Biomedical subjects

Arnold D Kim

Publications and source records attributed to Arnold D Kim.

8 recordsLinked to original sources

PubMed2006

Estimating optical properties in layered tissues by use of the Born approximation of the radiative transport equation.

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.

Algorithms↗

PubMed2006

Self-consistent scattering theory for the radiative transport equation.

We study light propagation in a random medium governed by the radiative transport equation. We present a theory for the transport equation with an inhomogeneous absorption coefficient. We obtain an analytical expression for the specific intensity in a uniform absorbing and scattering medium containing a point absorber. Using that result we derive a self-consistent system of integral equations to study a collection of point absorbers. We show numerical results that demonstrate the use of this theory.

Journal Article↗

PubMed2004

Light propagation in biological tissues containing an absorbing plate.

We study light propagation in biological tissue containing an absorbing obstacle. In particular, we solve the infinite-domain problem in which an absorbing plate of negligible thickness prevents a portion of the light from the source from reaching the detector plane. Inasmuch as scattering in the medium is sharply peaked in the forward direction, we replace the governing radiative transport equation with the Fokker-Planck equation. The problem is solved first by application of the Kirchhoff approximation to determine the secondary source distribution over the surface of the plate. That result is propagated to the detector plane by use of Green's function. The Green's function is given as an expansion of plane-wave modes that are calculated numerically. The radiance is shown to obey Babinet's principle. Results from numerical computations that demonstrate this theory are shown.

Biological Phenomena↗

PubMed2004

Backscattering of beams by forward-peaked scattering media.

For a beam impinging on a scattering medium the diffusion approximation to the radiative transport equation is not valid for analyzing the radiance near the source, especially if the medium scatters strongly with a sharp forward peak. To analyze the radiance, we use the Fokker-Planck approximation to the radiative transport equation. Numerical results show a backscattered ring appearing around the beam center. It also appears in Monte Carlo simulations of the radiative transport equation. This ring is manifested from successive near-forward scattering events, so it requires a directional description. Therefore the diffusion approximation cannot predict this ring.

Journal Article↗

PubMed2004

Beam propagation in sharply peaked forward scattering media.

We calculate the radiance of a light beam propagating in a uniformly scattering and absorbing slab and determine the point-spread function. We do this by solving numerically the governing radiative transport equation by use of plane-wave mode expansions. When scattering is sharply peaked in the forward direction and it becomes difficult to solve the radiative transport equation, we replace it with either the Fokker-Planck or the Leakeas-Larsen equation. We also solve these equations by using plane-wave mode expansions. Numerical results show that these two equations agree with the radiative transport equation for large anisotropy factors. The agreement improves as the optical thickness increases.

Journal Article↗

PubMed2004

Transport theory for light propagation in biological tissue.

We study light propagation in biological tissue using the radiative transport equation. The Green's function is the fundamental solution to the radiative transport equation from which all other solutions can be computed. We compute the Green's function as an expansion in plane-wave modes. We calculate these plane-wave modes numerically using the discrete-ordinate method. When scattering is sharply peaked, calculating the plane-wave modes for the transport equation is difficult. For that case we replace it with the Fokker-Planck equation since the latter gives a good approximation to the transport equation and requires less work to solve. We calculate the plane-wave modes for the Fokker-Planck equation numerically using a finite-difference approximation. The method of computing the Green's function for it is the same as for the transport equation. We demonstrate the use of the Green's function for the transport and Fokker-Planck equations by computing the point-spread function in a half-space composed of a uniform scattering and absorbing medium.

Light↗

PubMed2003

Light propagation in biological tissue.

Biological tissue scatters light mainly in the forward direction where the scattering phase function has a narrow peak. This peak makes it difficult to solve the radiative transport equation. However, it is just for forward-peaked scattering that the Fokker-Planck equation provides a good approximation, and it is easier to solve than the transport equation. Furthermore, the modification of the Fokker-Planck equation by Leakeas and Larsen provides an even better approximation and is also easier to solve. We demonstrate the accuracy of these two approximations by solving the problem of reflection and transmission of a plane wave normally incident on a slab composed of a uniform scattering medium.

Biological Phenomena↗

PubMedDate not supplied

Light transport in two-layer tissues.

We study theoretically light backscattered by tissues using the radiative transport equation. In particular we consider a two-layered medium in which a finite slab is situated on top of a half space. We solve the one-dimensional problem in which a plane wave is incident normally on the top layer and is the only source of light. The solution to this problem is obtained formally by imposing continuity between the solutions for the upper and lower layers. However, we are interested solely in probing the top layer. Assuming that the optical properties in the lower layer are known, we remove it from the problem yielding a finite slab problem by prescribing an alternate boundary condition. This boundary condition is derived using the theory of Green's functions and is exact. Hence, one needs only to solve the transport equation in a finite slab using this alternate boundary condition. We derive an asymptotic solution for the case when the slab is optically thin. We extend these results to the three-dimensional problem using Fourier transforms. These results are validated by comparisons with numerical solutions for the entire two-layered problem.

Biological Transport↗