Explicit treatment of mutual inductance in eight-column birdcage resonators

Open birdcage coil for head imaging at 7T

PURPOSE

To theoretically describe, design, and test the new geometry of the birdcage coil for 7 Tesla anatomical brain imaging, which includes a large window on top, without deliberately jeopardizing its homogeneity and efficiency. This opencage will not only improve patient comfort but also enable the volunteer to follow functional MRI stimuli. This design could also facilitate the tracking of patient compliance and enable better correction of the movement.

METHODS

Via the transfer matrix approach, a birdcage-like coil with a nonperiodic distribution of rungs is constructed with optimized currents in the coil rungs. Subsequently, the coil is adjusted in full-wave simulations. Then, the coil is assembled, fine-tuned, and matched on the bench. Finally, these results are confirmed experimentally on a phantom and in vivo.

RESULTS

Indeed, the computed isolation of -14.9 dB between the feeding ports of the coil and the symmetry of the circular polarized mode pattern transmit RF magnetic field ( B 1 + ) showed that the coil was properly optimized. An experimental assessment of the developed coil showed competitive transmit efficiency and coverage compared with the conventional birdcage coil of similar size.

CONCLUSION

The proposed opencage coil can be designed and work without a dramatic drop of performance in terms of the B 1 + field homogeneity, transmit efficiency ( B 1 + / P ref ), peak local specific absorption rate ( S A R 10 g ) and SAR efficiency ( B 1 + / S A R 10 g ).

Recent Progress in Birdcage RF Coil Technology for MRI System

The radio frequency (RF) coil is one of the key components of the magnetic resonance imaging (MRI) system. It has a significant impact on the performance of the nuclear magnetic resonance (NMR) detection. Among numerous practical designs of RF coils for NMR imaging, the birdcage RF coil is the most popular choice from low field to ultra-high field MRI systems. In the transmission mode, it can establish a strong and homogeneous transverse magnetic field B1 for any element at its Larmor frequency. Similarly, in the reception mode, it exhibits extremely high sensitivity for the detection of even faint NMR signals from the volume of interest. Despite the sophisticated 3D structure of the birdcage coil, the developments in the design, analysis, and implementation technologies during the past decade have rendered the development of the birdcage coils quite reasonable. This article provides a detailed review of the recent progress in the birdcage RF coil technology for the MRI system.

Application of copper plates for frequency tuning of surface wired and wireless MRI coils

This study shows how a copper plate could be used for frequency tuning of surface wired and wireless MRI coils. For this purpose, it is proposed to place the copper plate directly on their conducting circuit. This leads to increase in the resonance frequency of coils. The effect is most perceptible if the copper plate is comparable in size to the conducting circuit of radiofrequency (RF) coil. The experimental work was performed on a 7.05 T MR scanner using surface MRI coils operating on different resonance frequencies: ¹H (300 MHz), ³¹P (121 MHz), ²³Na (79 MHz), ¹³C (75 MHz). Application of copper plate for frequency tuning of wireless multi-turn multi-gap transmission line resonator (MTMG-TLR) was considered for the first time. The proposed method can be claimed if the nominal variable inductance or capacitance is not enough for tuning the resonance frequency of the MRI coil to a higher frequency range.

High-pass two-dimensional ladder network resonators for magnetic resonance imaging

A novel two-dimensional ladder network resonator design is introduced for signal transmission and detection in magnetic resonance imaging. It is shown that planar structures consisting solely of inductively coupled elements have a high-pass eigenmode spectrum and exhibit eigenfunctions which can be used for magnetic resonance imaging, including quadrature operation. Two 5 x 5 element prototypes, a planar surface coil and a volume head coil, are presented to demonstrate the suitability of the design for imaging at 3.0 Tesla.

An efficient design for birdcage probes dedicated to small-animal imaging experiments

We are presenting, in this paper, a simple, easily reproducible and easily tuneable design for home-built birdcage probes inducing a linearly polarised B1 field. A simple tuning method is proposed which preserves the induced field homogeneity that characterises in general the birdcage design. This is achieved by adding two extra rings (link rings) that allow one to connect two opposed points on the birdcage end rings via tuning capacitors. All the development stages, from design to practical realisation, are presented, step by step, in order to facilitate experimentalist work. Some images obtained with the birdcage probe are presented, accompanied by the B1 maps in transverse as well as longitudinal planes. Finally, a few suggestions are made for obtaining a circularly polarised magnetic field configuration.

