A Flexible Nested Sodium and Proton Coil Array with Wideband Matching for Knee Cartilage MRI at 3 Tesla

Abstract

Purpose

We describe a 6×2 channel sodium/proton array for knee MRI at 3 Tesla. Multi-element coil arrays are desirable because of well-known signal-to-noise ratio advantages over volume and single-element coils. However, low coil-tissue coupling that is characteristic of coils operating at low frequency can make the potential gains from a phased array difficult to realize.

Methods

The issue of low coil-tissue coupling in the developed six channel sodium receive array was addressed by implementing 1) a mechanically flexible former to minimize coil-to-tissue distance and reduce the overall diameter of the array and 2) a wideband matching scheme that counteracts preamplifier noise degradation caused by coil coupling and a high quality factor. The sodium array was complemented with a nested proton array to enable standard MRI.

Results

The wideband matching scheme and tight-fitting mechanical design contributed to greater than 30% central SNR gain on the sodium module over a mono-nuclear sodium birdcage coil, while the performance of the proton module was sufficient for clinical imaging.

Conclusion

We expect the strategies presented in this work to be generally relevant in high density receive arrays, particularly in x-nuclei or small animal applications, or in those where the array is distant from the targeted tissue.

INTRODUCTION

Quantitative sodium MRI is a non-invasive technique that is highly specific to the glycosaminoglycan (GAG) content (1,2) in knee cartilage and can be used as a means of detection and assessment of the degree of biochemical degradation in osteoarthritis (OA) (3,4). One of the fundamental challenges in sodium MRI is the relatively low sensitivity due to low sodium concentration in the body. In healthy cartilage, the average sodium concentration is generally in the range 200-300 mmol/L, which is around 260-400 times lower than the in vivo water proton concentration (5). This is compounded by low sodium receptivity (which is associated with a low gyromagnetic ratio that causes both reduced polarization and lower coil sensitivity). These factors result in a sodium MRI signal that is approximately 3000-4500 times lower than the proton signal in cartilage. These inherent disadvantages in sodium MRI can result in undesirable compromises in spatial resolution that can be unacceptable for cartilage visualization as well as long examination times that make it difficult to combine both proton and sodium knee imaging into a single protocol. Efficient pulse sequences and advanced reconstruction techniques have recently been developed to help alleviate these limitations (6-12). Further signal-to-noise ratio (SNR) enhancement can be achieved with optimized radiofrequency coils. Recently, dual-nuclei coil development has seen a shift from volume (13-22) and single-channel surface (23-30) to multi-channel phased arrays (31-37), which coincides with a renewed interest in “x-nuclei” or “low gamma” applications. While the advantages of proton multi-channel arrays have been well documented, sodium arrays have been less developed due to their role as a research, rather than clinical, tool.

Along with the promise for SNR gain from a multi-channel array come engineering challenges that arise in a low gamma regime in which low tissue-coil coupling can result in an unfavorable noise balance and degrade expected performance advantages over a traditional volume coil. Low tissue-coil coupling in a phased array has the additional disadvantage of accentuating preamplifier noise coupling, where noise generated in the transistor projects into the coil and is transferred to other elements via their mutual impedance (38-44). While this effect is generally ignored in proton arrays where high tissue-coil coupling and hence a reduced quality factor diminish its significance, SNR degradation can be substantial when inductive coupling to the tissue is low and/or high coil coupling conditions are present. In this work, we detail the design strategy in a multi-channel sodium and proton knee coil that counteracts low coil-tissue coupling on the sodium module by implementing a wideband matching scheme and a mechanically flexible former (45). We further tackle the challenge of providing proton imaging capability in the ensemble array without substantially compromising the performance of the sodium module.

METHODS

Coil Overview

The dual-nuclei sodium/proton knee array can be divided into three functional modules: 1) a high-pass birdcage coil for sodium transmission was built on the outer housing layer, which was divisible into anterior and posterior sections for patient entry, 2) a six-channel array for sodium reception was built on the inner layer, and 3) a six-channel array for proton transmission and reception, whose elements were nested within the sodium array, was also built on the inner layer. The schematic diagram and photographs in Figure 1 and Figure 2 illustrate this arrangement. More details are given on each module in the following sections.

