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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.
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Vaginal wall prolapse is the most common type of pelvic organ prolapse and is mainly associated with collagen bundle changes in the lamina propria. Neodymium (Nd:YAG) laser treatment was used as an innovative, minimally invasive and non-ablative procedure for the treatment of early-stage vaginal wall prolapse. The purpose of this pilot study was to assess connective tissue changes in the vaginal wall under prolapse without treatment and after Nd:YAG laser treatment using cross-polarization optical coherence tomography (CP OCT) with depth-resolved attenuation mapping. A total of 26 freshly excised samples of vaginal wall from 26 patients with age norm (n = 8), stage I-II prolapses without treatment (n = 8) and stage I-II prolapse 1-2 months after Nd:YAG laser treatment (n = 10) were assessed. As a result, for the first time, depth-resolved attenuation maps of the vaginal wall in the B-scan projection in the co- and cross-polarization channels were constructed. Two parameters within the lamina propria were target calculated: the median value and the percentages of high (≥4 mm-1) and low (<4 mm-1) attenuation coefficient values. A significant (p < 0.0001) decrease in the parameters in the case of vaginal wall prolapse compared to the age norm was identified. After laser treatment, a significant (p < 0.0001) increase in the parameters compared to the normal level was also observed. Notably, in the cross-channel, both parameters showed a greater difference between the groups than in the co-channel. Therefore, using the cross-channel achieved more reliable differentiation between the groups. To conclude, attenuation coefficient maps allow visualization and quantification of changes in the condition of the connective tissue of the vaginal wall. In the future, CP OCT could be used for in vivo detection of early-stage vaginal wall prolapse and for monitoring the effectiveness of treatment.
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Optical coherence tomography (OCT) is a promising tool for intraoperative tissue morphology determination. Several studies suggest that attenuation coefficient derived from the OCT images, can differentiate between tissues of different morphology, such as normal and pathological structures of the brain, skin, and other tissues. In the present study, the depth-resolved method for attenuation coefficient calculation was adopted for the real-world situation of the depth-dependent OCT sensitivity and additive imaging noise with nonzero mean. It was shown that in the case of sharp focusing (~10 µm spot full width at half maximum [FWHM] or smaller at 1.3 µm central wavelength) only the proposed method for depth-dependent sensitivity compensation does not introduce misleading artifacts into the calculated attenuation coefficient distribution. At the same time, the scanning beam focus spot with FWHM greater than 10 µm at 1.3 µm central wavelength allows one to use multiple approaches to the attenuation coefficient calculation without introducing noticeable bias. This feature may hinder the need for robust corrections for the depth-resolved attenuation coefficient estimations from the community.
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Pele , Tomografia de Coerência Óptica , Tomografia de Coerência Óptica/métodos , Encéfalo/diagnóstico por imagem , Algoritmos , CarmustinaRESUMO
Intraoperative differentiation of tumorous from non-tumorous tissue can help in the assessment of resection margins in breast cancer and its response to therapy and, potentially, reduce the incidence of tumor recurrence. In this study, the calculation of the attenuation coefficient and its color-coded 2D distribution was performed for different breast cancer subtypes using spectral-domain CP OCT. A total of 68 freshly excised human breast specimens containing tumorous and surrounding non-tumorous tissues after BCS was studied. Immediately after obtaining structural 3D CP OCT images, en face color-coded attenuation coefficient maps were built in co-(Att(co)) and cross-(Att(cross)) polarization channels using a depth-resolved approach to calculating the values in each A-scan. We determined spatially localized signal attenuation in both channels and reported ranges of attenuation coefficients to five selected breast tissue regions (adipose tissue, non-tumorous fibrous connective tissue, hyalinized tumor stroma, low-density tumor cells in the fibrotic tumor stroma and high-density clusters of tumor cells). The Att(cross) coefficient exhibited a stronger gain contrast of studied tissues compared to the Att(co) coefficient (i.e., conventional attenuation coefficient) and, therefore, allowed improved differentiation of all breast tissue types. It has been shown that color-coded attenuation coefficient maps may be used to detect inter- and intra-tumor heterogeneity of various breast cancer subtypes as well as to assess the effectiveness of therapy. For the first time, the optimal threshold values of the attenuation coefficients to differentiate tumorous from non-tumorous breast tissues were determined. Diagnostic testing values for Att(cross) coefficient were higher for differentiation of tumor cell areas and tumor stroma from non-tumorous fibrous connective tissue: diagnostic accuracy was 91-99%, sensitivity-96-98%, and specificity-87-99%. Att(co) coefficient is more suitable for the differentiation of tumor cell areas from adipose tissue: diagnostic accuracy was 83%, sensitivity-84%, and specificity-84%. Therefore, the present study provides a new diagnostic approach to the differentiation of breast cancer tissue types based on the assessment of the attenuation coefficient from real-time CP OCT data and has the potential to be used for further rapid and accurate intraoperative assessment of the resection margins during BCS.
