Determination of thermal conductivity of inhomogeneous orthotropic materials from temperature measurements

We consider the two-dimensional inverse determination of the thermal conductivity of inhomogeneous orthotropic materials from internal temperature measurements. The inverse problem is general and is classified as a function estimation since no prior information about the functional form of the thermal conductivity is assumed in the inverse calculation. The least-squares functional minimizing naturally the gap between the measured and computed temperature leads to a set of direct, sensitivity and adjoint problems, which have forms of direct well-posed initial boundary value problems for the heat equation, and new formulas for its gradients are derived. The conjugate gradient method employs recursively the solution of these problems at each iteration. Stopping the iterations according to the discrepancy principle criterion yields a stable solution. The employment of the Sobolev -gradient is shown to result in much more robust and accurate numerical reconstructions than when the standard -gradient is used

Assessment of Hyperbolic Heat Transfer Equation in Theoretical Modeling for Radiofrequency Heating Techniques

Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier’s theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode surface. Our results therefore suggest that HHTE should be considered for RF heating of the cornea (which requires very small electrodes and a heating time of 0.6 s), and for rapid ablations in cardiac tissue (less than 30 s)