Steady-state analysis of self-heated thermistors using finite elements.

The purpose of this work is to validate, using numerical, finite element methods, the thermal assumptions made in the analytical analysis of a coupled thermistor probe-tissue model upon which a thermal conductivity measurement scheme has been based. Analytic, closed form temperature profiles generated by the self-heated thermistors can be found if three simplifying assumptions are made: the thermistor is spherical; heat is generated in all regions of the bead; and heat is generated uniformly in the bead. This analytic solution is used to derive a linear relationship between tissue thermal conductivity and the ratio of thermistor temperature rise over electrical power required to maintain that temperature rise. This derived, linear relationship is used to determine thermal conductivity from the observed experimental data. However, in reality, the thermistor bead is a prolate spheroid surrounded by a passive shell, and the heating pattern in the bead is highly nonuniform. In the physical system, the exact relationship between the tissue thermal conductivity and parameters measured by the thermistor is not known. The finite element method was used to calculate the steady-state temperature profiles generated by thermistor beads with realistic geometry and heating patterns. The results of the finite element analysis show that the empirical, linear relationship remains valid when all three simplified assumptions are significantly relaxed.