Towards the estimation of three-dimensional temperature fields from noisy temperature measurements during hyperthermia

Abstract

The temperatures at most locations are unknown during clinical hyperthermia because temperature data are obtained at only a few discrete locations. In an attempt to further develop a technique for possibly solving this problem, the feasibility of using state and parameter estimation methods to predict three-dimensional temperature fields during hyperthermia treatments is investigated. Previous studies attempting to solve this problem have been limited to only one or two spatial dimensions. This paper investigates some conditions for which an estimation method can predict the complete three-dimensional temperature field for controlled numerical experiments with additive measurement noise. For the range of perfusion patterns considered, results show that the steady-state temperature field can be estimated to within 1°C if there is no measurement noise, no model mismatch, and as few as three measurement locations for seven perfusion zones. The addition of measurement noise degrades the performance of this estimation algorithm, especially when the number of measurement locations is small. Use of Tikhonov regularization of order zero significantly improves the performance of the algorithm for these cases. It was found that there is an optimal regularization parameter which maximizes the algorithm performance. This optimal value is a function of the perfusion magnitude and pattern. The present numerical results indicate that the approach used to solve this difficult and ill-posed problem could potentially be extended to estimate the complete temperature field in more realistic clinical conditions, but considerably more progress must be made before that goal can be reached.