Magnetic resonance angiography of collateral vessels in a murine femoral artery ligation model

The in vivo detection of growing collateral vessels following arterial occlusion is difficult in small animals. We have addressed the feasibility of performing high resolution time-of-flight angiograms to monitor the growth of collateral vessels after femoral artery occlusion in mice. We will also present a low-pass quadrature birdcage coil construction with a sufficient signal-to-noise ratio to produce high resolution. After a 4-month recovery period a C57BL/6 mouse with a surgical occlusion of the right femoral artery was used to assess the image quality and time requirements to produce magnetic resonance angiograms sufficient to assess collateral artery development using a two-dimensional gradient echo sequence. At a resolution of 100 x 100 x 100 microm and a matrix size of 256 x 128 x 256 for a 2.56 cm isometric volume, three scans were performed with one, two and four repetitions resulting in signal-to-noise ratios for the femoral artery proximal to the ligation site of 58, 126 and 194, respectively. Five C57BL/6 mice were additionally measured 4 weeks after occlusion using two repetitions and the visual collateral vessels were assessed for number and location: 2.0 +/- 1.2 in quadriceps muscle, 0.6 +/- 0.5 in adductor (deep adductor vessel), 0.0 +/- 0.0 in adductor (surface adductor vessels). The results showed a significant difference, two-sided t-test, p < 0.05, in number of vessels in all the locations. We have shown that this method can be utilized to elucidate the contribution of collateral vessels to arterial flow.

A fast and accurate simulator for the design of birdcage coils in MRI

The birdcage coils are extensively used in MRI systems since they introduce a high signal to noise ratio and a high radiofrequency magnetic field homogeneity that guarantee a large field of view. The present article describes the implementation of a birdcage coil simulator, operating in high-pass and low-pass modes, using magnetostatic analysis of the coil. Respect to other simulators described in literature, our simulator allows to obtain in short time not only the dominant frequency mode, but also the complete resonant frequency spectrum and the relevant magnetic field pattern with high accuracy. Our simulator accounts for all the inductances including the mutual inductances between conductors. Moreover, the inductance calculation includes an accurately birdcage geometry description and the effect of a radiofrequency shield. The knowledge of all the resonance modes introduced by a birdcage coil is twofold useful during birdcage coil design: --higher order modes should be pushed far from the fundamental one, --for particular applications, it is necessary to localize other resonant modes (as the Helmholtz mode) jointly to the dominant mode. The knowledge of the magnetic field pattern allows to a priori verify the field homogeneity created inside the coil, when varying the coil dimension and mainly the number of the coil legs. The coil is analyzed using equivalent circuit method. Finally, the simulator is validated by implementing a low-pass birdcage coil and comparing our data with the literature.

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

The performance modeling of RF resonators at high magnetic fields of 4.7 T and more requires a physical approach that goes beyond conventional lumped circuit concepts. The treatment of voltages and currents as variables in time and space leads to a coupled transmission line model, whereby the electric and magnetic fields are assumed static in planes orthogonal to the length of the resonator, but wave-like along its longitudinal axis. 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. The loading involves a homogeneous cylindrical dielectric insert of variable radius and length. This model formulation is capable of estimating the resonance spectrum, field distributions, and certain types of losses in the coil, while requiring only modest computational resources. The boundary element method is adopted to compute all relevant transmission line parameters needed to set up the transmission line matrices. Both the theoretical basis and its engineering implementation are discussed and the resulting model predictions are placed in context with measurements. A comparison between a conventional lumped circuit model and this distributed formulation is conducted, showing significant departures in the resonance response at higher frequencies. This MTL model is applied to simulate two small-bore animal systems: one of 7.5-cm inner diameter, tuned to 200 MHz (4.7 T for proton imaging), and one of 13.36-cm inner diameter, tuned to both 200 and 300 MHz (7 T).

A birdcage coil tuned by RF shielding for application at 9.4 T

The design and performance of an inductively fed low-pass birdcage radiofrequency (RF) coil for applications at 9.4 T are described where tuning is accomplished by mechanically moving a concentric RF shield about the longitudinal axis of an RF coil. Moving the shield about the RF coil effectively changes the mutual inductance of the system, providing a mechanism for adjusting the resonant frequency. RF shield tuning eliminates adjustable capacitors on the legs of the RF coil, eliminates current imbalances and field distortions, and results in improved B1 field homogeneity and high quality (Q) factors. RF shield tuning and inductive matching provide an isolated resonance structure which is both physically and electrically unattached. Experimental analysis of shield position on both B1 field homogeneity and resonant frequency is provided. Computer simulations of B1 field homogeneity as a function of shield position and shield diameter are also presented. Magnetic resonance microimaging substantiates the usefulness of this design.

Theory and application of array coils in MR spectroscopy

The theory and application of array coils are reviewed in the context of phased array spectroscopy. The optimization of the signal-to-noise ratio from an array of coils is developed by considering the efficiency of a phased array transmit coil. This approach avoids the need to consider noise correlation, and should be useful in future considerations of transmit phased array coils for MR spectroscopy. Methods to characterize array coil performance, including fields and coupling are briefly summarized, along with methods to minimize the effects of mutual inductance. The signal-to-noise advantages of array coils over single coils are examined for both planar and cylindrical arrays. Numerical simulations of planar arrays of 2 x 2, 4 x 4 and 8 x 8 elements and constant overall dimension are compared to a single coil of the same size. The results demonstrate a significant improvement in sensitivity near the array coil. Although the benefits of the array decrease as a function of distance from the array, the array sensitivity never drops below that of a single coil with the same overall dimensions, or that of a single element of the array. Similar results are obtained for a sixteen element cylindrical array, which is compared to a standard quadrature birdcage coil using both computational methods and phantom measurements. The phased array techniques reviewed are demonstrated with proton spectroscopic images of the brain.

