Linear scheme for time-domain fluorescence molecular tomography

Based on the generalized pulse spectrum technique that was previously developed for time-domain diffuse optical tomography, we propose a linear framework of time-domain fluorescence molecular tomography for simultaneous reconstruction of both the yield and lifetime of multi-fluorophores. The methodology is exemplified for mono-component case and validated with simulated data.     

Experimental validation for time-domain fluorescence diffuse optical tomography of linear scheme

We present a full three-dimensional, featured-data algorithm for time-domain fluorescence diffuse optical tomography that inverts the Laplace-transformed time-domain coupled diffusion equations and employs a pair of appropriate transform-factors to effectively separate the fluorescent yield and lifetime parameters. By use of a time-correlation single-photon counting system and the normalized Born formulation, we ex-perimentally validate that the proposed scheme can achieve simultaneous reconstruction of the fluorescent yield and lifetime distributions with a reasonable accuracy.     

Statistical characteristics of photon distributions in a semi-infinite turbid medium: Analytical expressions and their application to optical tomography

The paper focuses on the determination of statistical characteristics of photon distributions in a semi-infinite turbid medium, specifically the photon average trajectory and the root-mean-square deviation of photons from the average trajectory, with an approach based on the diffusion approximation to the radiative transfer equation. We show that the Dirichlet and Robin boundary conditions used for this purpose give close results. We derive exact analytical expressions for the case of the Dirichlet boundary condition. To demonstrate the practical value of our results we consider approximate solution of the inverse problem of time-domain diffuse optical tomography with the flat layer transmission geometry. The problem is solved with the method of photon average trajectories which are constructed with analytical expressions derived for a semi-infinite medium.     

A CTRW-based model of time-resolved fluorescence lifetime imaging in a turbid medium

We develop an analytic model of time-resolved fluorescent imaging of photons migrating through a semi-infinite turbid medium bounded by an infinite plane in the presence of a single stationary point fluorophore embedded in the medium. In contrast to earlier models of fluorescent imaging in which photon motion is assumed to be some form of continuous diffusion process, the present analysis is based on a continuous-time random walk (CTRW) on a simple cubic lattice, the objective being to estimate the position and lifetime of the fluorophore. This can provide information related to local variations in pH and temperature with potential medical significance. Aspects of the theory were tested using time-resolved measurements of the fluorescence from small inclusions inside tissue-like phantoms. The experimental results were found to be in good agreement with theoretical predictions provided that the fluorophore was not located too close to the planar boundary, a common problem in many diffusive systems.     

Depth-resolved fluorescence measurement in a layered turbid medium by polarized fluorescence spectroscopy

We show that, when a turbid medium with a layered fluorophore distribution is excited by linearly polarized light, measurement of angle-resolved polarized fluorescence can provide depth-resolved fluorescence measurements.     

Simple time-domain optical method for estimating the depth and concentration of a fluorescent inclusion in a turbid medium

A simple time-domain optical method for estimating the depth and concentration of fluorescent inclusions in turbid media is described. We demonstrate direct depth estimation of a localized fluorescent object from the temporal position of the temporal point-spread function maximum. The depth estimation permits recovery of the fluorophore concentration, both of which are essential quantities for optical molecular imaging studies. Since the maximum is independent of the fluorophore concentration, excitation laser power, detector gain, and other system-dependent factors, this method ensures a robust and efficient approach.     

Early-photon guided reconstruction method for time-domain fluorescence lifetime tomography

A reconstruction method guided by early-photon fluorescence yield tomography is proposed for time-domain fluorescence lifetime tomography(FLT) in this study. The method employs the early-arriving photons to reconstruct a fluorescence yield map, which is utilized as a priori information to reconstruct the FLT via all the photons along the temporal-point spread functions. Phantom experiments demonstrate that, compared with the method using all the photons for reconstruction of fluorescence yield and lifetime maps, the proposed method can achieve higher spatial resolution and reduced crosstalk between different targets without sacrificing the quantification accuracy of lifetime and contrast between heterogeneous targets.     

Comparison of frequency-domain and time-domain fluorescence lifetime tomography

We compare frequency-and time-domain formulations of deep-tissue fluorescence imaging of turbid media. Simulations are used to show that time-domain fluorescence tomography, implemented via the asymptotic lifetime-based approach, offers a significantly better separability of multiple lifetime targets than a frequency-domain approach. We also demonstrate experimentally, using complex-shaped phantoms, the advantages of the asymptotic time-domain approach over a Fourier-based approach for analyzing time-domain fluorescence data.     

Estimating the depth and lifetime of a fluorescent inclusion in a turbid medium using a simple time-domain optical method

A simple time-domain optical method for estimating the depth (d) and lifetime (tau) of fluorescent inclusions in a turbid medium is described. We demonstrate the method for depth and lifetime estimation of a fluorescent inclusion directly by fitting a monoexponential decay (tau(eff)) of the temporal position of the temporal point-spread function and the measurement of its maximum temporal position (t(max)). Since both of these measurements are intensity independent, this method provides a robust and efficient approach. This method is validated with experimental data.     

