morphological components of the tissue by comparing the OCE-based stiffness maps and histology. Such pre-calibration allows one to perform morphological segmentation of OCE-images demonstrating excellent correlation with segmentation of conventional histological images, but can be performed using freshly-extracted samples and even in vivo.

We present a robust semi-analytical multi-factor model of OCT-scan formation with rigorous accounting for the beam-focusing effects. It is based on numerical summation of the contributions of the localized sub-resolution scatterers, accounting for variations in the phase-amplitude parameters of the incident and backscattered optical waves, with a subsequent integration of the latter over the objective aperture. The main advantage of presented model is its convenience to account for scatterer motions in comparison with classical Monte-Carlo OCT-simulation approaches. In view of difficulties in performing highly-controlled phantom experiments, application of an adequate numerical model opens very flexible and convenient possibilities for evaluating the influence of scatter motions using numerically simulated OCT scans. The numerical model readily allows one to introduce various (e.g., regular/irregular or mixed) types of scatterer motions.

The possibility to assess molecular-biological and morphological features of particular breast cancer types can improve the precision of resection margin detection and enable accurate determining of the tumor aggressiveness, which is important for treatment selection. To enable reliable differentiation of breast-cancer subtypes and evaluation of resection margin, without performing conventional histological procedures, here we apply cross-polarization optical coherence tomography (CP-OCT) and compare it with a novel variant of compressional optical coherence elastography (C-OCE) in terms of the diagnostic accuracy (Ac) with histological verification. The study used 70 excised breast cancer specimens with different morphological structure and molecular status (Luminal A, Luminal B, Her2/Neo+, non-luminal and triple-negative cancer). Our first aim was to formulate convenient criteria of visual assessment of CP-OCT and C-OCE images intended (i) to differentiate tumorous and non-tumorous tissues and (ii) to enable more precise differentiation among different malignant states. We identified such criteria based on the presence of heterogeneities and characteristics of signal attenuation in CP-OCT images, as well as the presence of inclusions/mosaic structures combined with visually feasible assessment of several stiffness grades in C-OCE images. Secondly, we performed a blinded reader study of the Ac of C-OCE versus CP-OCT, for delineation of tumorous versus non-tumorous tissues followed by identification of breast cancer subtypes. For tumor detection, C-OCE showed higher specificity than CP-OCT (97.5% versus 93.3%) and higher Ac (96.0 versus 92.4%). For the first time, the Ac of C-OCE and CP-OCT were evaluated for differentiation between non-invasive and invasive breast cancer (90.4% and 82.5%, respectively). Furthermore, for invasive cancers, the difference between invasive but low-aggressive and highly-aggressive subtypes can be detected. For differentiation between non-tumorous tissue and low-aggressive breast-cancer subtypes, Ac was 95.7% for C-OCE and 88.1% for CP-OCT. For differentiation between non-tumorous tissue and highly-aggressive breast cancers, Ac was found to be 98.3% for C-OCE and 97.2% for CP-OCT. In all cases C-OCE showed better diagnostic parameters independently of the tumor type. These findings confirm the high potential of OCT-based examinations for rapid and accurate diagnostics during breast conservation surgery.

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.

As was shown earlier in the animal experiments, compression optical coherence elastography (OCE) is a highly sensitive method for studying the morphological features of biological tissues. An attempt was made to study the possibilities of the OCE method for identifying and differentiating from each other various morphological structures in human tissues. Postoperative samples of human breast cancer and human colon cancer were studied. Histological examination identified areas of morphological structures - (I) adipose tissue, (II) stroma and (III) tumor tissue in breast cancer samples; and areas of (I) mucous membrane and (II) tumor tissue in colon cancer samples. For these areas, an accurate comparison was made with OCE images and stiffness ranges for morphological structures were obtained. This observation allows us to make a conclusion that OСE can be a promising method for studying the structure of human tissue in clinics.

We report a new application of compressional optical coherence elastography (OCE) to discriminate morphological constituents of biological tissues by analyzing OCE images obtained either in vivo or for freshly excised samples. The new technique enables quantitative morphological segmentation of OCE images with delineation of several (~4-6) tissue constituents. As the first step, the method uses compressional OCE to reconstruct stiffness maps for a pre-chosen standardized pressure over the entire area of the OCE image. Then specific stiffness ranges (characteristic "stiffness spectra") are initially determined by careful comparison of the OCE-based stiffness maps with the results of segmentation of "gold-standard" histological slices. After such pre-calibration, the stiffness maps can be automatically segmented into regions, for which the Young’s modulus (stiffness) falls in specific ranges corresponding to the morphological constituents to be discriminated. The results of such automated segmentation of OCE-images demonstrate a striking correlation with the results of conventional segmentation of histological slices in terms of percentages of the segmented zones. High sensitivity of the OCE-method to histological alterations was demonstrated in vivo in comparative studies of various types of anti-tumor therapies using murine tumor models. Studies of >100 samples of freshly excised breast cancer samples revealed strong correlation between the tumor-tissue subtype and its morphological composition determined by the developed OCE method. Thus, the developed approach can be used as a basis for express OCE-based biopsy (feasible intraoperatively). Longitudinal in vivo monitoring of morphological alterations in tumors under therapy or during natural development is also possible for locations accessible to OCT.

