Effect of the refractive index mismatch on light propagation through diffusive layered media

Two-layer reconstruction of Raman spectra in diffusive media based on an analytical model in the time domain

We derive and validate an analytical model that describes the migration of Raman scattered photons in two-layer diffusive media, based on the diffusion equation in the time domain. The model is derived under a heuristic approximation that background optical properties are identical on the excitation and Raman emission wavelengths. Methods for the reconstruction of two-layer Raman spectra have been developed, tested in computer simulations and validated on tissue-mimicking phantom measurements data. Effects of different parameters were studied in simulations, showing that the thickness of the top layer and number of detected photon counts have the most significant impact on the reconstruction. The concept of quantitative, mathematically rigorous reconstruction using the proposed model was finally proven on experimental measurements, by successfully separating the spectra of silicone and calcium carbonate (calcite) layers, showing the potential for further development and eventual application in clinical diagnostics.

Negative dispersion of a form birefringence in subwavelength gratings

An achromatic response is required in most optical systems for wideband and straightforward configurations. The chromatic response of the optical system depends on the optical dispersion of the elements in the system. Here we study the dispersion of subwavelength grating (SWG) known to have a form birefringence. The birefringence of SWG was numerically analyzed with Bloch wave analysis (BWA) and finite element method (FEM). The sandwiched SWG with two identical substrates was studied for practical applications. We successfully demonstrated the negative dispersion form birefringence of SWG with an optimal duty cycle. This extraordinary dispersion was also shown considering the intrinsic dispersion of materials. Dispersion- and the angular response were in a tradeoff relationship while they depended on periodicity. The optical interference between the grating and the substrates can be eliminated by controlling the duty cycle. Our analysis offers optimal SWG with achromatic birefringence and high transparency, promising in the widespread applications of polarization control devices.

Recent progress in optical clearing of eye tissues

The growing need for viewing the detailed 3D structures of various tissues and organs requires advanced tissue processing and imaging techniques. However, light scattering by tissues hinders detailed structural observations. To overcome this, the emerging technique of "tissue optical clearing" has been flourishing in recent decades, providing excellent opportunities for imaging deep, micro-scale structures of various organs, or even of the whole body. In recent years, advanced tissue clearing techniques have been optimized for specific tissues and organs. Among these tissues, the eye is unique owing to its delicate structure and pigmented retinal epithelial cells, calling for more work on making these tissues "transparent". In this review, we searched Medline and Embase for studies published between January 2006 and August 2021 using the terms "tissue optical clearing", "ophthalmology", "eye", and "optical clearing agents", and we reviewed the publications on the optical clearing techniques of eye tissue from 2006 to the present, including both the clearing procedures and the subsequent analytical processes, thus gaining more insight into the application of tissue optical clearing in basic eye research. Furthermore, we discuss the future potential of optical clearing applications in clinical ophthalmology.

Time-Domain Near-Infrared Spectroscopy and Imaging: A Review

This article reviews the past and current statuses of time-domain near-infrared spectroscopy (TD-NIRS) and imaging. Although time-domain technology is not yet widely employed due to its drawbacks of being cumbersome, bulky, and very expensive compared to commercial continuous wave (CW) and frequency-domain (FD) fNIRS systems, TD-NIRS has great advantages over CW and FD systems because time-resolved data measured by TD systems contain the richest information about optical properties inside measured objects. This article focuses on reviewing the theoretical background, advanced theories and methods, instruments, and studies on clinical applications for TD-NIRS including some clinical studies which used TD-NIRS systems. Major events in the development of TD-NIRS and imaging are identified and summarized in chronological tables and figures. Finally, prospects for TD-NIRS in the near future are briefly described.

Modified reciprocity relation for the time-dependent diffusion equation

The classical reciprocity relation of radiative transfer fails for two points placed in regions having different indices of refraction. A modified reciprocity relation that involves the relative refractive index between the two points considered was previously derived for the continuous wave (cw) radiative transfer equation and for the cw diffusion equation (DE) [J. Opt. Soc. Am. A14, 486 (1997)]. In this paper, we extend these findings to the time-dependent DE and we discuss some implications to diffuse optical tomography.