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Introduction: To improve the quality of brain tumor resections, it is important to differentiate zones with myelinated fibers destruction from tumor tissue and normal white matter. Optical coherence tomography (OCT) is a promising tool for brain tissue visualization and in the present study, we demonstrate the ability of cross-polarization (CP) OCT to detect damaged white matter and differentiate it from normal and tumor tissues. Materials and methods: The study was performed on 215 samples of brain tissue obtained from 57 patients with brain tumors. The analysis of the obtained OCT data included three stages: 1) visual analysis of structural OCT images; 2) quantitative assessment based on attenuation coefficients estimation in co- and cross-polarizations; 3) building of color-coded maps with subsequent visual analysis. The defining characteristics of structural CP OCT images and color-coded maps were determined for each studied tissue type, and then two classification tests were passed by 8 blinded respondents after a training. Results: Visual assessment of structural CP OCT images allows detecting white matter areas with damaged myelinated fibers and differentiate them from normal white matter and tumor tissue. Attenuation coefficients also allow distinguishing all studied brain tissue types, while it was found that damage to myelinated fibers leads to a statistically significant decrease in the values of attenuation coefficients compared to normal white matter. Nevertheless, the use of color-coded optical maps looks more promising as it combines the objectivity of optical coefficient and clarity of the visual assessment, which leads to the increase of the diagnostic accuracy of the method compared to visual analysis of structural OCT images. Conclusions: Alteration of myelinated fibers causes changes in the scattering properties of the white matter, which gets reflected in the nature of the received CP OCT signal. Visual assessment of structural CP OCT images and color-coded maps allows differentiating studied tissue types from each other, while usage of color-coded maps demonstrates higher diagnostic accuracy values in comparison with structural images (F-score = 0.85-0.86 and 0.81, respectively). Thus, the results of the study confirm the potential of using OCT as a neuronavigation tool during resections of brain tumors.
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A pilot post-mortem study identifies a strong correlation between the attenuation coefficient estimated from the OCT data and some morphological features of the sample, namely the number of nuclei in the field of view of the histological image and the fiber structural parameter introduced in the study to quantify the difference in the myelinated fibers arrangements. The morphological features were identified from the histopathological images of the sample taken from the same locations as the OCT images and stained with the immunohistochemical (IHC) staining specific to the myelin. It was shown that the linear regression of the IHC quantitative characteristics allows adequate prediction of the attenuation coefficient of the sample. This discovery opens the opportunity for the usage of the OCT as a neuronavigation tool.
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Forward-viewing endoscopic optical coherence tomography (OCT) provides 3D imaging in vivo, and can be combined with widefield fluorescence imaging by use of a double-clad fiber. However, it is technically challenging to build a high-performance miniaturized 2D scanning system with a large field-of-view. In this paper we demonstrate how a 1D scanning probe, which produces cross-sectional OCT images (B-scans) and 1D fluorescence T-scans, can be transformed into a 2D scanning probe by manual scanning along the second axis. OCT volumes are assembled from the B-scans using speckle decorrelation measurements to estimate the out-of-plane motion along the manual scan direction. Motion within the plane of the B-scans is corrected using image registration by normalized cross correlation. En-face OCT slices and fluorescence images, corrected for probe motion in 3D, can be displayed in real-time during the scan. For a B-scan frame rate of 250 Hz, and an OCT lateral resolution of approximately 20 µ m , the approach can handle out-of-plane motion at speeds of up to 4 mm/s.