Figure 1.

Illustration of the developed 6×2 channel sodium/proton array that consists of three functional modules on two cylindrical layers. The flexible inner shell (15 cm diameter) houses the six channel sodium receive array (red) and six channel proton transceive array (blue). Paired concentric sodium/proton coil pairs are built on individual units linked with a hinge to the neighboring unit (see the photographs in Figure 2). Coil channel numbers are overlaid. Arrows between coils 1 and 6 indicate a discontinuity in the inner housing to allow patient entry. The rigid outer shell (25 cm diameter) houses the sodium birdcage (green), which is divisible into anterior and posterior halves for patient entry.

Figure 2.

Photographs of the sodium/proton knee array illustrate its modules and the patient positioning process: (a) the anterior half of the outer layer containing the sodium birdcage is separated from the posterior half and the flexible inner layer containing the sodium receive and proton transceive arrays is expanded while the patient's left knee is inserted, (b) six individual rigid units containing the sodium/proton arrays are outfitted with hinges to provide flexibility with the neighboring unit to combine the robustness of a rigid system with the sensitivity advantage of a tight-fitting flexible array, (c) the sodium/proton array is positioned around the patient, and (d) the anterior sodium birdcage is connected.

Sodium Receive Array

High performance of the sodium receive module was the key design criteria for the ensemble sodium/proton array. Two strategies were implemented to improve sodium sensitivity, which distinguish the proposed 3T dual-nuclei sodium/proton knee coil from conventional dual-nuclei knee coils: 1) a mechanically flexible housing system and 2) wideband matching. First, the sodium receive array was designed to minimize coil-tissue distance and reduce the allowable former diameter, both of which can be expected to improve SNR over rigid designs. Whereas rigid knee coils typically require ~18 to 21 cm diameter to accommodate a range of patient sizes, the proposed coil was built on flexible housing that allowed its nominal diameter to be reduced to 15 cm without compromising accessibility. This strategy helped counteract the low coil-tissue coupling that is characteristic of coils operating at a low resonance frequency (in this case 32.6 MHz). The flexible housing consisted of six rigid modules linked together by five hinges built in-house whose axes were along the z-axis. A discontinuity between two coils allowed the array to be opened and wrapped around the knee for subject positioning. Given the interest in patellar cartilage in the anterior region of the knee, the discontinuity was chosen to be at the posterior position (between coils 1 and 6 in Figure 1). The rationale was that the posterior coil gap required to accommodate large subjects would not affect performance in the anterior region. The coil count of six [7.9 cm (arc length) × 15 cm (head/foot)] was selected empirically based on target unloaded-to-loaded quality factor (Q) ratio of two and desired head/foot coverage of roughly 12 cm. Coils were built using 3 mm diameter copper tubing built onto FR4 circuit board, which have favorable shielding and resistance properties compared to flat copper traces (46,47). Neighboring coils were decoupled by choosing the appropriate value for the capacitance in their shared legs (48).

To maximize array performance in a regime where the operating frequency is low and coil coupling can be high, preamplifier noise coupling should be considered. In this phenomenon, noise generated in a given preamplifier is projected into the associated coil and further transferred to other coils in the array (38,40,41,43). The additional noise appears on the diagonal elements of the correlation matrix and therefore cannot be counteracted by decorrelation or matched filter image reconstruction techniques (38). Preamplifier noise coupling is a function of the noise figure of the preamplifier itself, match conditions, the normalized magnetic coupling coefficient (defined as the ratio of the width of the split resonance frequency in a two-coil system and the resonance frequency of an isolated coil k = Δf/f₀), and the coil Q. Small coil elements operating at low frequencies result in poor tissue-coil coupling, which is associated with high Q values and preamplifier noise coupling, as will become clear in the following section. Note that this noise source is routinely and appropriately ignored in typical clinical proton applications where the coil Q and coil interaction are both low due to heavy coupling to the sample and the use of decoupling strategies (geometrical overlapping, capacitive decoupling, etc.).

