An Eight-Channel Sodium/Proton Coil for Brain MRI at 3 Tesla

Abstract

The purpose of this work is to illustrate a new coil decoupling strategy and its application to a transmit-receive sodium-proton phased-array for MRI of the human brain. We implemented an array of eight triangle-shaped coils that encircled the head. The ensemble of coils was arranged to form a modified degenerate mode birdcage whose eight shared rungs were offset from the z-axis at interleaved angles of +/− 30°. This key geometric modification resulted in triangular elements whose vertices were shared between next-nearest neighbors, which provided a convenient location for counter-wound decoupling inductors, while nearest-neighbor decoupling was addressed with shared capacitors along the rungs. This decoupling strategy alleviated strong interaction that is characteristic of array coils at low frequency (32.6 MHz in this case) and allowed the coil to operate efficiently in transceive mode. The sodium array provided a 1.6-fold signal-to-noise ratio advantage over a dual-nuclei birdcage coil in the center of the head and up to 2.3-fold gain in the periphery. The array enabled sodium MRI of the brain with 5-mm isotropic resolution in approximately 13 minutes, which has helped overcome low-sodium MR sensitivity and improved quantification in neurological studies. An eight channel proton array was integrated into the sodium array to provide anatomical imaging.

Graphical abstract

An eight channel coil array was constructed to enable simultaneous sodium/proton brain imaging at 3.0 Tesla. The coil incorporated triangular elements to provide seamless neighbor and next nearest neighbor decoupling. The constructed coil array achieved significantly improved sodium sensitivity and adequate proton performance for anatomical localization when compared to a dual tuned birdcage coil.

Introduction

Sodium MRI has the potential to provide new metabolic information on tissue viability such as ion homeostasis and cell membrane integrity in brain, which is not available with standard proton MRI, in a non-invasive and a quantitative manner^1–3. This information could lead to a better understanding of normal physiological processes such as aging^4,5 and improved diagnosis and treatment monitoring of central nervous system disorders such as Alzheimer’s Disease⁶, multiple sclerosis (MS)⁷, and brain neoplasia⁸.

Sodium MRI in the human brain suffers from lack of sensitivity due to the low sodium concentration in the human brain (~44mM vs. 80M for water protons), low gyromagnetic ratio, and fast T2 relaxation associated with the sodium nucleus.³ The sodium nucleus has a spin of 3/2 and thus possesses a quadrupolar moment which interacts with the electric field gradients from its surroundings. This quadrupolar interaction is the main relaxation mechanism for the sodium spins, leading to short (quasi-monoexponential) T1 and biexponential T2 in biological tissues. For example in brain tissues, T1~15-35 ms in gray matter (GM) and white matter (WM), T1~50-60 ms in cerebrospinal fluid (CSF), T2_short~0.8-3 ms and T2_long~15-30 ms in GM and WM, and monoexponential T2~50-60 ms in CSF. The short T1 facilitates a short repetition time (TR) and fast averaging which can partially compensate for low sodium concentration, while due to very short T2s, ultrashort TE (UTE) sequences are recommended to acquire images. The inherent challenges of sodium MRI can therefore be addressed with high main magnetic fields, low resolution, signal averaging and UTE pulse sequences⁹, along with optimized radio frequency (RF) coils. Recent publications have demonstrated that dual-nuclei multi-channel phased array coils can achieve improved sodium sensitivity compared to birdcage volume coils and simultaneously enable standard proton MRI^10–15,16.

One of the engineering challenges associated with a sodium/proton phased-array comes from the need for a sodium transmit module, which dictates either dedicated transmit-only/receive-only (ToRo) or transceive (Tx/Rx) coil elements. Although in principle, a ToRo structure may be expected to provide better transmit field (B₁⁺) uniformity, we chose a Tx/Rx structure in order to preserve sodium signal-to-noise ratio (SNR) that could be degraded by shielding from a stand-alone transmit structure and lossy circuitry such as active and passive detuning circuits and fuses that accompanies ToRo coils. One caveat is that Tx/Rx structures require adequate isolation between coil elements to efficiently generate a uniform B₁⁺. We address this obstacle with an eight-channel array whose unique triangular elements enable neighbor and next-nearest neighbor decoupling. The coil additionally includes an integrated eight-channel nested proton array for anatomical localization. The manuscript details the coil design, implementation and performance.

