MULTIPLE MINIMA IN INVERSE HYPERTHERMIA TEMPERATURE ESTIMATION PROBLEMS

Using one-, two-, and three-dimensional numerical simulation models it is shown that multiple minima solutions exist for some inverse hypert hermia temperature estimation problems. This is a new observation that has important implications for all potential applications of these in verse techniques. The general conditions under which these multiple m inima occur are shown to be solely due to the existence of symmetries in the bio-heat transfer model used to solve the inverse problem. Gene ral rules for determining the number of these global minimum points in the unknown parameter (perfusion) space are obtained for several geom etrically symmetric (with respect to the sensor placement and the in v erse case blood perfusion model) one-, two- and three-dimensional prob lem formulations with multiple perfusion regions when no model mismatc h is present. As the amount of this symmetry is successively reduced, all but one of these global minima caused by symmetry become local min ima. A general approach for (a) detecting when the inverse algorithm h as converged to a local minimum, and (b) for using that knowledge to d irect the search algorithm toward the global minimum is presented. A t hree-dimensional, random perfusion distribution example is given which illustrates the effects of the multiple minima on the performance of a state and parameter estimation algorithm. This algorithm attempts to reconstruct the entire temperature field during simulated hyperthermi a treatments based on knowledge of measured temperatures from a limite d number of locations.