ECE532 Biomedical Optics © 1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute

Mie scattering from cellular structures

Soft tissue optics are dominated by the lipid content of the tissues. Such lipid constitutes the cellular membranes, membrane folds, and membranous structures such as the mitochondria (about 0.5 µm). While other objects such as protein aggregates and the nucleus are also sources of scattering, the lipid/water interface of membranes presents a strong refractive index mismatch and so plays a major role is scattering. The following graph summarizes the lipid contents of various tissues:

Lipid contents of tissues

Mie theory provides a simple first approximation to the scattering of soft tissues [ref. 2]. The approximation involves a few assumptions:

• Assume the refractive index of the lipid membranes of cells is 1.46, based on the reported 1.43-1.49 range for hydrogenated fats [ref. 3].
• Assume the refractive index of the cytosol of cells is 1.35, based on the reported value for cellular cytoplasms [ref. 1].
• Assume the lipid content of soft tissue is about 1-10% (f_v = 0.02-0.10). Let's choose f_v = 0.02 for this example to match the value for several typical soft tissues such as lungs, spleen, prostate, ovary, intestine, liver, arteries, to name a few.
• Assume all the lipid is packaged as small spheres of various sizes whose number density maintains a constant volume fraction f_v.
• Ignore the interference of scattered fields from particles which can alter the apparent scattering properties based on isolated particles.

In the following graphs, a 2% volume fraction of lipid is packaged as spheres of one size, for a series of choices of sphere diameter (radius a), adjusting the number density to maintain a constant volume fraction:

Scattering coefficient µ_s

Scattering anisotropy, g

Reduced Scattering µ_s(1 - g)

This picture includes the experimental values of µ_s(1 - g) for dog prostate, illustrating that the prostate is mimicked by a 2% volume fraction of lipid spheres in the 0.200-0.600 µm diameter range. Other soft tissues vary only a little from this general pattern for prostate tissue.

In summary

The wavelength dependence of light scattering in soft tissues such as the prostate suggests that cellular structures equivalent to spheres with diameters in the range of 0.200-0.600 µm contribute most of the scattering. The magnitude of the scattering suggests that a volume fraction of 0.02 or 2%, which is roughly the reported lipid content of prostate and many other soft tissues, yields a magnitude for µ_s(1 - g) which matches the magnitude of µ_s(1 - g) for prostate. Deviations from our assumed values for n_p based on lipid and n_med based on cytosol and from our assumed value for f_v will affect the magnitude of µ_s(1 - g). But in general,soft tissues with higher (or lower) lipid content will show increased (or decreased) scattering, while the wavelength dependence of µ_s(1 - g) should not change greatly.