A dual-tuned quadrature volume coil with mixed λ/2 and λ/4 microstrip resonators for multinuclear MRSI at 7T

Abstract

In this work, an 8-element by 8-element dual-tuned quadrature volume coil with a mix of capacitor terminated half-wavelength (λ/2) and quarter-wavelength (λ/4) microstrip resonators is proposed for multinuclear MRI/S studies at 7T. In the proton channel, λ/2 microstrip resonators with capacitive terminations on both ends are employed for operation at higher frequency of 298.1 MHz; in the heteronucleus channel, capacitor terminated λ/4 resonators, suitable for low frequency operations, are used to meet the low frequency requirement. This mixed structure design is particularly advantageous for high field heteronuclei MR applications with large difference in Larmor frequency of the nuclei in question. The proposed design method makes it much easier to perform frequency tuning for heteronucleus channel using a variable capacitor with a practical capacitance range. As an example, a dual-tuned volume coil for ¹H/¹³C mouse spectroscopic imaging was proposed to demonstrate the feasibility of this method. The finite-difference time-domain (FDTD) method is first used to model this dual-tuned volume coil and calculate the B₁ field distributions at two frequencies. Transmission parameters (S₂₁) measured between the proton channel and the carbon channel are −50 dB at 75 MHz and −35 dB at 298 MHz, showing the excellent isolation between the two channels at 7T. The proton image and ¹³C FID CSI image of a corn oil phantom on the axial plane at 7T demonstrate the feasibility of the proposed method. A preliminary proton image of a mouse on the sagittal plane is also acquired using the proposed dual-tuned volume coil at 7T, illustrating a fairly uniform B₁ field and sufficient image coverage for imaging in mice.

1. Introduction

Due to low natural abundance of heteronuclei, leading to low signal intensity, multinuclear MR applications, such as ¹H/¹³C [1–5], ¹H/²³Na [6–8] and ¹H/³¹P [9–12] spectroscopic imaging that are capable of depicting metabolic process in vivo, have brought forward urgent demand for efficient double-frequency RF coils to utmost detect the MR signals. Dual-tuned RF coils have been designed using different techniques such as lumped element method [13–18] and transverse electromagnetic resonator (TEM) technique [19–21], and have demonstrated great advantages in multinuclear spectroscopic imaging. However, involvement of two independently controlled frequencies makes the design of dual-tuned RF coils complicated and technically challenging, particularly at high and ultrahigh fields due to the required high frequency [22]. The high operation frequency of the ultrahigh field MR results in the increased conductor/radiation losses, degraded quality factors, augmented electromagnetic interactions between the two resonant frequencies, and difficulties in achieving required high resonant frequency of RF coils. These problems are more prominent in the presence of a living animal loaded to RF coils.

In recent years, it has been demonstrated that microstrip transmission line (MTL) RF coils are advantageous to high field in vivo MR applications with high quality factor, high frequency operation capability, reduced radiation losses, and thus improved MR sensitivity. This technique has been successfully applied to designs of surface coils [23,24], volume coils [25–28], and coil array [23,29–35] for high and ultrahigh field MR applications in humans. Because of the high frequency property of the microstrip resonator and the behavior of resonator length dependence of the frequency, the microstrip coil design shows challenges in reducing the resonant frequency for heteronuclear MR studies especially for the small animal applications where the coil size is much smaller than that used in humans. The capacitive termination [25,26,29] is one of methods to reduce the resonant frequency. However, in many multinuclear MR studies, the Larmor frequency of the heteronucleus is much lower than that of proton. It often requires impractically large capacitance to tune the resonant frequency down to the Larmor frequency of the heteronucleus in question. This makes its frequency tuning difficult and potentially increases the interaction between proton and heteronuclear channels.

