Analysis of the spatial distribution of detector sensitivity in a multilayer randomly inhomogeneous medium with strong light scattering and absorption by the Monte Carlo method

The spatial distribution of sensitivity in the domain of detection of a fiber-optic sensor used for spectrophotometric studies of skin and other biological tissues is studied. The method and results of modeling the propagation of optical radiation in multilayer randomly inhomogeneous media with strong light scattering and absorption are presented. Owing to the small distances between the source and detector (100–800 μm), the propagation of radiation in the medium under study is modeled by the Monte Carlo method combining the calculation of true paths and the use of statistical weights. For the same reason, we represent the surface and interfaces of layers of skin as rough randomly periodic surfaces corresponding to the actual structure of human skin. The method presented can be recommended as a means for the optimum selection of an arrangement for radiation incoupling and outcoupling.     

Combined spectroscopic method for determining the fluorophore concentration in highly scattering media

The spectroscopic analysis of composition of highly scattering media, in particular, biological tissues, is associated with difficult interpretation of the spectrum of radiation subjected to both absorption and multiple scattering in a medium. The proposed technique of the combined analysis of spectra of laser radiation fluorescence and diffuse reflection by highly scattering biological media allows quantitative determination of concentrations of basic chromophores and fluorophores in tissues with simultaneous estimation of structural changes in objects under study. To determine the effect of structural parameters on the intensity of backscattered laser and fluorescent radiation, numerical simulation and physical modeling of the interaction of exciting and fluorescent radiation with highly scattering media are performed. The dependences of the measured signal on the concentrations of scatterers and fluorophore (protoporphyrin IX) under study are measured.     

Calculation of Transfer Functions of Multilayer Biotissues in the Problems of Correction of Their Fluorescence Spectra

A method for rapid calculation of a flux of stimulated fluorescence of a multilayer optically dense medium with inhomogeneous distribution of the fluorophore has been developed. The light field in the medium at the excitation wavelength of fluorescence is represented by a superposition of incident collimated, incident diffuse, and reflected diffuse fluxes. A two-stream approximation is used to describe the light field in the medium at the wavelength of emission of the fluorescence. Fluxes in adjacent elementary layers of the medium and on its surface are connected by simple matrix operators that are obtained using a combination of engineering approaches of radiation-transfer theory and single-scattering approximation. The calculations of fluorescence fluxes of a four-layer biotissue that are excited and recorded at 400–800 nm are compared with their Monte Carlo simulation with a discrepancy of 1%. The effect of the propagation medium on the fluorescence spectra of 5-ALA-induced protoporphyrin IX that are recorded from human skin was studied, and a technique for their correction that is based on measurements and quantitative analysis of the diffuse reflectance spectrum of skin was proposed.     

Fluorescence tomography with simulated data based on the equation of radiative transfer

The quantification of a nonuniform quantum yield or fluorophore absorption distribution is of major interest in molecular imaging of biological tissue. We introduce what is believed to be the first fluorescence image reconstruction algorithm based on the equation of radiative transfer that recovers the spatial distribution of light-emitting fluorophores inside a highly scattering medium from measurements made on the surface of the medium. We obtain images of either the quantum yield or the fluorophore absorption.     

Laser heating of biological tissue with blood vessels: Modeling and clinical trials

The spatial distribution of the energy absorbed by a unit volume of a laser-irradiated biological tissue is calculated by the Monte Carlo method. Based on these calculations, the temperature fields in biological tissues subjected to laser radiation at 810 nm are modeled. The temperature fields in subcutaneous blood vessels are modeled separately taking into account the inhomogeneous volumetric distribution of heat sources inside the vessels. The results of the modeling showed that laser heating can be efficiently used both for small-diameter and large vessels. Experimental clinical trials of therapy of vascular skin changes by pulsed diode laser radiation (at 810 nm) confirmed these results.     

Correlation characteristics of optical coherence tomography images of turbid media with statistically inhomogeneous optical parameters

Noisy structure of optical coherence tomography (OCT) images of turbid medium contains information about spatial variations of its optical parameters. We propose analytical model of statistical characteristics of OCT signal fluctuations from turbid medium with spatially inhomogeneous coefficients of absorption and backscattering. Analytically predicted correlation characteristics of OCT signal from spatially inhomogeneous medium are in good agreement with the results of correlation analysis of OCT images of different biological tissues. The proposed model can be efficiently applied for quantitative evaluation of statistical properties of absorption and backscattering fluctuations basing on correlation characteristics of OCT images.     

Synthesis of novel fluorescently labeled water-soluble fullerenes and their application to its cellar uptake and distribution properties

Fullerene is a well-known carbon nanomaterial, which can be potentially used for drug manufacture or delivery. Despite several successful examples of utilizing fullerene derivatives as drug candidate materials, their low water solubility under physiological conditions negatively affects the cell penetration efficiency after treatment. In this work, we successfully synthesized two fullerene derivatives with covalently attached fluorescein and boron dipyrromethene (BODIPY) fluorophore moieties, which exhibited cellular uptake and intracellular localization. While both fluorophores decreased their fluorescence intensity in the vicinity of fullerene, the cellar uptake of the fluorescein-modified fullerene was detected via fluorescence microscopy observations. Moreover, decreases in the fluorescence intensities of the intact fluorescein and BODIPY species were observed when both fluorophores and fullerene coexisted in aqueous media.     