We use novel possibilities opened by compressional Optical Coherence Elastography (OCE) to characterize both natural interstitial gaps and laser-irradiation-produced porosity in collagenous tissues (corne and cartilage). Under increasing moderate compression up to strains ~several percent, the current Young modulus of cornea gradually increases from initial values below 100 kPa to values >MPa that are closer to Young's modulus of cartilages in which collagen fibers are much denser packed. The lower stiffness of cornea can reasonably be attributed to the initially looser packed collagenous fiber layers, so that initial high compressibility of cornea is dominated by interlayer voids (gaps). By analogy with geophysics, we apply a model describing the reduction in the tissue elastic modulus due to the presence of a system of nearly parallel, thin "crack-like" voids/pores between the collagenous fiber layers. Initially they are highly compressible, but with increasing compression are getting closed, so that the material gets stiffer. Characterization of such porous component in water-saturated packing of collagenous layers in the natural state is inaccessible to AFM and conventional microscopy, whereas OCE enables earlier unavailable possibility to non-invasively characterize such pores/gaps (their total volume and distribution over the aspect ratio) by analogy with crack characterization in geophysics. Also we apply OCE to characterize spatially-inhomogenous modification of pore characteristics by moderate IR-laser-irradiation in regimes typical of collagenous-tissue reshaping. The obtained results are important for obtaining better insight in the structural modificatons in collagenous packings in the context of the development of novel methods of laser-assisted non-surgical methods of cornea-refraction correction and biologically non-destructive reshaping of cartilaginous samples for fabrication of implants in otolaryngology and maxillofacial surgery.

Numerical beam refocusing in OCT is used to increase lateral resolution in the out-of-focus areas for strongly focused beams. However, this approach is based on overlapping lateral scanning in the assumption of the same scatterers positions. In the presence of scatterer motions the numerical refocusing approach can fail. It limit the applicability of the numerical refocusing approach to such based on scatterer motion evaluation modalities as angiography and elastopgraphy. Due to hard controlling phantom experiments we evaluate the influence of motion of scatterers on numerical beam refocusing on the base of numerical simulated OCT scans. The motions of the scatterers are well controlled in the numerical model and its effect on the numerical refocusing approach can be quantified. For this study, a full-wave model for simulating images in spectral-domain optical coherence tomography (OCT) with rigorous accounting for the beam-focusing effects is used.

Compressional optical coherence elastography (OCE) is the emerging tool to evaluate Young modulus of the tissue with resolution close to optical coherence tomography. Recent versions of compressional OCE based on the strain comparison within the tissue and the calibrated reference silicone layer (sensor) located between the OCT probe and tissue. For standard realizations of compressional OCE the evaluation of the strain within the tissue and the sensor performed only at one point of the stress-strain curve. In the same way the applied stress can be easily estimated in a wide range on the base on the stress-strain relation for calibrated sensor strain that allow to evaluate the stress-strain relation for the underlying tissue not in one point but in the wider range. In this report we demonstrate this approach to nonlinear parameter evaluation for wide range of the tissues. We demonstrate the application of this new tool to breast tissue, vaginal wall, bladder, brain, cartilages, coronary arteries walls in various states. The preliminary results shows that several states of the tissues such as vaginal wall state in case of pelvic organ prolapse, benign breast tumor and coronary arteries plague can be determined on the base of elastic nonlinear parameters.

