A concentric-loops coil enhancing RF coil B₁ efficiency and reducing imaging noise compared to traditional single-loop coil

Abstract

We proposed a simple approach to optimize a concentric-loops RF coil, consisting of an inner primary coil as the driving coil and an outer secondary coil as a passive resonator. By adjusting the tuning capacitor in the secondary loop to raise its self-resonance frequency to be slightly above the operating Larmor frequency, we enabled the preferred operation condition (additive mode), where both secondary and primary loops contributed to the largely enhanced RF coil transmit and receive magnetic fields $\left(B_1\right)$ within the area enclosed by the primary loop as compared to a single-loop secondary coil. Compared to a single secondary loop coil as control, electromagnetic (EM) simulations and phantom MRS/MRI at 10.5T ¹⁷O (60.6 MHz), 7T ³¹P (120.7 MHz), and 1.5T ¹H (63.8 MHz) operating frequencies show that the concentric-loops coil (8 cm diameter for the secondary loop coil) provides 1.2 to 1.4-fold higher $B_1$ and coil sensitivity in the near-coil region (0–3cm). In the far region, it offers slightly enhanced $B_1$ and coil sensitivity, which becomes similar to the control coil at 9 cm away from the coil plane. Additionally, the concentric-loops coil reduces imaging noise by 15–30%, collectively, resulting in an ~1.7× SNR gain at the near-coil region. The concentric-loops coil with the presented optimization strategy provides an effective and simple coil design with largely improved imaging SNR compared to a conventional single-loop coil for a broad range of MRS/MRI applications across different field strengths.

1. Introduction

Radiofrequency (RF) coils are a fundamental component in MRI technology and directly influence the imaging signal-to-noise ratio (SNR) and performance. Since the introduction of the surface coil for in vivo MRS [1], the circular loop resonator has been widely used for X-nuclear (non-proton) magnetic resonance spectroscopy imaging (MRSI) application such as ²H, ¹⁷O and ³¹P for studying the human brain metabolism [2–6]. However, X-nuclear MRSI is largely limited by low temporal and spatial resolution due to the low natural abundance of X nuclei (e.g., ²H, ¹⁷O and ¹³C) or low metabolites concentration and low intrinsic detection sensitivity compared to proton, and limited RF coil sensitivity. The circular solenoid or planar spiral coil design has been used to improve the RF coil sensitivity and imaging SNR as the use of many loop turns increases the overall RF coil magnetic field $\left(B_1\right)$ strength compared to a single-turn surface loop coil [7–9]. In addition, the spiral coil integrated with dielectric materials such as the Meta-metallic coil [10] and multi-turn split-conductor transmission-line resonators (MSTR) [11, 12] further increases the RF coil $B_1$ efficiency. However, as the number of the coil turns increases, the length of conductor trace of the multi-turn coil also increases, resulting in higher ohmic resistance of the multi-turn coil, thus, higher imaging noise and limiting the SNR gain [13]. Thus, the number of turns and the spacing between adjacent conductor traces must be carefully designed to optimize the coil layout in order to improve the overall multi-turn coil sensitivity and imaging SNR [14]. There has been limited exploration of simpler surface coil designs that avoid introducing complicated coil geometries and structures while improving overall MRI performance.

The planar concentric-loops coil design, consisting of an inner loop and an outer loop, is a simpler modification to the conventional single loop surface coil design as compared to the multi-turn loop or spiral coil design. The planar concentric-loops coil design has been widely used in MRS/MRI applications, such as serving as an inductive matching probe to couple to the main NMR resonating coils in order to match it to 50 ohms of the coaxial cable [15, 16]. Additionally, the concentric-loops coil design is used for dual-tuned X-nucleus/proton imaging, such as the nested loop designs [17, 18], where the center loop is used for X-nuclei imaging and the outer loop is used for proton imaging. Moreover, multiple concentrically placed loop-coil elements have also been used as a concentric array for parallel imaging [19]. Surprisingly, little attention has been given to examine how the self-resonance frequency of the inner or outer loop can be controlled and adjusted to provide optimal performance for the overall concentric-loops design for the single-frequency imaging application, and rigorously compare its performance with that of a traditional single-loop (control) coil.

In this work, we optimized the performance of a concentric-loops coil design consisting of an inner primary loop as the driving coil and a co-planar outer secondary loop as a passive resonator without wire connection between them. Compared to a single secondary loop coil as control, electromagnetic (EM) simulations and phantom MRS/MRI tests at 10.5T ¹⁷O (60.6 MHz), 7T ³¹P (120.7 MHz), and 1.5T ¹H (63.8 MHz) operating frequencies show that the optimized concentric-loops coil can significantly reduce imaging noise and increase the overall $B_1$ strength and coil sensitivity, thus, largely enhancing imaging SNR compared to a single-loop control coil.

