Modelling of biological tissue damage process with application of interval arithmetic

Abstract

In the paper, the numerical analysis of thermal processes proceeding in a 2D soft biological tissue subjected to laser irradiation is presented. The transient heat transfer is described by the bioheat transfer equation in Pennes formulation. The internal heat source resulting from the laser-tissue interaction based on the solution of the diffusion equation is taken into account. Thermophysical and optical parameters of the tissue are assumed as directed intervals numbers. At the stage of numerical realization. the interval finite difference method has been applied. In the final part of the paper, the results obtained are shown.

Numerical analysis of the temperature impact to the oxygen distribution in the biological tissue

“…In task related to determination of the temperature, Arrhenius injury integral and perfusion coefficient (equations (2), (3), (12)) the following data was used:  = 0.75 Wm -1 K -1 , c = 3 MJm -3 K -1 , c B = 3.9962 MJm -3 K -1 , T B = 37°C, Q met = = 250 Wm -3 , q 0 = 15 kWm -2 ,  = 10 Wm -2 K -1 , T amb = 20°C, T init = 37°C, t exp = 20 s, A = 3.1e+98 s -1 , E = 6.27e+5 J mol -1 , R = 8.314 J mol -1 K -1 , t = 0.05 s [14,15]. The value of initial perfusion coefficient was assumed on the basis of estimation of capillary density in muscle as w 0 = 0.041 s -1 [4,5].…”

“…At the stage of numerical realization the finite difference method has been applied with grid based on three-point stencils [15,19,20].…”

“…where w(Arr) and w 0 denote damage-dependent and initial perfusion coefficients [s -1 ] respectively, while Arr is the tissue damage degree estimated on the basis of Arrhenius injury integral [15][16][17]…”

“…In additional 1D task associated with temperature distribution and damage--dependent perfusion coefficient w(Arr) estimation, the Pennes equation with adequate boundary-initial conditions were used, in form [15,18,19]  …”

Mathematical Modeling of Breast Tumor Destruction Using Fast Heating during Radiofrequency Ablation

“…To estimate the degree of tissue destruction the Arrhenius integral, which describes the relationship between temperature and tissue damage, is used [39][40][41][42][43][44], where the relation between the tissue death with the temperature and the treatment time is given by…”