Objective: The motivation behind this work is facilitation of real-time Magnetic Resonance (MR) guided temperature steering and focusing in real-time.

Methods: Achieving this goal requires knowledge of how the temperature distribution will be affected by changing each antenna individually, at every point in time during the steering procedure. Acquiring this knowledge requires time expenditure on the order of the square of the number of antennas, at regular intervals during treatment. This can be prohibitively expensive in time, especially for a large number of antennas. Here we present a reduced order model approach that can reduce this time expenditure by using a smaller number of “virtual” antennas. Each virtual antenna is a specific weighted combination of real antennas. Thus, turning on a single virtual antenna is equivalent to simultaneously turning on all real antennas with specific phases and specific ratio of amplitudes. The virtual antennas are computed as eigenvectors corresponding to the eigenvalues of a tumor heating matrix (virtual antennas are arranged in order of decreasing heating efficiency, i.e., decreasing eigenvalues). Thus, these virtual antennas are dependent on the actual geometry of the patient and location of the tumor. Prior to treatment, the virtual antennas can be computed from a CT model of the patient or even approximately from a generic patient geometry. The virtual antenna concept was tested on patient leg geometry, heated using a 10-antenna mini annular phased array.

Results: Simulations showed that using less than two virtual antennas resulted in large errors in the optimized temperature distribution, compared to the full optimization with all 10 real antennas. The agreement improved greatly with 3 or more virtual antennas. Using as few as 4 virtual antennas produced results in close agreement to the full optimization (see Figure).

Conclusions: The proposed reduced order approach reduces the time required for system identification and optimization, and is thereby conducive to our future goal of real-time MR guided temperature control.