2. Theory

2.1. Optimize coil currents and $B_1$ field

Figure 1 schematically shows a traditional single-loop coil (Fig. 1A) and planar concentric-loops coil (Fig. 1B). For the concentric-loops equivalent circuits shown in Fig. 2B, the circuit on the left is the primary coil (sniffer coil), and its left end is connected to a coaxial cable with driving voltage $\left({\text{V}}_0\right)$. The inner primary coil is the driving coil, and outer secondary coil is a passive resonator (see Fig. 1B). The primary and secondary loops are magnetically coupled without any wire connection. The primary coil has a tuning capacitor $\left({\text{C}}_{\text{p}}\right)$, resistance $\left({\text{R}}_{\text{p}}\right)$ and inductance $\left({\text{L}}_{\text{p}}\right)$; and the secondary coil has inductance $\left({\text{L}}_{\text{s}}\right)$, capacitance $\left({\text{C}}_{\text{s}}\right)$ and resistance $\left({\text{R}}_{\text{s}}\right)$. Assuming that the magnetic flux generated by the secondary loop is uniformly distributed within the area of the primary loop with a smaller size, the mutual inductance (M) between the primary and secondary loops is:

$$M=-{\mu }_0\pi \frac{r_p^2}{2r_s},$$ [1]

Figure 1.

(A) A traditional 8-cm diameter single loop coil with conductor cross section width $\left(w_1\right)$. (B) The concentric-loops coil consists of an inner primary loop of conductor width $\left(w_2\right)$ and an outer secondary loop of conductor width $\left(w_1:<w_2\right)$. The inner primary coil is the driving coil, and outer secondary coil is a passive resonator. The primary and secondary loops are magnetically coupled without any wire connection. There is an optimal capacitance $\left({\text{C}}_{\text{s}}\right)$ for the secondary loop to adjust its self-resonant frequency $\left(f_{\text{s}}\right)$, which can maximize the $B_1$ (transmit and receive magnetic fields) and imaging SNR for the concentric-loops coil.

Figure 2.

(A) The concentric-loops coil, where ${\text{I}}_{\text{p}}$ is the current in the primary loop and ${\text{I}}_{\text{s}}$ is the current in the secondary loop. (B) The equivalent circuits of concentric-loops coil, where the primary loop is inductively coupled to the secondary loop with mutual coupling inductance M. (C) The phase difference between ${\text{I}}_{\text{s}}$ and ${\text{I}}_{\text{p}}$. When $f\text{s}$ is above the Larmor frequency (60.6MHz), ${\text{I}}_{\text{p}}$ and ${\text{I}}_{\text{s}}$ flow in the same direction (additive mode); when $f\text{s}$ is below the Larmor frequency, they flow in the opposite directions (subtractive mode).

where ${\mu }_0$ is the permeability constant, $r_p$ and $r_s$ are the radiuses of the primary loop and the secondary loop, respectively. The secondary coil has a self-resonating frequency $f\text{s}$:

$$f_s=\frac{1}{2\pi \sqrt{L_s{C}_s}}.$$ [2]

The $f_s$ is increased by decreasing the tuning capacitor $\left({\text{C}}_{\text{s}}\right)$ on the secondary loop, conversely, it is decreased by increasing ${\text{C}}_{\text{s}}$. The currents in the primary coil $\left({\text{I}}_{\text{p}}\right)$, and secondary coil $\left({\text{I}}_{\text{s}}\right)$ and their phase difference are labeled and presented in Fig. 2A–2C. Notably, when ${\text{I}}_{\text{p}}$ and ${\text{I}}_{\text{s}}$ have a phase shift of 180 degrees, the current directions of the primary coil and secondary coil are opposite. When ${\text{I}}_{\text{p}}$ and ${\text{I}}_{\text{s}}$ are in 0-degree phase shift, the currents of primary coil and secondary coil are in the same direction. Applying Kirchhoff’s voltage law, we can solve for the current in the primary loop coil:

$$I_p=\frac{v0}{R_p+j\omega L_p+\frac{-j}{\omega C_p}+\frac{-{\left(j\omega M\right)}^2}{R_s+j\omega L_s+\frac{-j}{\omega C_s}}},$$ [3]

where $\omega$ is the coil operating (or Larmor) frequency. The current in the secondary coil is:

$$I_s=\frac{-j\omega M{I}_p}{R_s+j\omega L_s+\frac{-j}{\omega C_s}}.$$ [4]

Based on Equations (3) and (4), we calculated the ${\text{I}}_{\text{s}}$ and ${\text{I}}_{\text{p}}$ at 10.5T ¹⁷O Larmor frequency (60.6 MHz) as a function of the self-resonant frequency of the secondary loop $\left(f_{\text{s}}\right)$ based on a given input voltage ${\text{V}}_0=1$ volt. Herein, we only focus on $f_{\text{s}}$ as an independent variable because the phase difference between the currents in the secondary and the primary loops only changes as a function of $f_{\text{s}}$, but not affected by the primary coil’s self-resonance frequency $\left(f_{\text{p}}\right)$. Figure 2C shows the phase difference between ${\text{I}}_{\text{s}}$ and ${\text{I}}_{\text{p}}$ as a function of $f_{\text{s}}$. When $f_{\text{s}}$ is above 60.6 MHz, the phase difference is near 0-degree and both ${\text{I}}_{\text{s}}$ and ${\text{I}}_{\text{p}}$ flow in the same direction, which we call the additive mode. In this mode, the magnetic fields generated by the primary and secondary loops within the area enclosed by the primary loop coil point in the same direction, creating an overall enhanced the $B_1$ field compared to the traditional single-loop coil. The concentric-loops coil is optimized when $f_{\text{s}}$ is between 61– 64MHz for this case. On the other hand, when fs is below 60.6 MHz, ${\text{I}}_{\text{s}}$ and ${\text{I}}_{\text{p}}$ flow in opposite directions (one in clockwise, and one in counterclockwise), operating in the subtractive mode and reducing the $B_1$ field.

