Some statistical characteristics of the rough surface of human skin

Abstract

The statistical properties of the skin surface have been described with the use of two approaches. The first approach is based on the probabilistic description of the skin topology at a given distribution density of rough surface heights and its correlation function. The Gaussian and quasi-periodic surfaces, whose parame- ters were estimated from the literature data, have been considered. The second approach is based on the ap- plication of the directional distribution function of microsurfaces of the skin. In the approximation of geometric optics, the shadowing effects of surface relief elements, as applied to the human skin, have been in- vestigated. The changes in the probability density of heights and slopes of parts of the surface irradiated with a directed beam due to the shadow regions have been estimated. The influence of shadowings on the electro- magnetic-field-quadratic photometric characteristics of the scattered light has been investigated. The results obtained are of interest for solving direct and inverse problems of biomedical optics — for analyzing the ra- diation fields in the biotissue and recovering its parameters by optical methods. Introduction. At the present time in medical practice various methods of irradiation of biological tissues and their diagnostics with the help of light are used widely. Of special value thereby are noninvasive methods realized through the skin because they are painless, cheap, and used in real time. Examples are photodynamic (1, 2) and low- intensity (3, 4) laser therapy of near-surface parts of the tissue, the determination of the structural and biophysical pa- rameters of the medium by the energy (5, 6) or polarization (6) characteristics of scattered light, and the investigation of the penetration depth of light into the tissue (7). The optical part of biomedical investigations and practical appli- cations is based on the methods of spectroscopy and optics of scattering media, and the radiation transport theory used for any absorbing and scattering media. In terms of theory, numerical (8) (mainly the Monte Carlo method) and ana- lytic (7, 9-11) approaches to the description of light fields inside and outside of biotissues have been well developed. In a particular realization of algorithms and computer programs, it is necessary to take into account the influ- ence of the structure of the skin surface on the radiation characteristics in such media. As a rule, the surface is as- sumed to be smooth (6, 8, 10, 11). This assumption is justified by a number of factors. First, the solution of the problem of the radiation transport in the medium is thus simplified considerably. At the same time, from general physical considerations it is clear that such an assumption may lead to errors in the calculation of the characteristics of the light fields in the medium. For example, in (2), the influence of the degree of roughness of the interface be- tween two media on the scattered radiation characteristics under different illumination conditions was estimated. It was shown that the coefficients of reflection and transmission of light under directed illumination of smooth and rough sur- faces may differ from one another by a factor of 1.5-2 or more. It is clear that for many optical problems these dif- ferences are very great. Second, there is a tangible lack of experimental data on the roughness characteristics of the skin surface which could form the basis for the statistical description of its structure. In other words, at present perti- nent initial physical data are absent. This is due to the wide variation of surface properties with the type of skin, am- bient conditions, age of a person, his/her physical and physiological condition, and many other factors. Third, to study the laws of scattering (reflection and transmission) of light by a statistically rough surface of any medium (including skin), special methods and algorithms are required.