| Summary: | <p>The Monte-Carlo method [1] already long ago proved itself as a powerful and universal tool for mathematical modelling in various areas of science and engineering. Researchers often choose this method when it is difficult to find a solution by other ways (or impossible at all), e.g. because of sophisticated analytical dependences, area of modelling or boundary conditions. Certainly, this necessarily statistical and flexible method requires significant computation time, but a continuously increasing computation capability makes it more and more attractive for a choice in specific situation.</p><p>One of the promising areas to use the method of statistical modelling is description of light propagation in the turbid (scattering) media. A high motivation for development of this approach is widely used lasers in biomedicine [3]. Besides, owing to its flexibility, the Monte-Carlo method is also of importance in theoretical researches, in particular, to estimate a degree of adequacy of the offered approximation methods for solving a radiative transfer equation [4].</p><p>It is known that key parameters of turbid media are an absorption coefficient (characterizes absorption probability of a photon per unit of path length) and a scattering coefficient (characterizes scattering probability of a photon per unit of path length). The ratio of each of the coefficients to their sum (extinction) defines a probability of "death" or "survival" of a photon, respectively, in interaction with lenses. Generally, in the scattering medium there is a non-coherent radiation component, which in turbid media such as biological tissues, already at the insignificant depth becomes prevailing over the coherent one (residual of the incident laser beam) [5].</p><p>The author used the Monte-Carlo method to simulate optical radiation propagation in the multilayer biological tissues with their optical characteristics corresponding to the skin and subcutaneous tissues. Such a biological tissue is the absorbing and scattering medium. The main absorbers in visible and near-IR spectral range in this case are melanin (contains in pigmented epidermis) and blood hemoglobin. Scattering is defined both by the fibrous structure of skin, and by the cell organellеs. The optical characteristics, absorbing and scattering properties of skin, and subcutaneous tissues are rather well studied [6][7][8].</p><p>The aim of modelling was to have both the stationary distribution of light radiation in multilayer biological tissue and the transitional characteristics corresponding to such biological tissue structure. These characteristics may appear when a biological tissue is subjected to short laser pulses. Discovering of such characteristics and their analysis allows us to formulate a criterion for the validity of stationary models of radiation transfer in multilayer biological tissue. As to transitional characteristics (i.e. time-allowed absorption coefficients in layers), the standard algorithm of the Monte-Carlo method [9][10] was modified to take into consideration a final speed value of light distribution in layers. In such a way, in particular, it was found that time about 60 Ps (for radiation with the wavelength of 633 nm) is necessary to obtain the steady-state (stationary) values of the absorbed power in skin and subcutaneous tissues. The entire modelling process (based on the i7 processor) took about 30 minutes, thus the number of the traceable photons made 100 million.</p><p>The results obtained for a beam of infinitesimal diameter allowed us to find the solution on distribution of light energy in biological tissue for a laser beam of a final width with a Gaussian profile of intensity. For this purpose, was used the mathematical apparatus of Green function. Its digital representation in this case is a modelling result for a beam of infinitesimal diameter. Since indexes of refraction of the adjacent layers in model were specified to be equal, the received function of integrated intensity for a Gaussian beam in the depth of biological tissue became a continuous and smooth function. In turn, it means that the function of absorbed power for the considered model of biological tissue will not be any more a continuous function, as the absorption coefficients of the adjacent layers are different.</p><p>Thus, the Monte-Carlo method applied to simulate a distribution of the optical radiation in multilayer biological tissue allowed us to have a required distribution of the resultant light field in a stationary case for the acceptable time, as well as to obtain time-allowed absorption coefficients in layers (transitional characteristics of light), which can be used to estimate the validity of stationary models of radiation transfer when biological tissue is subjected to short light pulses.</p>
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