Photon diffusion near the point-of-entry in anisotropically scattering turbid media

Abstract

From astronomy to cell biology, the manner in which light propagates in turbid media has been of central importance for many decades. However, light propagation near the point-of-entry (POE) in turbid media has never been analytically described, until now. Here we report a straightforward and accurate method that overcomes this longstanding, unsolved problem in radiative transport. Our theory properly treats anisotropic photon scattering events and takes the specific form of the phase function into account. As a result, our method correctly predicts the spatially dependent diffuse reflectance of light near the POE for any arbitrary phase function. We demonstrate that the theory is in excellent agreement with both experimental results and Monte Carlo simulations for several commonly used phase functions.

Light scattering spectroscopy identifies the malignant potential of pancreatic cysts during endoscopy

“…It is precisely these photons which are sensitive to the structure of the epithelial layer. Fortunately, our recently published work 27 solves this long-standing problem in radiative transport 28,29 , and provides a highly accurate analytic expression for the spatially dependent reflectance near the point of entry and provides a means to evaluate the backscatter signal from the signals measured by the spatial gating probe. This allows obtaining the same diagnostic parameter, Δ, from spatially gated data that we used with polarization gated data (see Methods).…”

“…3c) collected with the spatial gating probe we utilize the fact that the contribution of backscattering to the total spatially resolved reflectance decreases with the increase in source-detector separation r , significantly faster than that of the multiple scattering signal 27 . Supplementary Figure 1 shows contribution of the single large angle backscattering component and the diffuse reflectance component in epithelial tissue with a reduced scattering coefficient 49 ${\mu }_s^{\prime }=3{\text{mm}}^{-1}$ for the closest ( r 1 = 120 μm ) and farthest ( r 2 = 240 μm ) fibers in the spatial gating probe.…”

Modeling subdiffusive light scattering by incorporating the tissue phase function and detector numerical aperture

“…[3][4][5] However, for overlapping source-detector geometries, challenges remain regarding incorporation of the tissue phase function. 3,4 To model light transport, solutions to the radiative transport equation (RTE) involve expanding the radiance into a series of i spherical harmonics and the phase function into i Legendre polynomials. The latter are weighted with their moments g i , where g 1 is commonly referred to as the scattering anisotropy.…”

Phase-function corrected diffusion model for diffuse reflectance of a pencil beam obliquely incident on a semi-infinite turbid medium

“…Unfortunately, accurate analytical models of light propagation in tissue near the point-of-entry and for cases where absorption is high or comparable with scattering have been difficult to obtain. Recently, Vitkin et al 28 described an elegant phase-function corrected (PFC) diffusion approximation to the radiative transport equation which permitted an analytical description of a pencil beam normally incident on a semi-infinite turbid medium. In this paper, we extend their work to include a pencil beam obliquely incident on a semi-infinite turbid medium, and investigate the accuracy of the models by comparing them with Monte Carlo simulations.…”

“…Vitkin et al 28 found that the time-independent radiative transport equation where L is radiance, S is the source radiance distribution, r is a field point, s is a unit vector, μ t ¼ μ a þ μ s is the total interaction coefficient, the sum of the absorption and scattering coefficients, respectively, with normally incident collimated pencil-beam L c ðr;…”