Speckle statistics in OCT images: Monte Carlo simulations and experimental studies

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.

MCOCT: an experimentally and numerically validated, open-source Monte Carlo simulator for optical coherence tomography

Here, we present MCOCT, a Monte Carlo simulator for optical coherence tomography (OCT), incorporating a Gaussian illumination scheme and bias to increase backscattered event collection. MCOCT optical fluence was numerically compared and validated to an established simulator (MCX) and showed concordance at the focus while diverging slightly with distance to it. MCOCT OCT signals were experimentally compared and validated to OCT signals acquired in tissue-mimicking phantoms with known optical properties and showed a similar attenuation pattern with increasing depth while diverging beyond 1.5 mm and proximal to layer interfaces. MCOCT may help in the design of OCT systems for a wide range of applications.

Importance sampling-accelerated simulation of full-spectrum backscattered diffuse reflectance

The Monte Carlo (MC) method is one of the most widely used numerical tools to model the light interaction with tissue. However, due to the low photon collection efficiency and the need to simulate the entire emission spectrum, it is computationally expensive to simulate the full-spectrum backscattered diffuse reflectance (F-BDR). Here, we propose an acceleration scheme based on importance sampling (IS). We derive the biasing sampling function tailored for simulating BDR based on the two-term scattering phase function (TT). The parameters of the TT function at different wavelengths are directly obtained by fitting the Mie scattering phase function. Subsequently, we incorporate the TT function and its corresponding biased function into the redefined IS process and realize the accelerated simulation of F-BDR. Phantom simulations based on the Fourier-domain optical coherence tomography (FD-OCT) are conducted to demonstrate the efficiency of the proposed method. Compared to the original simulator without IS, our proposed method achieves a 373× acceleration in simulating the F-BDR of the multi-layer phantom with a relative mean square error (rMSE) of less than 2%. Besides, by parallelly computing A-lines, our method enables the simulation of an entire B-scan in less than 0.4 hours. To our best knowledge, it is the first time that a volumetric OCT image of a complex phantom is simulated. We believe that the proposed acceleration method can be readily applied to fast simulations of various F-BDR-dependent applications. The source codes of this manuscript are also publicly available online.

Retinal OCT speckle as a biomarker for glaucoma diagnosis and staging

This paper presents a novel image analysis strategy that increases the potential of macular Optical Coherence Tomography (OCT) by using speckle features as biomarkers in different stages of glaucoma. A large pool of features (480) were computed for a subset of macular OCT volumes of the Leuven eye study cohort. The dataset contained 258 subjects that were divided into four groups based on their glaucoma severity: Healthy (56), Mild (94), Moderate (48), and Severe (60). The OCT speckle features were categorized as statistical properties, statistical distributions, contrast, spatial gray-level dependence matrices, and frequency domain features. The averaged thicknesses of ten retinal layers were also collected. Kruskal-Wallis H test and multivariable regression models were used to infer the most significant features related to glaucoma severity classification and to the correlation with visual field mean deviation. Four features were selected as being the most relevant: the ganglion cell layer (GCL) and the inner plexiform layer (IPL) thicknesses, and two OCT speckle features, the data skewness computed on the retinal nerve fiber layer (RNFL) and the scale parameter (a) of the generalized gamma distribution fitted to the GCL data. Based on a significance level of 0.05, the regression models revealed that RNFL skewness exhibited the highest significance among the features considered for glaucoma severity staging (p-values of 8.6×10-6 for the logistic model and 2.8×10-7 for the linear model). Furthermore, it demonstrated a strong negative correlation with the visual field mean deviation (ρ=-0.64). The post hoc analysis revealed that, when distinguishing healthy controls from glaucoma subjects, GCL thickness is the most relevant feature (p-value of 8.7×10-5). Conversely, when comparing the Mild versus Moderate stages of glaucoma, RNFL skewness emerged as the only feature exhibiting statistical significance (p-value = 0.001). This work shows that macular OCT speckle contains information that is currently not used in clinical practice, and not only complements structural measurements (thickness) but also has a potential for glaucoma staging.

