Modelling the sampling volume for skin blood oxygenation measurements

Human skin, especially the epidermis, contains several major solar ultraviolet-radiation- (UVR-) absorbing endogenous chromophores including DNA, urocanic acid, amino acids, melanins and their precursors and metabolites. The lack of solubility of melanins prevents their absorption spectra being defined by routine techniques. Indirect spectroscopic methods show that their spectral properties depend on the stimulus for melanogenesis. The photochemical consequences of UVR absorption by some epidermal chromophores are relatively well understood whereas we lack a detailed understanding of the consequent photobiological and clinical responses. Skin action spectroscopy is not a reliable way of relating a photobiological outcome to a specific chromophore but is important for UVR hazard assessment. Exogenous chromophores may be administered to the skin in combination with UVR exposure for therapeutic benefit, or as sunscreens for the prevention of sunburn and possibly skin cancer.

This paper addresses the problem of tomographic reconstruction of absorption and scattering parameters in the optical region from measurements of transilluminated light. Specifically, the question of the sensitivity of different measurement schemes on the boundary of an object to perturbations of the optical parameters within the object are addressed. The concept of a photon-sampling volume [Appl. Opt. 33, 448 (1994)] and a photon-hitting density [Appl. Opt. 32, 448 (1993)] is extended to a photon-measurement density function (PMDF). The PMDF is derived from the Green's function of the diffusion equation and can be expressed for measurements such as the time-varying intensity, integrated intensity, temporal moments, and phase shift, as well as for both absorption and diffusion perturbations. Closed-form solutions are given for a number of these functions in infinite space, half-space, and slab geometries. Example results are given in terms of three-dimensional images.