To take advantage of the microstrip resonator and overcome the technical design difficulties facing in practical designs, we propose a design method for dual-tuned quadrature volume coil using a mix of capacitor terminated half-wavelength (λ/2) and quarter-wavelength (λ/4) microstrip resonators for multinuclear MR studies at ultrahigh fields. Compared with λ/2 microstrip resonators, λ/4 resonators with the same physical length operate at significantly lower frequency. This low frequency feature of λ/4 resonators is well suitable for heteronuclear MR applications. To demonstrate the proposed design technique, we have designed a 16-element dual-tuned volume coil in which 8 elements are λ/2 microstrip resonators for ¹H channel while another set of 8 elements are λ/4 microstrip resonators for ¹³C channel. This volume coil is capable of quadrature driving for both ¹³C channel and ¹H channel for improved sensitivity and reduced RF power for spin excitation. The resonant frequency of the λ/4 resonator is only half of that of the λ/2 resonator, therefore the terminated capacitor of the λ/4 resonator for ¹³C channel can be greatly reduced, making the frequency tuning much easier [36]. The finite-difference time-domain (FDTD) method is used to model the dual-tuned volume coil, determine the capacitance and calculate the B₁ field distributions at the two frequencies. Bench tests and in vivo MR experiments are performed to validate the feasibility and performance of the proposed 7T dual-tuned volume coil design.

2. Materials and methods

2.1 Dual-tuned microstrip volume coil design for ¹H and ¹³C MRI/S

The dual-tuned quadrature microstrip volume coil was designed for ¹H imaging and ¹³C spectroscopy at 7T, corresponding to the resonant frequencies of 298.1 MHz and 75 MHz respectively. A cross-sectional view of the volume coil is shown in Fig.1. There are totally 16 microstrip elements of 8 λ/2 resonators for ¹H and 8 λ/4 resonators for ¹³C equidistantly distributed on a Teflon cylinder which serves as both dielectric substrate and mechanical support. These 8 λ/2 resonators and 8 λ/4 resonators are alternately placed along the Teflon cylinder. Teflon is a low loss dielectric material with loss tangent smaller than 0.0002 and a permittivity of 2.1 at the frequency of interest and has been used as substrate for microstrip surface coil. The dimensions of this cylinder are 6.6cm OD by 5.2 cm ID by 10.1 cm in length. On the inner surface of the Teflon cylinder, 8 microstrip conductors of ¹H channel and 8 microstrip conductors of ¹³C channel were interleaved built. Each microstrip conductor was made from a copper tape with 0.32 cm width and 36 µm thickness (3M, St. Paul, Minnesota). The structure and equivalent circuit of the elements of ¹H channel and ¹³C channel are illustrated in Fig.2 and Fig. 3 respectively, as well as those of the typical microstrip resonator for comparison. For the typical microstrip resonator, the resonant frequency is:

$$f_{\mathit{\text{element}}}=\frac{c}{2l\sqrt{{\epsilon }_{\mathit{\text{eff}}}}}$$ (1)

where l and c denote the length of the microstrip conductor and the velocity of light in free space, respectively. ε_eff is the effective permittivity of the microstrip resonator.

Figure 1.

The cross-sectional view of the dual-tuned quadrature microstrip volume coil with mixed λ/2 and λ/4 resonators. The λ/2 and λ/4 resonators are alternately arranged along the circumference of the cylindrical volume coil. With this structure, both channels can be driven in quadrature for improved SNR and reduced excitation power.

Figure 2.

Diagrams of (a) typical open-circuited MTL resonator, (b) capacitor terminated λ/2 MTL resonator and (c) capacitor terminated λ/4 MTL resonator.

Figure 3.

Equivalent circuits of (a) the typical open-circuited MTL resonator, (b) capacitor terminated λ/2 MTL resonator and (c) capacitor terminated λ/4 MTL resonator.

For the ¹H channel, a λ/2 microstrip resonator with capacitive termination on both ends was adopted. The resonant frequency of such a λ/2 resonator can be predicted by solving the following equation [26]:

$$f_{\mathit{\text{re}}}=\frac{{\left(2\pi f_{\mathit{\text{re}}}{Z}_0\right)}^2{C}_{t1}{C}_{t2}-1}{2\pi Z_0(C_{t1}+C_{t2})}\text{tan}(\frac{2\pi l\sqrt{{\epsilon }_{\mathit{\text{eff}}}}}{c}{f}_{\mathit{\text{re}}})$$ (2)

where C_t1 and C_t2 are the capacitance of the termination capacitors of the microstrip resonator shown in Fig.2b. Z₀ is the characteristic impedance of the microstrip resonator. Compared with Eq. (1) of the typical microstrip resonator, the resonant frequency can be significantly reduced for the same conductor length l. This enables the microstrip volume coil to be designed for small size coil.

