Modeling Light Scattering in Tissue as Continuous Random Media Using a Versatile Refractive Index Correlation Function

Abstract

Optical interactions with biological tissue provide powerful tools for study, diagnosis, and treatment of disease. When optical methods are used in applications involving tissue, scattering of light is an important phenomenon. In imaging modalities, scattering provides contrast, but also limits imaging depth, so models help optimize an imaging technique. Scattering can also be used to collect information about the tissue itself providing diagnostic value. Therapies involving focused beams require scattering models to assess dose distribution. In all cases, models of light scattering in tissue are crucial to correctly interpreting the measured signal. Here, we review a versatile model of light scattering that uses the Whittle–Matérn correlation family to describe the refractive index correlation function Bn (rd). In weakly scattering media such as tissue, Bn (rd) determines the shape of the power spectral density from which all other scattering characteristics are derived. This model encompasses many forms such as mass fractal and the Henyey–Greenstein function as special cases. We discuss normalization and calculation of optical properties including the scattering coefficient and anisotropy factor. Experimental methods using the model are also described to quantify tissue properties that depend on length scales of only a few tens of nanometers.

Subdiffusion reflectance spectroscopy to measure tissue ultrastructure and microvasculature: model and inverse algorithm

“…Unfortunately, the HGPF provides an inherently unphysical form of the phase function due to its lack of a dipole/Raleigh scattering component, a fact that is confirmed by the observed mismatch between the HGPF and goniometric measurements of cells. 12,29 In order to remedy this shortcoming, the modified HGPF 30 was developed by adding a cos 2 ðθÞ dipole term and introducing a weighting parameter that scales the relative contribution of the HGPF and dipole term. Nonetheless, while it may provide more satisfying fits with measured data, the modified HGPF remains largely empirically based and therefore provides a limited connection to the underlying physical origin of the phase function.…”

“…1. Rogers et al 12 provide a more thorough argument for modeling light scattering as a continuous random medium. We also note an exception to this argument in biological samples, such as adipose tissue or cell suspensions, in which it can be well argued that the spherical geometry justifies a proper application of Mie theory.…”

“…11 Taking insight from the way in which absorption analysis is applied, we and others have proposed a scattering model, which takes its main inspiration from considering the physical structure of tissue. [12][13][14] Assuming the validity of the Born approximation (a safe assumption for most solid tissues 15 ), the fundamental physical tissue characteristic, which gives rise to light scattering, is the spatial refractive index (RI) autocorrelation function, B n ðr d Þ. [16][17][18] If B n ðr d Þ is known, a series of simple mathematical transformations can be used to first derive PðθÞ and subsequently optical properties, such as the scattering coefficient μ s and anisotropy factor g as well as higher order shape parameters, such as γ, D, etc.…”

“…[16][17][18] If B n ðr d Þ is known, a series of simple mathematical transformations can be used to first derive PðθÞ and subsequently optical properties, such as the scattering coefficient μ s and anisotropy factor g as well as higher order shape parameters, such as γ, D, etc. 10,19 Since B n ðr d Þ can similarly be defined for discrete particles (e.g., spheres, 12 red bloods cells, 20 rods, 18 etc.) as well as continuous random media, it can serve as a universal mediator between all models of light scattering.…”

“…12,21 From a mathematical standpoint, this model encompasses a wide range of plausible functional forms for the shape of B n ðr d Þ, including Gaussian, stretch-exponential, and power-law distributions. As an added benefit for the optics community, one special case of the Whittle-Matérn model includes the commonly used modified Henyey-Greenstein model.…”