The Steady-State Spatially Resolved Reflectance of a Three-Layered Mismatched Medium (original) (raw)
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Applied Optics, 1997
The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.
Hybrid diffusion and two-flux approximation for multilayered tissue light propagation modeling
Applied Optics, 2011
Accurate and rapid estimation of fluence, reflectance, and absorbance in multilayered biological media has been essential in many biophotonics applications that aim to diagnose, cure, or model in vivo tissue. The radiative transfer equation (RTE) rigorously models light transfer in absorbing and scattering media. However, analytical solutions to the RTE are limited even in simple homogeneous or plane media. Monte Carlo simulation has been used extensively to solve the RTE. However, Monte Carlo simulation is computationally intensive and may not be practical for applications that demand real-time results. Instead, the diffusion approximation has been shown to provide accurate estimates of light transport in strongly scattering tissue. The diffusion approximation is a greatly simplified model and produces analytical solutions for the reflectance and absorbance in tissue. However, the diffusion approximation breaks down if tissue is strongly absorbing, which is common in the visible part of the spectrum or in applications that involve darkly pigmented skin and/or high local volumes of blood such as port-wine stain therapy or reconstructive flap monitoring. In these cases, a model of light transfer that can accommodate both strongly and weakly absorbing regimes is required. Here we present a model of light transfer through layered biological media that represents skin with two strongly scattering and one strongly absorbing layer.
Model for photon migration in turbid biological media
Journal of the Optical Society of America A, 1987
Various characteristics of photon diffusion in turbid biological media are examined. Applications include the interpretation of data acquired with laser Doppler blood-flow monitors and the design of protocols for therapeutic excitation of tissue chromophores. Incident radiation is assumed to be applied at an interface between a turbid tissue and a transparent medium, and the reemission of photons from that interface is analyzed. Making use of a discrete lattice model, we derive an expression for the joint probability r(n, p)d 2 p that a photon will be emitted in the infinitesimal area d 2 p centered at surface point p = (x, y), having made n collisions with the tissue. Mathematical expressions are obtained for the intensity distribution of diffuse surface emission, the probability of photon absorption in the interior as a function of depth, and the mean path length of detected photons as a function of the distance between the site of the incident radiation and the location of the detector. We show that the depth dependence of the distribution of photon absorption events can be inferred from measured parameters of the surface emission profile. Results of relevant computer simulations are presented, and illustrative experimental data are shown to be in accord with the theory.
Applied Optics, 1992
When a picosecond light pulse is incident upon a turbid medium such as tissue, the temporal distribution of diffusely reflected and transmitted photons depends on the optical absorption and scattering properties of the medium. From diffusion theory it is possible to derive analytic expressions for the pulse shape in terms of the optical interaction coefficients of a homogeneous semi-infinite medium. Experimental tests of this simple model in tissue-simulating liquid phantoms of different geometries are presented here. The results of these tests show that, in a semi-infinite phantom, the application of the diffusion model provides estimates of the absorption and transport-scattering coefficients that are accurate to better than 10%. Comparable accuracy was also obtained with this simple model for finite slab, cylindrical, and spherical volumes as long as the objects were of sufficient size. For smaller volumes the absorption coefficient was overestimated because of the significant loss of photons at the boundaries of the object.
1989
Abstruct-Using optical interaction coefficients typical of mammalian soft tissues in the red and near infrared regions of the spectrum, calculations of fluence-depth distributions, effective penetration depths and diffuse reflectance from two models of radiative transfer, diffusion theory, and Monte Carlo simulation are compared for a semi-infinite medium. The predictions from diffusion theory are shown to be increasingly inaccurate as the albedo tends to zero andlor the average cosine of scatter tends to unity.
Journal of Biomedical Optics, 2007
The use of perturbation and differential Monte Carlo ͑pMC/ dMC͒ methods in conjunction with nonlinear optimization algorithms were proposed recently as a means to solve inverse photon migration problems in regionwise heterogeneous turbid media. We demonstrate the application of pMC/dMC methods for the recovery of optical properties in a two-layer extended epithelial tissue model from experimental measurements of spatially resolved diffuse reflectance. The results demonstrate that pMC/dMC methods provide a rapid and accurate approach to solve two-region inverse photon migration problems in the transport regime, that is, on spatial scales smaller than a transport mean free path and in media where optical scattering need not dominate absorption. The pMC/dMC approach is found to be effective over a broad range of absorption ͑50 to 400%͒ and scattering ͑70 to 130%͒ perturbations. The recovery of optical properties from spatially resolved diffuse reflectance measurements is examined for different sets of source-detector separation. These results provide some guidance for the design of compact fiber-based probes to determine and isolate optical properties from both epithelial and stromal layers of superficial tissues.
Monte Carlo simulation of near-infrared light propagation through homogeneous mixed media
Journal of Biomedical Optics, 2013
Noninvasive blood analysis devices that can measure levels of small constituents of blood are of interest in the medical community. An important step in creating these devices is to understand the interaction of photons with human tissue in increasingly greater physiological detail. Models based on layered biological materials give excellent results for many applications but may not be as accurate as needed when those materials are finely intertwined to the point of resembling a homogeneous mixture. To explore the ramifications of treating materials as layers versus a mixture, we have modeled, using a Monte Carlo technique, the interaction of photons through epidermis, blood, and water arranged both in layers and in a homogeneous blend. We confirm the expected linear relation between photon attenuation and material volumetric percentage in two-layer models. However, when the materials are homogeneously mixed together and volumetric percentage is replaced with interaction volume percentage, this relationship becomes nonlinear. These nonlinearities become significant when the values of the interaction coefficient, μ t , differ by an order of magnitude or more.
Optics Letters, 2006
We use the Born approximation of the radiative transport equation to recover simultaneously the absorption and scattering coefficients in a single layer of a two-layer tissue sample from reflectance data. This method reduces the estimation of both optical properties to a single linear, least-squares problem. It is valid over length scales smaller than a transport mean free path and hence is useful for epithelial tissue layers. We demonstrate the accuracy of this method by using spatially resolved reflectance data computed with Monte Carlo simulations.
IEEE Transactions on Biomedical Engineering, 1989
Abstruct-Using optical interaction coefficients typical of mammalian soft tissues in the red and near infrared regions of the spectrum, calculations of fluence-depth distributions, effective penetration depths and diffuse reflectance from two models of radiative transfer, diffusion theory, and Monte Carlo simulation are compared for a semi-infinite medium. The predictions from diffusion theory are shown to be increasingly inaccurate as the albedo tends to zero andlor the average cosine of scatter tends to unity.