Photon Migration In Turbid Media Research Articles

Equivalence of four Monte Carlo methods for photon migration in turbid media

In the field of photon migration in turbid media, different Monte Carlo methods are usually employed to solve the radiative transfer equation. We consider four different Monte Carlo methods, widely used in the field of tissue optics, that are based on four different ways to build photons' trajectories. We provide both theoretical arguments and numerical results showing the statistical equivalence of the four methods. In the numerical results we compare the temporal point spread functions calculated by the four methods for a wide range of the optical properties in the slab and semi-infinite medium geometry. The convergence of the methods is also briefly discussed.

Solution of the direct problem in turbid media with inclusions using Monte Carlo simulations implemented in graphics processing units: new criterion for processing transmittance data

The study of light propagation in diffusive media requires solving the radiative transfer equation, or eventually, the diffusion approximation. Except for some cases involving simple geometries, the problem with immersed inclusions has not been solved. Also, Monte Carlo (MC) calculations have become a gold standard for simulating photon migration in turbid media, although they have the drawback large processing times. The purpose of this work is two-fold: first, we introduce a new processing criterion to retrieve information about the location and shape of absorbing inclusions based on normalization to the background intensity, when no inhomogeneities are present. Second, we demonstrate the feasibility of including inhomogeneities in MC simulations implemented in graphics processing units, achieving large acceleration factors ( approximately 10(3)), thus providing an important tool for iteratively solving the forward problem to retrieve the optical properties of the inclusion. Results using a cw source are compared with MC outcomes showing very good agreement.

Acceleration of Monte Carlo modeling of light transport in turbid media; an approach based on hybrid, theoretical and numerical, calculations

A novel method to accelerate Monte Carlo (MC) simulations of photon migration in turbid media is presented. It is specifically suited for transillumination studies in slab geometries including some deep inhomogeneity. Propagation up to the inhomogeneity, at a given depth S 1 , is replaced by theoretical calculations using well established models. Then, photon propagation is continued inside the complete slab using MC rules until detection or absorption occurs. We report improvements in speed in factors up to approximately 10; the deeper the inhomogeneity, the larger the improvement. Examples are given showing that information remains unchanged with respect to pure MC simulations.

Controlled Monte Carlo method for light propagation in tissue of semi-infinite geometry

The controlled Monte Carlo method is generalized to model photon migration in turbid media of arbitrary geometries. Its implementation for the reflection geometry is exemplified in this paper. The most probable diffuse direction of light is used as the local attractive vector that serves as the basis of biased sampling of scattering angles. Consequently, path-length resolved photon trajectories can be generated with a significantly improved efficiency. We report a more than 29 times reduction in simulation time for early arriving photons in a typical configuration.

Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions

In this paper, a coupled radiative transfer equation and diffusion approximation model is extended for light propagation in turbid medium with low-scattering and non-scattering regions. The light propagation is modelled with the radiative transfer equation in sub-domains in which the assumptions of the diffusion approximation are not valid. The diffusion approximation is used elsewhere in the domain. The two equations are coupled through their boundary conditions and they are solved simultaneously using the finite element method. The streamline diffusion modification is used to avoid the ray-effect problem in the finite element solution of the radiative transfer equation. The proposed method is tested with simulations. The results of the coupled model are compared with the finite element solutions of the radiative transfer equation and the diffusion approximation and with results of Monte Carlo simulation. The results show that the coupled model can be used to describe photon migration in turbid medium with low-scattering and non-scattering regions more accurately than the conventional diffusion model.

Photon migration in turbid media with anisotropic optical properties

We analyse properties of photon migration in reflectance measurements made on a semi-infinite medium bounded by a plane, in which optical parameters may vary in directions neither parallel to, nor perpendicular to the bounding plane. Our aim in doing this is to develop the formulae necessary to deduce parameters of directionality from both time-gated and continuous wave measurements. The mathematical development is based on a diffusion picture, in which the bounding plane is regarded as being totally absorbing so that all photons reaching the surface contribute to the reflectance.

A finite element-spherical harmonics radiation transport model for photon migration in turbid media

In this paper, we solve the steady-state form of the Boltzmann transport equation in homogeneous and heterogeneous tissue-like media with a finite element-spherical harmonics (FE- P N ) radiation transport method. We compare FE-transport and diffusion solutions in terms of the ratio of absorption to reduced scattering coefficient, ( μ a/ μ s′) and the anisotropy factor g. Two different scattering phase function formulas are employed to model anisotropic scattering in the slab media with high g-value. Influence of void-like heterogeneities, and of their boundaries with the surrounding medium on the transport of photons are also examined.

