Dipoles & Traveling Waves
David Brunner1

1Institute for Biomedical Engineering, ETH Zurich and University of Zurich, Zurich, Switzerland

Synopsis

NMR and MRI signal detection is traditionally based on Faraday induction. The local magnetic moment produced by the nuclear spins is thereby excited and detected by near-field magnetic interaction with the coil. However, the basic physical regime governing the electrodynamics of the RF detector alters at ultra-high frequencies and therefore the instruments applied in these systems have to cope with a different situation than at lower field strengths. The emergence of field propagation phenomena and radiation allows and necessitates the application of new RF topologies that are not only targeted at producing and detecting magnetic fields in their reactive near field.

Introduction

NMR and MRI signal detection is traditionally based on Faraday induction [1]. The local magnetic moment produced by the nuclear spins is thereby excited and detected by near-field magnetic interaction mostly with one or multiple electromagnetic resonators tuned to the particular nuclear precession / Larmor frequency. Theses resonators produce large magnetic fields inside the sample by storing electromagnetic energy in their reactive near field. The idea of a direct inductive coupling between the RF detector and the nuclear magnetization in an MR experiment guided the development of these devices from the very beginning. This is also exemplified by the fact that despite the wide variety of existing designs MR RF detectors are widely doubted as “coils”, although the most commonly used implementations show hardly any resemblance with wound conductors. However, the basic physical regime governing the electrodynamics of the RF detector alters at ultra-high frequencies and therefore the instruments applied in these systems have to cope with a different situation than at lower field strengths. The emergence of field propagation phenomena and radiation allows and necessitates the application of new RF topologies that are not only targeted at producing and detecting magnetic fields in their reactive near field.

Physical background

The efficiency of MRI coils is determined by the ratio of circularly transverse polarized magnetic field produced in the region of interest and the involved losses [2]. For systems that are substantially smaller than the electromagnetic wavelength the magnetic field is produced by currents flowing on the coil conductor in the sense of Biot-Savart’s law. The involved losses are mainly ohmic. They are caused by the finite conductivity of the deployed conductors, dissipative losses in the components and by eddy currents in the conductive sample material / tissue. At the port connecting to the coil, the produced magnetic field represents as an inductance and the losses as equivalent series resistance. For typical NMR/MRI samples the inductive reactance is significantly higher than the resistive component, therefore the coil has a high quality factor (Q). In order to couple a signal in and out of the coil, this largely reactive impedance has to be matched to the real impedances of the connecting transmission lines/cables. The reactive nature of the coil forces the matching to be highly resonant and narrowband [3]. The quality factor of the resonance is thereby directly linked to that of the coil. The final SNR efficiency is however weighted by the filling factor which is the ratio between the NMR active magnetic field that permeates the region of interest and the total reactive magnetic field components adding to the inductance of the structure but not to the signal gain. With increasing frequency the radiative field components rise and concomitantly the power propagating away from the antenna that is not directly dissipated in the material. Then the generated RF fields detach from the coil conductor and are not in-phase throughout the sample anymore. Furthermore, a magnetic field generated in the sample can originate from an electric field close to the coil/antenna conductor. This enables antenna topologies to become efficient NMR/MRI coils that do not primarily produce a reactive magnetic near field in their close vicinity. This effect allowed remote excitation and detection by traveling waves [4]. The radiated power is furthermore adding to the equivalent series resistance of the coil however it does not primarily represent an ohmic loss in the system. Consequently, such antenna structures can be efficient while exhibiting very low unloaded quality factors and a correspondingly low Q-drop. Thereby they can offer high bandwidths and low load dependence. However, when considering RF problems at ultra-high fields it has always to be taken into account, that the coil/antenna will be operating inside the bore of an MRI scanner and not in free space. The bore wall is conductive and sets therefore boundary conditions to the electric and the magnetic field. This induces decisive differences to considerations typically made for free field antennas as for instance used in radio communication applications. I.e. only electromagnetic modes with a cut-off frequency below or close to the Larmor frequency can propagate RF power, however they can be individually fed and detected enabling remote parallel excitation and reception [5]. Furthermore, the derivation of the antenna/coil system’s properties cannot be separated from a particular loading situation since the interaction with the sample is typically very strong and alters the field pattern significantly. This leads to a considerably reduced validity of many coil design rules which are based on low perturbation approximations of the antenna’s free field properties when interacting with the sample.