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INTRODUCTION: Despite the introduction of increasingly multifaceted diagnostic techniques and the general advances in emergency abdominal and vascular surgery, the outcome of treatment of patients with acute impaired intestinal circulation remains unsatisfactory. The non-invasive and high-resolution technique of optical coherence tomography (OCT) can be used intraoperatively to assess intestine viability and associated conditions that frequently emerge under conditions of impaired blood circulation. This study aims to demonstrate the effectiveness of multimodal (MM) OCT for intraoperative diagnostics of both the microstructure (cross-polarization OCT mode) and microcirculation (OCT angiography mode) of the small intestine wall in patients with acute mesenteric ischemia (AMI). METHODS AND PARTICIPANTS: A total of 18 patients were enrolled in the study. Nine of them suffered from AMI in segments II-III of the superior mesenteric artery (AMI group), whereby the ischemic segments of the intestine were examined. Nine others were operated on for adenocarcinoma of the colon (control group), thus allowing areas of their normal small intestine to be examined for comparison. Data on the microstructure and microcirculation in the walls of the small intestine were obtained intraoperatively from the side of the serous membrane using the MM OCT system (IAP RAS, Russia) before bowel resection. The MM OCT data were compared with the results of histological examination. RESULTS: The study finds that MM OCT visualized the damage to serosa, muscularis externa, and blood vessels localized in these layers in 100% of AMI cases. It also visualized the submucosa in 33.3% of AMI cases. The MM OCT images of non-ischemic (control group), viable ischemic, and necrotic small intestines (AMI group) differed significantly across stratification of the distinguishable layers, the severity of intermuscular fluid accumulations, and the type and density of the vasculature. CONCLUSION: The MM OCT diagnostic procedure optimally meets the requirements of emergency surgery. Data on the microstructure and microcirculation of the intestinal wall can be obtained simultaneously in real time without requiring contrast agent injections. The depth of visualization of the intestinal wall from the side of the serous membrane is sufficient to assess the volume of the affected tissues. However, the methodology for obtaining MM OCT data needs to be improved to minimize the motion artefacts generated in actual clinical conditions.
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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.
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A method for numerical estimation and correction of aberrations of the eye in fundus imaging with optical coherence tomography (OCT) is presented. Aberrations are determined statistically by using the estimate based on likelihood function maximization. The method can be considered as an extension of the phase gradient autofocusing algorithm in synthetic aperture radar imaging to 2D optical aberration correction. The efficacy of the proposed method has been demonstrated in OCT fundus imaging with 6λ aberrations. After correction, single photoreceptors were resolved. It is also shown that wave front distortions with high spatial frequencies can be determined and corrected.
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Algoritmos , Tomografia de Coerência Óptica , Fundo de Olho , Funções VerossimilhançaRESUMO
A numerical method that compensates image distortions caused by random fluctuations of the distance to an object in spectral-domain optical coherence tomography (SD OCT) has been proposed and verified experimentally. The proposed method is based on the analysis of the phase shifts between adjacent scans that are caused by micrometer-scale displacements and the subsequent compensation for the displacements through phase-frequency correction in the spectral space. The efficiency of the method is demonstrated in model experiments with harmonic and random movements of a scattering object as well as during in vivo imaging of the retina of the human eye.