Photothermal modulation speckle optical coherence tomography of microvascular nondestructive imaging in vivo with high effective resolution

To achieve non-invasive and high effective resolution microvascular imaging in vivo, photothermal modulation speckle optical coherence tomography (PMS-OCT) imaging technology is proposed in this Letter to enhance the speckle signal of the bloodstream for improving the imaging contrast and image quality in the deeper depth of Fourier domain optical coherence tomography (FD-OCT). The results of simulation experiments proved that this photothermal effect could disturb and enhance the speckle signals, because the photothermal effect could modulate the sample volume to expand and change the refractive index of tissues, leading to the change in the phase of interference light. Therefore, the speckle signal of the bloodstream will also change. With this technology we obtain a clear cerebral vascular nondestructive image of a chicken embryo at a certain imaging depth. This technology expands the application fields of optical coherence tomography (OCT) especially in more complex biological structures and tissues, such as the brain, and provides a new way, to the best of our knowledge, for the application of OCT in brain science.

Monte Carlo-based full-wavelength simulator of Fourier-domain optical coherence tomography

Monte Carlo (MC) simulation has been widely used to study imaging procedures, including Fourier-domain optical coherence tomography (FD-OCT). Despite the broadband nature of FD-OCT, the results obtained at a single wavelength are often used in previous studies. Some wavelength-relied imaging applications, such as spectroscopic OCT (S-OCT), are unlikely to be simulated in this way due to the lack of information from the entire spectrum. Here, we propose a novel simulator for full-wavelength MC simulation of FD-OCT. All wavelengths within the emission spectrum of the light source will be simulated, and the optical properties derived from Mie theory will be applied. We further combine the inverse discrete Fourier transform (IDFT) with a probability distribution-based signal pre-processing to combat the excessive noises in the OCT signal reconstruction, which is caused by the non-uniform distribution of the scattering events at different wavelengths. Proof-of-concept simulations are conducted to show the excellent performance of the proposed simulator on signal reconstruction and optical properties extraction. Compared with the conventional method, the proposed simulator is more accurate and could better preserve the wavelength-dependent features. For example, the mean square error (MSE) computed between the backscattering coefficient extracted by the proposed simulator and the ground truth is 0.11, which is far less than the value (7.67) of the conventional method. We believe this simulator could be an effective tool to study the wavelength dependency in FD-OCT imaging as well as a preferred solution for simulating spectroscopic OCT.

A novel algorithm for multiplicative speckle noise reduction in ex vivo human brain OCT images

Optical coherence tomography (OCT) images of ex vivo human brain tissue are corrupted by multiplicative speckle noise that degrades the contrast to noise ratio (CNR) of microstructural compartments. This work proposes a novel algorithm to reduce noise corruption in OCT images that minimizes the penalized negative log likelihood of gamma distributed speckle noise. The proposed method is formulated as a majorize-minimize problem that reduces to solving an iterative regularized least squares optimization. We demonstrate the usefulness of the proposed method by removing speckle in simulated data, phantom data and real OCT images of human brain tissue. We compare the proposed method with state of the art filtering and non-local means based denoising methods. We demonstrate that our approach removes speckle accurately, improves CNR between different tissue types and better preserves small features and edges in human brain tissue.

Lateral image reconstruction of optical coherence tomography using one-dimensional deep deconvolution network

BACKGROUND AND OBJECTIVES

Optical coherence tomography (OCT) is a cross-sectional imaging method utilizing a low coherence interferometry. The lateral resolution of the OCT is limited by the numerical aperture (NA) of the imaging lens. Using a high NA lens improves the lateral resolution but reduces the depth of focus (DOF). In this study, we propose a method to improve the lateral resolution of OCT images by end-to-end training of a deep 1-D deconvolution network without use of high-resolution images.

MATERIALS AND METHODS

To improve the lateral resolution of the OCT, we trained the 1-D deconvolution network using lateral profiles of OCT images and the beam spot size. We used our image-guided laparoscopic surgical tool (IGLaST) to acquire OCT images of nonbiological and biological samples ex vivo. The OCT images were then blurred by applying Gaussian functions with various full width half maximums ranging from 40 to 160 µm. The network was trained using the blurred OCT images as input and the non-blurred original OCT images as output. We quantitatively evaluated the developed network in terms of similarity and signal-to-ratio (SNR), using in-vivo images of mesenteric tissue from a porcine model that was not used for training. In addition, we performed knife-edge tests and qualitative evaluation of the network to show the lateral resolution improvement of ex-vivo and in-vivo OCT images.

