Theoretical Analysis of Diffuse Reflectance from a Two-Layer Tissue Model

A three-dimensional diffuse reflectance equation for a two-layer tissue model was developed using photon diffusion theory. In this model, tissue was considered to consist of two homogeneous isotropically scattering layers whose scattering and absorption constants were expressed as a linear sum of those of whole blood and a blood-free tissue component; tissue hemoglobin content and oxygen saturation were then expressed in terms of these total tissue parameters. Reflectance predictions given by the two-layer equation were used to investigate the effects of various tissue and system parameters on the partial reflectance from the second tissue layer; among such parameters significantly affecting deep-layer reflectance are the tissues scattering constants, its geometry, and the geometry of the optical transducer. When the penetration depth of the incident photons is small compared with the thickness of the first layer, reflectance contributions from the second layer are negligible, and a single-layer approximation would be adequate; resultant reflectance errors range from 6 to 8 percent of the total reflectance, for source-detector separations in the range from 1 to 4 mm. However, when the photon penetration depth is large with respect to first-layer thickness, the effects of deep layers are both important and strongly dependent on transducer geometry; partial reflectances range to 50 percent of the total when the source-detector separation is 4 mm.