Ultrasound phased array control of thermal dose: High efficient constrained MPC

In this paper, a novel model-based treatment control system that manipulates the focal zone trajectory and intensity of ultrasound phased arrays to safely deliver prescribed thermal dose to the target in the minimum-time was developed. The system is characterized by its time-optimal performance, direct incorporation of normal tissue constraints, and computationally efficient implementation even in the presence of massive amount of magnetic resonance (MR) thermometry measurement data. A set of empirical basis functions is identified during pre-treatment planning using proper orthogonal decomposition (POD). Using the same reduced-order basis, thermal images are compressed and used in the feedback of the treatment controller. The controller has a cascaded structure, with a nonlinear thermal dose controller in the outer loop and a low-dimensional model predictive controller (MPC) in the inner loop. The controller solves on-line optimization problem, which allows for robust delivery of the desired thermal dose despite modeling errors and disturbances. The feasibility and performance of the developed control system were tested in a computer simulated treatment of a three-dimensional (3D) inhomogeneous tissue with ultrasound transducer arrays.