2-D Thermal Dose Optimization in High Intensity Focused Ultrasound Treatments Using the Adjoint Method

Abstract

Abstract A previously reported numerical technique, which uses adjoint method when optimizing 1D space variation of thermal dose in hyperthermia treatment is extended to the case of 2D problems [1]. Using a 2D transient computational model in the Penne’s bio-heat equation, optimization of thermal treatment during hyperthermia is shown to be effective and accurate. Numerical simulations are carried out with the 2D computational method to retrieve the prescribed thermal dose from the solution of an inverse thermal problem. The non-continuity of the temperature variation of thermal dose around the reference temperature is linearized over a small temperature interval. The adjoint method in conjunction with the conjugate gradient algorithm are employed to perform the optimization of the objective function. The results are obtained in terms of the computed thermal dose and the heat source to be applied. The numerical results, obtained for a simple treatment case show a good agreement between the estimated and desired thermal dose. However, the non-uniqueness of the obtained solution (the control function: heat source to be applied) is still under investigation and supports the need for further fundamental research.