Thermal dose optimization in high intensity focused ultrasound treatments using the adjoint method

摘要

In the treatment of cancerous tumores, the thermal dose is the time temperature history required to treat or destroy the undesirable tissue. The aim of this paper is to calculate the optimum history of heat source that, in one dimensional Biot-heat transfer model results in the desired thermal dose. The time dependent strength of this source defines the accumated energy at the end of a single heat treatment period. First the optimum control problem is formulated in infinitie dimensional form. The associated adjoint problem is obtained using the calculus of variations and an analytical formula is derived for the gradient of the functional of interest. Then, a parameteric representation of the control parameter in developed and the adjoint method is performed in conjugation with the conjugate gradient method for the solution of this control problem in finite dimensional form. A one dimensioinal numerical case is analyzed and discussed to demonstrate the performance and the rubustness of the present method.