Methods

Sodium Array

Given the low sensitivity of sodium MR, we prioritized sodium over proton coil performance and thus begin by describing the rationale behind the sodium array. The first design choice was to utilize a Tx/Rx rather than a ToRo structure because it reduces construction complexity and is expected to provide the following performance advantages: 1) Tx/Rx arrays do not require lossy detuning circuitry such as active and passive detuning circuits and fuses, and 2) Tx/Rx arrays do not require a dedicated transmit structure, which can introduce noise via copper shielding. A challenge associated with Tx/Rx structures is that coupling between elements can reduce B₁⁺ efficiency.

We initially explored a degenerate mode birdcage structure¹⁷, which in principle can provide B₁⁺ efficiency associated with a traditional birdcage in addition to the SNR advantage of a phased-array. Three rectangular elements of a degenerate mode birdcage were built on an elliptical cylinder (20 cm L/R × 25 cm A/P × 20 cm H/F) that fit closely to the human head to maximize loading. The elements were 17.8 cm long (H/F) with 8.9 cm arc length in order to match the dimensions required for an eight-channel encircling array. Nearest neighbors were tuned and decoupled at 32.6 MHz (sodium resonance frequency at 3 Tesla) by adjusting the capacitance ratio in the shared rungs and end ring. The reflection coefficient was measured on one element while the neighbor and next-nearest neighbor elements were terminated with 50 Ω to emulate ideal match conditions (network analyzer model 8712ES, Agilent, Santa Clara, CA). We found deleterious resonance frequency splitting between next-nearest neighbor coils that is generally understood to reduce B₁⁺ efficiency.

We addressed this problem by implementing triangular elements, which was originally proposed as a means to generate magnetic field variations in the head/foot direction¹⁸. The ensemble of triangular elements took the form of a modified degenerate mode birdcage whose shared rungs were tilted away from the z-axis. This key geometric adjustment provided the means to decouple next-nearest neighbor coils using counter-wound inductors at the shared triangle vertices. Further, nearest-neighbors were decoupled with capacitors along shared rungs.

We built an array of eight triangular loops with a height of 17.8 cm (H/F) and base of 17.8 cm on the elliptical former mentioned above (Figure 1). We chose an eight-element structure because the unloaded-to-loaded quality factor (Q) ratio of each coil was ~2.5 (~150:60), which indicates sample noise dominance while loaded with a tissue-equivalent head phantom¹⁹. The ratio between the shared rung and end ring capacitors was chosen to decouple nearest neighbor coils at 32.6 MHz. In addition, counter-wound inductors were inserted at the triangle vertices to decouple next-nearest neighbors. Scattering (S) parameters were used to determine decoupling efficacy.

Figure 1.

Photograph of the eight-channel sodium/proton coil array. One sodium and one proton element are highlighted in white and red, respectively.

The triangle array was interfaced to the scanner with a one-to-eight way power splitter. To achieve circularly polarized transmit excitation, home-built lumped element phase shift networks were added to provide 45° phase offsets according to the azimuthal location of the coil elements. Individual power splitter outputs were connected to Tx/Rx switches²⁰ to protect the preamplifiers during sodium excitation (Figure 2a). Two cable traps tuned to the sodium and proton frequencies separated the coil ground from the common ground shared by the interface. Preamplifier decoupling was achieved by adding a phase shift network in the receive path that transformed the low input impedance of the preamplifier into an inductance that formed a parallel resonant circuit with the match capacitor²¹.

Figure 2.

Flattened two-dimensional schematic diagram (a) of the eight-channel sodium/proton coil array and interface. For simplicity, a single sodium (black) and proton coil (red) are highlighted, while neighboring elements are displayed in gray. Approximate capacitor values are: C_M^23Na = 390 pF, C₁^23Na = 290 pF, C₂^23Na = 216 pF, C_M^1H = 40 pF, C₁^1H = 31 pF, and C₂^1H = 12 pF. Decoupling inductors were hand wound using 20 AWG wire with 3 turns and 6.4 mm inner diameter for M^Na, and 2 turns and 4.1 mm inner diameter for M^H. Abbreviations: RFS = radiofrequency short (1000 pF) and RFC = radiofrequency choke (10 μH). The status of the DC bias is forward in transmission and reverse in receive mode. A detailed block diagram of the proton power divider is shown in (b).

A rational question regarding the triangle coil is how does its efficiency compare to a rectangular loop whose rungs are aligned with the z-axis. To answer this question, we performed full wave electromagnetic simulations using the finite difference time domain method in Computer Simulation Technology (CST) Studio Suite (Framingham, MA). One triangle (height = 17.8 cm and base = 17.8 cm) and one rectangle (8.9 cm L/R × 17.8 cm H/F) loop with the same area were simulated. The coils were loaded with a phantom with relative permittivity = 51 and conductivity = 0.44 S/m at 32.6 MHz. The coils were tuned, matched and excited with 50 Ω ports and the transmit fields were normalized to 1 W accepted power. Accepted power was defined as input power minus the reflected power from the coil element.