Traveling wave NMR/MRI

The basic principle of the traveling wave approach is to excite the electromagnetic modes established by the circumferential conductive surface of the bore lining. If these modes have cut-offs below or close to the Larmor frequency, power can be efficiently coupled into these modes by use of patch antennas, feeding struts, electric or magnetic dipoles which are located at the bore end [4, 5] (Fig. 1a&b) or at the isocenter [6]. The approach showed that NMR can be excited and detected solely by propagative fields (Fig. 1c) without the presence of a closely coupled resonator. Importantly the progression of the RF phase present in propagative RF field components has the potential to mitigate uniformity problems of the excitation field. Since the underlying wave equation forces the complex fields to have a certain curvature choosing the solutions with a strong spatial phase modulation helps to reduce the variation in the amplitude of the magnetic fields (see Fig. 1d). Furthermore the power for the RF excitation has in some cases to be delivered to locations with a distance from the coil conductor on the order of the RF wavelength or beyond. These regions reside outside the reactive near field and can often be reached more efficiently using radiative antennas in comparison to typical coil structures that primarily produce strong reactive near fields in their vicinity. However, when considering the spatial power flow of the corresponding fields one has to keep in mind that the Pointing vectors represents the power flow irrespective if it is of propagative or of dissipative nature. Therefore also for traditional surface loop coils the Pointing vectors are in the loaded case pointing mainly perpendicular to the conductor plain into the lossy sample following the power flowing from the coil into the sample tissue where it is deposited. On the other hand an unloaded loop coil in free space would generate Pointing vectors directing radially away in the plane of the coil conductors.

Surface antenna topologies for propagative RF fields

In a quasi-stationary regime loop structures and arrays thereof offer a very high efficiency for producing reactive magnetic near fields. At higher frequencies the use of microstrip transmission lines (Fig. 4a) was introduced for transmission arrays [7]. The strong concentration of the magnetic and electric near fields in the element cause a comparably low resistive coupling to the sample tissue and thereby a lower load dependence of the structure and coupling to other elements. In particular large portions of the reactive electric fields can be concentrated in the capacitors at the end of the transmission line. However, these elements are typically fed from one of end-points which requires a careful balancing of the matching and exposes the RF cable to strong electric fields emanating from capacitively shorted end of the transmission line. Feeding the element from the center (Fig. 1b, [8]) allows to connect the cable with very low electric field exposure. Effectively these elements form a capacitively shortened dipole over a ground backplane. Removing the backplane or locating it very distantly from the strip line results in an effective dipole structure. These dipoles are not capacitively shortened and consequently the capacitive reactance of the element is largely caused by the electric field evanescent from the dipole’s tips. These electric fields can be concentrated in a high dielectric material [9] in order to prevent them from penetrating the sample causing loss and high local SAR depositions. Also monopole antennas (Fig. 1d) have been proposed for the use as MRI antennas [10]. Although their conductive surfaces suggest an entirely different topology than a dipole the structure is from a field theoretical standpoint largely equivalent to a dipole rotated by 90°. This becomes apparent considering the image charges and currents generated by the monopole in its backplane.

Acknowledgements

No acknowledgement found.

References

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Figures

Figure 1: Implementation and results of traveling wave NMR. a) A folded dipole antenna excites a circularly polarized propagative mode in the bore which then excites the NMR in the sample. b) Implementation with a human subject and a patch antenna. c) NMR spectra of ethanol excited and received over large distances. d) in-vivo results of feet imaging with traveling wave (left) and a classical resonator setup (right).

Figure 2:a) Side fed microstrip transmission line coil element, b) Centrally fed microstrip transmission line, c) dipole element, d) shield backed monopole. The arrows denote the direction of current flow, the double sided arrows mark the feed points.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)