Fast temperature optimization of multi-source hyperthermia applicators with reduced-order modeling of 'virtual sources'

The goal of this work is to build the foundation for facilitating real-time magnetic resonance image guided patient treatment for heating systems with a large number of physical sources ( e. g. antennas). Achieving this goal requires knowledge of how the temperature distribution will be affected by changing each source individually, which requires time expenditure on the order of the square of the number of sources. To reduce computation time, we propose a model reduction approach that combines a smaller number of predefined source configurations ( fewer than the number of actual sources) that are most likely to heat tumor. The source configurations consist of magnitude and phase source excitation values for each actual source and may be computed from a CT scan based plan or a simplified generic model of the corresponding patient anatomy. Each pre-calculated source configuration is considered a 'virtual source'. We assume that the actual best source settings can be represented effectively as weighted combinations of the virtual sources. In the context of optimization, each source configuration is treated equivalently to one physical source. This model reduction approach is tested on a patient upper-leg tumor model ( with and without temperature-dependent perfusion), heated using a 140 MHz ten-antenna cylindrical mini-annular phased array. Numerical simulations demonstrate that using only a few pre-defined source configurations can achieve temperature distributions that are comparable to those from full optimizations using all physical sources. The method yields close to optimal temperature distributions when using source configurations determined from a simplified model of the tumor, even when tumor position is erroneously assumed to be similar to 2.0 cm away from the actual position as often happens in practical clinical application of pre-treatment planning. The method also appears to be robust under conditions of changing, nonlinear, temperature-dependent perfusion. The proposed approach of using virtual sources reduces the number of variables that must be optimized to achieve a tumor-focused temperature distribution, thereby reducing the calculation time required in real-time control applications to about 1/3 to 1/4 of that required for full optimization.