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Purpose: In local hyperthermia, precise temperature control throughout the entire target region is key for swift, safe, and effective treatment. In this article, we present a model predictive control (MPC) algorithm providing voxel-level temperature control in magnetic resonance-guided high intensity focused ultrasound (MR-HIFU) and assess the improvement in performance it provides over the current state of the art. Materials and methods: The influence of model detail on the prediction quality and runtime of the controller is evaluated and a tissue mimicking phantom is characterized using the resulting model. Next, potential problems arising from modeling errors are evaluated in silico and in the characterized phantom. Finally, the controller's performance is compared to the current state-of-the-art hyperthermia controller in side-by-side experiments. Results: Modeling diffusion by heat exchange between four neighboring voxels achieves high predictive performance and results in runtimes suited for real-time control. Erroneous model parameters deteriorate the MPC's performance. Using models derived from thermometry data acquired during low powered test sonications, however, high control performance is achieved. In a direct comparison with the state-of-the-art hyperthermia controller, the MPC produces smaller tracking errors and tighter temperature distributions, both in a homogeneous target and near a localized heat sink. Conclusion: Using thermal models deduced from low-powered test sonications, the proposed MPC algorithm provides good performance in phantoms. In direct comparison to the current state-of-theart hyperthermia controller, MPC performs better due to the more finely tuned heating patterns and therefore constitutes an important step toward stable, uniform hyperthermia. ARTICLE HISTORY

Purpose: This article will report results from the in-vivo application of a previously published model-predictive control algorithm for MR-HIFU hyperthermia. The purpose of the investigation was to test the controller's in-vivo performance and behavior in the presence of heterogeneous perfusion. Materials and methods: Hyperthermia at 42 C was induced and maintained for up to 30 min in a circular section of a thermometry slice in the biceps femoris of German landrace pigs (n¼5) using a commercial MR-HIFU system and a recently developed MPC algorithm. The heating power allocation was correlated with heat sink maps and contrast-enhanced MRI images. The temporal change in perfusion was estimated based on the power required to maintain hyperthermia. Results: The controller performed well throughout the treatments with an absolute average tracking error of 0.27 ± 0.15 C and an average difference of 1.25 ± 0.22 C between T 10 and T 90 : The MPC algorithm allocates additional heating power to sub-volumes with elevated heat sink effects, which are colocalized with blood vessels visible on contrast-enhanced MRI. The perfusion appeared to have increased by at least a factor of $1.86 on average. Conclusions: The MPC controller generates temperature distributions with a narrow spectrum of voxel temperatures inside the target ROI despite the presence of spatiotemporally heterogeneous perfusion due to the rapid thermometry feedback available with MR-HIFU and the flexible allocation of heating power. The visualization of spatiotemporally heterogeneous perfusion presents new research opportunities for the investigation of stimulated perfusion in hypoxic tumor regions.

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A hybrid integrator-gain system is discussed that aims for improved low-frequency disturbance rejection, while, at the same time, does not deteriorate overshoot and settling times when compared with a linear integrator. The hybrid integrator has similar phase advantages as the well-known Clegg integrator but without inducing the discontinuous behavior resulting from resetting system state values. Optimal tuning of the controller parameters of the hybrid integrator is strongly influenced by machine-specific properties and therefore favors a data-driven optimization approach. However, as a time-domain optimization algorithm can easily lead to nonrobust solutions in the sense of large peaking of the closed-loop frequency response functions, frequency-domain robustness constraints will be imposed. By means of an adaptive weighting filter design, the parameter updates are penalized upon violation of said robustness constraints. Posed in an unconstrained problem formulation, this is subsequently solved by applying a Gauss-Newton-based parameter update scheme.Closed-loop stability of the linear time-invariant plant and controller in feedback connection with a hybrid integrator-gain system element follows from a circle-criterion-like analysis, which is based on evaluating (measured) frequency response data. Measurement results obtained from an industrial wafer scanner demonstrate the effectiveness of the approach.