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The methods used for digital processing of optical coherence tomography (OCT) and crosspolarization (CP) OCT images are focused on improving the contrast ratio of native structural OCT images. Such advances are particularly important for the intraoperative detection of glioma margins where the visual assessment of OCT images can be difficult and lead to errors. The aim of the study was to investigate the application of optical coefficients obtained from CP OCT data for the differentiation of glial tumorous tissue from a normal brain. Pseudocolor en-face OCT maps based on two optical coefficients (the commonly used rate of attenuation in the cochannel, and in addition, the interchannel attenuation difference) were constructed for normal rat brain coronal cross sections and for brains with a 101.8 rat glioblastoma model. It was shown that the use of optical coefficients significantly increased the available information from the OCT data in comparison with unprocessed images. As a result, this allowed contrasting of the white matter from the gray matter and tumorous tissue ex vivo, and for this purpose, the interchannel attenuation difference worked better. The interchannel attenuation difference values of white matter were at least seven and two times higher than corresponding values of the cortex and tumorous tissue, whereas the same parameter for cochannel attenuation coefficient values of white matter are about 4 and 1.4. However, quantitative analysis shows that both coefficients are suitable for the purpose of glioblastoma detection from normal brain tissue regardless of whether a necrotic component was present (in all compared groups p < 0.001 ).
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We report a compact rigid instrument capable of delivering en-face optical coherence tomography (OCT) images alongside (epi)-fluorescence endomicroscopy (FEM) images by means of a robotic scanning device. Two working imaging channels are included: one for a one-dimensional scanning, forward-viewing OCT probe and another for a fiber bundle used for the FEM system. The robotic scanning system provides the second axis of scanning for the OCT channel while allowing the field of view (FoV) of the FEM channel to be increased by mosaicking. The OCT channel has resolutions of 25 / 60 µm (axial/lateral) and can provide en-face images with an FoV of 1.6 × 2.7 mm2. The FEM channel has a lateral resolution of better than 8 µm and can generate an FoV of 0.53 × 3.25 mm2 through mosaicking. The reproducibility of the scanning was determined using phantoms to be better than the lateral resolution of the OCT channel. Combined OCT and FEM imaging were validated with ex-vivo ovine and porcine tissues, with the instrument mounted on an arm to ensure constant contact of the probe with the tissue. The OCT imaging system alone was validated for in-vivo human dermal imaging with the handheld instrument. In both cases, the instrument was capable of resolving fine features such as the sweat glands in human dermal tissue and the alveoli in porcine lung tissue.
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Derme/diagnóstico por imagem , Diagnóstico por Imagem/métodos , Microscopia de Fluorescência/métodos , Procedimentos Cirúrgicos Robóticos/métodos , Tomografia de Coerência Óptica/métodos , Animais , Humanos , Alvéolos Pulmonares/diagnóstico por imagem , Reprodutibilidade dos Testes , Glândulas Sudoríparas/diagnóstico por imagem , SuínosRESUMO
This paper considers valuable visual assessment criteria for distinguishing between tumorous and non-tumorous tissues, intraoperatively, using cross-polarization OCT (CP OCT)-OCT with a functional extension, that enables detection of the polarization properties of the tissues in addition to their conventional light scattering. Materials and Methods: The study was performed on 176 ex vivo human specimens obtained from 30 glioma patients. To measure the degree to which the typical parameters of CP OCT images can be matched to the actual histology, 100 images of tumors and white matter were selected for visual analysis to be undertaken by three "single-blinded" investigators. An evaluation of the inter-rater reliability between the investigators was performed. Application of the identified visual CP OCT criteria for intraoperative use was performed during brain tumor resection in 17 patients. Results: The CP OCT image parameters that can typically be used for visual assessment were separated: (1) signal intensity; (2) homogeneity of intensity; (3) attenuation rate; (4) uniformity of attenuation. The degree of match between the CP OCT images and the histology of the specimens was significant for the parameters "signal intensity" in both polarizations, and "homogeneity of intensity" as well as the "uniformity of attenuation" in co-polarization. A test based on the identified criteria showed a diagnostic accuracy of 87-88%. Intraoperative in vivo CP OCT images of white matter and tumors have similar signals to ex vivo ones, whereas the cortex in vivo is characterized by indicative vertical striations arising from the "shadows" of the blood vessels; these are not seen in ex vivo images or in the case of tumor invasion. Conclusion: Visual assessment of CP OCT images enables tumorous and non-tumorous tissues to be distinguished. The most powerful aspect of CP OCT images that can be used as a criterion for differentiation between tumorous tissue and white matter is the signal intensity. In distinguishing white matter from tumors the diagnostic accuracy using the identified visual CP OCT criteria was 87-88%. As the CP OCT data is easily associated with intraoperative neurophysiological and neuronavigation findings this can provide valuable complementary information for the neurosurgeon tumor resection.
