Traveling Wave MRI. David O. Brunner. Institute for Biomedical Engineering University and ETH Zurich

Transcription

1 Traveling Wave MRI David O. Brunner Institute for Biomedical Engineering University and ETH Zurich Introduction NMR and MRI signal detection is traditionally based on Faraday induction [1]. The local magnetic moment produced by the nuclear spins is excited and detected by near-field electromagnetic interactions mostly with one or multiple electrical resonators tuned to the particular frequency. This means that the energy to excite the spin system is coupled from the coil to the spins similarly as from one coil of a transformer to the other and vice versa in the receive phase of the experiment. 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, as it will be explained in the section below, the basic physical regime governing the electrodynamics of the RF detector can drastically and quite abruptly alter at ultra-high frequencies and therefore the instruments applied in these systems have to cope with a different situation than at lower field strengths. Physical background The dynamics of electromagnetism is generally governed by Maxwell s equations. But, the solution of the full set of equations can become complicated to obtain on the one hand and also difficult to interpret on the other. It is therefore very instructive to consider the Helmholtz equation, that is equivalent in systems with only piecewise constant material parameters: ( 2 + k(r ) 2 )ψ(r ) = f(r ); k 2 (r ) = ωμ(r ) ωε(r ) + iσ(r ), [1] where k represents the local wave number, Ψ a time harmonic field (electric or magnetic) and f the driving term (f is zero except at the sources driving the system). This equation basically states, that the field curvature expressed by the Laplacian has to equal the wave number in every point if no source is close by (f=0). Although the exact pattern of the resulting fields can be very complex it can still be seen that the wavelength (given by the wave number) introduces a characteristic scale to the electrodynamic system. Since the fields locally bend, the product of the wave number and the size of the electrodynamic system (R) considered (k R) gives a good indication of the total field variation and hence of the regime the system is working in. If this product is very small (<<1), k can basically be neglected in the equation and we end up with a pure Poisson s equation. This is the same equation governing electrostatics and magnetostatics resulting in certain characteristics: First, phase delays due to propagation do not exist and all phase differences are accrued due to losses via the imaginary part of k 2 [2]. Although the fields vary harmonically in time, the change is much slower than the speed of propagation of the induced change across the system and hence the field is in synch in all positions. This is why this regime is also dubbed quasi-stationary. In this approximation

2 (k 0), the field pattern generated by a given current/charge distribution does not differ from a stationary solution. Because the fields do not detach from the source driving it, coupling the magnetic field to a lossy sample is directly linked to an increase of the resistance seen by the source in the quasi stationary regime. A result with major implication for MR is that the uniform field (B (r ) = c where f(r ) = 0) is a solution to this equation. Regarding the homogeneous part of the equation ( 2 ψ(r ) = 0)for an unbound region this fact is trivial, but more importantly also sheetcurrent distributions on the surface of finite volumes (f(r ); r ε Ω) can be found realizing a uniform field inside the volume. In fact, uniform volume resonator structures such as birdcages [3] or TEM resonators [4] approximate such a current distribution on their discrete conductor lattice in order to achieve a uniform circularly polarized field in the imaging volume. The quasi-stationary regime is of eminent importance for almost all RF devices applied in NMR and MRI since the RF scaling of almost all systems allows applying the corresponding simple equations. This is shown in Figure 1 comparing the electrodynamic size (k R) of various NMR systems. Obviously, only human ultra-high-field systems violate the quasi-stationary condition to a significant degree and the continuous thrive of even higher fields and larger imaging volumes will lead even more strongly away from a quasi-stationary behavior. Figure 1: Electrodynamic scaling of NMR and MRI systems. Only human whole body MRI systems reach beyond the quasistationary regime. This consideration already shows the uniqueness of the newest generation of human ultra high field systems in that respect. Therefore these systems are probably the only ones where the design principles based on the quasi-stationary approximation get majorly challenged. Indeed it was reported that long standing RF concepts did not yield anymore the performance regarding uniformity and efficiency as expected from lower frequencies. How drastic the consequences of this change are can be considered by regarding the bore of such a system as a cylindrical conductive hollow waveguide. It is found that the fields inside such a waveguide can only have a discrete number of transverse patterns ( ET( xy, ), BT( xy, )), the so called modes. Each mode has a characteristic cutoff frequency ω c that determines above which frequency it propagates with an axial wave number k z. Below that frequency the mode extends into the waveguide evanescently, meaning that it dies off exponentially with a decay constant λ z = 2π k. For a given oscillation frequency ω, the cut-off z frequency determines the axial wave number