Nonstationary two-flux model of radiation transport for optical tomography of scattering media

A nonstationary two-flux model is formulated for the transport of radiation in an inhomogeneous scattering medium and is applied to the situation where such a medium is irradiated by the narrow beam of a pulsed laser. It is shown that when the time distribution of the transmitted photons is measured it is possible simultaneously to reconstruct the two spatial functions (the coefficients of absorption coefficient and of scattering of the radiation by the medium) by means of an inverse Radon transformation and the solution of a system of nonlinear differential equations on the projection lines. An analytic solution is obtained in quadratures for these differential equations. The results constitute a method of solving problems in optical tomography in an inhomogeneous scattering medium Zh. Tekh. Fiz. 67, 61–65 (May 1997)     

Localization of radiation in two-dimensional random media of finite extent

The localization of electromagnetic waves in a two-dimensional random medium composed of strong scatterers is studied theoretically. It is shown that an allowance for the spatial radiation intensity distribution inside the medium, along with an analysis of the distance dependence of the transmission coefficient, is needed to reveal the localization states in media of finite extent.     

Application of the Monte Carlo method for modeling passage of ultrashort laser pulses through an inhomogeneous medium with moving scatterers

We present the results of numerical modeling of passage of ultrashort laser pulses through an inhomogeneous layered medium with moving scatterers, based on solution of the nonsteady-state radiation transport equation by the Monte Carlo method. We consider the effects of Doppler broadening of the backscattered radiation spectrum in biological tissues. We have analyzed the dynamics of propagation of a short laser pulse within a multilayer model of human skin. We have studied the possibilities for tomography of different layers of biological tissue based on analysis of the spectrum of the scattered radiation pulse.     

Influence of Magnetic-Field and Plasma-Density Inhomogeneities on the Propagation and Amplification of Radio Waves in the Solar Corona

We analyze the maser generation of millisecond spikes of the solar radio emission at the cyclotron resonance of a fast extraordinary wave in an inhomogeneous medium. It is shown that the magnetic-field inhomogeneity with parameters typical of the solar corona drastically reduces the time of electromagnetic-wave amplification, which is explained by the fact that these waves leave the resonance region in the wave-vector space. As a result, an unstable electron distribution can be formed. The efficient generation of radiation becomes possible only in such local regions where the influence of the magnetic-field inhomogeneity is compensated by small-scale inhomogeneities of the plasma density with typical scales ranging from tens to hundreds of kilometers. Taking the effect of inhomogeneous medium into account allows us to explain spatial and temporal characteristics of the spikes.     

Retrieval of optical characteristics of an inhomogeneous turbid medium based on time-resolved diffuse reflectometry data: Studying by the Monte Carlo method

Formation of a signal in an optical diffuse reflectometry system using pulse probing radiation from a medium with a layered distribution of the absorption coefficient has been simulated by the Monte Carlo method. The influence of absorption inhomogeneities on the pulse shape and photon travel path was studied. Analysis of statistical characteristics (mean propagation time and broadening magnitude) of detected scattered pulses was performed. Variations in the spatial distribution of travel trajectories of photons forming the signal of optical diffuse reflectometry were analyzed. Based on a comparison of the obtained characteristics with theoretical data, conclusions have been drawn on the agreement of the retrieved values of the absorption and scattering coefficients with their true values depending on the distance between the source and receiver.     

Helmholtz integral in the acoustics of an inhomogeneous medium

Integral relations that generalize the Helmholtz integral for an inhomogeneous medium with arbitrary gradients of its density and the sound velocity in it are obtained. Expressions that determine the Helmholtz integral for problems related to the diffraction and radiation of sound in an inhomogeneous medium are derived. It is shown that, in the case of an inhomogeneous medium, an additional factor depending on the density distribution in the medium appears in the integrand.     

Conditions for generation of X-ray cherenkov radiation during motion of charges in realistic media

The influence of the spatial distribution of electrons, atoms, and nuclei in condensed media on a medium’s susceptibility and on the conditions for the formation of short-wavelength Cherenkov radiation are considered. It is shown that taking into account the inhomogeneous (atomic and electronic) structure of material media in which fast charged particles travel leads to a change in the effective susceptibility and permittivity in the X-ray range, as compared with cases of model homogeneous media with the same average concentration of electrons. The influence of the distribution functions of electrons and nuclei in a target on the conditions for Cherenkov radiation generation and its parameters and on the threshold energy of fast charged particles required to generate such radiation is studied. It is shown that the function of the spatial distribution of electrons and nuclei in a target affects the conditions for generating laser radiation in the X- and λ-ray ranges (on the problem of X- and λ-ray lasers). The obtained results show that using the Fresnel approximation in the X-ray range is insufficiently justified and can lead to significant errors.     

