Optimization and comparison of two practical dual-tuned birdcage configurations for quantitative assessment of articular cartilage with sodium magnetic resonance imaging

Introduction

Osteoarthritis (OA) is a degenerative joint disease with a high prevalence in the aging population. The early stages of OA can be associated with a reduction in glycosaminoglycan (GAG) concentration, changes in the size and organization of collagen fibers, and increased water content (1-3). When the disease progresses, morphologic changes like thinning and lesions of the cartilage occur that can be captured by radiography and conventional magnetic resonance imaging (MRI). To maximize the effectiveness of therapeutic approaches to OA, there is high demand for imaging techniques that are sensitive to the early stages of OA. Recently, more advanced MRI techniques have been developed to detect and quantify the early molecular changes that precede the morphological changes of the cartilage. The most popular quantitative MRI techniques of this kind are delayed gadolinium-enhanced magnetic resonance imaging contrast (dGEMRIC) (4,5), T_1ρ relaxation mapping (6) and sodium MRI (7-9). Although sodium MR imaging has been shown to strongly correlate with the GAG concentration in the cartilage, its implementation is still challenging because of the low sensitivity of the ²³Na nucleus, low in vivo concentrations, fast transverse relaxation times and the requirement for x-nuclei compatible scanner hardware and RF coils. Dual-tuned coils provide heteronuclear images and anatomical hydrogen background images without repositioning the subject thus avoiding co-registration errors. Furthermore the hydrogen channel can be used for efficient B₀ shimming, which is often required in heteronuclear imaging applications.

Due to the anatomy of the human leg, the birdcage with its cylindrical structure is well suited to perform imaging of the knee joint. Several approaches to achieve dual tuning of a birdcage structure have been proposed over the years: double tuning LC circuits on rungs (10), filters on rungs (11,12), concentric birdcages (13), four-ring birdcages (14) and birdcages with alternating low and high frequency tuned rungs (15,16). All of these designs have their advantages and weaknesses in regard to B₁ field homogeneity, coil efficiency, complexity and geometric requirements. Generally, inserting tank circuits or filters into the coil structure to facilitate dual tuning is cumbersome and leads to additional losses which might be unacceptable at the low gamma nucleus. In contrast two designs, the four-ring birdcage (FRB) (14) and the alternating rungs birdcage (ARB) (15) are especially attractive under practical considerations since they combine both frequency modes in one easy-to-build structure, but don’t require additional lossy dual tuning circuits. Thus the efficiency of the low gamma nucleus is only slightly degraded compared to a single-tuned coil. To find a practical and well performing coil for future sodium and hydrogen MRI studies of the human knee, a FRB and ARB coil were designed and then characterized using workbench and MRI measurements.

Methods

Coil structures

Four-ring birdcage (FRB)

The 1.5 T ²³Na/¹H dual-tuned FRB coil consists of three connected, low-pass birdcages with 16 legs (Figure 1A,B). The inner ²³Na birdcage is tuned at 16.8 MHz with the central capacitors C_low and acts very similar to a single-tuned low-pass birdcage. The outer birdcages are tuned with capacitors C_high and couple through space and through the rungs to provide together a homogenous ¹H mode at 63.6 MHz. A drawback often encountered with FRB structures is the increase of the axial coil length due to the outer birdcage structures. The diameter of the human thigh is considerable bigger than the diameter of the knee and the calf, thus a long coil makes it difficult to place the knee in the center of the coil without increasing the diameter of the coil. This would be detrimental to the coil efficiency due to a decreased filling factor. Additionally the increased length might cause patient discomfort. Duan et al. (17) computationally optimized the lengths of the FRB structure while taking these geometric considerations, field homogeneity and coil efficiency of both nuclei into account. Considering these simulations, the lengths of the inner and outer birdcage were set to 15 cm (l_inner) and 2.5 cm (l_outer) for the 18 cm diameter coil built in this study.

Figure 1 Schematic structures and photographs of the four-ring birdcage (FRB) and the alternating rungs birdcage (ARB). l_inner and l_outer indicate the length of the inner (sodium) and outer (hydrogen) sections of the FRB (A). l indicates the length of the ARB structure and lguard ring the distance of the guard rings (C). Clow and Chigh indicate the capacitors of the low (sodium) and high (hydrogen) resonance for both, FRB (A) and ARB (C). Photographs of the assembled coils are shown in (B) (FRB) and (D) (ARB).

Alternating rungs birdcage (ARB)

The 1.5 T ²³Na/¹H dual-tuned ARB coil consists of a low-pass birdcage with 16 rungs which are alternatingly populated with capacitors C_low and C_high to resonate the coil at 16.8 MHz and 63.6 MHz (Figure 1C,D). The length l of 15 cm and the diameter of 18 cm of the ARB were chosen to provide the same ²³Na FOV as the FRB.