For the ¹³C channel, a capacitor terminated λ/4 microstrip resonator was adopted. The resonant frequency of such a structure can be deduced by calculating the limitation of the Eq. (2). Thus the resonant frequency of the capacitor terminated λ/4 microstrip resonator can be predicted by solving the following equation:

$$2\pi Z_0{C}_t{f}_{\mathit{\text{re}}}\text{tan}(\frac{2\pi l\sqrt{{\epsilon }_{\mathit{\text{eff}}}}}{c}{f}_{\mathit{\text{re}}})=1$$ (3)

where C_t is the capacitance of the termination capacitor of the microstrip resonator shown in Fig.2c. Compared with Eq. (2), the resonant frequency can be significantly reduced for the same capacitance and conductor length. This makes it possible to apply the microstrip resonator to ¹³C which has a much lower resonant frequency than ¹H.

The ground plane of the coil was built by ringing a cylindrical copper foil with 36 µm thickness on the outer surface of the Teflon cylinder. This continuous ground plane can effectively enhance the coupling between the elements.

The resonant frequency of the microstrip volume coil is expressed as [26]:

$$f_{\mathit{\text{vc}}}=\frac{1}{\sqrt{1+\frac{1}{L}{\displaystyle {\sum }_{i=1}^{N-1}{k}_{1,i+1}}\text{cos}(\frac{2\pi }{N}i)}}{f}_{\mathit{\text{re}}}$$ (4)

where k_{1, i+1} is the mutual inductance between the 1^st element and the (i+1)th elements, N denotes the number of elements and L denotes the inductance of each microstrip resonant element. In this volume coil design the magnetic coupling dominates the coupling between the elements, therefore the electric coupling was ignored and only mutual inductance to coil induced voltage from the other resonator elements was considered. The resonant element frequency f_re denotes that of the ¹H channel or the ¹³C channel. From Eq. (4), it can be seen that the resonant frequency of the volume coil is smaller than that of each element due to the mutual coupling between them.

2.2 FDTD simulations

Based on the structure described above, a coil model was first built and the B₁ field distributions at the two frequencies were numerically simulated using the FDTD. A cylinder-shaped mouse muscle phantom with permittivity of 58 and conductivity of 0.8 was modeled within a 16-element dual-tuned microstrip volume coil. The diameter of the phantom was 4.2 cm which is about 80% of the volume coil ID. Each element of the coil was modeled as a 0.32 cm wide and 10.1 cm long thin strip of copper and placed equal spacing on the surface of a cylinder with 5.2 cm ID, 6.6 cm OD and 10.1 cm length. The permittivity of this cylinder is 2.1, which is the same as that of the Teflon. On the inside surface of this cylinder the ground plane of the volume coil was modeled as a continuous wrapping copper with thickness of 0.36 µm. For the mixed λ/2 resonator of ¹H channel, capacitors were connected on both ends of the copper strip as passive load. For the mixed λ/4 resonator of ¹³C channel, on one end the strip was directly connected to the ground plane using a copper strip with the same width of the strip; on the other end a capacitor was connected between the strip and the ground using a perfect electric conductor. The coaxial cable of the volume coil was modeled as a series voltage source with 50 ohm impedance which was connected to each driven port of the coil model. Linear drive was used for each channel. The Yee cell was 1 mm which was small enough for satisfying the simulation accuracy. The Gauss waveform was used to determine the value of the terminated capacitors and the stop criteria were that the calculation converged to −35 dB or reached the maximum iteration number of 10⁶. Then, the Sine waveform was used to calculate the B₁ field distributions and the stop criteria were that the calculation converged to −40 dB or the iteration number reached 300,000. All the FDTD calculation was performed using the software XFDTD 6.4 (Remcom, Inc.) on a PC with 2.33 GHz CPU and 4 GB memory.