RESULTS

The proposed method showed an improvement of image quality on both blurred images and non-blurred images. When the proposed deconvolution network was applied, the similarity to the non-blurred image was improved by 1.29 times, and the SNR was improved by 1.76 dB compared to the artificially blurred images, which was superior to the conventional deconvolution method. The knife-edge tests at distances at 200 to 1000 µm from the imaging probe showed an approximately 1.2 times improvement in lateral resolution. In addition, through qualitative evaluation, it was found that the image quality of both ex-vivo and in-vivo tissue images was improved with clear structure and less noise.

CONCLUSIONS

This study showed the ability of the 1-D deconvolution network to improve the image quality of OCT images with variable lateral resolution. We were able to train the network with a small amount of data by constraining the network in 1-D. The quantitative evaluation showed better results than conventional deconvolution methods for various amount of blurring. Qualitative evaluation showed analogous results with quantitative results. This simple yet powerful image restoration method provides improved lateral resolution and suppresses background noise, making it applicable to a variety of OCT imaging applications.

Indirectly assessing changes in corneal properties with OCT speckle after crosslinking in porcine eyes

The aim of this study was to assess the effect of the standard crosslinking (CXL) procedure on corneal properties and subsequent changes in collagen bonds formation using optical coherence tomography (OCT) corneal speckle statistics and vibrational spectroscopy. Porcine eyes with intact corneal epithelium were randomly selected to one of the four study groups: (1) untreated eyes moistened with phosphate-buffered saline (PBS); (2) eyes after the epithelial debridement and riboflavin application; (3) eyes after CXL procedure according to the Dresden protocol; and (4) eyes after corneal epithelial debridement, regularly moistened with PBS. Before and after this selection, each eyeball was subjected to the constant intraocular pressure of 20 mmHg. Then, ocular biometry was performed and the central cornea was imaged using spectral-domain OCT. Following this, a nonparametric approach to speckle modeling (the Contrast Ratio (CR)) was utilized within the region of interest for each B-scan covering the central corneal stroma. To verify whether the CXL performed ex-vivo results in formation of new bonds in the cornea, Fourier Transform Infrared Attenuated Total Reflectance (ATR-FTIR) spectra of dried corneas, dissected from examined eyeballs, were collected and analyzed. Corneal epithelium removal alone or with the riboflavin application leads to a statistically significant decrease in the CR median value (the Wilcoxon signed-rank test, p < 0.05). However, the most pronounced change in CR median value, which decreases with the increased number of scatterers, was shown after the complete CXL procedure including riboflavin soaking and UVA irradiation (the Wilcoxon signed-rank test, p = 0.004). Analysis of ATR-FTIR spectra revealed influence of UVA irradiation on collagen matrix. The study has shown the increased dehydration accompanied by almost no alteration of collagen native triple-helical structure. Significant changes have been observed for bands related to collagen crosslinks. Specifically, the predominant changes occurred in the sugar region from 1150 to 975 cm^-1, as well as in the absorbance of carbonyl groups. Furthermore, the ratio of two Amide I components at approximately 1660 cm^-1 and 1675 cm^-1 decreased after UVA irradiation. Together, these results provided the evidence for the creation of new corneal crosslinks. In conclusion, this study clearly indicates that the UVA exposure causes the substantial difference in optical scattering occurring in corneal stroma as a result of the induced biochemical changes at the molecular level in this tissue assessed with ATR-FTIR. The proposed speckle-based methodology brings a new insight into the development of OCT technology useful in an indirect assessment of some collagen changes.

Local Burr distribution estimator for speckle statistics

Speckle statistics in ultrasound and optical coherence tomography have been studied using various distributions, including the Rayleigh, the K, and the more recently proposed Burr distribution. In this paper, we expand on the utility of the Burr distribution by first validating its theoretical framework with numerical simulations and then introducing a new local estimator to characterize sample tissues of liver, brain, and skin using optical coherence tomography. The spatially local estimates of the Burr distribution's power-law or exponent parameter enable a new type of parametric image. The simulation and experimental results confirm the potential for various applications of the Burr distribution in both basic science and clinical realms.

Signal-carrying speckle in optical coherence tomography: a methodological review on biomedical applications

SIGNIFICANCE

Speckle has historically been considered a source of noise in coherent light imaging. However, a number of works in optical coherence tomography (OCT) imaging have shown that speckle patterns may contain relevant information regarding subresolution and structural properties of the tissues from which it is originated.