2.2. Noise calculation

The noise voltage is given by $V_{noise}=\sqrt{4k_B\left(R_{sample}+R_{coil}\right)T\times \Delta f}$, where $k_B$ is the Boltzmann constant, $R_{sample}$ and $R_{coil}$ are sample and coil ohmic resistance respectively, whereas $\text{T}$ is the coil and sample temperature and $\Delta f$ is the receiver bandwidth. For low RF frequency, the noise caused by the sample resistance is small compared to the coil resistance [20, 21], we can simplify the $\text{SNR}$ as

$$SNR=\frac{B_1}{\sqrt{R_{coil}}}.$$ [5]

The single loop coil resistance can be approximated by the product of the loop coil’s diameter $\left(\text{D}\right)$ and resistivity $\left(\mathrm{\rho }\right)$ divided by the skin effect $\left(\mathrm{\delta }\right)$ and conductor cross section width ($w_1$ and $w_2$) and conductor thickness $\left(\text{t}\right)$ [9, 22]:

$$R_{Control}=\frac{\rho \left(\pi D_1\right)}{w_{1}t-\left(w_1-2\delta \right)\left(t-2\delta \right)},$$ [6]

where

$$\delta =\sqrt{\frac{\rho }{\pi {\mu }_{0}f}}.$$ [7]

$D_1$ and $D_2$ are secondary loop and primary loop diameters, respectively. The control coil has the same diameter and same conductor cross section width as the secondary loop. For the concentric-loop coils, the mutual inductance $\left(\text{M}\right)$ between the primary and the secondary loops needs to be considered (Fig. 2B), where $\text{M}$ is derived from Equations (1). The coil resistance of the concentric-loops coil in the real part is:

$$\begin{array}{l}{R}_{Concen}=real\left(R_p-\frac{{\left(j\omega M\right)}^2}{R_s-\frac{j}{\omega C_s}+j\omega L_s}\right)\hfill \\ =real\left(\frac{\rho \left(\pi D_2\right)}{w_{2}t-\left(w_2-2\delta \right)\left(t-2\delta \right)}-\frac{{\left(j\omega M\right)}^2}{\frac{\rho \left(\pi D_1\right)}{w_{1}t-\left(w_1-2\delta \right)\left(t-2\delta \right)}-\frac{j}{\omega C_s}+j\omega L_s}\right).\hfill \end{array}$$ [8]

The primary loop coil has a smaller coil dimeter $\left(D_2<D_1\right)$ and wider conductor cross section width $\left(w_2>w_1\right)$ than the control single loop coil (Fig. 1). Based on Equations (6) and (7), the primary loop resistance $\left({\text{R}}_{\text{p}}\right)$ is nearly 2-fold smaller than the single loop coil resistance $\left({\text{R}}_{\text{Control}}\right)$. The mutual inductance between the primary and secondary loops is 29 nH. At the Larmor frequency of 60.6 MHz (10.5T ¹⁷O), the primary loop inductance $\left({\text{L}}_{\text{p}}\right)$ is 70 nH, and the secondary loop or control single loop coil inductance $\left({\text{L}}_{\text{s}}\right)$ is 135 nH. Based on Equation (8), the concentric-loops coil resistance $\left({\text{R}}_{\text{Concen}}\right)$ is dominated by ${\text{R}}_{\text{p}}$ in the additive mode. Therefore, based on Equation (5), the noise voltage ratio between the single loop control and the concentric-loops $\left(\sqrt{R_{Control}}/\sqrt{R_{Concen}}\right)$ is in the range of 1.3–1.4, or 23 to 28% noise reduction in the concentric-loops design.

3. Method

3.1. Imaging coil setups:

For the concentric-loops coil, the secondary loop coil self-resonance $\left(f_{\text{s}}\right)$ is adjusted to 63 MHz for 10.5T ¹⁷O, 67MHz for 1.5T ¹H, and 125 MHz for 7T ³¹P imaging, while the reflection coefficients from the primary coil of the concentric-loops coil and the control single-loop coil are adjusted to < −20 dB for the actual Larmor frequencies at 60.6 MHz for 10.5T ¹⁷O , 63.8MHz for 1.5T ¹H, and 120.3 MHz for 7T ³¹P imaging under the loaded condition, respectively. A spherical phantom jar (16 cm diameter) filled with 50 mM NaCl solution and a cylindrical phantom filled with 50 mM NaCl solution are used as the imaging phantom for ¹⁷O MRSI at 10.5T. The RF coil is positioned 2cm away from the phantom during imaging. The Q-factors under unloaded and loaded condition using the spherical phantom for four different coil types: a secondary coil, a concentric-loops coil in subtractive mode, a concentric-loops coil in addictive mode and a primary loop coil are measured and presented in Table 1. The concentric-loops coil in the additive mode shows a slightly higher unloaded/loaded Q-factor ratio. For 7T ³¹P MRSI experiments, NaH₂PO₄ and Gadolinium (Gd) are added in the cylindrical phantom for shortening the inorganic phosphate (Pi) longitudinal relaxation time $\left({\text{T}}_1\right)$. All RF coils are used in transceiver mode.

