Solutions of the Direct Problem in Turbid Media with Inclusions using Monte Carlo Simluations and Transmited Light Experiments

CARBONE, NICOLÁS ABEL; DI ROCCO, H. O.; IRIARTE, D. I.; POMARICO, D. A.; RANEA SANDOVAL, H. F.

Lima

Congreso; RIAO-OPTILAS 2010; 2010

Pontificia Universidad Católica del Perú

Near Infrared (NIR) Light propagation inside turbid media, like polymers, milky solutions and biological tissues, is dominated by multiple scattering. Its study is of great interest in biomedical optics, including diagnostic techniques like detection of breast cancer and bedside monitoring of organs oxygenation. Turbid media are completely characterized by three parameters, namely: absorption coefficient, scattering coefficient, and anisotropy factor. A reduced scattering coefficient, , can also be defined, being the transport mean free path(1). The real ultimate goal is to solve the so called inverse problem, that is, to retrieve the optical properties of a turbid medium given the light distribution at its output. On the contrary, one refers to the (much easier) direct problem if the light distribution is to be obtained from a given set of optical properties inside the medium (homogeneous or not). The solution of the direct problem for light propagation in these media requires solving the (relatively) complicated Radiative Transfer Equation. However, in most practical cases, where scattering dominates light propagation is described by the Diffusion Approximation (DA), given by , where U(r) is the desired diffuse intensity, D is the diffusion coefficient and E(r) is the photons source. Solutions of the DA can be obtained with relative ease for homogeneous media but become more complicated for media with inclusions, which are of real interest for practical biomedical problems. Because of its flexibility, Monte Carlo (MC) numerical simulations are appropriate for these complex cases. The only drawback is that MC simulations are computationally very intensive(2-5). Recently(6,7), parallel processing using Graphics Processing Units (GPU), based on Compute Unified Device Architecture (CUDA), has reduced calculation times by a factor of 102 to 103. This allows iteratively solving the direct problem until the optical properties of the inclusion(s) is (are) obtained, by matching the light transmittance obtained by MC with the corresponding experimental one. This is the approach presented in this contribution and it requires two steps: 1) Locating the inhomogeneities inside the medium. This is done by normalization of a transmittance image of the turbid medium with the inclusions by an image of it without inclusions (See Results I). 2) After that, MC simulations implemented in CUDA are iteratively run for the medium with inclusions, which optical properties are varied from one simulation to another until the experimental profiles are matched by the simulations. As a figure of merit least squares is used. Examples for a highly absorbing inclusion and for an inclusion with absorption similar to tumors are presented in Results II. The nominal and retrieved optical properties are given in the table.