Theory of the quadrature elliptic birdcage coil

This paper presents the theory of the quadrature birdcage coil wound on an elliptic cylindrical former. A conformal transformation of the ellipse to a circular geometry is used to derive the optimal sampling of the continuous surface current distribution to produce uniform magnetic fields within an elliptic cylinder. The analysis is rigorous for ellipses of any aspect ratio and shows how to produce quadrature operation of the elliptic birdcage with a conventional hybrid combiner. Insight gained from the transformation is also used to analyze field homogeneity, find the optimal RF shield shape, and specify component values to produce the correct current distribution in practice. Measurements and images from a 16-leg elliptic birdcage coil at both low and high frequencies show good quadrature performance, homogeneity, and sensitivity.

Mutual Inductance in the Bird-Cage Resonator

Formulas are derived to account for the effect of the mutual inductances, between all meshes, upon the electrical resonance spectra bird-cage resonators, and similar structures such as the TEM resonator of P. K. H. Roschmann (United States Patent 4,746,866) and J. T. Vaughan et al. (Magn. Reson. Med. 32, 206, 1994). The equations are parameterized in terms of isolated mesh frequencies and coupling coefficients, and ought therefore apply not only to simple magnetic couplings used in the derivation, but to electromagnetic couplings as well. A method for measuring the coupling coefficients-applicable to shielded as well as unshielded resonators-is described, based upon the splitting of frequencies in pairs of coupled resonators; and detailed comparisons are given between calculated and measured resonance spectra: for bird-cage resonators, with and without shields, and for the TEM resonator.

Multiple tuning of birdcage resonators

A theoretical framework is presented for designing birdcage resonators for MRI and MR spectroscopy. The analogy between the birdcage problem and the phonon problem in solid-state physics is used to achieve multiple tuning. Allowing that the capacitances in the columns of the cage assume unequal values, it is possible to achieve multiple tuning and simultaneously preserve the sinusoidal current distribution necessary to set a homogeneous magnetic field. Given the physical dimensions of the columns and branches of the cage as well as the desired resonant frequencies, the corresponding values of the capacitances can be calculated exactly. Closed-form expressions for the capacitances are given in terms of the mutual inductances and the desired resonant frequencies. A detailed analysis for a symmetrical low-pass birdcage is presented. The expressions for the resonant frequencies reduce to those given by other authors when only nearest-neighbor mutual inductances are included.

High frequency volume coils for clinical NMR imaging and spectroscopy

A tuned transmission line resonator has been developed in theory and in practical design for the clinical NMR volume coil application at 4.1 tesla. The distributed circuit transmission line resonator was designed for high frequency, large conductive volume applications where conventional lumped element coil designs perform less efficiently. The resonator design has made use of a resonant coaxial cavity, which could be variably tuned to the Larmor frequency of interest by tunable transmission line elements. Large head- and body-sized volumes, high efficiencies, and broad tuning ranges have been shown to be characteristic of the transmission line resonator to frequencies of 500 MHz. The B1 homogeneity of the resonator has been demonstrated to be a function of the electromagnetic properties of the load itself. By numerically solving Maxwell's equations for the fully time-dependent B1 field, coil homogeneity was predicted with finite-element models of anatomic structure, and inhomogeneities corrected for. A how-to exposition of coil design and construction has been included. Simple methods of quadrature driving and double tuning the transmission line resonator have also been presented. Human head images obtained with a tuned transmission line resonator at 175 MHz have clearly demonstrated uncompromised high field advantages of signal-to-noise and spatial resolution.

Transmission line analysis of noncylindrical birdcage resonators

Transmission line theory, validated for the standard cylindrical birdcage coil, has been employed for the analysis of a rectangular birdcage resonator which is useful for MR imaging of the hand. Due to lack of cylindrical symmetry in the rectangular coil, RF field uniformity was evaluated and found to be critically dependent upon the choice of column from which the coil was linearly driven. Effective L1 and L2 inductance elements were determined using known formulas for self and mutual inductance contributions, and compensation of the different inductance elements of the hand coil was performed to produce cylindrically symmetric birdcage current patterns. RF field mapping using the Biot-Savart law demonstrated a rectangular coil sensitivity 22% greater than a comparable cylindrical version. MR hand and wrist images were acquired using the rectangular birdcage coil. In addition, transmission line analysis was extended to other noncylindrical birdcage geometries.

Use of transmission line analysis for multi-tuning of birdcage resonators

A general analysis for double- and higher order tuning of birdcage resonators is presented based on a lumped element transmission line model. Expressions were developed for the determination of the resonant frequencies of bandstop and bandpass birdcage coils and, with specific restrictions, for capacitor values required to obtain any two desired mode one resonant frequencies. Experimental measurements on three variants each of an eight-column bandstop and an eight-column bandpass were in excellent agreement with theory; the average absolute frequency difference and percent deviation were 1.51 +/- 1.57 MHz and 2.61 +/- 2.36%, respectively. In addition, 31P and 1H phantom images were obtained at 2.0 T using a representative bandstop coil.