Constraint-Adaptive Model Predictive Control for Radio Frequency Hyperthermia Cancer Treatments

During a mild hyperthermia treatment, tumors are heated to temperatures ranging from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$39~^{\circ } $ </tex-math></inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$45~^{\circ } $ </tex-math></inline-formula>C for 60–90 min. This thermal therapy can be a successful adjuvant to conventional cancer treatments such as chemotherapy and radiotherapy. In order to extract the maximum potential from the thermal therapy, it is crucial to heat the tumor to the desired therapeutic temperature while minimally heating the healthy tissue. Due to the recent development of magnetic resonance (MR)-compatible heating devices, MR thermometry techniques can be employed to noninvasively monitor the internal patient temperature in real time. This development enables closed-loop control strategies to improve the clinical value of the hyperthermia treatment. In this article, we propose a novel model predictive control (MPC) solution based on the alternating direction method of multipliers in combination with constraint removal techniques to compute optimal control inputs for radio frequency (RF)-based mild hyperthermia in real time based on models with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{5}$ </tex-math></inline-formula>–<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{6}$ </tex-math></inline-formula> states and temperature safety constraints. We validated the proposed controller on high-fidelity patient models with and without patient model mismatches. We will show that the proposed control strategy can track a desired tumor temperature reference, while ensuring patient safety through <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{5}$ </tex-math></inline-formula>–<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{6}$ </tex-math></inline-formula> constraints and maintaining real-time feasibility with a computation time of 6 s, which is sufficiently fast considering the thermal dynamics.