Materials

For both birdcage coils formers with 18 cm diameter were chosen to comfortably fit around a human knee. Some commercial knee coils can be split in two halves to allow easier patient access (18). This complicates the coil construction process and introduces additional connector losses and coil asymmetries. Thus it was decided to build the coils on closed cylinders. The diameter of 18 cm of the coils built for this study allows accessing the coils by slightly flexing the ankle which was found unproblematic. The coil structures were constructed with adhesive-back copper strips (3M, St. Paul, MN, USA) with a thickness of 35 μm. Coaxial HF-shields with a diameter of 24 cm were used to minimize the interaction of the coils with the scanner bore and avoid aliasing from the other leg. Non-magnetic capacitors (TEMEX Ceramics, Pessac, France) and variable trimmer capacitor (Voltronics, Denville, NJ, USA) were used to tune the coils.

Bench tests

An Agilent (Santa Clear, CA, USA) E5071B vector network analyzer was used to measure the S-parameters and resonance patterns.

Tuning

The capacitors required to resonate the FRB and ARB at the desired frequencies can be calculated by the equations provided in (14) and (15). In practice it is sufficient to start by calculating the capacitors needed for a single-tuned low pass birdcage at the ²³Na frequency. The additional ¹H tuning rungs with their low capacitance represent high impedance at the ²³Na frequency and therefore have little influence on the tuning of the ²³Na mode. In contrast, the capacitors of the ²³Na structure represent low impedance, i.e., almost shorts at the ¹H frequency. Thus, tuning of the ¹H and ²³Na modes is a largely independent procedure. The final capacitor values are listed in Table 1. To suppress gradient eddy currents, two equally spaced 100 nF bypass capacitors were added per end ring (19).

Table 1 Capacitor values of the four-ring birdcage (FRB) and the alternating rungs birdcage (ARB)
Full table

Matching and interfacing

Both coils were capacitively matched to 50 Ohm with symmetric networks. Both nuclei are driven in quadrature with custom-built quadrature hybrids. Cable traps and low/high-pass filters in the feed lines tuned to the appropriate frequencies were incorporated to ensure coil safety and stability.

MR experiments

All MR experiments were performed on a 1.5 T clinical scanner (Siemens Medical Solutions, Erlangen, Germany) with x-nuclei capability.

Acquisition of B₁ maps

A cylindrical phantom (11 cm diameter) containing a saline water solution (5 g/L NaCl and 1.25 g/L NiSO₄) was used to characterize the coils. B₁ mapping was performed on both nuclei to assess the coil homogeneity and efficiency. To obtain high quality sodium B₁ maps a phase-sensitive method (20,21) with a 3D gradient echo (GRE) readout (resolution 5×5×10 mm³, TE: 7 ms, TR: 100 ms, Bandwidth: 80 Hz/pixel, TA: 35:00 min) was used. The B₁ field of the ¹H channel was mapped with a 3D GRE sequence with a Bloch-Siegert shift (22) preparation (resolution 5×5×5 mm³, TE: 7 ms, TR: 20 ms, Bandwidth: 250 Hz/pixel, TA: 0:45 min).

Evaluation of the B₁ field homogeneity, efficiency and signal-to-noise ratio (SNR)

To quantitatively evaluate the field homogeneity the relative uniformity (RU) within the central FOV (11 cm diameter, 8 cm length) of the B₁ maps was calculated. RU represents the percentage of pixels inside the FOV whose relative deviation is not bigger than 10% of the mean B₁ field Eq. [1] (23):

The B₁ maps were also used to calculate the required voltage amplitude for a 180° block pulse of 1 ms length at the center of the coil. This voltage serves as a measure of the coil efficiency and SNR since B₁ is direct proportional to the SNR (24).

In vivo imaging

In vivo data of a volunteer was acquired with the FRB to verify that the coil performance is sufficient to perform sodium and hydrogen imaging of the human knee. For ¹H imaging a high resolution 3D MEDIC (multi-echo data imaging combination) sequence (resolution: 0.47×0.51×1.5 mm³, TR: 37 ms, TE: 20 ms, flip angle: 20°, TA: 8 min) was used. For ²³Na imaging a 3D GRE dataset was acquired (resolution: 2.7×2.7×8 mm³, TR: 11.4 ms, TE: 4 ms, Bandwidth: 85 Hz/pixel, TA: 30 min). The in vivo SNR is given as the signal intensity of each pixel divided by the standard deviation of the noise of the background.

