Feedforward and feedback control of ultrasound surgery

In this paper, a two stage method is used to control the thermal dose distribution in ultrasound surgery. In the first stage, a model-based nonlinear optimal control problem is solved, leading to an optimal feedforward thermal dose distribution. The control inputs are the real and the imaginary parts of the ultrasound transducer excitations and the feedforward control give the trajectories for control input and temperature that provide the optimal thermal dose distribution in tissues. A quadratic cost criteria is used to weight the thermal dose distribution and inequality constraints are used to limit the maximum input amplitude. In the second stage, the original nonlinear system equation is linearized with respect to the feedforward trajectories and an LQG feedback controller is derived from the linearized equations. The quadratic cost function is used to weight the error between the feedforward and measured temperature trajectories. With feedback, modeling errors in feedforward control can be corrected during the sonication and numerical simulations show that the derived method leads to a feasible solution, even when large modeling errors are present.