Reconstruction of Experimental Hyperthermia Temperature Distributions: Application of State and Parameter Estimation

Subsets of data from spatially sampled temperatures measured in each of nine experimental heatings of normal canine thighs were used to test the feasibility of using a state and parameter estimation (SPE) technique to predict the complete measured data set in each heating. Temperature measurements were made at between seventy-two and ninety-six stationary thermocouple locations within the thigh, and measurements from as few as thirteen of these locations were used as inputs to the estimation algorithm. The remaining (non “input”) measurements were compared to the predicted temperatures for the corresponding “unmeasured” locations to judge the ability of the estimation algorithm to accurately reconstruct the complete experimental data set. The results show that the predictions of the “unmeasured” steady-state temperatures are quite accurate in general (average errors usually < 0.5°C; and small variances about those averages) and that this reconstruction procedure can yield improved descriptors of the steady-state temperature distribution. The accuracy of the reconstructed temperature distribution was not strongly affected by either the number of perfusion zones or by the number of input sensors used by the algorithm. One situation extensively considered in this study modeled the thigh with twenty-seven independent regions of perfusion. For this situation, measurements from ninety-six to thirteen sensors were used as input to the estimation algorithm. The average error for all of these cases ranged from −0.55°C to +0.75°C, respectively, and was not strongly related to the number of sensors used as input to the estimation algorithm. For these same cases the maximum prediction error (the maximum absolute difference between the measured temperature and the predicted temperature determined by a search over all locations) ranged from 0.92°C to 5.08°C, respectively. To attempt to explain the magnitude of the maximum error, several possible sources of model mismatch and of experimental uncertainty were considered. For this study, a significant source of error appears to arise from differences between the true power deposition field, the power deposition model predictions, and the experimentally measured powers. In summary, while large errors can be present for a few isolated locations in the predicted temperature fields, the SPE algorithm can accurately predict the average characteristics of the temperature field. This predictive ability should be clinically useful.