To detect small-scale changes in tissue with optical techniques, small sampling volumes are required. Single fiber reflectance (SFR) spectroscopy has a sampling depth of a few hundred micrometers. SFR spectroscopy uses a single fiber to emit and collect light. The only available model to determine optical properties with SFR spectroscopy was derived for tissues with modified Henyey–Greenstein phase functions. Previously, we demonstrated that this model is inadequate for other tissue phase functions. We develop a model to relate SFR measurements to scattering properties for a range of phase functions, in the absence of absorption. Since the source and detector overlap, the reflectance cannot be accurately described by diffusion theory alone: SFR measurements are subdiffuse. Therefore, we describe the reflectance as a combination of a diffuse and a semiballistic component. We use the model of Farrell et al. for the diffuse component, solved for an overlapping source and detector fiber. For the semiballistic component, we derive a new parameter, psb, which incorporates the integrals of the phase function over 1 deg in the backward direction and 23 deg in the forward direction. Our model predicts the reflectance with a median error of 2.1%, compared to 9.0% for the currently available model.
To detect small-scale changes in tissue, small sampling volumes and, therefore, short source–detector separations are required. In this case, reflectance measurements are not adequately described by the diffusion approximation. It has been shown that such subdiffusive measurements are sensitive to the phase function of tissue (the probability distribution of scattering angles). Three parameters related to the tissue phase function have been proposed to describe subdiffusive reflectance: gamma, sigma, and RpNA. For an overlapping source-detector geometry (e.g. Single Fiber Reflectance spectroscopy, or SFR), it has been shown that RpNA outperforms gamma and sigma. RpNA was derived using the assumptions that detected photons undergo only a single backscatter event in combination with an arbitrary number of forward scattering events, and that all scattering angles occur within the acceptance angle of the detector, theta_NA, where theta_NA = arcsin(NA/nsample).
We further investigated the phase function influence, by determining the distribution of scattering angles for detected photons – which we term the ‘effective phase function’. We will show that the assumption that all scattering angles occur within the acceptance angle of the detector is incorrect. Based on our results for the effective phase function, we derived a new parameter, Rpeff. We performed Monte Carlo simulations for overlapping source/detector geometries for a range of phase functions, reduced scattering coefficients, NAs, and source/detector diameters, which showed that Rpeff improves the prediction of the measured reflectance compared to gamma, sigma, and RpNA. We developed a model for an overlapping source-detector geometry incorporating Rpeff, to derive scattering and absorption properties of tissue.