Models that adequately describe the effect of crack-like defects on the elastic moduli of solids are one of the key "ingredients" needed to obtain diagnostic conclusions about the structural features of the material. The change in the velocities of longitudinal and shear elastic waves depending on the pressure is one of the most popular methods of measuring the connection of these moduli with the cracks present in the material. For commonly considered models with an isotropic crack orientation (which makes the medium on average isotropic), the measurement of these two velocities is sufficient to determine two independent moduli (for example, the shear and bulk moduli) through which other characteristics of interest can be expressed. In this case, the applied pressure, gradually closing the cracks, is a control parameter that regulates the concentration of cracks.It is quite natural when constructing models to obtain expressions relating the elastic moduli with the crack concentration (the latter cannot be to directly monitored when the applied pressure is varied). In this regard, some additional considerations are used about the relationship of crack concentration to pressure, which allows one to relate the model expressions with the moduli measured during the pressure variation. Assuming some approximations relating the pressure and concentration with free fitting parameters in the model, it is possible to achieve the best agreement of model with the experimental dependences on pressure. This approach looks natural and is conventionally used, resulting in apparently satisfactory agreement between the model predictions and the measurement data.Here we show that this apparent agreement is often achieved at the expense of strong violation of self-consistency between the input data fed into the model and the output of the model. This violation is far from obvious in conventional approaches based on the use of an auxiliary (and not directly measurable) relationship between concentration and pressure. To find out the fact of either violation or fulfillment of the condition of self-consistency, here we describe such a form of the model, in which its input parameters can be expressed in terms of experimentally measured values (in contrast to the crack concentration that cannot be monitored as a function of pressure). In the proposed description of the fractured material, the cracks are characterized by the shear- and normal compliances, the ratio of which is not a priori fixed and can be extracted from the experimental data.The proposed procedure of interpretation of experimental pressure dependences allows one to explicitly verify the model self-consistency and assess the elastic properties of real cracks that is many cases appear to be strongly different from the properties intrinsic to the standard penny-shape-crack model.The reported study was supported by RFBR, project number 19-05-00536.

A multimodal optical coherence tomography (MM OCT) combining microstructural cross-polarization (CP) imaging and compression OCT-elastography (OCE) was employed in this study. The research was carried out on the noninvasive and invasive subtypes of human breast cancer. This study demonstrates how CP OCT combined with OCTelastography identifies an example of DCIS cancer that progresses into invasive breast cancer. OCE images more clearly show the cross sections of the ducts filled with tumor cells for DCIS (high-contrast structures with clear boundaries and high stiffness values) surrounded by areas with lower stiffness corresponding to fibrous stroma regions. The regions of invasive breast cancer in OCE-scans look as zones with strongly increased stiffness, which well agrees with the histology. Percentage of pixels with different characteristic stiffness ("stiffness spectrum") in the OCTelastography images was assessed to quantitatively visualize stiffness of tumor. The demonstrated ability of MM OCT imaging for breast cancer subtypes differentiation and breast cancer margin assessment is important for improved managements of patients.

We consider application of optical coherence elastography (OCE) to problems of laser-assisted structural modification/reshaping of avascular collagenous tissues used for fabrication of cartilaginous implants and corneal tissue reshaping for perspective technologies of vision-correction. The developed OCE technique allows one to quantitatively visualize aperiodic strains during the IR-laser irradiation of the tissue samples and evaluate cumulative strains produced by the laser irradiations. OCE can assess stability of laser-modeled implants via monitoring of post-irradiation slow strains and to study the interplay of temperature and thermal stresses to optimize tissue reshaping. Irradiation-induced micro-porosity in the tissue can be assessed via combination of strain mapping with compressional optical elastography.

We present a differential formulation of effective-medium model in which the normal and shear compliances of the high-compliance porosity are explicitly decoupled. This feature of the decoupled-compliance model (DC model) is in contrast to conventional models in which such defect's properties are implicitly assumed and are subject to strong limitations defined by the used particular crack model. Comparison with the DC model makes it possible to reveal such implicit assumptions in the conventional models. Furthermore, for the conventional cracks, our approach gives the same results as the conventional models. The ability of the DC model to incorporate arbitrary defect properties in terms of their normal-to-shear compliance ratio ( q -ratio) is used to formulate an analogue of Hashin-Shtrikman constraints on the range of feasible crack-induced variations in the moduli. Comparison of the DC model with experimental pressure dependences of elastic-wave velocities in rocks makes it possible to extract the q -ratio for real crack-like defects. These results demonstrate that properties of real cracks usually noticeably differ from those of popular crack models such as cracks with free faces (e.g., penny-shape) or pure shear cracks. We discuss an example of sandstone with pronouncedly negative Poisson's ratio that is due to the fact that the ratio of normal-to-shear compliances of voids in this rock ( q ~7–8) is significantly higher than for the conventional cracks ( q ~2). Ability of the DC model to accurately extrapolate pressure dependences of the moduli from relatively low pressures to several times greater is demonstrated, including the cases, for which the conventional models give huge errors. The introduced parameter q – the ratio of normal-to-shear compliances of voids – provides additional insight into properties of real crack-like defect in rocks.

