Study of Inhomogeneities in Turbid Media: Experimental and Numerical Results

CARBONE, NICOLÁS ABEL; DI ROCCO, H. O.; IRIARTE, D. I.; POMARICO, D. A.; RANEA SANDOVAL, H. F.; PARDINI, PAMELA; WAKS SERRA, MARÍA VICTORIA

Pueblo

Congreso; Congreso General ICO; 2011

Diffuse transmission of Near Infrared light through tissue is a tool for noninvasive imaging for diagnostic purposes. Most of the research has been focused over breast cancer imaging; however, major efforts have been also done in cerebral tomography and topography imaging, as well as in small animal imaging systems. Optical systems are currently under study for the functional imaging of the brain and the detection of breast tumours1,2. Despite its relative low spatial resolution compared to X- Rays, the interest in this novel non-invasive tool relies on its capability to optically characterize inhomogeneities and to obtain functional information of the tissues3, thus improving and complementing the techniques used for localization. The optical parameters to be measured are the absorption coefficient μa, the scattering coefficient, μs, the anisotropy factor g and the reduced scattering coefficient given by μ’s= μs(1 - g), which is the inverse of the transport mean free path. The propagation of light in turbid media is best described by the Radiative Transfer Equation (RTE)4,5, which is the expression of the balance of energy inside a volume element of the scattering medium. An analytical model widely used to describe this phenomenon is the Diffusion Approximation (DA) to the RTE, , where is the diffuse intensity, is the diffusion coefficient and is the photon source. DA has shown to be precise even in fairly complex systems, but much simpler to implement than the RTE. Diffusion theory describes light transport accurately only in the strong scattering regime that is, where the reduced scattering coefficient is much larger than the absorption coefficient, μ ‘s >> μa, and the observation point, where light is collected, is far from the sources and boundaries.11 Experimentally, there are three different techniques for studying turbid media: Time Resolved (TR)6,7, using short pulses, Frequency – Domain (FD)8,9, by high frequency modulation of continuous sources, and Continuous Wave(CW)10,11. In this work, we use the TR approach. The shape and amplitude of time resolved transmittance, which is the Distribution of Times of Flight (DTOF) of photons, depends on both the scattering and the absorption properties. Thus from the analysis of the shape of a DOTF it is possible to obtain information about the optical properties of the medium. This shape analysis can be made by using the different moments of the distribution. In particular, the zero order moment is the total integrated intensity, the first order moment is the Mean Time of Flight of the photons, etc. In this contribution we analyze the transilluminance profiles when absorbing cylindrical inclusions are submerged in rectangular tanks of liquid phantoms made of a solution containing water, milk and india ink. The free surfaces of the tank are scanned using a pulsed (70ps) NIR laser to illuminate one face and a colineal fiber at the other face of the tank to collect light. Inclusions are made from similar solutions but are gelified by adding 2% of Agarose to the solution. The ink proportion in the inclusion relative to that of the liquid bulk determines the “more” or “less” absorbing nature of the inclusion. The spatial profiles obtained from the zero order moment (which is equivalent to a CW experiment) under some experimental conditions show an apparently contradictory effect when the absorption coefficient of the inclusion is higher than that of the bulk. In this case, the profiles may present a peak of higher intensity (less absorption?) at the inclusion. In the experiments To study this effect we designed a controlled experiment using the same inclusion, but the scattering coefficient of the bulk was varied from a small one (low milk proportion) one to a concentrated one (high milk proportion). Simultaneously, the corresponding ink amount was added, to keep constant the absorption coefficient of the bulk. We show that the absorption alone is not the relevant parameter, but the product k=μa μs . If this product for the inclusion is lower than that of the bulk, the zero order moment (integrated intensity profile) has a peak where the inclusion is located. On the contrary, the first order moment (Mean Time of Flight) presents a dip at the more absorbing inclusion, apparently solving this problem. However, a complete analysis involving higher order moments is required to address all possible combinations of absorption and scattering parameters. A comparison was made between an experiment and a theoretical model for cylindrical inclusions and with Monte Carlo (MC) simulations using Graphics Processing Units12 based on Compute Unified Device Architecture (CUDA) that reduce the times of calculations.