To investigate the RF efficiency and field homogeneity of our proposed design, a conventional 16-strut dual-tuned birdcage coil was modeled and compared with the microstrip coil model. The conventional birdcage was in the same size as the microstrip coil: the diameter was 5.2 cm and the length was 10.1 cm. 8 struts of ¹H channel and 8 struts of ¹³C channel were alternately placed. Each strut was made from a copper tape with 0.32 cm width and 36 um thickness (3M, St. Paul, Minnesota). The capacitor value for ¹H channel was 7.4 pF while that for ¹³C channel was 59 pF. The same phantom was modeled within the coil. All the other settings for the FDTD simulation were kept the same.

2.3 Bench test

Based on the simulation results, a dual-tuned microstrip volume coil for ¹H and ¹³C was then built as shown in Fig.4. To generate a circularly polarized B₁ field, the coil operated in quadrature with connection to a 3-dB 90° quadrature hybrid. In both ¹H and ¹³C channels, two driving elements of the volume coil were 90° apart in phase. The frequency tuning of the two channels can be achieved by adjusting the termination capacitors. The impedance matching of the volume coil can be achieved by varying the trimmer capacitor (Voltronics, Denville, NJ) which was connected in series to the microstrip conductors of the driving element.

Figure 4.

(a) Structure of the proposed 8-element by 8-element dual-tuned volume coil using alternately placed λ/2 and λ/4 microstrip resonators for in vivo ¹³C/¹H MRSI applications at 7T and (b) Prototype of this dual-tuned microstrip volume coil with two sets of quadrature feedings.

An Agilent E5070B network analyzer was used for testing the coil resonance modes, the isolation between two quadrature ports and that between the proton and carbon channels. As shown in Fig.1, there are totally 4 ports on the dual-tuned volume coil: 0° ¹H port, 90° ¹H port, 0° ¹³C port and 90° ¹³C port. The resonance modes of the 4 ports were tested using the reflection parameter S₁₁ firstly. Then the isolation between two pair of quadrature ports of ¹H channel and ¹³C channel were tested using the transmission parameter S₂₁. To test the isolation between the ¹H and ¹³C channels, the S₂₁ between them was also measured at both resonant frequencies.

2.4 Phantom and in vivo MRI

Both phantom and in vivo images were tested using a commercial 7T General Electric Signa™ scanner. In the phantom experiment, the ¹H images and ¹³C spectroscopic images of a cylindrical corn coil phantom were obtained in axial plane. The ¹H image of the phantom was acquired using a gradient echo (GRE) sequence with FOV =10 cm, encoding matrix = 256×128, slice thickness = 3 mm, TR= 100 ms, TE= 6.8 ms, FA = 30° and Average number = 1. The ¹³C spectroscopic image was acquired using the FIDCSI sequence (GE Healthcare, Waukesha, WI, USA) with TR = 2 sec, 10 mm in plane slice and 20 mm thickness. The FIDCSI is 2D chemical shift imaging by using a set of phase-encoded free induction decay signals. A proton image of a mouse was also acquired in sagittal plane using a fast spin echo (FSE) sequence with the following imaging parameters: FOV = 9 cm, encoding matrix = 192×192, slice thickness = 1.6 mm, TR= 4000 ms, TE= 104.08 ms, FA = 90° and Average number = 1.

3. Results

3.1 simulations

Theoretical calculation based on the analytical equations was first applied to estimate the capacitance for each element of the ¹H and ¹³C channel. Then these estimated capacitances were used to build the numerical model for the dual-tuned microstrip volume coil in xFDTD environment and the Gauss waveform was used to sweep frequency to determine the value of each capacitor. After several iterations, proper capacitances were found: for the λ/2 resonator in ¹H channel the terminated capacitors are 13.6 pF and 6.8 pF, and for the λ/4 resonator in ¹³C channel the terminated capacitance was 70 pF. Using this setting, the sine waveform was used to calculate the B₁ field distribution of each channel. Both the ¹H channel and ¹³C channel generate a homogeneous RF field within the interested area of the phantom. As shown in Fig.5a, when the 298.1 MHz sine wave signal was input into the driven port of the ¹H channel, the elements of the ¹H channel were all excited except the elements which were orthogonal to the driven element, while all the elements of the ¹³C channel were suppressed. When the 75 MHz Sine waveform was used, the ¹³C channel excited and the ¹H channel was quiet, which is shown in Fig.6a. The sinusoid distributions of the currents for both ¹H and ¹³C channels along the circumference of the coil are clearly illustrated. These results show excellent isolation between ¹H and ¹³C channels, which is desired in dual-tuned RF coil design.

