Analytical modeling of laser pulse heating of embedded biological targets: An application to cutaneous vascular lesions

Detailed understanding of the thermal processes in biological targets undergoing laser irradiation continues to be a challenging problem. For example, the contemporary pulsed dye laser (PDL) delivers a complex pulse format which presents specific challenges for theoretical understanding and further development. Numerical methods allow for adequate description of the thermal processes, but are lacking for clarifying the effects of the laser parameters. The purpose of this work is to derive a simplified analytical model that can guide the development of future laser designs. A mathematical model of heating and cooling processes in tissue is developed. Exact analytical solutions of the model are found when applied to specific temporal and spatial profiles of heat sources. Solutions are reduced to simple algebraic expressions. An algorithm is presented for approximating realistic cases of laser heating of skin structures by heat sources of the type found to have exact solutions. The simple algebraic expressions are used to provide insight into realistic laser irradiation cases. The model is compared with experiments on purpura threshold radiant exposure for PDL. These include data from four independent groups over a period of 20 years. Two of the data sets are taken from previously published articles. Two more data sets were collected from two groups of patients that were treated with two PDLs (585 and 595 nm) on normal buttocks skin. Laser pulse durations were varied between 0.5 and 40 ms; radiant exposures were varied between 3 and 20 J/cm(2). Treatment sites were evaluated 0.5, 1, and 24 hours later to determine purpuric threshold. The analytical model is in excellent agreement with a wide range of experimental data for purpura threshold radiant exposure. The data collected by independent research groups over the last 20 years with PDLs with wavelengths ranged from 577 to 595 nm were described accurately by this model. The simple analytical model provides an accurate description of a wide range of experimental data. The model can be used to guide the development of future laser designs and help refine laser parameters.