Table 1.

Measured RF coil Q-factors under unloaded and loaded conditions using the a NaCl phantom for a single 5.5 cm diameter primary loop, a single 8-cm diameter secondary loop, a concentric-loops coil in additive mode, and a concentric-loops coil in subtractive mode.

RF coil	Unloaded Q-factor	Loaded Q-factor	Q-ratio (unloaded/loaded)
Single Primary loop (5.5-cm diameter)	250	120	2.1
Single Secondary loop (8-cm diameter)	350	70	5
Concentric-loops coil (Additive Mode)	400	65	6.2
Concentric-loops coil (Subtractive Mode)	50	30	1.7

3.2. MRSI/MRI Experiment:

The 10.5T ¹⁷O MRSI and 7T ³¹P MRSI experiments were performed on 10.5T and 7T human scanners (SIEMENS, Germany), respectively. The 3D Fourier Series Window Chemical Shift Images (FSW-CSIs) [23] were acquired. For the 10.5T ¹⁷O MRSI, , a field of view (FOV) of 17×17×17 and a matrix size of 19×19×15 were used for spherical phantom jar MSRI, and a FOV of 10×10×10 cm with a matrix size of 9×9×7 were used for cylindrical phantom MRSI. For ¹⁷O MRSI at10.5T, data were acquired with a 200ms repetition time (TR) under fully relaxed condition, using a 1ms excitation hard pulse, 30 kHz bandwidth and 1024 FID points. For ³¹P MRSI at 7T, we used 1s TR (fully relaxation condition with Gd), 5 kHz bandwidth, and 1024 FID points. We processed the CSI spectrum with zero filling, line broadening and zero-order phase correction. After obtaining a set of 3D CSI data acquired with gradually increasing RF pulse voltages, we fitted the set of spectral resonance signals over corresponding RF hard pulse voltages based on the “SINE” shape function to calculate and generate the transmit magnetic field ($B_1^{+}$ in absolute scale) and coil sensitivity ($B_1^{-}$ in relative scale) maps [24]. The real part of the CSI spectrum peak was used to determine the values of $B_1^{+}$ and $B_1^{-}$$\left(\propto \text{SNR}\right)$, where $B_1^{+}$ is inversely proportional to the RF hard pulse voltage for reaching a 90° RF pulse flip angle, and $B_1^{-}$ presents the maximum spectral signal $\left(S_{90°}\right)$ reached at 90° RF pulse flip angle (FA) under fully relaxed condition [24]. Additionally, we obtained the noise standard deviation $\left(\mathrm{\sigma }\right)$ from the CSI spectra acquired at 0-volt RF pulse voltage. The SNR maps were then obtained by normalizing the $B_1^{-}$ maps with the noise level.

The 1.5T ¹H MRI experiment was conducted on a custom 1.5T human scanner using similar imaging setup and phantom (Fig. S1). The actual flip-angle imaging (AFI) [25] was used to acquire the flip angle (FA) maps, with $\text{TR1}=180\text{ms}$,$\text{TE}=16\text{.2}\text{ms}$. The FA maps were then converted to relative transmit field strength $\left(B_1^{+}\right)$ by normalizing the FA maps with the actual pulse voltage used.

3.3. Electromagnetic simulations:

The electromagnetic (EM) simulation was performed in CST studio suite 2020 (Dassault Systèmes, Vélizy-Villacoublay, France). The hexahedral time-domain solver was used with a 0.5-mm isotropic resolution mesh. The RF coils were modeled with pure copper (electric conductivity = 5.966×e⁷ S/m), with no loss assumed for the lumped capacitors. For the EM simulation used in Fig. 3, a cubic phantom of 18cm side length were modeled with a relative permittivity $\left({\mathrm{\epsilon }}_{\text{r}}\right)$ of 79 and conductivity of 0.4 S/m. The RF coils are position 1.5cm above the top of the cubic phantom. For the EM simulation used in Fig. 4, a cylindrical phantom (8cm diameter, 8cm height) was modeled with ${\mathrm{\epsilon }}_{\text{r}}$ of 79, and conductivity of 0.4 S/m. The $B_1^{+}$ fields normalized by input voltage and coil surface currents are exported for analysis and investigation.

Figure 3.