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Optical coherence tomography (OCT) is a promising method for detecting cancer margins during tumor resection. This study focused on differentiating tumorous from nontumorous tissues in human brain tissues using cross-polarization OCT (CP OCT). The study was performed on fresh ex vivo human brain tissues from 30 patients with high- and low-grade gliomas. Different tissue types that neurosurgeons should clearly distinguish during surgery, such as the cortex, white matter, necrosis and tumorous tissue, were separately analyzed. Based on volumetric CP OCT data, tumorous and normal brain tissue were differentiated using two optical coefficients - attenuation and forward cross-scattering. Compared with white matter, tumorous tissue without necrotic areas had significantly lower optical attenuation and forward cross-scattering values. The presence of particular morphological patterns, such as necrosis and injured myelinated fibers, can lead to dramatic changes in coefficient values and create some difficulties in differentiating between tissues. Color-coded CP OCT maps based on optical coefficients provided a visual assessment of the tissue. This study demonstrated the high translational potential of CP OCT in differentiating tumorous tissue from white matter. The clinical use of CP OCT during surgery in patients with gliomas could increase the extent of tumor resection and improve overall and progression-free survival.
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Neoplasias Encefálicas/diagnóstico por imagem , Neoplasias Encefálicas/patologia , Encéfalo/diagnóstico por imagem , Tomografia de Coerência Óptica , Encéfalo/citologia , Encéfalo/patologia , Feminino , Glioma/diagnóstico por imagem , Glioma/patologia , Humanos , Processamento de Imagem Assistida por Computador , Masculino , Curva ROCRESUMO
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.
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Colágeno/química , Colágeno/metabolismo , Técnicas de Imagem por Elasticidade , Fenômenos Mecânicos , Temperatura , Animais , Fenômenos Biomecânicos , Módulo de Elasticidade , Coelhos , Esclera/diagnóstico por imagem , Esclera/metabolismoRESUMO
This work is dedicated to the development of the OCT system with angiography for everyday clinical use. Two major problems were solved during the development: compensation of specific natural tissue displacements, induced by contact scanning mode and physiological motion of patients (eg, respiratory and cardiac motions) and online visualization of vessel cross-sections to provide feedback for the system operator.
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Angiografia/instrumentação , Tomografia de Coerência Óptica/instrumentação , Humanos , Processamento de Imagem Assistida por Computador , Fatores de TempoRESUMO
A novel machine-learning method to distinguish between tumor and normal tissue in optical coherence tomography (OCT) has been developed. Pre-clinical murine ear model implanted with mouse colon carcinoma CT-26 was used. Structural-image-based feature sets were defined for each pixel and machine learning classifiers were trained using "ground truth" OCT images manually segmented by comparison with histology. The accuracy of the OCT tumor segmentation method was then quantified by comparing with fluorescence imaging of tumors expressing genetically encoded fluorescent protein KillerRed that clearly delineates tumor borders. Because the resultant 3D tumor/normal structural maps are inherently co-registered with OCT derived maps of tissue microvasculature, the latter can be color coded as belonging to either tumor or normal tissue. Applications to radiomics-based multimodal OCT analysis are envisioned.
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Algoritmos , Angiografia , Imageamento Tridimensional/métodos , Tomografia de Coerência Óptica , Animais , Linhagem Celular Tumoral , Camundongos , Camundongos Endogâmicos BALB C , MicrovasosRESUMO
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 10-100â 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.
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Córnea/diagnóstico por imagem , Lasers , Estresse Mecânico , Tomografia de Coerência Óptica/métodos , Córnea/citologia , TemperaturaRESUMO
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.