Coupled microstrip line transverse electromagnetic resonator model for high‐field magnetic resonance imaging

Abstract

The transverse electromagnetic (TEM) resonator design (1,5-7) as an RF coil has received heightened attention as a superior replacement for the standard birdcage coil (4) in high-field 4.7-9.4 T MRI applications. It has been demonstrated (1-3) that at the corresponding operating frequencies of 200 and 400 MHz, the TEM resonator can achieve better field homogeneity and a higher quality factor than an equivalent birdcage coil, resulting in improved image quality.In our opinion, the primary difference between a TEM resonator and a birdcage coil is the cylindrical shield, which functions as an active element of the system, providing a return path for the currents in the inner conductors. In a birdcage coil, the shield is a separate entity, disconnected from the inner elements, only reflecting the fields inside the coil to prevent excessive radiation losses. Because of this shield design, the TEM resonator behaves like a longitudinal multiconductor transmission line (MTL), capable of supporting standing waves that occur at high frequencies. Unlike a birdcage coil, the TEM resonator's inner conductors do not possess connections to their closest neighbors, but instead connect directly to the shield through capacitive elements. Resonance mode separation is accomplished though mutual coupling between the inductive inner conductors. Since all the conductors connect to the shield with tunable capacitive elements, the field distribution can be adjusted to achieve the best homogeneity.The first descriptions of TEM resonator structures appeared in patents (5,6). Subsequently, several works (1,8 -11) have been published on the subject of modeling the TEM resonator. The models are typically based on transmission line concepts. Vaughan et al. (1) derived an estimate for the resonance frequency by treating the resonator as a section of coaxial transmission line terminated by capacitors. Tropp (8) developed a lumped circuit model for a TEM resonator, wherein the inner conductors are treated as inductors with mutual coupling and the terminating elements are capacitors. The model predicts all resonant modes of the TEM resonator and shows good agreement with experimental data. However, the measurements are conducted at a relatively low frequency of 143 MHz. Rö schmann (9) and Chingas et al. (10) developed TEM resonator models based on simplified coupled transmission line equations. These models are accurate at predicting particular resonance frequencies, but require complete symmetry of the structure and its terminating elements.Baertlein et al. (11) developed a resonator model based on MTL theory, which included accurate calculations of per-unit-length parameter matrices, resonance frequencies, and field distributions inside the coil. The TEM coil can be modeled under linear or quadrature drive conditions. The resonance frequency predictions compared well with measurements and a full-wave finite-difference time domain (FDTD) model, developed separately in Ref.12. The transmission line model is suitable for studying the resonance beh...

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“…used to predict the behaviour of resonating coils in high-field magnetic resonance imaging (Bogdanov and Ludwig 2002). While the MTL method is quite general and can quickly approximate the overall behaviour of the sensor, it can only be used within the constraints of the transverse electromagnetic theory excluding radiation effects and conductive loss mechanisms in the glottal load models.…”

“…These matrices characterize the physical behaviour of the transmission line configuration as a function of angular frequency ω = 2πf and per-unit-length resistance R, conductance G, inductance L and capacitance C matrices. As discussed in Bogdanov and Ludwig (2002), a standard electrostatic boundary element technique is invoked to compute these matrices for an xy-plane cross sectional slice of the sensor shown in figure 3. Following basic linear, first order differential matrix equation theory, (3) has the general solution…”

Interaction between the RF Field of MRI Apparatus and Pacemakers

“…These coils are driven by sources connected to the end of one or more conductors. Theoretical studies on TEM resonators have shown that they behave like loaded multiconductor transmission lines capable of supporting standing waves (Bogdanov & Ludwig 2002). In the absence of excitation, and for symmetrically placed tubes, the condition for resonance results in:…”

“…where h n is the transverse vector mode function (Bogdanov & Ludwig 2002). Because circular polarization is necessary to excite the MR signal, coils are commonly driven in quadrature so as to produce circularly-polarized fields.…”

Comparing Saddle, Slotted-tube and Parallel-plate Coils for Magnetic Resonance Imaging

“…The characteristics of the birdcage resonator, including the effects of a conducting shield, have been analyzed by using the boundary element method. In this work a multiconductor transmission line (MTL) model is developed and successfully applied to analyze a 12-element unloaded and loaded microstrip line transverse electromagnetic (TEM) resonator coil for animal studies [1]. To produce a uniform B 1 field along the coil (z-direction), a multi-section alternating impedance microstrip element was investigated in Akgun [2].…”