A detailed theoretical outline of noise coupling and its mitigation through wideband matching has been given by Vester et al (43). We focus on the application of the technique in this section. The effective noise factor of a preamplifier in a two-coil system is

$$F^{\prime }=F\cdot \left(\frac{1}{2z}+\frac{z}{2}+\frac{{\left(kQ\right)}^2}{2z}\right),$$ [1]

where F is the noise factor of the isolated preamplifier in linear units and z is the impedance transformation ratio that defines the ratio of the impedance required for a classic noise match (commonly 50 Ω) to that presented by the coil at the preamplifier input. The classic match strategy implies z = 1 and the effective added noise factor from Eq.[1] is $F_c^{\prime }=F\cdot [1+{\left(kQ\right)}^2∕2]$. The optimal impedance transformation ratio under the wideband match strategy is

$$z=\mid 1+jkQ\mid ,$$ [2]

which reduces Eq. [1] to $F_w^{\prime }=F\cdot \sqrt{1+{\left(kQ\right)}^2}$. The additional noise factor can be related to the SNR by recognizing $SNR\propto 1\sqrt{1+F^{\prime }}$, where unity represents the baseline noise from sources such as the subject and coil and the square root accounts for the measurement of voltage SNR in MRI. Given that F’ reduces to F when coil coupling is not present (k = 0) and a classic match is implemented (z = 1), the ratio of SNR without preamplifier noise coupling to that with coupling follows as

$$\eta =\sqrt{1+F}∕\sqrt{1+F^{\prime }}.$$ [3]

Figure 3 shows the predicted normalized SNR values of a coil element in a two-channel array matched using the classic and wideband match strategies, along with the optimal reflection coefficient for a range of kQ values. The reflection coefficient for optimal wideband matching is determined by converting the impedance transformation ratio given in Eq. [2]: $S_{11}^w=(z\cdot Z_0-Z_0)∕(z\cdot Z_0+Z_0)$, where Z₀ = 50Ω is the impedance corresponding to the classic match.

Figure 3.

Plot of the theoretical SNR of a coil element in a two-channel array, where unity represents that of an isolated coil (whose preamplifier noise factor is set to 1.122). SNR_w (solid line) is that predicted using the optimal wideband match, where the corresponding optimal wideband reflection coefficient is given by the $S_{11}^w$ curve (long dashed line) for a range of kQ values. SNR_c (short dashed line) is that predicted using a classic match where S₁₁ = 0. The plot shows that the wideband match scheme mitigates SNR degradation and provides substantial SNR gain over the classic strategy at high kQ values.

In the developed array, preamplifier noise coupling was exacerbated between coils 1 and 6, whose close proximity but lack of a decoupling mechanism was a design choice required to accommodate the mechanically flexible housing. With the housing in its nominal position, the magnetic coupling coefficient was measured using a double probe by dividing the resonance frequency of a given coil (measured with all other coils open-circuited) by the difference in resonance frequencies between two coupled modes (measured with all but two coils open circuited). The coupling coefficients were: k = 0.12 for gapped coils 1 and 6, k = 0.03 for next-nearest neighbor pairs (coils 1 and 3, 2 and 4, 3 and 5, and 4 and 6), and k ≈ 0 for capacitively decoupled pairs (coils 1 and 2, 2 and 3, 3 and 4, 4 and 5, and 5 and 6). The Q was approximately 95 when loaded with a 1.9 L water phantom doped with [NaCl] = 46.8mM (5.2 g) and [NiSO₄] = 18.4mM (5.4 g) to approximate knee loading. Inserting the appropriate values into Eq. [2] gives |z| = 11.4 for coils 1 and 6, and 3.1 for all other coils. To apply wideband matching in these conditions, |S₁₁| was set to 0.84 for coils 1 and 6, and to 0.51 for all other coils by making appropriate adjustments to the capacitor values (Figure 4). The match strategies were compared through SNR measurements in a phantom with the array matched using the wideband scheme and the classic scheme where |S₁₁| was adjusted to zero in all coils as illustrated in the Smith Chart traces in Figure 5. In both experiments, the phase lengths between the sodium preamplifiers and receive coils was adjusted to achieve preamplifier decoupling (49).

Figure 4.