The shape of emission lines from a spatially inhomogeneous gas containing macroscopic particles

A theoretical study of the shape of spectral lines emitted from a spatially inhomogeneous gas in the presence of a condensed phase has been carried out. The gas-phase atoms emit and absorb light while the macroscopic particles and the walls emit, absorb, and scatter light.The spatial inhomogeneity is described by distribution of the gas-phase temperature with a homogeneous core and a monotone change at the periphery, corresponding to a linear change of the blackbody radiation. The radiation transport equation is solved by using successive approximations. The dependence of the radiation intensity on the radiation characteristics and the inhomogeneity characteristics of the two-phase medium has been established. The calculation of the shape of spectral lines takes into account the fact that, inside the line, the optical density of the layer, the probability of photon survival, and radiation sources in the two-phase medium change simultaneously.     

Spatially Periodic Inhomogeneous States in a Nonlinear Crystal with a Nonlinear Defect

Spatially periodic inhomogeneous stationary states are shown to exist near a thin defect layer with nonlinear properties separating nonlinear Kerr-type crystals. The contacts of nonlinear self-focusing and defocusing crystals have been analyzed. The spatial field distribution obeys a time-independent nonlinear Schrödinger equation with a nonlinear (relative to the field) potential modeling the thin defect layer with nonlinear properties. Both symmetric and asymmetric states relative to the defect plane are shown to exist. It has been established that new states emerge in a self-focusing crystal, whose existence is attributable to the defect nonlinearity and which do not emerge in the case of a linear defect. The dispersion relations defining the energy of spatially periodic inhomogeneous stationary states have been derived. The expressions for the energies of such states have been derived in an explicit analytical form in special cases. The conditions for the existence of periodic states and their localization, depending on the defect and medium characteristics, have been determined.     

Angular spectrum approach to electromagnetic wave propagation in inhomogeneous media

The angular spectrum representation of the electromagnetic wave field is employed to solve the wave propagation in a weakly inhomogeneous medium. Taking the two-dimensional spatial Fourier transform of the radiation field as well as of the dielectric constant, the angular amplitude is shown to satisfy an integro-differential equation. A similar equation is also applicable for the propagation of radiation in a non-linear medium. This integro-differential equation is solved for two specific cases of interest, namely that of a stratified medium and of a square-law medium.     

Behaviour of Fluorescence Emission of Cyanine Dyes,Cyanine Based Fluorescent Nanoparticles and CdSe/ZnS Quantum Dots in Water Solution Upon Specific Thermal Treatments

Fluorescence techniques are widely used as detection methods in a wide range of biological imaging and analytical applications. The purpose of this work is to determine a measurement method which leads to a comparison between different classes of fluorophores in term of stability of the fluorescence signal upon thermal treatment cycles. This kind of investigation can determine whether the fluorophore performance is affected by heating/cooling cycles and to what extent. The fluorophores considered in this work were organic fluorophores belonging to the family of indocyanine dyes (IRIS3 by Cyanine Technologies S.p.A.) in their molecular form or encapsulated within silica nanoparticles, and CdSe/ZnS carboxyl quantum dots (Qdots 565 ITK by Invitrogen). The NIST Standard Reference Material® SRM 1932 fluorescein solution was used in the certified concentration as reference material in order to evaluate the repeatability of the used spectrofluorimeter. The proposed measurement protocol allows to characterize all kind of fluorophores upon thermal treatments. This allows direct comparison of their performance under temperature changes, giving useful guidelines for the selection of the most suitable fluorophore for the envisaged application. Moreover the method appears to be a promising tool for the characterisation of reference fluorescent materials. The experimental results demonstrate that each fluorophore class shows a specific behaviour. The experimental data analysis points out an important hysteresis effect for quantum dots that was not detected for cyanine molecules and was only slightly detected for cyanine doped silica nanoparticles.     

Theory of a stationary microwave discharge with multiply charged ions in an expanding gas jet

The formation of a jet of a nonequilibrium multiply charged ion plasma is studied in the inhomogeneous gas jet. It is shown that the geometrical divergence of the jet restricts the maximum ion charge state and results in the spatial localization of the discharge. Stationary solutions corresponding to such regimes are constructed. The model proposed can be used to optimize modern experiments on generation of hard UV radiation due to the line emission of multiply ionized atoms in a gas jet heated by high-power millimeter and submillimeter radiation.     

The fluorescence of a molecular gas excited a strong monochromatic standing wave radiation field

Among the different methods of nonlinear spectrosccpy the method of analysing the fluorescence light is useful in investigating weak absorbing molecular transitions. In this paper the fluorescence of a molecular gas in the resonator of a high-power single mode laser is investigated. By tuning the standing wave field frequency to centre of the absorption line one observes a narrow local minimum for the fluorescence. This minimum is determined by the homogeneously broadened line of the molecular transition and gives information of the different molecular relaxation processes. The influence of vibrational-rotational relaxations, velocity changing collisions and spatial inhomogeneous distribution of the population caused by the standing wave field on the width and contrast of the minimum is theoretically investigated. It will be shown, that vibrational-rotational and velocity changing collisions increase the intensity of the fluorescence. The spatial inhomogeneous distribution of population caused by the excitation decreases the contrast.Results have been partially presented in reference [12].