Experimental setup for transfer function measurement to assess RF heating of medical leads in MRI: Validation in the case of a single wire

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Magnetic resonance imaging is an irreplaceable diagnostic tool that may become hazardous when patients are implanted with an active medical device—especially the radiofrequency (RF) field, which presents a heating risk at the bare electrode of an implanted lead. The influence of various parameters on the lead heating has been reported in literature 1. For example, the resonance behavior as a function of the cable length has been studied with different geometrical parameters and material properties of the cable 1. The effect of the conductivity of the medium where the cable is embedded has also been studied 2. The influence of the position of a simple cable or a pacemaker lead in a phantom has also been reported 3. The structure of different pacemaker/defibrillator leads has been studied 5, as well as the influence of the termination conditions of pacemaker/defibrillator leads 6. Among these studies, an important result is the influence of the phase distribution of the incident field on the lead heating 8.
Indeed, a lot of the early studies analyzed the behavior of leads for a constant amplitude and constant phase incident electrical field (E‐field) 1, especially the behavior as a function of the length of the lead showing (in this case) a resonant effect. As mentioned previously, Yeung et al 8 showed the key importance of the phase distribution of the incident field on the possible heating at the electrode of a lead. Interesting experiments on cables have been made by Bottomley et al 9 to confirm this by folding cables along themselves with different folding lengths to change the incident field phase. These experiments show that a long cable that does not heat under a constant phase and constant amplitude incident field because it is above the resonant length can heat significantly once folded along a certain length. For example, in a human body, the incident field along a pacemaker lead has a distribution that is far from being constant 10 and is very different from the distribution in the American Society for Testing Material (ASTM) phantom 11 under the usual test conditions along the side of the phantom 11. The incident field in a human body has a distribution so complex that it cannot be reproduced experimentally in a phantom. Therefore, the only way to estimate the heating of a lead in vivo is by simulating the lead in a human body model. Nevertheless, some leads such as pacemaker leads are too complex to simulate because of a very fine helicoidal structure 13. Park et al therefore introduced the transfer function concept 14. This concept comes directly from the formulation of the electromagnetic problem by the method of moments and it is implicit in the work by Yeung et al 8. The scattered field at the electrode is considered to be the linear superposition of the effect of the tangential incident field all along the cable given by the transfer function, which is a complex function of the position along the cable. This transfer function can be measured for complex cables that are too complicated to simulate. Knowing the incident field in a human model from a simulation, the heating can be estimated for a complex cable, thanks to the measured transfer function according to the following equation 14: JOURNAL/mrim/04.02/01445475-201803000-00056/math_56MM1/v/2018-01-24T161827Z/r/image-png where α is a calibration coefficient determined from an experiment in a phantom with a known incident field Einc(z) and TF(z) is the complex transfer function at the position along the cable z.
The problem arising is how to measure the transfer function.

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