Bellia, S. Aliouat; Saidane, A.; Benzohra, M.; Saiter, J. M.; Hamou, A. Dimensional soft tissue thermal injury analysis using transmission line matrix (TLM) method. (English) Zbl 1154.80002 Int. J. Numer. Model. 21, No. 6, 531-549 (2008). The authors use a TLM method in order to model the impact of the exposition of the skin to a high temperature heat source. They use Pennes’ bioheat 3D equation \[ \nabla ^{2}\theta (x,t)=(\rho _{t}C_{t}/K_{t})\partial \theta /\partial t(x,t)+\omega _{b}C_{b}/K_{t}\theta (x,t) \] for the description of the evolution of the temperature inside the skin. A damage function is built as \(\Omega (x)=\int_{0}^{t}A\exp (\Delta E/RT(x,t))dt\). The authors then use a model inspired from the transmission line circuit replacing the thermal wave heat flow (resp. temperature) by a RC network (resp. voltage). Delta voltage pulses are simultaneously incident on all parts of the nodes. They are instantaneously scattered into reflected pulses. The authors indicate the relations between reflected and incident pulses. In order to illustrate this TLM method and to validate the method, the authors introduce 1D and 2D models. In the 1D model, the authors compare the temperature computed applying either the TLM method or the FEM method (applied to Pennes’ equation) as a function of the depth inside the skin. They take from the literature the values of the parameters associated to the thermal and the geometrical properties of the multilayered skin. They observe a quite good agreement between the two approximate solutions, taking \(\Delta x=0,04mm\) and \(\Delta t=10^{-3}s\). In the 2D model, the authors consider a small region of the skin surface exposed to a high temperature heat source. They again compare the approximate solutions obtained using the TLM or the FEM methods. They end their paper exposing the advantage of the TLM method because of its simplicity. Reviewer: Alain Brillard (Riedisheim) Cited in 1 Document MSC: 80A20 Heat and mass transfer, heat flow (MSC2010) 78M20 Finite difference methods applied to problems in optics and electromagnetic theory 94C05 Analytic circuit theory Keywords:TLM method; Pennes’ bioheat transfer equation; multilayered skin; skin burn; burn injury analysis; FEM method PDFBibTeX XMLCite \textit{S. A. Bellia} et al., Int. J. Numer. 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