(A) The electromagnetic (EM) simulation setup with a concentric-loops coil placed on the top of a cubic box phantom. (B) The current densities of the concentric-loops coil, showing the primary $\left({\text{I}}_{\text{p}}\right)$ and secondary $\left({\text{I}}_{\text{s}}\right)$ loop currents at $f\text{s}=58\text{MHz}$, where the current vectors on the primary and secondary loops flow in the opposite directions (subtractive mode), and at $f\text{s}=61\text{MHz}$, where the current vectors on the primary and secondary loops flow in the same direction (additive mode). (C) The EM simulation results showing the $B_1^{+}$ (transmit magnetic field) in RF coil and the cubic box phantom in the sagittal view for following RF coil setups: a single 8cm diameter loop coil (i.e., secondary loop coil only), a concentric-loops coil (both secondary and primary loops) in the subtractive mode, a concentric-loops coil in the addictive mode, and a single 5.5cm diameter loop coil (primary loop). The cylindrical phantom is outlined by white dashed line, and elevations from the coil plane at 0, 2, 4, 6 and 9cm are annotated. In all cases, the RF coils were matched and tuned to the 10.5T ¹⁷O Larmor frequency of 60.6MHz. (D) The 1D $B_1^{+}$ profiles within the phantom in vertical direction away from the RF coil plane (0cm) for the different RF coil setups. (E) The 1D $B_1^{+}$ profiles within the phantom in horizontal direction at elevations of 2, 4, 6 and 9cm above the RF coil plane for the different RF coil setups.

Figure 4.

(A) Spatial distributions of the simulated $B_1^{+}$ strength for the 8cm loop only, 8cm-6.5cm loops, 8cm-5.5cm loops, 8cm-2.5 cm loops. All coils are tuned and matched to 60.6 MHz at −20 dB. The white dashed line outlines the phantom jar. (B) One-dimensional $B_1^{+}$ plot through the cylindrical phantom. The x-axis indicates the vertical distance from the coil plane (at 0cm). The 8cm-5.5cm loops demonstrated 1.5- to 1.7- fold increase in $B_1^{+}$ compared the 8cm loop within the distance of 0–2.8cm above the coil plane.

Electric losses in the cubic phantom at 60.6 MHz were calculated and normalized to 1-watt RF input power for imaging with the concentric-loops coil in additive mode and the secondary loop coil as shown in Fig. S3. Both coils showed similar loss levels within the sample. On the other hand, the real part of the impedance measured at the driving port of the primary loop in the concentric-loops coil is approximately half that of the real part of the impedance measured at the driving port of the secondary loop coil, consistent with the prediction based on Equations (6) and (8).

4. Results

4.1. Surface current density and simulated $B_1$

The EM simulation setup is shown in Fig. 3A, and the current density vector plots on the primary and secondary loops of the concentric-loops coil under different $f_{\text{s}}$ conditions are shown in Fig. 3B. For all cases, the RF coils are tuned and matching at 60.6 MHz. The EM simulated current density vector plot agrees with the circuit analysis result shown in Fig. 2C. When $f_{\text{s}}=58\text{MHz}$, the ${\text{I}}_{\text{p}}$ and ${\text{I}}_{\text{s}}$ are in the subtractive mode and they flow in opposite directions, resulting in the $B_1^{+}$ cancelation; in contrast, when $f_{\text{s}}=61\text{MHz}$, the ${\text{I}}_{\text{p}}$ and ${\text{I}}_{\text{s}}$ are in the additive mode and they flow in the same direction, resulting in the enhanced $B_1^{+}$ in space. The optimum condition for concentric loops coil is achieved as the $f_{\text{s}}$ frequency is slightly above the Larmor frequency (61–64MHz) for the ¹⁷O MRSI at 10.5T. The sagittal view of the normalized $B_1^{+}$ rofile within the phantom for four different coil types: a secondary coil, a concentric-loops coil in subtractive mode, a concentric-loops coil in addictive mode and a primary loop coil are shown in Fig. 3C. The 1D $B_1^{+}$ field profiles in the vertical and horizontal directions are plotted in Fig. 3D and Fig. 3E, respectively. From 1.5cm to 4cm above the coil plane, the concentric-loops coil in the additive mode shows the strongest $B_1^{+}$ field in both center and periphery of the phantom, compared to other three RF coils. Compared to the secondary loop coil, the concentric-loops coil in the additive mode achieved a 1.2- to 1.4-fold $B_1^{+}$ enhancement from 1.5cm to 3cm depth. As approaching far region (9cm elevation from the coil plane), the $B_1^{+}$ field of the concentric-loops coil in the additive mode gradually approaches a similar level as the single-loop secondary coil.

4.2. Effect of the primary coil size

The overall strength of RF coil transmit field $\left(B_1^{+}\right)$ is also affected by the size of the primary loop. The spatial distributions of $B_1^{+}$ at 60.6 MHz (i.e., ¹⁷O Larmor frequency at 10.5T) for the control coil: “8cm loop” and the concentric-loops coils: “8cm+6.5cm loops”, “8cm+5.5cm loops”, and “8cm+2.5 cm loops” are shown in Fig. 4. In all cases, the secondary coil $f_{\text{s}}$ is tuned to within the optimum frequency range (61–64 MHz). At this condition, the concentric-loops coils are in the additive mode, where the magnetic flux density enclosed by the primary loop is enhanced. The 1D $B_1^{+}$ profiles (perpendicular to the coil center) through the jar phantom positioned on different types of coils are shown in Fig. 4B. For all concentric-loops coils with varied primary coil size, the $B_1^{+}$ within the phantom is significantly higher than that of the single-loop control coil, especially within the distance of 0–2cm from the coil plane. As the primary coil size decreases, $B_1^{+}$ near the coil grows larger, but becomes relatively weaker when away from the coil. For “8cm + 5.5cm loops”, the $B_1^{+}$ is slightly higher compared to other types of concentric-loops deigns for distance >1.5cm from the coil plane, and produced a 1.5- to 1.7-fold $B_1^{+}$ gain compared to the single-loop coil within a 0–2cm distance from the coil plane; thus, the “8cm + 5.5cm loops” concentric-loops coil was used for the phantom imaging experiment and testing.

