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.

Nondestructive label-free detection of peritumoral white matter damage using cross-polarization optical coherence tomography.

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.

Brain white matter morphological structure correlation with its optical properties estimated from optical coherence tomography (OCT) data.

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.

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.

Numerical method for axial motion artifact correction in retinal spectral-domain optical coherence tomography.

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.

Optical coefficients as tools for increasing the optical coherence tomography contrast for normal brain visualization and glioblastoma detection.

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 ).

Cross-Polarization Optical Coherence Tomography for Brain Tumor Imaging.

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.

Quantitative nontumorous and tumorous human brain tissue assessment using microstructural co- and cross-polarized optical coherence tomography.

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.

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).

Deformation-induced speckle-pattern evolution and feasibility of correlational speckle tracking in optical coherence elastography.

Feasibility of speckle tracking in optical coherence tomography (OCT) based on digital image correlation (DIC) is discussed in the context of elastography problems. Specifics of applying DIC methods to OCT, compared to processing of photographic images in mechanical engineering applications, are emphasized and main complications are pointed out. Analytical arguments are augmented by accurate numerical simulations of OCT speckle patterns. In contrast to DIC processing for displacement and strain estimation in photographic images, the accuracy of correlational speckle tracking in deformed OCT images is strongly affected by the coherent nature of speckles, for which strain-induced complications of speckle "blinking" and "boiling" are typical. The tracking accuracy is further compromised by the usually more pronounced pixelated structure of OCT scans compared with digital photographic images in classical DIC applications. Processing of complex-valued OCT data (comprising both amplitude and phase) compared to intensity-only scans mitigates these deleterious effects to some degree. Criteria of the attainable speckle tracking accuracy and its dependence on the key OCT system parameters are established.

Hybrid M-mode-like OCT imaging of three-dimensional microvasculature in vivo using reference-free processing of complex valued B-scans.

We propose a novel OCT-based method for visualizing microvasculature in three-dimension using reference-free processing of individual complex valued B-scans with highly overlapped A-scans. In the lateral direction of such a B-scan, the amplitude and phase of speckles corresponding to vessel regions exhibit faster variability and, thus, can be detected without comparison with other B-scans recorded in the same plane. This method combines elements of several existing OCT angiographic approaches and exhibits: (1) enhanced robustness with respect to bulk tissue motion with frequencies up to tens of Hz, (2) resolution of microcirculation images equal to that of structural images, and (3) possibility of quantifying the vessels in terms of their decorrelation rates.

Elastographic mapping in optical coherence tomography using an unconventional approach based on correlation stability.

An approach to elastographic mapping in optical coherence tomography (OCT) using comparison of correlation stability of sequentially obtained intensity OCT images of the studied strained tissue is discussed. The basic idea is that for stiffer regions, the OCT image is distorted to a smaller degree. Consequently, cross-correlation maps obtained with compensation of trivial translational motion of the image parts using a sliding correlation window can represent the spatial distribution of the relative tissue stiffness. An important advantage of the proposed approach is that it allows one to avoid the stage of local-strain reconstruction via error-sensitive numerical differentiation of experimentally determined displacements. Another advantage is that the correlation stability (CS) approach intrinsically implies that for deformed softer tissue regions, cross-correlation should already be strongly decreased in contrast to the approaches based on initial reconstruction of displacements. This feature determines a much wider strain range of operability than the proposed approach and is favorable for its free-hand implementation using the OCT probe itself to deform the tissue. The CS approach can be implemented using either the image elements reflecting morphological structure of the tissue or performing the speckle-level cross-correlation. Examples of numerical simulations and experimental demonstrations using both phantom samples and in vivo obtained OCT images are presented.

Optical coherence tomography for in situ monitoring of laser corneal ablation.

OBJECTIVE: To improve the precision of refractive surgery, a new approach for determination of the removed corneal thickness profile in situ with laser ablation by optical coherence tomography (OCT) is developed. STUDY DESIGN/MATERIALS AND METHODS: The traditional method for precision (less than 10 microm) measurements of intraocular distances is based on the use of the reflected component of probing radiation. This component is characterized by a small range of operating angles between a probing beam and a normal to the surface under study. To enhance this range of operating angles we suggest using a light component backscattered from a biological object. This will enable precision measurements over the entire surface of the cornea without any changes in the orientation between a probing beam and the eye, a necessary condition for in situ monitoring of laser refraction correction in the eye. We suggest a specially developed algorithm of OCT signal processing to measure the corneal thickness by the backscattered light component for a single longitudinal scan (A scan). The corneal thickness profile is obtained by a series of such A scans acquired by successively scanning a probing beam along the corneal surface. The thickness profile of removed layer is determined by changes in the corneal thickness profile in the process of ablation. When the cornea is ablated by a beam with a fixed transverse profile, we propose using integral characteristics of the ablated layer profile, for example, the maximum ablation depth, as criteria of changes in refractive power of the eye. The measurement precision by these characteristics is considerably higher than by a single A scan. Since the cornea is a poorly scattering medium, the Fourier filtering is employed to increase reliability and precision of the method. Model experiments on monitoring the ablation process in a lavsan film and ex vivo human cornea are described. Preliminary experiments on in vivo measurements of human corneal thickness are performed. RESULTS: In model experiments the precision of measurement of laser ablation depth by one A scan was 5-20 microm, depending on the signal-to-noise ratio (SNR), whereas the precision of measurement of laser ablation depth as the integral characteristic of the ablated layer profile was 0.3-5 microm. The experimental results showed that at small SNR Fourier filtering might considerably increase reliability and precision of measurements. When SNR is high, the measurement precision does not change. The precision of measurements of the corneal thickness in preliminary in vivo experiments was higher than in ex vivo experiments. This factor is very promising for application of the method suggested herein in refractive surgery.

In vivo optical coherence tomography feasibility for bladder disease.

PURPOSE: Optical coherence tomography is a new imaging modality capable of imaging luminal surface of biological tissue in the near infrared range with a spatial resolution close to the cellular level. We identified characteristic optical coherence tomography patterns for nonproliferative and proliferative inflammation, and malignant alterations of the bladder. MATERIALS AND METHODS: Optical coherence tomography was performed to image the bladder of 66 patients. The probe passed through the operating channel of a cystoscope and was pressed onto the mucosal site of interest. A mucosal biopsy of the image site was obtained. Optical coherence tomography was used to construct 680 images of the bladder and the images were compared with histology slides. RESULTS: Optical coherence tomography images of normal bladder showed 3 layers, namely the mucosa or transitional epithelium, submucosa and smooth muscle. In exudative processes there were poor light scattering areas in the connective tissue layer. Images of bladders with proliferative cystitis revealed nonuniform thickening of the epithelium or hyperplasia. Squamous metaplasia appeared as thicker and less transparent epithelium with a jagged boundary. Images of transitional cell carcinoma were characterized by the complete loss of a regular layered structure of the bladder wall and the penetration depth of optical imaging was slight. CONCLUSIONS: This study provides the characteristic optical coherence tomography pattern of nonproliferative and proliferative inflammation, and the characteristic appearance of severe dysplasia and transitional cell carcinoma. This technique may be useful as a guide for biopsy and for assisting in establishing resection margins.