Influence of boundary conditions on photon diffusion through an interface between two turbid media with different refractive indices

The photon migration in two semi-infinite highly scattering media with different refractive indices is studied in the diffusion approximation for two sets of boundary conditions at the interface. In commonly used boundary conditions, the ratio of the intensity (fluence rate) to the squared refractive index is assumed continuous across an interface and the normal component of flux is required to be continuous. However, a more rigorous approach shows that the boundary condition for the intensity may be different. As was shown by Aronson [J. Opt. Soc. Am. A12, 2532 (1995)], the ratio of the intensity to the squared refractive index undergoes a jump across an interface that is proportional to the diffuse flux. A diffusion model with an instantaneous point source that can be solved analytically for both sets of boundary conditions is considered. The analytical solutions are derived and compared with the results of Monte Carlo simulations that take into account the reflections and refractions at the interface according to Fresnel's formulas. It is shown that the analytical solutions with the Aronson boundary condition for intensity match the Monte Carlo results better than the solutions with a continuous ratio of the intensity to the squared refractive index.

Microcirculatory changes and skeletal muscle oxygenation measured at rest by non-infrared spectroscopy in patients with and without diabetes undergoing haemodialysis

Introduction

Haemodialysis has direct and indirect effects on skin and muscle microcirculatory regulation that are severe enough to worsen tolerance to physical exercise and muscle asthenia in patients undergoing dialysis, thus compromising patients' quality of life and increasing the risk of mortality. In diabetes these circumstances are further complicated, leading to an approximately sixfold increase in the incidence of critical limb ischaemia and amputation. Our aim in this study was to investigate in vivo whether haemodialysis induces major changes in skeletal muscle oxygenation and blood flow, microvascular compliance and tissue metabolic rate in patients with and without diabetes.

Methods

The study included 20 consecutive patients with and without diabetes undergoing haemodialysis at Sant Andrea University Hospital, Rome from March to April 2007. Near-infrared spectroscopy (NIRS) quantitative measurements of tissue haemoglobin concentrations in oxygenated [HbO₂] and deoxygenated forms [HHb] were obtained in the calf once hourly for 4 hours during dialysis. Consecutive venous occlusions allowed one to obtain muscular blood flow (mBF), microvascular compliance and muscle oxygen consumption (mVO₂). The tissue oxygen saturation (StO₂) and content (CtO₂) as well as the microvascular bed volume were derived from the haemoglobin concentration. Nonparametric tests were used to compare data within each group and among the groups and with a group of 22 matched healthy controls.

Results

The total haemoglobin concentration and [HHb] increased significantly during dialysis in patients without and with diabetes. Only in patients with diabetes, dialysis involved a [HbO₂], CtO₂ and increase but left mVO₂ unchanged. Multiple regression StO₂ analysis disclosed a significant direct correlation of StO₂ with HbO₂ and an inverse correlation with mVO₂. Dialysis increased mBF only in diabetic patients. Microvascular compliance decreased rapidly and significantly during the first hour of dialysis in both groups.

Conclusions

Our NIRS findings suggest that haemodialysis in subjects at rest brings about major changes in skeletal muscle oxygenation, blood flow, microvascular compliance and tissue metabolic rate. These changes differ in patients with and without diabetes. In all patients haemodialysis induces changes in tissue haemoglobin concentrations and microvascular compliance, whereas in patients with diabetes it alters tissue blood flow, tissue oxygenation (CtO₂, [HbO₂]) and the metabolic rate (mVO₂). In these patients the mVO₂ is correlated to the blood supply. The effects of haemodialysis on cell damage remain to be clarified. The absence of StO₂ changes is probably linked to an opposite [HbO₂] and mVO₂ pattern.

Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model

A diffusion-based model for photon migration through a three-layer medium is described. The main purpose of this work is to investigate the performance of a diffusion equation (DE)-based forward model for studying photon migration through a diffusive layered medium having a low scattering layer. This geometrical model can be used as a simple model of the adult head. Numerical results are shown for a set of values of the optical properties typical of the adult human head, where scalp and skull are lumped in the first layer while the second and third layer are associated with the cerebrospinal fluid (CSF) and the brain, respectively. Due to the presence of the CSF, which is a relatively clear layer, the diffusion-based model yields an approximate solution of photon migration. Nevertheless, comparisons with MC simulations show that the model can predict the total and the partial mean path length in the different layers with an error less than 20%. In particular, the partial mean path length in the third layer, representative of the brain, is calculated with an error less than 10% if the reduced scattering coefficient of the second layer, representative of the CSF, is assumed 0.25 mm(-1).

Skin and cutaneous melanocytic lesion simulation in biomedical optics with multilayered phantoms

The complex inner layered structure of skin influences the photon diffusion inside the cutaneous tissues and determines the reflectance spectra formation. Phantoms are very useful tools to understand the biophysical meaning of parameters involved in light propagation through the skin. To simulate the skin reflectance spectrum, we realized a multilayered skin-like phantom and a multilayered skin phantom with a melanoma-like phantom embedded inside. Materials used were Al(2)O(3) particles, melanin of sepia officinalis and a calibrator for haematology systems dispersed in transparent silicon. Components were optically characterized with indirect techniques. Reflectance phantom spectra were compared with average values of in vivo spectra acquired on a sample of 573 voluntary subjects and 132 pigmented lesions. The phantoms' reflectance spectra agreed with those measured in vivo, mimicking the optical behaviour of the human skin. Further, the phantoms were optically stable and easily manageable, and represented a valid resource in spectra formation comprehension, in diagnostic laser applications and simulation model implementation, such as the Monte Carlo code for non-homogeneous media.

Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry

We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.

Absorption and scattering perturbations in homogeneous and layered diffusive media probed by time-resolved reflectance at null source-detector separation

We characterize the capability of time-resolved reflectance measurements at small source-detector separation (less than 5 mm) to localize small inhomogeneities embedded in an otherwise homogeneous or layered diffusive medium. By considering both absorption and scattering inhomogeneities, we demonstrate the improvement of this approach in terms of contrast and spatial resolution, as compared to more typical set-ups involving larger source-detection separations (few centimeters). Simulations are performed exploiting an analytical perturbation approach to diffusion theory and a four-layer heterogeneous time-resolved Monte Carlo code, considering realistic tissue geometries. Exhaustive investigation in the parameters space is reported.

Analytical solution for light propagation in a two-layer tissue structure with a tilted interface for breast imaging

Reflectance measurement of breast tissue is influenced by the underlying chest wall, which is often tilted as seen by the detection probe. We develop an analytical solution of light propagation in a two-layer tissue structure with tilted interface and refractive index difference between the layers. We validate the analytical solution with Monte Carlo simulations and phantom experiments, and a good agreement is seen. The influence of varying the tilting angle of the interface on the reflectance is discussed for two types of layered structures. Further, we apply the developed analytical solution to obtain the optical properties of breast tissue and chest wall from clinical data. Inverse calculation using the developed solution applied to the data obtained from Monte Carlo simulations shows that the optical properties of both layers are obtained with higher accuracy as compared to using a simple two-layer model ignoring the interface tilt. This is expected to improve the accuracy in estimating the optical properties of breast tissue, thus enhancing the accuracy of optical tomography of breast tumors.

Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging

We propose a novel approach to imaging in diffusive media based on time-resolved reflectance measurements at null source-detector separation. This approach yields better spatial resolution and contrast as compared to the classical approach, which typically employs a separation of 20-40 mm. Results are obtained by an analytical perturbation approach to diffusion theory and on Monte Carlo simulations. Practical implementation with state-of-the-art technology and performance of a complementary approach based on the use of small but not null source-detector separation are also discussed.

Perturbation model for light propagation through diffusive layered media

A fast and novel perturbation approach is proposed to account for the effects of absorbing inhomogeneities on light propagation through layered media. The calculation has been implemented with the Born approximation. Examples of results are reported both for a two- and for a three-layered medium. The method presented has been validated with the results of Monte Carlo simulations. The forward solver presented in this paper can be of significant use in investigating the feasibility of real experiments, e.g. for functional imaging studies.