4.3. Magnetic field sniffer measurements

Figure 5 shows the experimentally measured $B_1^{+}$ of the concentric-loops coil operating at the 10.5T ¹⁷O Larmor frequency of 60.6MHz, with the secondary loop tuned to different $f_{\text{s}}$ by adjusting the tuning capacitor $\left({\text{C}}_{\text{s}}\right)$ on the secondary loop. As illustrated in Fig. S1, the outer secondary loop is first tuned and fixed to a self-resonating frequency $f_{\text{s}}$, an inner primary loop is then placed on top of the secondary loop. The inner primary loop is connected to a vector network analyzer (VNA, Rohde & Schwarz ZNBT8 16-port VNA) via a coaxial cable. The concentric-loops loop is tuned and matched to the Larmor frequency (60.6 MHz) by only adjusting the trimmer capacitors on the primary loop. The output $B_1^{+}$ field at 2.8 cm above the center of the concentric-loops coil was measured using a 2cm diameter $B_1$ probe (Magnetic field sniffer, the method is described in [26]) coupled to the coil and connected to the VNA. Based on our calibration, 0dB measurement of the $B_1$ probe is 2 μT/volt. Figure 5 shows that the output $B_1^{+}$ field at 2.8cm above the center of an 8cm single-loop control coil (Fig. 1A) is −10dB (horizontal dashed line as a reference). When $f_{\text{s}}<60\text{MHz}$, the concentric-loops coil operates in the subtractive mode, and its $B_1^{+}$ is smaller than the control single-loop coil. When $f_{\text{s}}$ is between 61 to 64 MHz (optimal condition), the concentric-loops coil operates in the additive mode, and the $B_1^{+}$ at the same position becomes −6.2 dB, which is approximately 1.6-fold increase in $B_1^{+}$ compared to the single-loop control coil. This value is consistent to the EM simulation results (Fig. 4), which indicate approximately a 1.5-fold increase in $B_1^{+}$ for the “8cm +5.5cm” concentric loops coil compared to the “8cm” loop for 1.5–2 cm above the RF coil plane. When $f_{\text{s}}$ is > 65 MHz (beyond the optimal frequency range), the measured concentric-loops coil $B_1$ gradually decreases as the secondary loop $B_1$ diminishes and the primary loop $B_1$ becomes dominate. Thus, for concentric-loops coil of 60.6 MHz Larmor frequency, the optimum $f_{\text{s}}$ frequency range is 61–64 MHz.

Figure 5.

Bench-measured $B_1^{+}$ using a magnetic field sniffer at 2.8 cm above the center of concentric-loops coil operating at the 10.5T ¹⁷O Larmor frequency of 60.6 MHz, where the secondary loop self-resonating frequency $f_{\text{s}}$ is tuned to different values. For all cases, the concentric-loops coil is matched and tuned to the same Larmor frequency (60.6MHz). For comparison, the measured $B_1^{+}$ of an 8cm-diameter single-loop coil matched and tuned to 60.6 MHz is −10dB as indicated by the black dash line. When $f\text{s}\mathrm{<}60\text{MHz}$ (in the subtractive mode), the measured concentric-loops coil $B_1^{+}$ is smaller than the control single-loop coil. When $f\text{s}$ is between 61 to 64 MHz (in the additive mode, an optimal condition), the concentric-loops coil $B_1^{+}$ is approximately 1.6-fold higher compared to a single-loop coil. When $f\text{s}\mathrm{>}65\text{MHz}$, the concentric-loops coil $B_1^{+}$ decreases as the secondary loop $B_1^{+}$ diminishes and the primary loop $B_1$ becomes dominant.

4.5. MRS/MRI imaging results

Using a head-size spherical phantom, we performed 10.5T ¹⁷O (60.6MHz) MRSI with four different coil types: a secondary coil, a concentric-loops coil in subtractive mode, a concentric-loops coil in addictive mode and a primary loop coil. The resulting coil sensitivity maps within the phantom are summarized in Fig. 6. A 1.2–1.4 times signal gain was observed with the concentric-loops coil in the additive mode compared to the secondary loop (control) coil at 3–4 cm above the coil plane. At 9cm depth, a similar level of coil sensitivity is observed between the concentric-loops coil in the addictive mode and the secondary loop coil. These measurement results are consistent with the EM simulation findings shown in Fig. 3. Using a cylindrical phantom (Fig. S1), we conducted the 10.5T ¹⁷O and 7T ³¹P (120.3MHz) imaging tests, the $B_1^{-}$, $B_1^{+}$ and SNR maps of a cylindrical phantom imaged by the single-loop and concentric-loops coils are shown in Figs. 7A and 7B, respectively. We observed a 1.5- to 1.8-fold increase for 10.5T ¹⁷O imaging, and a 1.5-fold increase for 7T ³¹P imaging, respectively, in $B_1^{-}$ and $B_1^{+}$ within 0–2.2cm from the coil plane. In addition to the signal improvement, we also observed an approximately 30% reduction and 15% reduction in the 0-volt excitation voltage noise level in the 10.5T ¹⁷O and 7T ³¹P CSI, receptively, acquired using the concentric-loops coil. Overall, the $B_1$ improvement and noise reduction result in approximately 1.9- to 2.6-fold SNR gain for 10.5T ¹⁷O imaging, and 1.8-fold SNR gain for 7T ³¹P imaging using the optimal concentric-loops coil. The zoomed in spectra and spectral noise level for representative CIS voxels acquired by the single loop control and concentric-loops coil are demonstrated in Fig. 7C for 10.5T ¹⁷O and Fig. 7D for 7T ³¹P, respectively, for comparison, showing again large SNR improvement using the concentric-loops coil.