Schematic diagram of the sodium receive array. Note that a parallel match capacitor (C₅) in channels 1 and 6 sets up a wideband match with S₁₁ = 0.86, while a series match capacitor (C₁) in channels 2 to 4 sets up S₁₁ = 0.49 (Smith Chart traces are shown in Figure 5). Azimuthal positions are indicated at the bottom (90° = anterior, 270° = posterior).

Figure 5.

Scattering parameter traces (S₁₁) for sodium receive coils matched to different reflection coefficients: standard 50 Ω match (blue), wideband match with S₁₁ = 0.51 measured on coil 2 and applicable to coils 3-5 (red), and wideband match with S₁₁= 0.84 measured on coil 1 and applicable to coil 6 (gold). Traces are shown from 27.6 MHz (square markers) to 37.6 MHz (triangular markers) with the sodium resonance frequency (32.6 MHz) indicated by circular markers.

After tuning and matching the sodium receive coils as described above, an active detuning circuit was added to each element to avoid RF field distortion during sodium excitation. With the detuning circuits tuned to the sodium frequency and positioned at each of the coil drive ports, an undesirable resonance mode near the proton frequency was observed when the circuits were forward biased. In light of this, the positions of the detuning circuits were alternated between the coil port and the capacitor position on the opposite side of the coil element, which provided the requisite detuning at the sodium frequency and did not produce a resonant mode near the proton frequency. Supplementary protection was provided by a fuse rated to 700 mA.

Detunable Sodium Birdcage

A concentric detunable sodium birdcage coil was installed to provide a homogeneous transmit field. An eight-rung high-pass birdcage was used because its uniform imaging mode and non-uniform high-order modes occur at frequencies well below the proton resonant frequency thus reducing the likelihood of birdcage and proton mode interaction. Full-wave simulations using a current mode expansion with Dyadic Green's functions (50,51) were used to guide the choice of birdcage dimensions using methods similar to those previously described (32). The selected birdcage dimensions (25 cm diameter × 15 cm length) were based on tradeoffs between high B₁⁺ uniformity that necessitates a larger length-to-diameter ratio and high peak B₁⁺ that calls for small diameter and smaller length-to-diameter ratio. Another requirement was that the birdcage fit around the sodium receive array in a concentric manner with minimal disturbance to the contralateral leg. In practice, the birdcage was tuned during sodium transmission and detuned during sodium reception and proton operation by appropriately biasing PIN diodes that were in series with each rung. The birdcage was physically divided into anterior and posterior half-cylinders in order to allow convenient patient positioning. Coaxial connectors provided robust electrical continuity between the two halves (part numbers 122-124-003-257-001 [female] and 122-124-004-257-001 [male], Odu-USA, Inc., Camarillo, CA).

Proton Transmit-Receive Array

The aim of the proton module was to provide anatomical imaging capability and static field shim analysis with minimal disturbance to the sodium receive array. This was accomplished using a nested strategy that has been previously demonstrated in various forms in which co-planar and concentric proton coils are added to the sodium array (26,27,29,32,33,52). Specifically, an array of six transceive proton coils was constructed. Coil dimensions of 3.2 cm (arc length) × 10 cm (head/foot) were empirically selected base coverage and uniformity of large coils and tolerable coupling offered by small coils.

Neighboring proton coils were coupled by less than −11 dB (next-nearest neighbors were coupled by < −22 dB) owing to their relatively small geometry, gapped structure, and shielding provided by the surrounding concentric sodium elements. The pertinent values for wideband match calculations were Q = 130 and k = 0.01. Although Eq. [2] indicated an optimal wideband match with z = 1.64, Eq. [3] predicted a negligible (1%) SNR difference between the wideband and classic strategy. Further, since the proton coils were to be operated in transceive mode, a 50 Ω match was implemented for optimal transmit efficiency. To assess the impact of the proton coils on the sodium elements and vice versa, Q measurements were recorded on both sets of coils with the other set in both active and deactivated (open circuited) states.

The proton array was driven through a cascade of Wilkinson splitters (a 1:3 splitter followed by two 1:2 splitters, which is represented as a 1:6 splitter in Figure 6) that divided the power into six equal parts, whose outputs were fed to a set of six transmit/receive switches. To generate a circular polarized magnetic field, a phase shift equal to each coil's azimuthal position was built-in using appropriate lumped element phase shifters and coaxial cable segments.

