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Using optical interaction coefficients typical of mammalian soft tissues in the red and near infrared regions of the spectrum, calculations of fluence-depth distributions, effective penetration depths and diffuse reflectance from two models of radiative transfer, diffusion theory, and Monte Carlo simulation are compared for a semi-infinite medium. The predictions from diffusion theory are shown to be increasingly inaccurate as the albedo tends to zero and/or the average cosine of scatter tends to unity.

It is possible to alter the interaction parameters characterizing neutral particle radiation transport without significantly altering the spatial distribution of the particle fluence rate. Practical mathematical relations specifying the constraints that such an alteration must satisfy are known as similarity relations. Similarity relations are derived in this work from integrated versions of the single energy neutral particle transport equation. The application of these relations in accelerating Monte Carlo deep penetration simulations is described and assessed. Computational reductions may exceed a factor of 10 in highly scattering media in which the scattering is highly forward peaked, such as applies to the propagation of red and near IR light through soft tissues.