Results

After building the structures of the FRB and the ARB the coils were tuned, matched and their coupling coefficients were determined with the cylindrical phantom. Figure 2 shows the S₁₁ plots of the FRB and ARB for ¹H (span 10 MHz) and ²³Na (span 5 MHz) in dB after tuning and matching the coil. All plots show well-defined resonance modes with sufficient mode separation. The worst case coupling coefficients can be found in Table 2. The goal to sufficiently match and isolate the ²³Na and ¹H channels was achieved without complications. To further increase the isolation between the ¹H and ²³Na channels to at least 20 dB, filters were added to the ²³Na feed lines on both coils and ²³Na filters on the ARB. For the FRB the least inter nuclei coupling was observed when the ¹H and ²³Na channels were 45° apart.

Figure 2 S11 plots of the four-ring birdcage (FRB) and the alternating rungs birdcage (ARB) for ¹H (span 10 MHz) and ²³Na (span 5 MHz) in dB. All plots show well-defined resonance modes with sufficient mode separation.

Table 2 ²³Na and ¹H bench measurements of the coupling and matching coefficients of the four-ring birdcage (FRB) and the alternating rungs birdcage (ARB) in dB
Full table

The acquired B₁ maps (Figure 3) were used to calculate the RU and the 180° pulse amplitude (Table 3). The ²³Na efficiencies of the two coils are almost identical (45.1 vs. 45.9 V) while the RU of the FRB is slightly higher (95.2% vs. 93.6%) than the ARB’s. Regarding the ¹H performance the FRB outperforms the ARB at both efficiency (69.2 vs. 75.4 V) and field homogeneity (94.4% vs. 74.4%).

Figure 3 Orthogonal slices of the normalized 3D B₁ maps of the four-ring birdcage (FRB) and the alternating rungs birdcage (ARB). The images correspond to axial, coronal and sagittal slices (from left to right) of the 3D B₁¹H (A) and ²³Na B₁ datasets (B). The labels on the images indicate the physical orientation of the B₁ maps: top-to-bottom (A-P), left-to-right (L-R), and front-to-back (I-S). The dashed lines mark the volume used for the calculation of the relative uniformity (RU).

Table 3 Relative uniformities (RU) of the central FOV in percent and 180° pulse amplitudes in Volt of the four-ring birdcage (FRB) and the alternating rungs birdcage (ARB) for ¹H and ²³Na
Full table

As results of the better performance in the phantom measurements, the FRB was chosen to acquire in vivo data of a volunteer. Figure 4 shows a sagittal slice of the acquired morphological 3D MEDIC data set and the 3D sodium data set. Additionally an overlay image of the segmented ²³Na cartilage signal onto the ¹H image was created. The ²³Na SNR of the cartilage is in the range of 6 to 14.

Figure 4 Sagittal images of a ²³Na and ¹H in vivo dataset acquired with the four-ring birdcage (FRB) coil. From left to right: ²³Na image (A), ¹H image (B) and overlay of the color-mapped ²³Na signal-to-noise ratio (SNR) of the cartilage onto the ¹H image (C). The colorbar indicates the SNR of the ²³Na image.

Discussion

Two practical dual-tuned quadrature birdcages for the human knee were designed and characterized. Both coils show well-defined resonance modes and the bench measurements of the matching and decoupling coefficients were well within the commonly accepted requirements (<−20 dB). Sodium and hydrogen B₁ maps were acquired to investigate the efficiency and RF field homogeneity of the coils. As expected the ²³Na efficiency of the FRB and the ARB is almost identical since the additional ¹H rungs have little influence on the ²³Na currents. The field homogeneity of a birdcage coil increases with its number of rungs. Correspondingly, the FRB with its 16 rungs is superior in field homogeneity to the ARB with its eight rungs contributing to the ²³Na field as indicated by the lower RU. The imaging coverage of ¹H and ²³Na in the axial direction is identical for the ARB (Figure 3). Unlike, the FRB’s axial imaging coverage for ¹H is considerably larger than for ²³Na due to the longer length of the ¹H structure (19 vs. 15 cm). This might be causing aliasing in the axial direction, if not addressed properly during image acquisition. The ²³Na rungs of the ARB support counter rotating currents at the ¹H frequency that have a negative impact on the ¹H field homogeneity. This effect is visible as periodic B₁ field attenuations near the rungs (Figure 3A). Accordingly, the FRB is superior to the ARB regarding the ¹H field homogeneity and efficiency. The achieved in vivo resolution and SNR of the sodium images acquired with the FRB allow quantification of the sodium concentration of the cartilage as shown by others researchers (18). High resolution anatomical ¹H images could be obtained without averaging.

Conclusions

Concluding, the ARB and FRB are both practical dual-tuned coils and deliver similar ²³Na efficiency. Due to its superior ¹H homogeneity and efficiency and its slightly better ²³Na homogeneity, the FRB is the overall preferred coil for the given requirements of this study.

Acknowledgements

Funding: This work was funded by the EU as part of the Seventh Framework Program (FP7) in the Health project 241719 “ADIPOA”.

Footnote

Conflicts of Interest: The authors have no conflicts of interest to declare.

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