Optical scattering properties of soft tissue: a discrete particle model

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Abstract
We introduce a micro-optical model of soft biological tissue that permits numerical computation of the absolute magnitudes of its scattering coefficients. A key assumption of the model is that the refractive-index variations caused by microscopic tissue elements can be treated as particles with sizes distributed according to a skewed log-normal distribution function. In the limit of an infinitely large variance in the particle size, this function has the same power-law dependence as the volume fractions of the subunits of an ideal fractal object. To compute a complete set of optical coefficients of a prototypical soft tissue (single-scattering coefficient, transport scattering coefficient, backscattering coefficient, phase function, and asymmetry parameter), we apply Mie theory to a volume of spheres with sizes distributed according to the theoretical distribution. A packing factor is included in the calculation of the optical cross sections to account for correlated scattering among tightly packed particles. The results suggest that the skewed log-normal distribution function, with a shape specified by a limiting fractal dimension of 3.7, is a valid approximation of the size distribution of scatterers in tissue. In the wavelength range 600 ≤ λ ≤ 1400 nm, the diameters of the scatterers that contribute most to backscattering were found to be significantly smaller (λ/4–λ/2) than the diameters of the scatterers that cause the greatest extinction of forward-scattered light (3–4λ).