Mathematical Model of Suppression of Laser Emission Dissipation in Biotissues with the Use of an Immersion Clearing Method

Experimental researches of kinetics of immersion suppression of laser emission dissipation in biological tissues have shown that time of clearing dependence of biotissue transmission has oscillating character. For explanation of this phenomenon we have designed a mathematical model of immersion suppression of laser emission dissipation in biotissues. Mathematical model consists of two phases. At the maiden phase, the spatially-temporal distribution of immersion liquid concentration in biological samples is calculated, and at the second phase (on the basis of data, obtained as a solution of the previous problem) collimated beam light transmission through the sample is calculated. To solve the problem of immersion liquid diffusion into biotissue sample, simple diffusion model, which takes into account difference between diffusion constants of immersion liquid in longitudinal and transverse directions, is used. Also the oscillating character of time dependence of diffusion constants is supposed. Transmission of homogeneous sample's stratum can be calculated using Bouguer law since the collimated beam light transmission is investigated. As sample of biotissue is not homogeneous, it is divided into quasi-homogeneous stratums and the total transmission of the entire sample is calculated as the product of transmission coefficients of every quasi-homogeneous stratum. On the basis of the model described above, the algorithm and the program code have been created, which allow one to calculate spatially-temporal function of immersion liquid concentration in biotissue and spatially-temporal function of biotissue sample transmission. Comparison of experimental and calculated spatially-temporal functions of biotissue sample transmition has shown their good coincidence.