Radiative transfer and optical imaging in biological media by low-order transport approximations: the simplified spherical harmonics (SP N ) approach

Abstract

Radiative transfer theory (RTT) is a valuable theoretical framework for describing the propagation of optical radiation in turbid media (Ishimaru, 1978; Wang and Wu, 2007). RTT has succeeded in fields such as astronomy and astrophysics (Chandrasekhar, 1960), remote sensing of the earth surface and atmosphere (Melnikova et al., 2012), heat transfer (Howell et al., 2010; Modest, 2003; Atalay, 2006), and, particularly, in biomedical optics (Wang and Wu, 2007; Hielscher et al., 2011; Klose, 2010a). The fundamental equation in RTT is the radiative transfer equation (RTE) (Wang and Wu, 2007). The RTE is the most accurate model for describing light propagation in biological tissue, with no approximation regarding the angular, spatial or temporal dependences (Hielscher et al., 2011). The RTE is an integrodifferential equation that depends on a set of optical parameters (index of refraction, absorption, scattering and scattering function) that describe the medium (Ishimaru, 1978). The validity limits of the RTE rest on the model conceived to describe light propagation, and should be established for each physical situation (Marti Lopez et al., 2003). Analytical solutions of the RTE are only known for simple geometries (Ishimaru, 1978; Liemert and Kienle, 2011b).