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.

In this chapter we consider applications of multimodal OCT for characterizing tumorous tissues. Namely, the following extensions of OCT are discussed: (1) polarization-sensitive OCT providing complementary images in the initial and cross-polarization channels (CP OCT), (2) OCT-based label-free angiography (OCA), and (3) compressional variant of OCT-based elastography (OCE). For each modality we briefly consider the principles of realization and present examples of various biomedical applications from utilization in laboratory experiments with model tumors on animals to demonstrations of possibilities of multimodal OCT in pre-clinical studies and usage in clinical conditions. Among such applications we present the results of using CP OCT for detection of tumorous and nontumorous regions in brain and breast tissues; application of OCA for monitoring the results of photodynamic therapy of murine model tumor CT26 and patients’ basal cell carcinoma; utilization of OCA for studying mucositis on patients during radiation therapy, as well as chemically induced cancer in hamster cheek pouch. In conclusion, we consider several examples of successful realization of compressional OCE for such applications as monitoring of tumor response to chemotherapy, visualization of morphological features of breast cancer and delineation of breast cancer from non-tumor tissue.

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.

Microvascular networks of human basal cell carcinomas (BCC) and surrounding skin were assessed with optical coherence angiography (OCA) in conjunction with photodynamic therapy (PDT). OCA images were collected and analyzed in 31 lesions pre-treatment, and immediately/24 hours/3–12 months post-treatment. Pre-treatment OCA enabled differentiation between prevalent subtypes of BCC (nodular and superficial) and nodular-with-necrotic-core BCC subtypes with a diagnostic accuracy of 78%; this can facilitate more accurate biopsy reducing sampling error and better therapy regimen selection. Post-treatment OCA images at 24 hours were 98% predictive of eventual outcome. Additional findings highlight the importance of pre-treatment necrotic core, vascular metrics associated with hypertrophic scar formation, and early microvascular changes necessary in both tumorous and peri-tumorous regions to ensure treatment success.

In recent pre-clinical studies, we have demonstrated that analysis of speckle statistics in low-scattering, low SNR regions may have applications for accurate lymphatic vessels (and nerves) mapping in optical coherence tomography (OCT) of biotissues. Specifically, we utilized a Rayleigh fitting goodness-of-fit threshold parameter to isolate low scattering biological structures, in particular to distinguish them from noise. The threshold as well as the size of region of interest (ROI) for such speckle statistics evaluation were both chosen empirically. Here we present a model simulation study aimed at optimizing and automatically determining these empirically chosen important parameters. We explore the Rayleigh fit and speckle contrast metrics parameter space to enable accurate label-free OCT mapping of weakly scattering structures such as lymphatic vessels.

Photodynamic therapy (PDT) is emerging as a common and efficacious method for basal cell carcinoma (BCC) treatment, and new non-invasive imaging technologies can further enhance it. Optical coherence angiography (OCA) was employed in this study. OCA is a non-invasive, label-free, real-time bioimaging method that has proven to be a helpful tool for visualizing normal and pathological vasculature, including vascular damage evaluation after using a vasculature-targeted therapy for predicting its success. In experimental study, it was shown that both the tumor and peritumorous vessels stasis (disappearance in OCA images) in 24 hours post treatment play significant roles in PDT success. On controllable mouse ear tumor model the following practical and robust OCA-based criterion of PDT success was formulated: there should be no visibly perfused vessels on OCA images inside the tumor borders, whereas in the 2 mm near-tumor proximity regions the vascular density should not exceed 1% from OCA image area in 24 hours post PDT. The criterion obtained on the experimental model was translated to clinical study. OCA monitoring of basal cell carcinoma reaction to PDT has shown that dramatic decrease in the vascular density in the tumor in 24 hours post PDT can predict tumor non-recurrence with high diagnostic accuracy for 12 months follow-up. The strong reaction of peritumorous vessels in 24 hours post PDT is associated with hypertrophic scar formation in 3-6 months, but the weak reaction of peri-tumorous vascular reaction leads to normotrophic scar formation.