Fluorescence-lifetime-based tomography for turbid media

We derive a novel algorithm to recover the in vivo distributions of fluorophores based on an asymptotic life-time analysis of time-domain fluorescence measurements with turbid tissue. We experimentally demonstrate the advantage offered by this method in localizing fluorophores with distinct lifetimes. This algorithm has wide applicability for diagnostic fluorescence imaging in the presence of several-centimeter-thick biological tissue, since fluorescence lifetime is a sensitive indicator of local tissue environment and interactions at the molecular level.     

Light propagation for time-domain fluorescence diffuse optical tomography by convolution using lifetime function

Time-domain light propagation in biological tissue is studied by solving the forward problem for fluorescence diffuse optical tomography using a convolution of the zero-lifetime emission light and the exponential function for a finite lifetime. We firstly formulate the fundamental equations in a time-domain assuming that the fluorescence lifetime is equal to zero, and then the solution including the lifetime is obtained by convolving the emission light and the lifetime function. The model is a two-dimensional (2-D) 10 mm-radius circle with the optical properties simulating biological tissue for the near infrared light, and contains some inclusions with fluorophores. Temporal and spatial profiles of excitation and emission light are calculated and discussed for several models with different inclusions. The results are physically reasonable and will be used for the inverse problem of fluorescence diffuse optical tomography.     

Relationship between depth of a target in a turbid medium and fluorescence measured by a variable-aperture method

The relationship between the depth of a target in a turbid medium and the fluorescence ratio profile measured by use of illumination and collection apertures with variable diameters and the same optical path is shown. The forward problem was studied by Monte Carlo simulations of the propagation of fluorescent light through a theoretical model of a biologically relevant system for a range of aperture diameters. The curve of the fluorescence ratio as a function of the aperture diameter is characterized by a maximum/minimum point whose position shifts linearly with the depth of the target. Furthermore, the position of the maximum/minimum is observed to be insensitive to variations in the fluorescence efficiency and to the optical properties of the target layer or the entire medium.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

Abstract

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Picosescond fluorescence lifetime standards for frequency- and time-domain fluorescence

We characterized a series of dimethylamino-stilbene derivatives as standards for time-domain and frequency-domain lifetime measurements. The substances have reasonable quantum yields, are soluble in solvents available with a high purity, and do not show significant sensitivity to oxygen quenching. All the fluorophores displayed single exponential intensity decays, as characterized by frequency-domain measurements to 10 GHz. The decay times vary from 880 to 57 ps, depending on structure, solvent, and temperature, which is a useful range for modern picosecond time-domain or gigahertz frequency-domain instruments. These fluorophores may be used either to test an instrument or as reference compounds to eliminate color effects. We also characterized two-fluorophore mixtures, with the decay times spaced twofold (150 and 300 ps), with varying proportions. These mixtures are useful for testing the resolution of other time- and frequency-domain instrumentation. The excitation wavelength ranges from 260 to 430 nm, and the emission from 350 to 550 nm. The decay times are independent of the excitation and emission wavelengths.     

Analysis of the characteristics of a two-fiber sensor for monitorship of a turbid medium

Summary Certain characteristics of a two-fiber sensor device, of the type proposed by Papaet al. for sea water turbidity monitorship, are examined. The extension of medium from which most of the received backscattered power originates is investigated, together with possible effects of multiple scattering on the received power. Laboratory measurements testing the results of the analysis are reported.

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Riassunto Sono esaminate alcune caratteristiche di un sensore a due fibre, del tipo di quello proposto da Papaet al. per il monitoraggio della torbidità dell'acqua di mare. è stata studiata l'estensione della zona del mezzo da cui proviene la maggior parte della radiazione retrodiffusa ricevuta. Sono stati considerati effetti di diffusione multipla. I risultati dell'analisi sono stati controllati con misure in laboratorio.

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Резюме Исследуются некоторые характеристики дву-qh-нитевого датчика, предложенного Папа и др. для мониторирования мутности морской воды. Исследуется расширение зоны в среде, из которой формируется основная часть рассеянного назад излучения. Также рассматриваются эффекты многократного рассеяния. На основе лабораторных измерений проводится проверка результатов анализа.

     

Two-dimensional isotropic scattering in a semi-infinite medium

Exact results are presented for the source function, radiative flux, and intensity at the boundary of a two-dimensional, isotropically scattering, semi-infinite medium subjected to collimated or diffuse radiation. The spatial distributions of incident radiation considered are (1) cosine-varying, (2) semi-infinite step, (3) step at the origin and (4) finite strip. Two-dimensional effects are most pronounced at large albedos.     

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain (SP-FDTD) algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field (TF/SF) formulation of high-order symplectic finite-difference time-domain (SFDTD) scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain (FDTD), the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.