Lanczos-Based Model-Order Reduction for Optimization and Control of Electromagnetically Induced Hyperthermia

Abstract

In this work, two procedures for the optimization of transient temperature fields in electromagnetically induced therapeutic hyperthermia are proposed. Both procedures employ numerical models of electromagnetic and heat transfer processes. The computational demands of the optimization procedures are mitigated by employing reduced-order numerical models obtained via the spectral Lanczos decomposition method (SLDM) in lieu of the original, high-order models. An open-loop optimization procedure based on quadratic programming (QP) is proposed that determines the time dependent RF power level necessary to reach therapeutic temperatures quickly without exposing healthy tissue to excesive temperatures. Additionally, a closed-loop optimization procedure is proposed based on linear-quadratic Gaussian (LQG) optimal control that employs feedback from temperature measurements such as those available from magnetic resonance thermography. The performance of both techniques is simulated on a realistic tissue model of the human trunk heated by an annular phased array (APA). It is shown that by optimizing the transient temperature fields in oncological hyperthermia, effective thermal dose can be increased for a fixed treatment time and level of risk to healthy tissue. Additionally, it is shown that in some cases the non-linear nature of the human thermoregulatory response (manifest as temperature dependent perfusion) can be compensated for by the proposed linear feedback controller.