Figure 6.

Schematic diagram of the six-channel proton transmit/receive array. Azimuthal positions are indicated at the bottom (90° = anterior, 270° = posterior).

Transmission Power Limits

To restrict tissue heating caused by the electric field of the proton transmit array, specific absorption rate (SAR) limits were set in accordance with those established by the International Electrotechnical Commission (IEC) (International Standard IEC 60601-2-33 2010). Local SAR was determined experimentally using methods similar to those described by Brown et al. (53). Briefly, the relative temperature change was measured in a homogeneous nonperfused cylindrical gelatin phantom composed of water doped with salt and sugar (54) such that its dielectric properties (conductivity = 0.64 S/m and relative permittivity = 65) were similar to those of muscle tissue (55). Proton gradient echo phase images were acquired before and after the application of a predetermined level of RF power. Oil phantoms were placed adjacent to the phantom to provide temperature insensitive phase references. Temperature change was determined using the proton resonance frequency shift method (56) and subsequently converted to SAR by applying $SAR\left(\overrightarrow{r}\right)=c\cdot \Delta T\left(\overrightarrow{r}\right)∕\tau$, where c = 2.5 kJ kg⁻¹ K⁻¹ is the heat capacity of the phantom (measured using a KD2 probe; Decagon Devices, Inc, Pullman, WA), $\Delta T\left(\overrightarrow{r}\right)$ is the local temperature change, and τ is the duration of the RF application. Note that the measurement was performed with the proton array in its nominal mechanical position. Given the mechanically flexible nature of the array, it is conceivable that the worst-case scenario in terms of constructive electric field interference was not reached. To account for this variable and other measurement inaccuracies, a two-fold safety margin was incorporated over the 20 W/kg local limit in the extremities set by the IEC and thus the proton time-averaged amplifier output was restricted to 37.6 W to establish a local SAR limit of 10 W/kg over a 360-second averaging period.

The sodium power limit was explored using an analogous procedure wherein the tissue-equivalent gel phantom was exposed to RF at 32.6 MHz. In this experiment, 24.4 W delivered for 604 s resulted in negligible heating (< 0.2 °C). No signs of reflected power, coil instability, or arcing were found, which could have potentially explained the lack of heating. Alternatively, the following rationale was used to determine the RF power limit. Assuming that the minimum volume of the extremity that will be exposed to RF is 0.68 L (57) with an estimated mass of 1 kg, the power limit is given by 10 W/ kg * 1 kg = 10 W. Accounting for the sodium transmit coil efficiency (1 − Q_loaded / Q_empty = 0.38), the time averaged power was limited to 10 W / 0.38 = 26.3 W, which is likely very conservative (only slightly above 24.4 W that resulted in no heating).

Imaging

Phantom and in vivo knee measurements were performed on a whole-body 3 Tesla scanner with multi-nuclear capability (TIM Trio, Siemens Healthcare, Erlangen, Germany) upon approval by our local IRB and with informed written consent from participants. The developed dual-nuclei array was compared to three single-nuclei coils available at our center: 1) sodium birdcage with 20 cm diameter × 17 cm length; 2) clinical proton knee coil with a birdcage transmitter and 15 channel receive array [approximately 18 cm diameter × 16.7 cm length, Quality Electrodynamics, Mayville, OH (58)]; and 3) clinical proton knee birdcage coil (approximately 21 cm diameter × 15 cm length, Invivo Corp., Gainesville, FL). Raw SNR measurements for both proton and sodium were made using a two-dimensional GRE pulse sequence in which images were acquired with and without RF excitation and processed using the method described by Kellman and McVeigh (59) (imaging parameters are listed in Table 1). Proton SNR is reported as SNR = SNR_raw/sin(FA), where FA is the flip angle measured using the method described by Fautz et al (60). Sodium B₁⁺ maps were generated by acquiring a series of gradient echo images over a range of pulse amplitudes, fitting the signal intensities to a sine curve, and scaling its period by the appropriate factors. Metabolic and anatomical imaging was demonstrated using three-dimensional non-Cartesian Fermat looped orthogonally encoded trajectories (FLORET) and fast spin echo (FSE) acquisitions (6,8).