Proton Array

Our intention was to integrate an array of eight transmit/receive triangular proton elements with the sodium array to enable B₀ shimming and standard proton MRI. RF simulations using the CST Studio Suite were performed to investigate the efficiency of the proton coils in the presence of the sodium coils and vice versa. A proton element was modeled as a triangular loop (15 cm base L/R and length = 15 cm H/F) that was tuned and matched to 123.2 MHz and 50 Ω in the presence of the simulated phantom described above. The proton loop was concentrically nested inside the sodium element whose dimensions are given above. The B₁⁺ of the proton and sodium elements was recorded in isolation (while the counterpart was removed from the simulation) and in the presence of its nested counterpart.

In practice, the proton coils were constructed using 12 American wire gauge (AWG) copper wires to reduce eddy currents induced by neighboring coils^22,23. The Q was approximately 180 (unloaded) and 50 (loaded). Each coil was tuned to 123.2 MHz using four distributed capacitors and matched to 50Ω in the presence of the tissue-equivalent head load. The neighboring proton elements were decoupled by linked counter-wound inductors (Figure 2a). Next-nearest neighbor decoupling was not necessary.

A proton interface was designed and constructed in house to facilitate transmit-receive operation. Transmission was driven through three stages of Wilkinson power dividers and quadrature hybrids²⁴ arranged to provide outputs with 45° phase offsets that corresponded to the azimuthal location of the proton coil elements (Figure 2b). Individual power splitter outputs were connected to Tx/Rx switches to protect the preamplifiers during proton transmission. Preamplifier decoupling and common mode current reduction were achieved in an analogous manner to that described for the sodium array.

MRI Measurements

All imaging experiments were performed on Siemens 3 Tesla Trio scanner that was upgraded to Prisma during the course of this work (Siemens Healthineers, Germany). Human subjects were scanned after obtaining their informed written consent. Sodium and proton transmit power was restricted to 5 W/kg based on MR thermometry measurements similar to that described in Ref.²⁵ to enforce a two-fold safety buffer below the 10 W/kg limit set by the International Electrotechnical Commission (IEC document 60601-2-33 2010). SNR and B₁⁺ benchmark measurements were performed with the developed array and a third-party dual-nuclei sodium/proton head coil (Stark Contrast, Erlangen, Germany) available at our center. The benchmark coil was a dual tuned birdcage coil with 16 rungs, 30 cm length and 27 cm diameter. High impedance trap circuits were incorporated to achieve resonance at 32.6 and 123.2 MHz^26,27. While its dimensions do not allow a strictly fair comparison to the developed coil, its familiar birdcage topology is expected to provide a good point of reference.

SNR maps were calculated from separate signal and noise (with the RF pulse amplitude set to zero) measurements acquired with a gradient echo pulse sequence and processed with the optimal array combination method²⁸. The sodium/proton SNR acquisition parameters were as follows: TR = 200/500 ms, TE = 2.9/3.82 ms, flip angle = 90/10°, voxel size = 7.8 × 7.8 × 30/0.9 × 0.9 × 3 mm³, and acquisition time = 3 min 26 s/2 min 07s. The proton B₁⁺ field was measured using the method described in Ref²⁹. Because the pulse sequence was not available for non-proton nuclei, sodium B₁⁺ maps were calculated by scaling the period of a sine curve to the pixel-wise signal intensities of a series of gradient echo sodium images that were collected with a range of imaging pulse amplitudes³⁰.

Sodium imaging was demonstrated using a three-dimensional non-Cartesian Fermat looped orthogonally encoded trajectories (FLORET) acquisition^31,32 with the following parameters: TR = 100 ms, TE = 0.2 ms, flip angle = 80°, resolution = 5 mm isotropic, acquisition time = 11 min 15 s. Proton anatomical imaging was performed with a magnetization-prepared rapid acquisition gradient echo (MPRAGE) sequence: TR = 2100 ms, TE = 2.52 ms, TI = 900 ms, flip angle = 8°, resolution = 1.6 mm isotropic, parallel acceleration factor = 2 (array)/1 (birdcage), and acquisition time = 3 min 09 s (array)/5 min 34 s (birdcage).