Development of noninvasive diagnostic techniques in clinical practice, especially sufficiently fast methods suitable for intraoperative use, remains a topical and challenging problem in modern medicine. Compressional Optical Coherence Elastography (OCE) that has a high potential to be intraoperatively applied. This study reports preliminary results on application of compressional OCE for identification of tumor margins and even differentiation of breast cancer types with low- and high- histological grades, i.e., a step towards creation of a kind of OCE-based optical biopsy. The reported variant of OCE utilized B-scans with scales ~2-4 mm comparable with typical scales of histological samples. The approach is based on the ability of OCE to quantitatively visualize distribution of the Young modulus (stiffness) in studied tissue samples, which then is used to perform "elasto-spectroscopy" generically resembling the mass-spectroscopy procedures. The procedures of the OCE examination do not require any special preparation of tissue samples and thus can be applied intraoperatively on time intervals ~ a few minutes with immediately available results. In the reported study, the samples after OCE examinations were subjected to histological studies and classification made by an experienced histopathologist. Comparison between the OCE results and histological data made it possible not only to distinguish between normal tissue and tumor (for determining resection boundary), but also to formulate OCE-based criteria allowing for differentiation between carcinomas of low grades and fairly good treatment prognosis and high-grade invasive tumors with poor prognosis. Similarly, identification of not only invasive breast tumors, but also benign breast lesions, intermediate between norm and malignant tumors can be made.

We present an optical coherence tomography (OCT) lymphangiography visualization approach based on analysis of speckle statistics. For in-vivo experimentation, normal and tumor tissues are examined in mouse dorsal skin window chamber model. In order to evaluate the speckle statistics, OCT datasets are acquired in 3 spatial and 1 temporal dimensions to be divided then into smaller volumes of interests. In temporal dimension, repeated same-location scanning is performed for simultaneous blood vessel detection through speckle variance processing. Speckle statistics in each volume of interest are tested for similarity to known distributions corresponding either to noise or to tissue. We show that lymphatic vessels could be detected using a specific parameter range of speckle statistics as a filter, to separate the surrounding tissues and blood vessels. The proposed approach does not require numerous post-processing steps that are often used in lymphatic detection methods that are based on low signal amplitude regions (e.g., OCT signal attenuation compensation, inversion, amplitude thresholding etc.). Instead, we use a fast 2-step filtering procedure to reveal lymphatic vessels in imaged tissues.

We present a realization of real-time OCT-based strain mapping by estimating interframe phase-variation gradient using the developed "vector" method. This technique allows for mapping both fairly fast and large, as well as rather small strains, slowly-varying on intervals ~tens of minutes. Optimization of interframe interval for improving signal-to-noise ratio is discussed and experimentally demonstrated. Ultimate stability of strain estimation with the designed OCT setup is experimentally estimated using stable phantoms. Examples of spatially resolved maps of slowly-varying strains are demonstrated. The developed methods can be used in emerging techniques of laser-assisted modification of collagenous tissues (e.g., for such perspective application as fabrication of cartilaginous implants).

A computationally efficient and fairly realistic model of OCT-scan formation in spectral-domain optical coherence tomography is described. The model is based on the approximation of discrete scatterers and ballistic character of scattering, these approximations being widely used in literature. An important feature of the model is its ability to easily account for arbitrary scatterer motions and computationally efficiently generate large sequences of OCT scans for gradually varying configurations of scatterers. This makes the proposed simulation platform very convenient for studies related to the development of angiographic processing of OCT scans for visualization of microcirculation of blood, as well as for studies of decorrelation of speckle patterns in OCT scans due to random (Brownian type) motions of scatterers. Examples demonstrating utilization of the proposed model for generation OCT scans imitating perfused vessels in biological tissues, as well as evolution of speckles in OCT scans due to random translational and rotational motions of localized (but not-point-like) scatterers are given. To the best of our knowledge, such numerical simulations of large series of OCT scans in the presence of various types of motion of scatterers have not been demonstrated before.

In this paper, we present a computationally highly efficient full-wave model of optical coherence tomography (OCT)-scan formation by focused beams in spectral-domain OCT. Similarly to some previous models, it is based on the summation of fields scattered by discrete sub-resolution scatterers, and enables one to account for the axial and lateral inhomogeneity of the illuminating Gaussian beam. The main feature ensuring the high computational efficiency of the described model is that, rather than numerical integration of the scattered signal over the receiving aperture, we apply an analytical description of both the illuminating-beam focusing and the collection of the scattered signals over the receiving aperture. Elimination of numerical integration over the receiving aperture increases the overall computation speed by a factor of ∼ 10 3 . This is of key importance in terms of the practical feasibility of simulations of 3D OCT data volumes for large amounts (∼ 10 5 − 10 7 ) of scatterers, corresponding to realistic densities of cells in biological tissues. We demonstrate the model’s possibilities by simulating the digital refocusing of strongly focused OCT beams in the presence moving scatterers, thereby presenting a novel principle of contrast-agent-free visualization of scatterer flows, with velocities typical of blood microcirculation.