Figure 6.

(A) The RF coils fabricated on the PCB board. From left to right: a single 8cm diameter secondary loop, a concentric-loops coil (both secondary and primary loops) in the subtractive mode, a concentric-loops coil in the addictive mode, and a single 5.5cm diameter primary loop. For the concentric-loops and secondary loop coils, the capacitors are connected through vias on the bottom side of the PCB boards. All RF coils are tuned and matched to 10.5T ¹⁷O Larmor frequency of 60.6 MHz. (B) The ¹⁷O MRSI imaging setup using a 16cm diameter spherical phantom filled with 50mM NaCl solution. The RF coil are placed at 2cm above the imaging phantom. (C) Measured sagittal-view RF coil sensitivity ($B_1^{-}$, arbitrary units) within the phantom for the four RF coil setups shown in (A). (D) The 1D $B_1^{+}$ profiles within the phantom in the vertical direction, moving away from the RF coil plane (0cm), for the different RF coil setups. (E) The 1D $B_1^{+}$ profiles in the horizontal direction at elevations of 4cm and 9cm above the RF coil plane for the difference RF coil setups.

Figure 7.

(A) Three selective axial-orientation slices of the measured RF transmit magnetic field $\left(B_1^{+}\right)$, RF coil sensitivity $\left(B_1^{-}\right)$, and imaging SNR maps of the cylindrical phantom imaged by the 8cm single-loop and concentric-loops coil at Larmor frequency of 60.6 MHz for 10.5T ¹⁷O MRSI, and (B) at 120.3 MHz for 7T ³¹P MRSI. The SNR is calculated as the $B_1^{-}$ divided by the spectra noise level acquired at 0-volt pulse voltage. The 10.5T ¹⁷O concentric-loops coil shows a 1.5- to 1.8-fold gain in $B_1^{+}$ and $B_1^{-}$, and a 1.9- to 2.6-fold gain in SNR compared to the single-loop control coil, while the 7T ³¹P concentric-loops coil shows 1.5-fold gain in $B_1^{+}$ and $B_1^{-}$, and a 1.8-fold gain in SNR compared to the single-loop control coil. Representative CSI spectra (red arrows) and zoomed-in spectral noises for the concentric-loops coil and single-loop are shown in (C) for 10.5T ¹⁷O MRSI and (D) for 7T ³¹P MRSI, respectively, for comparison, indicating a denoising effect in the concentric-loops coil.

We also conducted a ¹H MRI study at 1.5T (63.8MHz), and the $B_1^{+}$ map results of the single-loop control coil and concentric-loops coil are shown in Fig. 8A. The $f_{\text{s}}$ was tuned to 66 MHz to optimize the performance of the concentric-loops coil at 63.8 MHz operating frequency. The 1D profiles of $B_1^{+}$ through the middle of the phantom are shown in Fig. 8C. Within the distance of 0–3 cm from the coil plane, the concentric-loops coil exhibits a 1.4- to 1.6-fold stronger $B_1^{+}$ compared to the single-loop coil again. In addition, the concentric-loops coil exhibits an 18% noise reduction compared to the single-loop coil (Fig. 8B), resulting in a near 1.7- to 1.9-fold SNR gain for the concentric-loops loops (Fig. 8D). For far regions (>50mm elevation from coil plane), the concentric-loops coil also achieved slightly enhanced $B_1^{+}$ (Fig. 8C) and SNR (Fig. 8D) compared to the single loop control coil.

Figure 8.

(A) The $B_1^{+}$ maps of the cylindrical saline jar phantom imaged by the single-loop and concentric- loops coils at 1.5T ¹H operating frequency (63.8 MHz). (B) The signal intensity distribution from the voxels outside of the phantom acquired using the small flip angle gradient echo imaging (GRE) was quantified to determine the noise levels for both coil types, indicating a 18% reduction in noise standard deviation $(\sigma )$ with the concentric-loops coil. (C) The 1D profiles of $B_1^{+}$ through middle of the phantom for both coil types, indicating 1.4- to 1.6-fold increases in $B_1^{+}$ for concentric-loops coil within the distance of 0–3 cm from the coil plane. (D) The 1D profiles of $B_1^{+}$ divided by the noise $(\sigma )$ through middle of the phantom for both coil types, showing a near 1.7- to 1.9-fold SNR gain within the distance of 0–3cm from the coil plane for the concentric-loops compared to the single-loop coil.