Results

The reflection curve (Figure 3) of a single element in the rectangular array shows significant coupling with the next-nearest neighbor that results in familiar resonant mode splitting. The match dropped from −15 dB in isolation to −4 dB in the presence of the next-nearest neighbor. The triangular element maintains a single resonance in the presence of its next nearest neighbor owing to the shared counter-wound inductors at the triangle vertices. Nearest-neighbor decoupling was preserved with shared rung capacitors.

Figure 3.

Reflection coefficient for one element of a three-channel rectangular array (left) shows a split resonance characteristic of strong coupling between next-nearest neighbor coils. Decoupling inductors in a triangular array remove next-nearest neighbor coupling and result in a single resonance (right).

Simulated sodium B₁⁺ fields showed that the triangular loop efficiency was about 90% of the rectangular loop at a depth of 150 mm along the main axis. The primary explanation for this difference is greater z-directed magnetic fields are generated by the angled rungs of the triangular compared to rectangular element.

B₁⁺ simulations show that a sodium loop is almost unaffected by the presence of the proton loop (Figure 4 top row). On the other hand, the proton loop is shielded by the sodium loop, which provides a minor improvement in transmit efficiency at the surface and reduction at depths greater than 98 mm along the main axis of the coil compared to an isolated proton element (Figure 4 bottom row).

Figure 4.

Simulated maps show the ratio of B₁⁺ for a sodium (top row) or proton (bottom row) triangle coil with its nested multinuclear counterpart to that of the same coil in isolation. The sodium coil provides approximately identical B₁⁺ in both the isolated and multinuclear environment. The presence of the sodium coil shields the proton coil, which increases efficiency near the surface but degrades efficiency at depths greater than approximately 9.8 cm.

The S-parameters for the eight-channel triangle array show that the lumped element decoupling provided −13.0 dB isolation between neighboring coils and −15.4 dB between next-nearest neighbors (Table 1). No mechanism was installed to counteract coupling between third and fourth-distant neighbors, which had an average value of −9.3 dB.

Table 1.

Scattering matrix measurements show coil match and isolation. The triangular elements enabled local lumped element decoupling between nearest and next-nearest neighbors. No mechanism was installed to counteract distant-neighbor coupling. Values indicate mean ± standard deviation (maximum value).

	S (dB)
Sodium coils
Diagonal elements	−15.8 ± 0.3 (−15.3)
Adjacent neighbors	−13.0 ± 0.4 (−12.4)
Next nearest neighbors	−15.4 ± 0.8 (−14.2)
Distant neighbors	−9.3 ± 0.2 (−8.8)
Proton coils
Diagonal elements	−21.7 ± 1.7 (−18.2)
Adjacent neighbors	−15.2 ± 1.1 (−13.3)
Next nearest neighbors	−13.2 ± 1.0 (−12.2)
Distant neighbors	−11.5 ± 1.0 (−10.6)

The eight-channel sodium array provided 1.6-fold higher SNR in the center of the head and up to 2.3-fold gain in the periphery compared to the dual-tuned birdcage reference coil (Figure 5). FLORET images show good coverage and adequate sensitivity for 5 mm isotropic resolution.

Figure 5.

FLORET (Fermat looped orthogonally encoded trajectories) sodium images acquired with the eight-channel array show excellent coverage and delineation of brain structures (top row). The sodium signal-to-noise ratio (SNR) maps show that the eight-channel array (second row) provided a 1.6-fold gain in the head center and up to 2.3-fold gain in the periphery compared with the dual-nuclei birdcage (fifth row). The transmit field (B₁⁺) was 62.7 ± 8.4 μT/√kW for the array and 59.5 ± 4.7 μT/√kW for the birdcage in the central transverse plane in the phantom.

The insertion loss of the sodium transmit module was −0.5 ± 0.2 dB with 45 ± 1° phase intervals at each output. B₁⁺ maps acquired in the head phantom show that the array generated a transmit field of 62.7 ± 8.4 μT/√kW, while the dual tuned birdcage generated 59.5 ± 4.7 μT/√kW in the central transverse slice.

The proton transmit module had −0.6 ± 0.3 dB insertion loss at 45 ± 3° phase intervals at each output. The proton SNR at the center of the head was similar to that of the dual-tuned birdcage (Figure 6). As expected, the array provided significant SNR gains in the periphery but limited coverage in the H/F direction. B₁⁺ maps acquired in vivo show that the array produced a transmit field of 14.6 ± 1.9 μT/√kW and the dual tuned birdcage produced a transmit field of 16.7 ± 2.0 μT/√kW in the central transverse plane with peripheral fat and skull regions removed. Example 1.6-mm isotropic MPRAGE images are shown in the top row of Figure 6.

