Scientific Research of the Institute of Mathematics and Computer Science PARAMETER SENSITIVITY ANALYSIS OF BURN INTEGRALS USING THE ADJOINT APPROACH Ewa Majchrzak 1, 2 , Marek Jasiński 1 1 Silesian University of Technology, Gliwice 2 Czestochowa University of Technology, Czestochowa Abstract. In the paper the numerical analysis of thermal processes proceeding in the do- main of biological tissue subjected to an external heat source is presented. Heat transfer in the skin tissue was assumed to be transient and one-dimensional. The degree of the skin burn can be predicted on the basis of so called Henriques integrals and the main subject of the paper is the sensitivity analysis of these integrals with respect to the thermophysical parameters. Here the adjoint approach of parameter sensitivity analysis has been applied. On the stage of numerical computations the boundary element method has been used. In the final part of the paper the results obtained are shown. 1. Introduction The skin is treated as a multilayer 1D domain, in which one can distinguish the following sub-domains: epidermis of thickness L 1 , m, dermis of thickness L 2 - L 1 and sub-cutaneous region Ω 3 of thickness L 3 - L 2 - L 1 . The thermophysical parameters of successive layers equal λ e , W/(mK) (thermal conductivity), and c e , J/(m 3 K) (specific heat per unit of volume). Thermal damage of skin begins when the temperature at the basal layer (the interface between epidermis and dermis) rises above 44°C (317 K). Henriques [1] found that the degree of skin damage could be predicted on the basis of the integrals 0 ( )exp d () F t b b b b E I PT t RT t   Δ = -     ∫ (1) and 0 ( ) exp d () F t d d d d E I PT t RT t   Δ = -     ∫ (2) where ΔE/R, K, is the ratio of activation energy to universal gas constant, P b , P d , 1/s, are the pre-exponential factors, while T b , T d , K, are temperatures of basal layer (the surface between epidermis and dermis) and dermal base (the surface between dermis and sub-cutaneous region). Please cite this article as: Ewa Majchrzak, Marek Jasiński, Parameter sensitivity analysis of burn integrals using the adjoint approach, Scientific Research of the Institute of Mathematics and Computer Science, 2004, Volume 3, Issue 1, pages 115-120. The website: http://www.amcm.pcz.pl/