Mie scattering from cellular structures

ECE532 Biomedical Optics
Steven L. Jacques, Scott A. Prahl

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

[ref. 1] Click figure to enlarge

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% (fv = 0.02-0.10). Let's choose fv = 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 fv.
• 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:

s = fv/((4/3)a3)

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µs

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g

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µs(1 - g)

This picture includes the experimental values of µs(1 - g) for dog prostate, illustrating that the prostate is mimiced 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 µs(1 - g) which matches the magnitude of µs(1 - g) for prostate. Deviations from our assumed values for np based on lipid and nmed based on cytosol and from our assumed value for fv will affect the magnitude of µs(1 - g). But in general,soft tissues with higher (or lower) lipid content will show increased (or decreased) scattering, while the wavelength dependence of µs(1 - g) should not change greatly.