AIM

The objective of this work is to provide a comprehensive overview of the methods developed for retrieving speckle information in biomedical OCT applications.

APPROACH

PubMed and Scopus databases were used to perform a systematic review on studies published until December 9, 2021. From 146 screened studies, 40 were eligible for this review.

RESULTS

The studies were clustered according to the nature of their analysis, namely static or dynamic, and all features were described and analyzed. The results show that features retrieved from speckle can be used successfully in different applications, such as classification and segmentation. However, the results also show that speckle analysis is highly application-dependant, and the best approach varies between applications.

CONCLUSIONS

Several of the reviewed analyses were only performed in a theoretical context or using phantoms, showing that signal-carrying speckle analysis in OCT imaging is still in its early stage, and further work is needed to validate its applicability and reproducibility in a clinical context.

Statistical analysis of corneal OCT speckle: a non-parametric approach

In biomedical optics, it is often of interest to statistically model the amplitude of the speckle using some distributional approximations with their parameters acting as biomarkers. In this paper, a paradigm shift is being advocated in which non-parametric approaches are used. Specifically, a range of distances, evaluated in different domains, between an empirical non-parametric distribution of the normalized speckle amplitude sample and the benchmark Rayleigh distribution, is considered. Using OCT images from phantoms, two ex-vivo experiments with porcine corneas and an in-vivo experiment with human corneas, an evidence is provided that the non-parametric approach, despite its simplicity, could lead to equivalent or better results than the parametric approaches with distributional approximations. Concluding, in practice, the non-parametric approach should be considered as the first choice to speckle modeling before a particular distributional approximation is utilized.

Statistical modeling of retinal optical coherence tomography using the Weibull mixture model

In this paper, a novel statistical model is proposed for retinal optical coherence tomography (OCT) images. According to the layered structure of the retina, a mixture of six Weibull distributions is proposed to describe the main statistical features of OCT images. We apply Weibull distribution to establish a more comprehensive model but with fewer parameters that has better goodness of fit (GoF) than previous models. Our new model also takes care of features such as asymmetry and heavy-tailed nature of the intensity distribution of retinal OCT data. In order to test the effectiveness of this new model, we apply it to improve the low quality of the OCT images. For this purpose, the spatially constrained Gaussian mixture model (SCGMM) is implemented. Since SCGMM is designed for data with Gaussian distribution, we convert our Weibull mixture model to a Gaussian mixture model using histogram matching before applying SCGMM. The denoising results illustrate the remarkable performance in terms of the contrast to noise ratio (CNR) and texture preservation (TP) compared to other peer methods. In another test to evaluate the efficiency of our proposed model, the parameters and GoF criteria are considered as a feature vector for support vector machine (SVM) to classify the healthy retinal OCT images from pigment epithelial detachment (PED) disease. The confusion matrix demonstrates the impact of the proposed model in our preliminary study on the OCT classification problem.

Speckle statistics of biological tissues in optical coherence tomography

The speckle statistics of optical coherence tomography images of biological tissue have been studied using several historical probability density functions. Here, we propose a new theoretical framework based on power-law functions, where we hypothesize that an underlying power-law distribution governs scattering from tissues. Thus, multi-scale scattering sites including the fractal branching vasculature will contribute to power-law probability distributions of speckle statistics. Specifically, these are the Burr type XII distribution for speckle amplitude, the Lomax distribution for intensity, and the generalized logistic distribution for log amplitude. Experimentally, these three distributions are fitted to histogram data from nine optical coherence tomography scans of various samples and biological tissues, in vivo and ex vivo. The distributions are also compared with classical models such as the Rayleigh, K, and gamma distributions. The results indicate that across OCT datasets of various tissue types, the proposed power-law distributions are more appropriate models yielding novel parameters for characterizing the physics of scattering from biological tissue. Thus, the overall framework brings to the field new biomarkers from OCT measures of speckle in tissues, grounded in basic biophysics and with wide applications to diagnostic imaging in clinical use.

