Dimensional soft tissue thermal injury analysis using transmission line matrix (TLM) method

Abstract

The skin is sensitive to temperature change and the effect may not be significant while the temperature at the surface is below 448C: However, higher surface temperatures (above 448C) will further incur time burning and carbonization so that irreversible damage may happen. An investigation of the heating intensity and the duration of the exposure to the heating source suggested that when the surface temperature is greater than 518C; the exposure time required to destroy the epidermis is so short that transepidermal necrosis may occur. In this paper, we present one-and two-dimensional numerical models based on transmission line matrix (TLM) method for a quantitative prediction of skin burn injury resulting from the exposure of the skin surface to a high temperature heat source. Transient temperatures are numerically estimated by solving the Pennes' bioheat equation, and the damage function denoting the extent of burn injury is calculated using the Arrhenius assumptions for protein damage rate. The TLM model is used to analyse the effects of exposure time and geometrical dimensions of mutlilayered skin, on the transient temperature distribution and damage extension. TLM results showed good agreement with other numerical sources, suggesting that TLM modelling can be used as a tool for an effective thermal diagnostic of burn injuries.

General node for transmission‐line modeling (TLM) method applied to bio‐heat transfer

“…This paper presents a general TLM formulation for bio‐heat transfer that can be simplified to previously published formulations . This formulation assumes that the unit vector normal to the border of the node is similar to the unit vector pointing from the center of the node to the midpoint of the border (Equation ), which becomes exact for regular geometries such as rectangles and parallelepipeds.…”

“…It is important to note that, with minor modifications, Equations to can be simplified to the previously published formulations …”

“…It is important to note that, with minor modifications, Equations 3 to 15 can be simplified to the previously published formulations. [11][12][13][14][15][16][17][18][19] 2.2 | Scattering, connection, boundary conditions, initial conditions, temperature calculation, and heat flux calculation Scattering is computed as the resultant voltage in the impedances Z n of the Thévenin's equivalent circuit ( Figure 3) of the general TLM node circuit ( Figure 2):…”

“…[7][8][9] Because of these advantages, TLM has become an increasingly popular method to solve problems in heat transfer in biological tissues. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] The limitation of the TLM method is that, for every control volume geometry, a new circuit node must be developed. The first developed TLM node formulation was for regular geometries (squares and cubes) 15,16 and was later expanded to include graded elements (rectangles and parallelepipeds) 11 and orthogonal curvilinear elements (such as cylinders).…”

“…[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] The limitation of the TLM method is that, for every control volume geometry, a new circuit node must be developed. The first developed TLM node formulation was for regular geometries (squares and cubes) 15,16 and was later expanded to include graded elements (rectangles and parallelepipeds) 11 and orthogonal curvilinear elements (such as cylinders). 29,30 However, bio-heat-transfer problems have inherently complex geometries that are difficult to accurately model using the node geometries previously described.…”