Analytical transient-time solution for temperature in non perfused tissue during radiofrequency ablation

Radiofrequency ablation (RFA) with internally cooled needle-like electrodes is a technique widely used to destroy cancer cells. In a previous study we obtained the analytical solution of the biological heat equation associated with the RFA problem in perfused tissue, i.e. when the governing equation which models the temperature distribution in tissue includes the blood perfusion therm. We also found that under these circumstances the temperature profiles always reach a steady state (limit temperature). However, the analytical solution of the RFA thermal problem without perfusion (e.g. conducted on an organ in which atraumatic vascular clamping is performed to temporally interrupt blood perfusion), cannot be directly obtained by setting the blood perfusion term to zero in the previously obtained solution. In fact, it is necessary to address the mathematical resolution in a totally different way. Our goal was to obtain the analytical expression of the temperature distribution in an RFA process with internally cooled needle-like electrodes when the biological tissue is not perfused. We consider two spatial domains: A finite domain which represents the real situation, and an infinite domain, which only makes sense from a mathematical point of view and which has been traditionally employed in analytical studies. Even though considering infinite time is not realistic, these approaches are surely worth considering in order to understand what happens “far from the electrode” or for “very long periods of time.” The results indicate that the temperature value is finite both when the spatial domain is finite (which implies that a steady state is reached), and when time is finite for any spatial domain. From this it can be concluded that a steady state is never reached if the spatial domain is infinite.