Figure 6.

The exemplary proton MPRAGE images acquired with the eight-channel array show good T1 contrast in the central brain but falloff in the head apex (top row). Images were acquired with parallel acceleration factor = 2 (array) and 1 (birdcage). The array provided similar SNR in the center of the brain and gains in the periphery compared to the proton channel of the dual nuclei birdcage (second and fourth rows). The B₁⁺ maps (third and bottom rows) show that the array provided a transmit field of 14.6 ± 1.9 μT/√kW, while the birdcage provided 16.7 ± 2.0 μT/√kW in the brain region (peripheral fat and skull excluded) in the transverse plane.

Discussion and Conclusions

We developed a modified degenerate mode birdcage using triangular elements. While a conventional degenerate mode birdcage has the potential for desirable excitation and reception properties, it is in practice difficult to achieve complete degeneracy due to coupling between non-adjacent neighbor elements³³. Although coupling can be dampened by strong tissue loading in high frequency implementations^34,35, we observed resonance frequency splitting at 32.6 MHz. By tilting the rungs away from the z-direction, the shared triangle vertices provided a means to decouple nearest and next-nearest neighbor coils using local lumped elements (Figure 3). This decoupling strategy allowed the modified degenerate mode birdcage to produce a uniform and circularly polarized B1+ field and provide the receive sensitivity gains associated with a multi-channel phased-array for sodium imaging (Figure 5). A secondary benefit is that it’s transmit/receive capability eliminated the need for lossy detuning circuitry that would be required in a ToRo array.

The choice of triangular sodium elements provided effective neighbor and next nearest neighbor decoupling, however there was no mechanism in place to counteract coupling between third and fourth-order neighbors, which had an average value of −9.3 dB (Table 1). The transmit field variations observed in the sodium B₁⁺ maps can be attributed to the higher order coupling observed between sodium elements. Further optimization such as customized transmit power distribution to the individual elements may also improve B₁⁺ uniformity.

Although our eight-channel array provided substantially improved SNR over the birdcage coil, its spatially varying B₁⁻ field (and to a lesser extent B₁⁺) can make sodium quantification less straightforward. The phantom replacement method^36,37, in which pre-scans are performed on a variety of phantoms in order to relate the spatially dependent signal intensity to sodium concentration, is a viable option for quantification.

We applied the triangle degenerate mode concept in an eight-channel array for sodium MRI of the brain. This application additionally called for proton MRI capability, which was pursued with proton elements that were inserted concentric to the sodium coils to reduce inter element coupling and overall design complexity. Though this design choice greatly reduced design complexity, it resulted in proton elements that were small in size with gaps between them. Gaps caused signal and B₁⁺ nulls that were mainly confined to peripheral fat and skull, while the B1+ uniformity in a transverse slice through the brain was similar to that of the reference birdcage. Further, counter-rotating currents were induced in the nested dual-nuclei arrays that reduced proton coil efficiency. Possible approaches to reduce counter rotating currents are to switch to an interleaved coil arrangement where the proton array is offset with respect to the sodium array^14,38 or to install proton filters in the sodium array, which can be expected to reduce sodium performance by about 5% on each element^31,32.

In conclusion, we designed and implemented a multi-channel sodium/proton array for brain MRI at 3 T. The triangular geometry provided convenient shared locations for nearest and next-nearest neighbor decoupling, which allowed Tx/Rx operation as a modified degenerate birdcage mode array. The sodium module provided at least a 1.6-fold SNR gain over a dual-nuclei sodium birdcage coil, while proton channel performance was sufficient for anatomical imaging. The coil has helped overcome low-sodium MR sensitivity and improve quantification in neurological studies including epilepsy, traumatic brain injury and multiple sclerosis^39,40.

Abbreviations used

MRI

magnetic resonance imaging

MS

multiple sclerosis

UTE

ultrashort echo time

RF

radio frequency

ToRo

transmit-only/receive-only

Tx/Rx

transcieve

SNR

signal-to-noise ratio

L/R

left - right

H/F

head – feet

A/P

Anterior-posetrior

Tx

transmit

IEC

International Electrotechnical Commission

TE

echo time

TR

repetition time

FLORET

fermat looped orthogonally encoded trajectories acquisition

TPI

twisted projection Imaging

MPRAGE

magnetization-prepared rapid acquisition gradient echo

FLAIR

fluid-attenuated inversion recovery

RFC

Radio frequency choke

RFS

Radio frequency short