Volumetric tumor delineation and assessment of its early response to radiotherapy with optical coherence tomography

Texture analyses of optical coherence tomography (OCT) images have shown initial promise for differentiation of normal and tumor tissues. This work develops a fully automatic volumetric tumor delineation technique employing quantitative OCT image speckle analysis based on Gamma distribution fits. We test its performance in-vivo using immunodeficient mice with dorsal skin window chambers and subcutaneously grown tumor models. Tumor boundaries detection is confirmed using epi-fluorescence microscopy, combined photoacoustic-ultrasound imaging, and histology. Pilot animal study of tumor response to radiotherapy demonstrates high accuracy, objective nature, novelty of the proposed method in the volumetric separation of tumor and normal tissues, and the sensitivity of the fitting parameters to radiation-induced tissue changes. Overall, the developed methodology enables hitherto impossible longitudinal studies for detecting subtle tissue alterations stemming from therapeutic insult.

Bayesian analysis of depth resolved OCT attenuation coefficients

Optical coherence tomography (OCT) is an optical technique which allows for volumetric visualization of the internal structures of translucent materials. Additional information can be gained by measuring the rate of signal attenuation in depth. Techniques have been developed to estimate the rate of attenuation on a voxel by voxel basis. This depth resolved attenuation analysis gives insight into tissue structure and organization in a spatially resolved way. However, the presence of speckle in the OCT measurement causes the attenuation coefficient image to contain unrealistic fluctuations and makes the reliability of these images at the voxel level poor. While the distribution of speckle in OCT images has appeared in literature, the resulting voxelwise corruption of the attenuation analysis has not. In this work, the estimated depth resolved attenuation coefficient from OCT data with speckle is shown to be approximately exponentially distributed. After this, a prior distribution for the depth resolved attenuation coefficient is derived for a simple system using statistical mechanics. Finally, given a set of depth resolved estimates which were made from OCT data in the presence of speckle, a posterior probability distribution for the true voxelwise attenuation coefficient is derived and a Bayesian voxelwise estimator for the coefficient is given. These results are demonstrated in simulation and validated experimentally.

Two-dimensional simulation of optical coherence tomography images

An algorithm for the simulation of two-dimensional spectral domain optical coherence tomography images based on Maxwell’s equations is presented. A recently developed and modified time-harmonic numerical solution of Maxwell’s equations is used to obtain scattered far fields for many wave numbers contained in the calculated spectrum. The interferometer setup with its lenses is included rigorously with Fresnel integrals and the Debye-Wolf integral. The implemented model is validated with an existing FDTD algorithm by comparing simulated tomograms of single and multiple cylindrical scatterers for perpendicular and parallel polarisation of the incident light. Tomograms are presented for different realisations of multiple cylindrical scatterers. Furthermore, simulated tomograms of a ziggurat-shaped scatterer and of dentin slabs, with varying scatterer concentrations, are investigated. It is shown that the tomograms do not represent the physical structures present within the sample.

Accurate Monte Carlo simulation of frequency-domain optical coherence tomography

Optical coherence tomography (OCT) relies on optical interferometry to provide noninvasive imaging of living tissues. In addition to its 3D imaging capacity for medical diagnosis, its potential use for recovering optical parameters of biological tissues for biological and pathological analyses has also been explored by researchers, as pathological changes in tissue alter the microstructure of the tissue and therefore its optical properties. We aim to develop a new approach to OCT data analysis by estimating optical properties of tissues from OCT scans, which are invisible in the scans. This is an inverse problem. Solving an inverse problem involves a forward modeling step to simulate OCT scans of the tissues with hypothesized optical parameter values and an inverse step to estimate the real optical par1meters values by matching the simulated scans to real scans. In this paper, we present a Monte Carlo (MC)-based approach for simulating the frequency-domain OCT. We incorporated a focusing Gaussian light beam rather than an infinitesimally thin light beam for accurate simulations. A new and more accurate photon detection scheme is also implemented. We compare our MC model to an analytical OCT model based on the extended Huygens-Fresnel principle (EHF) to demonstrate the consistency between the two models. We show that the two models are in good agreement for tissues with high scattering and high anisotropy factors.