Figure 5.

B₁ field distributions of the ¹H channel of (a) microstrip dual-tuned volume coil and (b) conventional dual-tuned birdcage coil calculated using FDTD method. (c) 1D plot of the field distribution along the central line of the 2D images. The red line denotes the microstrip coil while the blue line denotes the birdcage coil. The RF efficiency of the microstrip coil is around 1 dB higher than that of the birdcage coil, while the homogeneity variation of both coils is within 1.8 dB range.

Figure 6.

B₁ field distributions of the ¹³C channel of (a) microstrip dual-tuned volume coil and (b) conventional dual-tuned birdcage coil calculated using FDTD method. (c) 1D plot of the field distribution along the central line of the 2D images. The red line denotes the microstrip coil while the blue line denotes the birdcage coil. The RF efficiency of the ¹³C channel of the microstrip coil is around 6 dB higher than that of the birdcage coil, while the homogeneity variation of both coils is within 1 dB range.

Fig.5b shows the RF field distribution of the ¹H channel of the 16-strut dual-tuned birdcage coil. Compared with Fig.5a, the RF field of the birdcage coil used in this work is slightly weaker than that of the microstrip. The 1D plot in Fig.5c shows this difference more clearly. The RF efficiency of the ¹H channel of the microstrip volume coil is approximately 1 dB higher than that of the birdcage coil, while the homogeneity variation of both coils are within 1.8 dB range. As a comparison of Fig.6a which shows the ¹³C RF field distribution of the microstrip volume coil, Fig.6b shows that of the conventional birdcage coil. The 1D plot in Fig.6c illustrates that, in this specific case, the RF efficiency of the ¹³C channel of the microstrip volume coil is approximately 6 dB higher than that of the birdcage coil, while the homogeneity variation of the two coils are both within 1 dB range.

3.2 Bench test

The resonance modes of one driving port of ¹H channel and the isolation between the two driving ports were plotted in Fig.6. When ¹H channel were tuned at 298.1 MHz, the reflection coefficient S₁₁ of the two ports are both better than −43 dB, and the transmission coefficient S₂₁ between the two quadurature ports is −26 dB. Fig.7 shows the resonance modes and the isolation between the two quadrature ports of the ¹³C channel when tuned at 74.94 MHz. The reflection coefficient S₁₁ of the two ports are better than −32 dB, while the transmission coefficient S₂₁ between the two quadurature ports is better than −27 dB. These results ensure excellent quadrature performance of both ¹H and ¹³C channels.

Figure 7.

(a) S₁₁ plot of one driving port of ¹H channel showing the multimodal behavior of the dual-tuned volume coil with 8 ¹H elements; (b) S₂₁ measurement of the two driving ports of ¹H channel, indicating the accuracy of the 900 phase requirement of the two quadrature ports in the 300 MHz range.

The isolation between the ¹H channel and the ¹³C channel is illustrated in Fig.8. The transmission coefficient S₂₁ between two channels was plotted at both 74.94 MHz and 298.1 MHz with 30 MHz span. Also, the S₂₁ from 50 MHz to 330 MHz span is shown. The S₂₁ at 74.94 MHz is better than −50 dB and that at 298.1 MHz is better than −35 dB, indicating that the two channels of ¹H and ¹³C are isolated sufficiently, which is essential for efficient acquisition of ¹³C MR signals.

Figure 8.

(a) S₁₁ plot of one driving port of ¹³C channel, showing the well-defined resonance modes of the dual-tuned coil with 8 elements; (b) S₂₁ measurement between the two quadrature driving ports of ¹³C channel. The sufficient isolation (~27dB) indicates accuracy of the 90° phase requirement of the two quadrature ports.