3 k ( ω ) = µε ω ω, [2] z 2 2 c whereas ε and µ denote the permeability and permittivity of the waveguide medium. Together with the mode patterns, the wave number defines the global field phasors E(r ) = E T (x, y) e i k z(ω)z and B(r ) = B T (x, y) e ik z(ω)z, [3] which reflect wave propagation if ω ω c and exponential axial decay otherwise. The plus or minus sign applies corresponding to the direction of propagation considered if the E T and B T field phasors refer to linear polarizations. Figure 2 depicts the behavior of the axial propagation as a function of the frequency. In regime 1 where most NMR systems and human MRI systems operate, the axial decay length of the evanescent fields from the source is very short. Therefore it becomes essential that the RF probe resides in close vicinity to the sample examined in order to get a strong coupling. In regime 2 the fields start to extend a bit further and in conjunction with losses first phase effects and visible propagation might occur, as is typically the case in whole body applications at field strengths like 3T. In regime 3 the transition around the lowest cut-off occurs. At cut-off already, the fields extend infinitely into a lossless waveguide (k z 0, λ z ), however the fields are everywhere still in phase. Clearly the lossless case shows an unrealistic behavior resulting in an infinite reactance and group delay for instance that is not seen in reality. Already slight losses smear out this sharp transition noticeably. Furthermore the net transmission losses in a lossy waveguide near cut-off are very high. But a small amount of high dielectric filling material is sufficient to lower the cut-off frequency of the bore to a degree that the lowest two modes (TE 11 ) can propagate over the needed distances. This is the regime in which an empty 60 cm bore of a human whole body 7T system is found with a cutoff frequency of around 300 MHz. In regime 4 multiple modes propagate allowing even transversally different field patterns to persist in the bore. This regime can be established in a typical 7T system by large dielectric loads [5] or a human body. Figure 2: Electromagnetic regimes of a hollow waveguide. The alteration below and above cut-off of the first mode is abrupt and has drastic consequences. Implications for RF systems at ultra-high fields By this it becomes clear that such a drastic change in regime imposes problems but maybe also opens chances for RF probe concepts. The fact that fields can extend over large distances can reduce for instance the necessity of bringing the probes very close to the subject, allowing the remote detection of NMR signals [6]. Placing RF probes remotely frees valuable space in the direct vicinity of the patient and also has potential electrical advantages. Close coupling resonators are strongly influenced by the subject loading and even their tuning can be shifted making them delicate to operate. This is less of a problem with a radiative antenna whose load is represented by a comparably large radiation resistance.

4 On the MR physics side the most important aspect that changes compared to the case using a close coupling resonator is that the retrieved MR signal has a spatially varying phase induced by the propagation delay of the RF wave exciting and inducing the signal in the RF probe. Since in the quasistationary regime all fields are in phase, no phase variation is induced at lower frequencies. However, such phase variation cannot only improve the spatial encoding capability of an RF detector but can even lead to directive radiation of the spin signal as it was theoretically proposed and measured [6, 7]. However, the most important advantage is expected from the propagation of RF waves inside the imaging volume itself. As stated above, the Helmholtz equation itself imposes the RF fields to bend according to the wave number that is not negligible at these frequencies. Uniform fields can therefore not extend over large volumes. This can be further illustrated by splitting up the time harmonic field phasor in magnitude and phase terms by which Equation 1 for one dimension becomes: Ψ = A(x)e iφ(x) ; A, φϵr x 2 A(x) + 2i x A x φ + ia x 2 φ A( x φ) 2 + k 2 A = 0. [4] In typical volume resonators an axially standing wave is established resulting in a field that oscillates in phase which nulls all the derivatives of the phase term in Eq. 4 (terms in blue & violet). Therefore the amplitude term (red) has to vary in space to match up with the wave number (black) resulting in a non-uniform axial coverage [8]. However, if the magnitude is constant, so all derivatives of it become zero, the phase term has to carry the needed bending. One way to achieve such a varying phase term is by propagation as seen by Eq. 3. This is good news for MR imaging, where the resolution of the resulting image is usually much higher than this phase variation and therefore partial volume effects do not occur. This can be different in large voxel spectroscopy leading to directive radiation of the spin signal [9]. Of course the used model here certainly oversimplifies the situation of an in-vivo human application, but the reasoning stays in its essence true, that if a uniform field magnitude shall be established, a form of wave propagation has to Figure 3: Implementation and first 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 samble. b) implementation with a human subject and a patch antenna. c) NMR spectras 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).