Table 1.

Pulse sequence parameters.

Description	B1+ mapping		SNR measurement		Anatomical	Metabolic
Pulse sequence	2D GRE		2D GRE		2D PDw FSE*	3D FLORET**
Nucleus	23Na	1H	23Na	1H	1H	23Na
Voxel size (mm3)	10.4×10.4×50.0	1.5×1.5×5.0	10.4×10.4×50	0.9×0.9×3.0	0.4×0.4×3.0	4.0×4.0×4.0
TE (ms)	3.1	2.4	3.1	4.1	29	0.2
TR (ms)	200	1000	200	200	3000	80
Flip angle (°)	-	-	90	20	90 (excitation) 156 (refocusing)	80
Bandwidth (Hz/pixel)	300	651	300	300	401	-
Number of slices	1	1	1	1	29	64
Field-of-view (mm2)	500×500	192×192	500×500	220×220	140×140	256×256
Acquisition time (s)	11	8	11	53	204	864

^*A turbo factor of five and parallel imaging acceleration factor of two was applied to the fast spin echo acquisition.

^**Other relevant parameters were: 3 hubs at 45°, 300 interleaves per hub, 12 averages, ADC duration = 6.25 ms, and dwell time = 10 us.

RESULTS

Sodium

The sodium receive coils had Q values of approximately 195 in isolation and 105 when loaded with a human leg. The sodium coil Q values changed by less than 5% when the proton coils were open-circuited, illustrating their low level of interaction.

Compared to the conventionally matched sodium array, the wideband match scheme provided a SNR gain of 10% in the center of the phantom and 50% in the posterior, which corresponded to the region covered by coils 1 and 6 (Figure 7a). The central SNR gain is in good agreement with Eq. [3], which predicts η = 1.09 for coils 3 to 5 (with F = 1.122), while that measured near posterior was less than the predicted gain (η = 1.94 for coils 1 and 6).

Figure 7.

Sodium coil performance comparison between the developed dual-nuclei array with classic 50 Ω matching (top row), wideband matching (middle row), and a conventional mono-nuclear sodium birdcage (bottom row). a) SNR measurements show the developed wideband-matched coil provided a 30% gain in the center and greater than two-fold in the periphery compared to the birdcage. The wideband match strategy provided a 50% SNR gain in the posterior portion of the phantom and 10% gain in the center compared to the conventional match. b) FLORET images of the knee and articular cartilage acquired with the developed array (top row) show qualitative advantages over those acquired with the sodium birdcage (bottom row).

The developed dual-nuclei array provided a 30% SNR gain over the mono-nuclear sodium birdcage in the center and greater than two-fold in the periphery. The higher central SNR for the dual-nuclei array can be attributed to the smaller overall dimensions and close-fitting nature of the coil compared to the birdcage. Sodium imaging using the FLORET pulse sequence showed similar qualitative advantages (Figure 7b). FLORET SNR was not calculated due to the complex nature of the sampling scheme and image reconstruction algorithm.

In the phantom, B₁⁺ uniformity of the sodium module was 96% in the central transverse slice of the knee phantom with the proposed coil (where uniformity was defined as one minus the standard deviation of the flip angle divided by its mean). In vivo transmit efficiency for both the constructed coil and mono-nuclear birdcage was 222 nT/V (corresponding to a 180° excitation with a 200 V hard pulse with 1 ms duration).

Proton

The proton coils had Q values of approximately 225 when unloaded and 130 when loaded by a human knee with the sodium coils resonant. The Q values were 235 (unloaded) and 100 (loaded) when the sodium coils were open circuited. In vivo transmit efficiency in the center of the knee was 91 nT/V and 100 nT/v for the constructed coil and mono-nuclear 15 channel array, respectively (corresponding to a 180° excitation with a 129 and 117 V hard pulse with 1 ms duration) (Figure 8a). Central SNR provided by the dual-nuclei array was 67% of that provided by the 15 channel mono-nuclear array (Figure 8b). The sparse local coils expectedly caused local B₁⁺ hot spots in the posterior knee, and limited coverage was observed in the head-foot direction; the full width at half maximum length of the B₁⁺ profile was 6.7 cm for the dual-nuclei array compared to 15.5 cm for the 15 channel mono-nuclear array. Nonetheless, coverage and central transmit uniformity provided by the developed array was adequate for PDw FSE imaging (Figure 8c). Additionally, the proton array provided a 15% SNR advantage in the center of a phantom over a traditional single-tuned knee birdcage coil.

