24 July 2006 On the problem of simple renormalization of diffusion asymptotics in optical beam reflectance by biological media
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Abstract
The problem of pencil optical beam reflectance by semi-infinite biological media is considered using microscopic hybrid approach to the radiative transfer equation (RTE). This approach is based on the reciprocity of the Green function for the radiative transfer theory and the iteration procedure of the solution to the integral equation for Green function written in reciprocal form. As a result the solution to the RTE is represented as a sum of two terms. The first one is diffusely reflected by biological media radiation with a finite-order scattering. The second term represents a convolution of the RTE Green function with an effective source function. The microscopic hybrid method enabled improving accuracy of the standard diffusion approximation in the problem of pencil optical beam reflectance by biological media. The relative error of the microscopic hybrid method with respect to Monte Carlo simulation is within 6% and included also the media with peak forwarded phase function of single scattering event. The main advantage of our method is that it does not use heuristic assumptions the well known in the literature hybrid models are based on. However, it is desirable to use a simple renormalization of standard diffusion asymptotics for practical applications, for example, to determine a blood oxygenation. It can significantly reduce processing time of experimental measurements. Such a simple renormalization of diffusion asymptotics is given in this work. The method lies in the selection of a factor for diffusion asymptotics at given interval distances from incident point along the surface. It is shown that acceptable accuracy for the measurements of relative values of reflectance by semi-infinite biological media is provided.
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Alexander Y. Appanov, Alexander Y. Appanov, Yuri N. Barabanenkov, Yuri N. Barabanenkov, } "On the problem of simple renormalization of diffusion asymptotics in optical beam reflectance by biological media", Proc. SPIE 6163, Saratov Fall Meeting 2005: Optical Technologies in Biophysics and Medicine VII, 61631F (24 July 2006); doi: 10.1117/12.697344; https://doi.org/10.1117/12.697344
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