Based on the simulation results and bench tests, the capacitance C_t1 and C_t2 on the ¹H element were 12.4 pF and 6.8 pF respectively. The capacitance C_t on the ¹³C element was 68 pF and a variable capacitor (Johneson9620, 0.5 – 2.5 pF) was parallel connected into the element to perform frequency tuning.

3.3 MRI tests

After B₀ shimming using the ¹H channel MR tests was performed. The ¹H GRE image and ¹³C spectroscopic image in the axial plane of a corn oil phantom was acquired sequentially and are shown in Fig.9. These two images illustrate high quality of proton image and carbon spectroscopic image of the microstrip volume coil. The chemical shift artifacts of the oil phantom at the ultrahigh field of 7T are also clearly observed in this image. Another proton in vivo image of a mouse on sagittal plane shown is also shown in Fig.10. This demonstrates that the proposed dual-tuned volume coil design can provide a fairly homogeneous B₁ field and image coverage with loading in the 300MHz range.

Figure 9.

S₂₁ measurements between the ¹³C channel and the ¹H channel (a) in frequency ranges of 50 – 330 MHz, (b) 75 MHz and (c) 298.1 MHz. Sufficient electromagnetic isolation between ¹³C channel and ¹H channel of the proposed dual-tuned volume coil is essential for efficient acquisition of ¹³C signals.

Figure 10.

MR images of the dual-tuned microstrip volume coil at 7T: (a) ¹H image of a corn oil phantom on axial plane (chemical shift artifacts of the oil phantom at the ultrahigh field of 7T are clearly observed in this image); (b) ¹³C FIDCSI spectroscopic image of the corn oil phantom (with natural abundance) on axial plane.

4. Discussion and Conclusion

A novel design for dual-tuned quadrature volume coil using a mix of capacitor terminated half-wavelength and quarter-wavelength microstrip resonators for multinuclear MR studies at 7T has been proposed. An example volume coil design for ¹H/¹³C spectroscopic imaging for mouse study has been presented to demonstrate the feasibility of this method. High quality proton image and carbon spectroscopic image of a corn oil phantom have been obtained using this dual-tuned microstrip volume coil. Both simulations and MR experiment results have shown the excellent performance of the proposed design method.

In this design, mixed λ/2 and λ/4 resonators were utilized to fit the different resonant frequencies of ¹H and ¹³C respectively. At the same length, λ/4 resonators operate at relatively low frequency compared with the commonly used λ/2 resonators in RF coil design. Therefore, the use of λ/4 resonators is advantageous for ¹³C channel and makes it much convenient to perform frequency tuning by using commercially available variable capacitors.

The FDTD simulation has shown that the dual-tuned microstrip volume coil can generate homogeneous B₁ fields at both ¹H and ¹³C resonant frequencies. When the elements of one frequency are excited there is nearly no signal in the elements of the other frequency, showing excellent isolation between the two channels, which is desired in dual-tuned RF coil designs because it can help to increase efficiency of heteronuclear MR signal excitation and detection. Quadrature driving has been applied to both the ¹H and ¹³C channels of the volume coil to improve the SNR and reduce RF excitation power. The transmission parameters S₂₁ between each pair of driving ports of ¹H and ¹³C channels are −26 dB and −27 dB respectively, ensuring excellent quadrature performance of both ¹H and ¹³C channels. Measured on a network analyzer, the transmission parameters S₂₁ between a driving port of ¹H and that of ¹³C is better than −50 dB at 75 MHz and −35 dB at 298.1 MHz. This measured result demonstrates that the ¹H and ¹³C channels have been isolated excellently and is in agreement with the FDTD simulation results. In summary, this dual-tuned microstrip volume coil with mixed λ/2 and λ/4 resonant elements is feasible and efficient, provided that sufficient radial separation is maintained between the strip conductor and the ground to provide sufficient coupling between elements. The characteristic of the microstrip provides a simple approach to design dual-tuned volume coil for in vivo multinuclear MR at ultrahigh fields.

Figure 11.

¹H in vivo image of a mouse on sagittal plane acquired using the ¹H channel of the proposed dual-tuned volume coil at 7T. This preliminary ¹H imaging result demonstrates that the proposed dual-tuned volume coil design can provide a fairly homogeneous B₁ field and image coverage with loading in the 300MHz range.