Figure 8.

Proton coil performance comparison between the developed dual-nuclei array (top row) and clinical 15-channel proton array by QED (bottom row): a) SNR, b) flip angle distribution, and c) anatomical image.

DISCUSSION AND CONCLUSIONS

At frequencies as low as 32.6 MHz tissue losses are small and the resulting low unloaded to loaded Q ratio can make the potential gains from a phased array difficult to realize. This issue was addressed by implementing a wideband matching scheme and a mechanically flexible former to minimize coil to tissue distance and reduce the overall diameter of the array. The resulting dual-nuclei array provided substantial SNR gain in articular cartilage regions compared to a mono-nuclear sodium birdcage coil. The wideband matching scheme provided additional gain over the conventionally matched sodium array, where preamplifier noise coupling is accentuated due to coil coupling inherent in the mechanically flexible design and a characteristically high loaded Q-factor. We expect the wideband match strategy to be broadly relevant in high density receive arrays, particularly when the loaded coil quality factor is high as can be the case in x-nuclei or small animal applications, or in those where the array is distant from the targeted tissue (61).

Note that the broadband match calculations were simplified to that of a two-coil array wherein a given coil was considered to be coupled exclusively to one other coil. An eigenmode analysis that accounts for all coupling combinations may produce more favorable match conditions and help explain the deviation between the expected and measured results.

Coil sensitivity correction, along with those related to B₀ inhomogeneity and partial volume effects (62,63) may be critical for accurate sodium quantification in the cartilage. Although the multi-channel array improves SNR over a volume coil, its spatially varying sensitivity can make sodium quantification less straightforward. So-called “phantom replacement” and similar methods (64-66) that utilize phantom images to relate signal intensity to sodium concentration may not be sufficient due to the coil's flexible nature and therefore subject-dependent sensitivity. One way to address the issue is to estimate subject-specific individual coil sensitivity maps from the ratio between images acquired using the array and those acquired with the birdcage (assuming that the birdcage provides a homogeneous receive pattern), or directly from low-frequency k-space data already obtained in an array acquisition. Alternatively, computer simulations could be utilized to generate sensitivity maps over a range of coil positions and subsequently matched to that in the experiment. Low-resolution sensitivity maps could then be combined using a matched filter approach and finally applied to convert the high-resolution sodium image to standard units.

To maximize performance on the sodium module, some compromises were made to the proton module. The compromises were evident in the central SNR, which was lower than that provided by the 15 channel mono-nuclear proton receive array. This suggests that the gapped structure and counter-rotating proton currents generated in the sodium array combine to reduce performance below the optimal level. One way to alleviate out-of-phase currents is to install proton blocking trap circuits that have been demonstrated to minimally compromise x-nuclei performance (30,67). Nonetheless, proton SNR was 15% better than a mono-nuclear knee birdcage, suggesting that the proposed design is more favorable than standard “trap-based” dual-nuclei coils where the efficiency of the high-frequency channel is generally sacrificed by approximately one-half (23). Finally, the gapped proton design resulted in compromised transmit uniformity, which was considered a reasonable trade-off given the sodium SNR priority and the desire to avoid shielding the proton coils from the tissue by the low-impedance sodium coils. We also note that proton uniformity may be further compromised due to non-optimal phase offsets when the former is flexed.

In summary, we have laid out a blueprint for a sodium/proton array for knee cartilage MRI at 3 Tesla that can be translated to applications with similar tissue loading conditions. The sodium array provided at least 30% SNR gain over a mono-nuclear sodium birdcage coil, while proton channel performance was sufficient for clinical imaging. The design included a mechanically flexible sodium array and wideband matching strategy, which were both straightforward to implement. These features will help overcome low sodium MR sensitivity and improve GAG quantification in OA studies.