PURPOSE: State of the art to access radiofrequency (RF) heating near implants is computer modeling of the devices and solving Maxwell's equations for the specific setup. For a set of input parameters, a fixed result is obtained. This work presents a theoretical approach in the alternating current (ac) limit, which can potentially render closed formulas for the basic behavior of tissue heating near metallic structures. Dedicated experiments were performed to support the theory. METHODS: For the ac calculations, the implant was modeled as an RLC parallel circuit, with L being the secondary of a transformer and the RF transmission coil being its primary. Parameters influencing coupling, power matching, and specific absorption rate (SAR) were determined and formula relations were established. Experiments on a copper ring with a radial gap as capacitor for inductive coupling (at 1.5 T) and on needles for capacitive coupling (at 3 T) were carried out. The temperature rise in the embedding dielectric was observed as a function of its specific resistance using an infrared (IR) camera. RESULTS: Closed formulas containing the parameters of the setup were obtained for the frequency dependence of the transmitted power at fixed load resistance, for the calculation of the resistance for optimum power transfer, and for the calculation of the transmitted power in dependence of the load resistance. Good qualitative agreement was found between the course of the experimentally obtained heating curves and the theoretically determined power curves. Power matching revealed as critical parameter especially if the sample was resonant close to the Larmor frequency. CONCLUSIONS: The presented ac approach to RF heating near an implant, which mimics specific values for R, L, and C, allows for closed formulas to estimate the potential of RF energy transfer. A first reference point for worst-case determination in MR testing procedures can be obtained. Numerical approaches, necessary to determine spatially resolved heating maps, can be supported.
PURPOSE: State of the art to access radiofrequency (RF) heating near implants is computer modeling of the devices and solving Maxwell's equations for the specific setup. For a set of input parameters, a fixed result is obtained. This work presents a theoretical approach in the alternating current (ac) limit, which can potentially render closed formulas for the basic behavior of tissue heating near metallic structures. Dedicated experiments were performed to support the theory. METHODS: For the ac calculations, the implant was modeled as an RLC parallel circuit, with L being the secondary of a transformer and the RF transmission coil being its primary. Parameters influencing coupling, power matching, and specific absorption rate (SAR) were determined and formula relations were established. Experiments on a copper ring with a radial gap as capacitor for inductive coupling (at 1.5 T) and on needles for capacitive coupling (at 3 T) were carried out. The temperature rise in the embedding dielectric was observed as a function of its specific resistance using an infrared (IR) camera. RESULTS: Closed formulas containing the parameters of the setup were obtained for the frequency dependence of the transmitted power at fixed load resistance, for the calculation of the resistance for optimum power transfer, and for the calculation of the transmitted power in dependence of the load resistance. Good qualitative agreement was found between the course of the experimentally obtained heating curves and the theoretically determined power curves. Power matching revealed as critical parameter especially if the sample was resonant close to the Larmor frequency. CONCLUSIONS: The presented ac approach to RF heating near an implant, which mimics specific values for R, L, and C, allows for closed formulas to estimate the potential of RF energy transfer. A first reference point for worst-case determination in MR testing procedures can be obtained. Numerical approaches, necessary to determine spatially resolved heating maps, can be supported.