Sensitivity analysis of temperature in heated soft tissues with respect to time delays

Abstract

Axisymmetric tissue region heated by an external heat flux is considered. The mathematical model is based on the dual-phase lag equation supplemented by appropriate boundary and initial conditions. This equation, in relation to the Pennes’ equation, has two additional parameters, namely the relaxation time and the thermalization time. The aim of this research is to estimate the temperature changes due to changes of these parameters. To achieve this, sensitivity analysis methods are used. The basic problem and additional ones related to the sensitivity functions are solved using the implicit scheme of the finite difference method. The performed computations show that the temperature changes caused by changes in the relaxation and thermalization times are larger for higher values of the external heat flux and shorter times of its action.

Numerical analysis of biological tissue heating using the dual-phase lag equation with temperature – dependent parameters

“…To solve the problem formulated, the implicit scheme of the finite difference method is applied [10,17]. The differential grid is shown in Figure 3.…”

“…On the remaining surfaces the no-flux condition qb = 0 is taken into account. It should be noted that in the dual-phase lag model the Neumann condition takes the form [17] λ ( )…”

Sensitivity of a Process for Heating Thin Metal Film Described by the Dual-Phase Lag Equation with Temperature-Dependent Thermophysical Parameters to Perturbations of Lag Times

“…Thus, the sensitivity model can be constructed using the differentiation of DPLE and the appropriate boundary-initial conditions with respect to the parameter p k . This rather obvious approach is called a direct method-e.g., [38][39][40].…”