Parameter estimation in reconstructing temperature fields during hyperthermia.

Abstract

In this dissertation, a state and parameter estimation algorithm is implemented and modified to predict the blood perfusions and thus the complete steady-state temperature fields based on input from a limited number of temperature measurements taken during simulated hyperthermia treatments. Several fundamental phenomena related to this inverse problem are investigated from simple direct models. The general conditions under which these multiple minima occur are shown to be solely due to the existence of symmetries in the inverse problem formulation. Both an adjoint formulation and a sensitivity equation method are derived and used to determine the elements in the Jacobian matrix associated with the inverse problem of estimating the blood perfusion and temperature fields during hyperthermia cancer treatments. These methods and a previously developed influence coefficient method for obtaining that matrix are comparatively evaluated by solving a set of numerically simulated inverse hyperthermia problems. An improved state and parameter estimation algorithm has been developed to reduce the total computational time required. If the change of the unknown perfusion parameters is small a linear approximation scheme is implemented in which the old Jacobian matrix (or sensitivity matrix) is used, instead of recalculating the new Jacobian matrix for the next iteration. Results show that if the temperature is approximated as a linear (or quasi-linear) function of the blood perfusion, the linearizing approach considerably reduces the CPU time required to accurately reconstruct the temperature field. One of the model mismatch problems between the actual tumor and the simulated models is selected and investigated for the one-dimensional case. The model mismatch present in this dissertation is caused by the discretization of a perfusion field into several discrete zones. It is our attempt to understand the effects of the model mismatch problems from a simple model, and then generalize to more complicated three-dimensional cases which could occur during hyperthermia treatments. To simulate the ultrasound hyperthermia treatments, a scanned focussed ultrasound power field is generated and then used to create the transient power-on data and the steady-state temperature field. The feasibility of using the transient power-on data to estimate the attenuation coefficient and the blood perfusion and thus reconstruct the steady-state temperature field is presented.