Photon migration in turbid media: a finite-element solution for the most favorable path

A better understanding of the fundamental principles of photon migration in highly scattering media is of great importance for developing new methods for disease diagnosis, imaging, and tomography. In this paper we present a most-favorable-path approach to the problem of light propagation in turbid media, based on the diffusion equation. The most favorable path, on which photons will be found, can be obtained from the path of the net flux propagation. The diffusion intensity and the direction of the net flux can be calculated with the finite-element method, which can deal with heterogeneous problems and frequency-domain problems within complex geometry, and can introduce boundary effects as well. Simulations were conducted for phantoms with different optical parameters and source-detector separations. Experiments have been performed to verify this new method. The most favorable path is found to be more sensitive to the source-detector separation and the absorption coefficient of the medium than to the scattering coefficient. The feasibility of using the theory in optical tomography for the recognition of objects hidden in turbid media is discussed.

Photon migration in turbid media using a cumulant approximation to radiative transfer

A photon transport model for light migration in turbid media based on a cumulant approximation to radiative transfer is presented for image reconstruction inside an infinite medium or a bounded medium with a planar geometry. This model treats weak inhomogeneities through a Born approximation of the Boltzmann radiative transfer equation and uses the second-order cumulant solution of photon density to the Boltzmann equation as the Green's function for the uniform background. It provides the correct behavior of photon migration at early times and reduces at long times to the center-moved diffusion approximation. At early times, it agrees much better with the result from the Monte Carlo simulation than the diffusion approximation. Both approximations agree well with the Monte Carlo simulation at later times. The weight function for image reconstruction under this proposed model is shown to have a strong dependence at both early and later times on absorption and/or scattering inhomogeneities located in the propagation direction of and close to the source, or in the field of view of and close to the detector. This effect originates from the initial ballistic motion of incident photons, which is substantially underestimated by the diffusion approximation.

Recent Advances in Optical Tomography Techniques for Biomedical Imaging.

Optical imaging of biological tissues is a fast growing field that brings state-of-the-art laser and optical technologiestogether with physical and clinical sciences. Many new concepts and detection techniques developedin the past several years have evolved this field from basic study of photon migration in turbid media to clinicalpractice. This paper reviews some of the recent developments in the study of optical tomography, which alsomay imply the future direction of biomedical imaging by means of optical methods.

The continuous-time random walk description of photon motion in an isotropic medium

Lattice random walk models are useful alternatives to diffusion theory for describing photon migration in turbid media. Results obtained from random walk models were, in the past, based on approximating the propagator as a Gaussian function. This is equivalent to assuming that a large number of steps have been taken. We show that a particular, physically plausible, continuous-time random walk (CTRW) model can be solved exactly. At sufficiently long times the solution reduces to that for a random walk in discrete time. We provide exact solutions to problems related to cw reflection measurements and indicate some generalizations to time-gated measurements made on a uniform medium.

Effect of the scattering delay on time-dependent photon migration in turbid media

We modified the diffusion approximation of the time-dependent radiative transfer equation to account for a finite scattering delay time. Under the usual assumptions of the diffusion approximation, the effect of the scattering delay leads to a simple renormalization of the light velocity that appears in the diffusion equation. Accuracy of the model was evaluated by comparison with Monte Carlo simulations in the frequency domain for a semi-infinite geometry. A good agreement is demonstrated for both matched and mismatched boundary conditions when the distance from the source is sufficiently large. The modified diffusion model predicts that the neglect of the scattering delay when the optical properties of the turbid material are derived from normalized frequency- or time-domain measurements should result in an underestimation of the absorption coefficient and an overestimation of the transport coefficient. These observations are consistent with the published experimental data.

Photon migration at short times and distances and in cases of strong absorption

Diffusion theory is widely used to describe photon migration in turbid media because it is simple and, in certain cases, can be accurate to within a few percent. However, it neglects the ballistic nature of photon propagation between successive scattering events and hence entirely breaks down for short times and distances, as well as for strong absorption. Here we generalize on the exact two-stream theory of one-dimensional photon migration to obtain a telegrapher equation that accounts for both diffusive and ballistic aspects of propagation in three-dimensional media. At long times and distances the standard diffusion theory is recovered, whereas at short times and distances we find improved predictions for such phenomena as pulse spreading, diffuse photon-density wave dispersion, transmission through a slab, and pulse reflection from a semi-infinite medium. Our theory should be useful for accurately characterizing turbid media, such as biological tissues, and may also aid in improving the spatial resolution of images made with diffuse light.