Analytic description of the laser-beam heating of multicomponent biological tissues

An analytic method is developed for solving a system of heat conduction equations in two-component biological tissues irradiated by a narrow laser beam. The axial and radial heat transfer in a medium, heat exchange between capillaries and the surrounding tissue, and heat transfer to an external medium are taken into account. Simple expressions describing the spatiotemporal distributions of the tissue temperature are obtained, which in fact do not require any software for calculations. The method was used for calculating temperature fields in a medium at different irradiation wavelengths in the region between 400 and 700 nm for a broad range of geometrical, optical, and thermal parameters of the problem. The time intervals are estimated in which a simpler approximation of an infinitely wide beam can be used to analyse the thermal regime of a tissue irradiated by a narrow light beam. The analytic representation of the Green function for the problem with a narrow beam obtained in the paper shows that the applicability of this approximation is determined not by the condition of a substantial excess of the beam width over the light penetration depth into the medium, but by the beam radius, the thermal diffusivity, and the instant of time after the onset of laser beam action.