Reduced-order modeling for hyperthermia control

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Abstract
This paper analyzes the feasibility of using reduced-order modeling techniques in the design of multiple-input, multiple-output (MIMO) hyperthermia temperature controllers. State space thermal models are created based upon a finite difference expansion of the bioheat transfer equation model of a scanned focused ultrasound system (SFUS). These thermal state space models are reduced using the balanced realization technique, and an order reduction criterion is tabulated. Results show that a drastic reduction in model dimension can be achieved using the balanced realization. The reduced-order model is then used to design a reduced-order optimal servomechanism controller for a two-scan input, two thermocouple output tissue model. In addition, a full-order optimal servomechanism controller is designed for comparison and validation purposes. These two controllers are applied to a variety of perturbed tissue thermal models to test the robust nature of the reduced-order controller. A comparison of the two controllers validates the use of open-loop balanced reduced-order models in the design of MIMO hyperthermia controllers.