Mixed-integer model predictive control for large-area MR-HIFU hyperthermia in cancer therapy

In hyperthermia treatments, cancer tissue is heated to enhance the desired effects of radio- and chemotherapies. A powerful technology for noninvasive feedback-controlled hyperthermia is magnetic-resonance-guided high-intensity focused ultrasound (MR-HIFU), which enables fast and millimeter-accurate heating inside the body. Electronic beam steering allows for volumetric heating, but due to its limited steering range can only be used to treat small tumors. For the treatment of larger tumors, the transducer itself must be mechanically relocated as well. Due to system limitations, however, the admissible transducer positions must be restricted to a finite set that is chosen a priori. Moreover, non-negligible time is needed for transducer relocation, during which no heating is possible. In this paper, we present a mixed-integer model predictive controller that simultaneously optimizes over the power deposition by electronic beam steering - a continuous subproblem - as well as the mechanical transducer motions - a discrete subproblem. By incorporating model knowledge of the tissue's thermal response and of the transducer carrier motion system into the predictive algorithm, the controller optimizes treatment temperature while respecting temperature and actuation constraints. The performance of the proposed feedback control setup is demonstrated by means of simulation.