5 be induced because a uniform field in amplitude and phase is not supported by the underlying physical equations. Implementations of traveling wave RF devices The first demonstrations of MR signal excitation and detection was performed using a patch antenna located at one end of the bore of a 7T human whole body 7T scanner (Figure 3). Since the bore is usually lined with a layer of conductive material it can be approximated as a circular waveguide. The antenna structure at the end of the bore excites one or several of the propagative modes inside the bore which then excites the NMR in the subject and by reciprocity receives the spin signal. This scheme allowed first remote detection of NMR by propagative fields in order to acquire spectra and images (Figure 3, [6]). Since the RF signals exciting and transporting the NMR signals propagate, the received signal drops off only slowly only due to losses and reflections along the waveguide and not as rapidly as due to the steep field decay occurring in the evanescent regime. It could also be shown that on axially tapered object a large axial coverage can be achieved. Another major advantage exhibited by such setups is their simplicity and more importantly that typically no space in the bore around the patient is occupied. This gives increased possibilities for placing additional hardware and for subject positioning [10]. Figure 4: Parallel transmission and reception by travelling waves. Remote excitation of different waveguide modes allows excitation of distinct field patterns in the sample (a). b) Parallel imaging g- factor maps. c) RF shimming field patterns of each channel (top) invivo results after RF shimming (bottom). However, in situations as they are encountered when imaging a human head or body, establishing propagating waves in complex dielectric structures is hampered by reflections and diffractions occurring at dielectric boundaries, generating significant standing wave ratios. A possible solution proposed was the use of dielectric materials to reduce reflections[11] by more smoothly tapering the distribution of dielectric materials in axial directions. In the case of body imaging numerical studies showed a comparable B 1 to SAR performance as for traditional resonators [12]. The efficiency of power delivery and SAR is certainly reduced in such cases where the exciting RF wave has to propagate over large distances heavily loaded with lossy sample material. A higher efficiency can in such cases be achieved by either bypassing the lossy material by inner conductive structures or shields [13, 14] or by exciting the propagative mode close to the imaging region [15]. Since different modes in a waveguide have different transverse field patterns (Figure 4), parallel transmission can also be established

6 by axially traveling waves [16-18]. For this however at least as many modes must propagate in the waveguide feed section as there are channels to be used in the system (Figure 4). In a typical human whole body 7T system only the TE 11 modes traveling. In order to get more modes to propagate either the frequency or the electrical size of the bore must be increased. The latter can be achieved by dielectric or conductive fillings that shorten the wavelength. Further different linear combinations of modes must be excited with each feeding channel. This is typically achieved by the positioning and angulation of the exciters. Interestingly these exciter structures can be very simple, such as a copper stub or a loop mounted on the center pin of a connector penetrating the outer shield and do not need high-power capable or tunable lumped elements. Once spatially distinct field patterns can be excited, RF shimming, acceleration of spatial localized pulses and imaging read-outs can be performed in the same manner as with close coupling arrays. As shown in Figure 4 showing results from Ref [17] the parallel imaging performance as measured by the g-factor in a 30 cm diameter conductive cylinder is comparable to a typical 8 channel close coupling array. By reduction of the dielectric loading in the feed section the number of propagating modes could be gradually reduced and the parallel imaging performance worsened correspondingly. This shows that the modes carry indeed independent information about the NMR signal distribution in the sample. A further approach extending the capability of traveling wave excitation is feeding propagating waves from both sides into the system. By this the uniformity and efficiency of the resulting excitation could be improved [19]. However, the emergence of propagative fields inside an MR scanner cannot only be used to excite axially traveling modes, but also in order to excite an RF wave transversely propagating to deeper tissue regions. These so called radiative element arrays [20] reduce the reactive near-field coupling to the sample by placing a high dielectric ceramic in between. This not only greatly reduces the local SAR deposition just below the transmitter element but also allows directing the RF power flow inwards to deeper regions of the body compared to stripline or loop structures that are designed to work in close-coupling regime. As a result, the excitation efficiency of tissue in deeper regions of the large objects could be significantly increased. Conclusion The change in the electrodynamic regime encountered in novel ultra-high field human systems compared to lower field equivalents alters the behavior of the RF fields and their interaction with the RF probes drastically. The most prominent consequence is certainly that RF fields can detach from the RF probe if the NMR frequency is above the cut-off of the bore s lowest mode. This allows remote excitation and detection of NMR by which valuable space is freed up in the imaging volume of the system. If the RF probe couples over radiated fields to the sample the loading of the detector becomes largely independent of the sample which greatly simplifies tuning and matching considerations. Further the concept of RF signal transmission through propagating waves prompts strong analogies to other fields such as microwave engineering, non-linear optics, laser physics and EPR which can provide seminal ideas for novel RF concepts and spin manipulation methods. Finally, taking electromagnetic radiation as a fundamental mechanism of NMR signal excitation and detection into the design considerations of future RF detector topologies will most probably further improve the performance of existing ultra-high field systems and will almost certainly be necessary for even higher frequencies in the future.

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