Statistical Models of Signal and Noise and Fundamental Limits of Segmentation Accuracy in Retinal Optical Coherence Tomography

Optical coherence tomography (OCT) has revolutionized diagnosis and prognosis of ophthalmic diseases by visualization and measurement of retinal layers. To speed up the quantitative analysis of disease biomarkers, an increasing number of automatic segmentation algorithms have been proposed to estimate the boundary locations of retinal layers. While the performance of these algorithms has significantly improved in recent years, a critical question to ask is how far we are from a theoretical limit to OCT segmentation performance. In this paper, we present the Cramèr-Rao lower bounds (CRLBs) for the problem of OCT layer segmentation. In deriving the CRLBs, we address the important problem of defining statistical models that best represent the intensity distribution in each layer of the retina. Additionally, we calculate the bounds under an optimal affine bias, reflecting the use of prior knowledge in many segmentation algorithms. Experiments using in vivo images of human retina from a commercial spectral domain OCT system are presented, showing potential for improvement of automated segmentation accuracy. Our general mathematical model can be easily adapted for virtually any OCT system. Furthermore, the statistical models of signal and noise developed in this paper can be utilized for the future improvements of OCT image denoising, reconstruction, and many other applications.

Fluence compensation in raster-scan optoacoustic angiography

Modern optical imaging techniques demonstrate significant potential for high resolution in vivo angiography. Optoacoustic angiography benefits from higher imaging depth as compared to pure optical modalities. However, strong attenuation of optoacoustic signal with depth provides serious challenges for adequate 3D vessel net mapping, and proper compensation for fluence distribution within biotissues is required. We report on the novel approach allowing to estimate effective in-depth fluence profiles for optoacoustic systems. Calculations are based on Monte Carlo simulation of light transport and account for complex illumination geometry and acoustic detection parameters. The developed fluence compensation algorithm was tested in in vivo angiography of human palm and allowed to overcome significant in-depth attenuation of probing radiation and enhance the contrast of lower dermis plexus while preserving high resolution of upper plexus imaging.

OCT Amplitude and Speckle Statistics of Discrete Random Media

Speckle, amplitude fluctuations in optical coherence tomography (OCT) images, contains information on sub-resolution structural properties of the imaged sample. Speckle statistics could therefore be utilized in the characterization of biological tissues. However, a rigorous theoretical framework relating OCT speckle statistics to structural tissue properties has yet to be developed. As a first step, we present a theoretical description of OCT speckle, relating the OCT amplitude variance to size and organization for samples of discrete random media (DRM). Starting the calculations from the size and organization of the scattering particles, we analytically find expressions for the OCT amplitude mean, amplitude variance, the backscattering coefficient and the scattering coefficient. We assume fully developed speckle and verify the validity of this assumption by experiments on controlled samples of silica microspheres suspended in water. We show that the OCT amplitude variance is sensitive to sub-resolution changes in size and organization of the scattering particles. Experimentally determined and theoretically calculated optical properties are compared and in good agreement.

Massively parallel simulator of optical coherence tomography of inhomogeneous turbid media

BACKGROUND AND OBJECTIVE

An accurate and practical simulator for Optical Coherence Tomography (OCT) could be an important tool to study the underlying physical phenomena in OCT such as multiple light scattering. Recently, many researchers have investigated simulation of OCT of turbid media, e.g., tissue, using Monte Carlo methods. The main drawback of these earlier simulators is the long computational time required to produce accurate results. We developed a massively parallel simulator of OCT of inhomogeneous turbid media that obtains both Class I diffusive reflectivity, due to ballistic and quasi-ballistic scattered photons, and Class II diffusive reflectivity due to multiply scattered photons.

METHODS

This Monte Carlo-based simulator is implemented on graphic processing units (GPUs), using the Compute Unified Device Architecture (CUDA) platform and programming model, to exploit the parallel nature of propagation of photons in tissue. It models an arbitrary shaped sample medium as a tetrahedron-based mesh and uses an advanced importance sampling scheme.

RESULTS

This new simulator speeds up simulations of OCT of inhomogeneous turbid media by about two orders of magnitude. To demonstrate this result, we have compared the computation times of our new parallel simulator and its serial counterpart using two samples of inhomogeneous turbid media. We have shown that our parallel implementation reduced simulation time of OCT of the first sample medium from 407 min to 92 min by using a single GPU card, to 12 min by using 8 GPU cards and to 7 min by using 16 GPU cards. For the second sample medium, the OCT simulation time was reduced from 209 h to 35.6 h by using a single GPU card, and to 4.65 h by using 8 GPU cards, and to only 2 h by using 16 GPU cards. Therefore our new parallel simulator is considerably more practical to use than its central processing unit (CPU)-based counterpart.

CONCLUSIONS

Our new parallel OCT simulator could be a practical tool to study the different physical phenomena underlying OCT, or to design OCT systems with improved performance.

