Frequency domain photon migration in the delta- P1 approximation: analysis of ballistic, transport, and diffuse...

The standard diffusion approximation (SDA) to the Boltzmann transport equation (BTE) is commonly used to describe radiative transport for biomedical applications of frequency-domain diffuse optical imaging and spectroscopy. Unfortunately, the SDA is unable to provide accurate radiative transport predictions on spatial scales comparable to the transport mean free path and for media in which optical scattering is not dominant over absorption. Here, we develop and demonstrate the use of the delta- P1 approximation to provide improved radiative transport estimates in the frequency domain via the addition of a Dirac delta function to both radiance and phase function approximations. Specifically, we consider photon density wave propagation resulting from the illumination of an infinite turbid medium with an embedded, intensity-modulated, spherical light source. We examine the accuracy of the standard diffusion and delta- P1 approximations relative to Monte Carlo simulations that provide exact solutions to the BTE. This comparison establishes the superior accuracy of the delta- P1 approximation relative to the SDA that is most notable at distances less than 3 transport mean free paths from the source. In addition, we demonstrate that the differences in photon density wave propagation in a highly forward scattering medium (g1=0.95) vs an isotropically scattering medium (g1=0) provides a basis to define three spatial regimes where the light field is dominated by (a) unscattered/ballistic light, (b) minimally scattered light, and (c) diffusely scattered light. We examine the impact of optical properties, source modulation frequency, and numerical aperture of detection on the spatial extent and location of these regimes.