Light Propagation In Biological Tissue Research Articles

Transport theory for light propagation in biological tissue: erratum

Transport theory for light propagation in biological tissue: erratum

Monte Carlo analysis of near‐infrared light propagation in a neonatal head model

AbstractIn brain function measurement using near‐infrared light, it is very important to make a theoretical analysis of light propagation in the head tissue, since it is impossible to measure the effect of optical fiber arrangement on the region of measurement or its sensitivity. The Monte Carlo method is widely used in the analysis of near‐infrared light propagation in biological tissue, since it allows light propagation analysis of heterogeneous tissue by a relatively simple algorithm. In this study, a model simulating the cross‐sectional structure of the neonatal head is constructed by using square elements, and the light propagation is analyzed. First, the variance‐reduction (VR) method and the delta‐scattering (DS) method, which are typical algorithms of the Monte Carlo method, are applied to the model composed of square elements, and the results of the analysis and the computation time for light propagation are compared and discussed. It is shown that the DS method is useful for a model composed of small square elements, since the computation time depends little on the size of the elements. As a result of analysis of light propagation in the neonatal head model using the DS method, we see that light propagation is greatly affected by the heterogeneity of the head tissue. © 2004 Wiley Periodicals, Inc. Syst Comp Jpn, 35(9): 60–69, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10246

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 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.

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.

ANALYSIS OF OPTICAL TOMOGRAPHY WITH NON-SCATTERING REGIONS

AbstractThis paper provides mathematical analysis of optical tomography in a situation when the examined object, for example the human brain, is strongly scattering with non-scattering inclusions. Light propagation in biological tissue is often modelled by the diffusion approximation of the radiative transfer equation. To be justified, the diffusion approximation demands that the medium is strongly scattering. Naturally, this is not true for non-scattering inclusions, for which some other model is needed. This is found through geometrical optics. Combination of the two models leads to an elliptic partial differential equation with boundary conditions on the outer boundary as well as on the boundaries of the non-scattering regions. The well-posedness of this forward problem is the main concern of this work.AMS 2000 Mathematics subject classification: Primary 35Q60; 35R30

Diffuse Optical Tomography by Inverse Problem Technique.

Diffuse optical tomography using near infrared light has been developed for the purpose of imaging oxygenation states in human body. The technology is classified into three groups by measuring techniques; CW, frequency and time domain techniques. This review describes light propagation in biological tissues and their optical properties for solving the forward problem in the image reconstruction algorithm which resorts to the technique of inverse problems. Recent development of the algorithms are also reviewed and future applications are described.

Experimental validation of Monte Carlo and finite-element methods for the estimation of the optical path length in inhomogeneous tissue

To validate models of light propagation in biological tissue, experiments to measure the mean time of flight have been carried out on several solid cylindrical layered phantoms. The optical properties of the inner cylinders of the phantoms were close to those of adult brain white matter, whereas a range of scattering or absorption coefficients was chosen for the outer layer. Experimental results for the mean optical path length have been compared with the predictions of both an exact Monte Carlo (MC) model and a diffusion equation, with two differing boundary conditions implemented in a finite-element method (PEM). The MC and experimental results are in good agreement despite poor statistics for large fiber spacings, whereas good agreement with the FEM prediction requires a careful choice of proper boundary conditions.

An ARX model for light propagation in biological tissue.

For many applications in biomedical engineering, and especially for precise dosimetry in photodynamic therapy, it is essential to determine the absorption and scattering of light in biological tissue very precisely. At present it is not possible to measure the absorption and scattering coefficient separately by using an endoscopic sensor based upon the backscattering phenomenon. In this paper, we propose a solution to this problem. We present a new model derived from Kubelka and Munk's theory, which is known to be suitable for the description of optical phenomena in tissue. Then we apply an algorithm often used in signal processing, the Auto Regressive with eXternal input or ARX model, which allows us to determine both optical coefficients separately. A first validation is done by numerical simulation, then measurements with phantoms were done. The results of both tests prove the model to be reliable and effective.

Contribution of an ARX Modeling of Light Propagation in Biological Tissue to Measurement by Backscattering in Pulse Oximetry

Contribution of an ARX Modeling of Light Propagation in Biological Tissue to Measurement by Backscattering in Pulse Oximetry

Low-degree polynomial phase-functions with high g-value (light propagation in biological tissues)

In an attempt to construct an analytic theory of anisotropic random flight, the need has arisen to construct phase-functions for which the expansion in spherical harmonics has only a limited number of terms, but which have a high value for the asymmetry parameter g. The authors describe the procedure to find the phase-function which has a maximum value of g for given N, where N is the number of spherical components of the phase-function. It appears that in order to attain g = 0.9, one needs a phase-function composed of at least nine spherical components, or equivalently a polynomial of degree nine.