Inference of Complete Tissue Temperature Fields from a Few Measured Temperatures: An Unconstrained Optimization Method

Abstract

In clinical applications of hyperthermia, tissue temperature measurements are made at only a few selected locations because of patient tolerance and practical clinical limitations. Since it is necessary to know the complete tumor temperature field in order to effectively evaluate a treatment, methods of interpolating and extrapolating must be developed to estimate the unmeasured tumor temperatures. The difficulty of making such estimates from only a few data points is compounded by a lack of knowledge of the tumor blood perfusion characteristics. To solve this problem we have developed an iterative state and parameter estimation algorithm to attempt to estimate complete tissue temperature fields from temperatures measured at selected locations when tissue perfusion values are unknown. This approach uses either a conjugate gradient or a relaxation method to minimize the difference between the measured temperatures and the temperatures predicted at those same locations by the bioheat transfer equation. To investigate the mathematical capabilities and limitations of this technique a sensitivity analysis has been performed by applying it to a large number of simulated one-dimensional hyperthermia treatments. To illustrate its applicability to clinical situations, the estimation algorithm is also applied to temperature measurements from an animal experiment. The simulation results show that the technique is promising for estimating the complete tumor temperature distribution from measurements at a small number of sampled locations, if some knowledge of the blood perfusion pattern is available.