Statistical model for OCT image denoising

Optical coherence tomography (OCT) is a non-invasive technique with a large array of applications in clinical imaging and biological tissue visualization. However, the presence of speckle noise affects the analysis of OCT images and their diagnostic utility. In this article, we introduce a new OCT denoising algorithm. The proposed method is founded on a numerical optimization framework based on maximum-a-posteriori estimate of the noise-free OCT image. It combines a novel speckle noise model, derived from local statistics of empirical spectral domain OCT (SD-OCT) data, with a Huber variant of total variation regularization for edge preservation. The proposed approach exhibits satisfying results in terms of speckle noise reduction as well as edge preservation, at reduced computational cost.

Influence of eye biometrics and corneal micro-structure on noncontact tonometry

Purpose

Tonometry is widely used as the main screening tool supporting glaucoma diagnosis. Still, its accuracy could be improved if full knowledge about the variation of the corneal biomechanical properties was available. In this study, Optical Coherence Tomography (OCT) speckle statistics are used to infer the organisation of the corneal micro-structure and hence, to analyse its influence on intraocular pressure (IOP) measurements.

Methods

Fifty-six subjects were recruited for this prospective study. Macro and micro-structural corneal parameters as well as subject age were considered. Macro-structural analysis included the parameters that are associated with the ocular anatomy, such as central corneal thickness (CCT), corneal radius, axial length, anterior chamber depth and white-to-white corneal diameter. Micro-structural parameters which included OCT speckle statistics were related to the internal organisation of the corneal tissue and its physiological changes during lifetime. The corneal speckle obtained from OCT was modelled with the Generalised Gamma (GG) distribution that is characterised with a scale parameter and two shape parameters.

Results

In macro-structure analysis, only CCT showed a statistically significant correlation with IOP (R² = 0.25, p<0.001). The scale parameter and the ratio of the shape parameters of GG distribution showed statistically significant correlation with IOP (R² = 0.19, p<0.001 and R² = 0.17, p<0.001, respectively). For the studied group, a weak, although significant correlation was found between age and IOP (R² = 0.053, p = 0.04). Forward stepwise regression showed that CCT and the scale parameter of the Generalised Gamma distribution can be combined in a regression model (R² = 0.39, p<0.001) to study the role of the corneal structure on IOP.

Conclusions

We show, for the first time, that corneal micro-structure influences the IOP measurements obtained from noncontact tonometry. OCT speckle statistics can be employed to learn about the corneal micro-structure and hence, to further calibrate the IOP measurements.

Probability density function formalism for optical coherence tomography signal analysis: a controlled phantom study

The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications.

Optical coherence tomography images simulated with an analytical solution of Maxwell's equations for cylinder scattering

An algorithm for the simulation of image formation in Fourier domain optical coherence tomography (OCT) for an infinitely long cylinder is presented. The analytical solution of Maxwell’s equations for light scattering by a single cylinder is employed for the case of perpendicular incidence to calculate OCT images. The A-scans and the time-resolved scattered intensities are compared to geometrical optics results calculated with a ray tracing approach. The reflection peaks, including the whispering gallery modes, are identified. Additionally, the Debye series expansion is employed to identify single peaks in the OCT A-scans. Furthermore, a Gaussian beam is implemented in order to simulate lateral scanning over the cylinder for two-dimensional B-scans. The fields are integrated over a certain angular range to simulate a detection aperture. In addition, the solution for light scattering by layered cylinders is employed and the various layers are identified in the resulting OCT image. Overall, the simulations in this work show that OCT images do not always display the real surface of investigated samples.

Monte Carlo modeling of angiographic optical coherence tomography

Optical coherence tomography (OCT) provides both structural and angiographic imaging modes. Because of its unique capabilities, OCT-based angiography has been increasingly adopted into small animal and human subject imaging. To support the development of the signal and image processing algorithms on which OCT-based angiography depends, we describe here a Monte Carlo-based model of the imaging approach. The model supports arbitrary three-dimensional vascular network geometries and incorporates methods to simulate OCT signal temporal decorrelation. With this model, it will be easier to compare the performance of existing and new angiographic signal processing algorithms, and to quantify the accuracy of vascular segmentation algorithms. The quantitative analysis of key algorithms within OCT-based angiography may, in turn, simplify the selection of algorithms in instrument design and accelerate the pace of new algorithm development.