4.6. Application in array coils

Concentric-loops coils can also be decoupled from each other using the geometric overlapping method, as shown in Fig. 9A, thus, to construct array coils. With an optimize overlap distance, we can achieve a good decoupling $\left({\text{S}}_{12}=-15\text{dB}\right)$ between the two adjacent concentric-loops coils, while the overly overlapped case results in split peaks in ${\text{S}}_{11}$ and worse decoupling $\left({\text{S}}_{12}=-6\text{dB}\right)$ as shown in Fig. 9B. The imaging results using two decoupled concentric-loops coils in the additive mode are shown in Figs. 9C & 9D. The quadrature driving concentric-loops array coils achieved the theoretic $\sqrt{2}\text{SNR}$ gain (i.e., 1.4-fold gain) within the phantom compared to the single-mode driven concentric-loops coil.

Figure 9.

(A) Two overlapped concentric-loops coils driving in quadrature mode are placed 2cm above an imaging phantom for ¹⁷O MRSI measurement at 10.5T. Each concentric-loops coil in the additive mode is fabricated on a PCB board and tuned and matched to Larmor frequency = 60.6 MHz (¹⁷O at 10.5T). (B) Under loaded conditions, the network analyzer shows the two optimally overlapped, matched-tuned concentric-loops coils were decoupled at −15 dB, while the non-optimally overlapped concentric-loops coils were decoupled at −6 dB. (C) The 1D coil sensitivity $\left(B_1^{-}\right)$ profiles within the phantom in vertical direction moving away from the RF coil plane (0cm) for single-mode driving (one concentric-loops coil) and quadrature-mode driving (two concentric-loops coils). The sensitivity ratio between the two modes closely matches the theoretical ratio of $\surd 2$. (D) Sagittal-view coil sensitivity maps within the phantom for single-mode concentric-loops coil and quadrature-mode driving concentric-loops coils, respectively.

5. Discussion

Both equivalent circuit analysis and EM simulation results show that by adjusting the tuning capacitor on the secondary loop the concentric-loops coil can operate in an additive mode where the currents in both primary loop and secondary loop flow in the same direction, generating an enhanced $B_1$ (transmit and receive magnetic fields) within the area enclosed by the primary loop, for both near coil and in distant regions in the phantom compared to the control single-loop coil. Conversely, the concentric-loops coil can operate in a subtractive mode: where currents in primary loop and secondary loop flow in the opposite directions, generating a reduced $B_1$. Using a concentric-loops coil with an optimized primary loop coil size and operated in the additive mode, we are able to achieve approximately 1.2–1.4-fold increase in $B_1^{+}$ and $B_1^{-}$ in imaging phantom within the distance of 0–3 cm from the coil plane than the control single-loop coil at 10.5T ¹⁷O (60.6MHz), 1.5T ¹H (63.8MHz), and 7T ³¹P (120.3MHz) operating Larmor frequencies, as compare to a single secondary loop coil. Additionally, slightly enhanced $B_1$ is observed for far region in the phantom using the concentric-loops coil compared to control single-loop coil (8cm diameter) at 4–8cm, with equal $B_1$ levels at 9cm. In addition, the concentric-loops coil’s ohmic resistance is dominated by the smaller primary coil with less ohmic resistance and exhibits noise reduction of 30% at 10.5T ¹⁷O, 18 % at 1.5T ¹H and 15% at 7T ³¹P operating frequency compared to the single-loop coil. As Larmor frequency increases, we observed less noise reduction as the sample noise becomes dominant compared to the coil noise [1, 7, 8]. However, our noise study did not consider other factors such the noise figure of the pre-amplifier and the noise introduced by RF cable resonance. Further investigations are needed to quantify the noise performance of the proposed concentric-loops at different RF frequencies. Overall, we observed 1.7-fold SNR gain for 10.5T ¹⁷O, 1.5T ¹H and 7T ³¹P imaging with the optimized coil design compared to the traditional single-loop coil in the near-coil imaging region.

The concentric-loops design provides a simple coil geometry to largely improve the coil sensitivity and boost imaging SNR. However, the mutual inductance between the secondary and primary loops calculated in Equation (1) does not consider the wave-effects. For an RF coil loop size of 8cm, the quasi-static approximation is valid up to 120 MHz. Thus, our concentric-loops design should be valid for RF frequencies in the range up to 120 MHz. This concentric-loops coil design can be effectively applied to array coil designs for ultrahigh field (7T) X-nuclei (e.g., ²H, ¹⁷O, ¹³C, ²³Na and ³¹P) MR or MRS imaging applications [2–5] or relative low field (≤3T) and very low field (≤0.5T) proton MRI. To optimize the concentric-loops coil for stronger $B_1^{+}$ and higher SNR at a given Larmor frequency, the $f_{\text{s}}$ should be increased slightly above the Larmor frequency by a few MHz, for instance, the optimum $f_{\text{s}}$ is within the 61–64 MHz for 10.5T ¹⁷O imaging, 65–67 MHz for 1.5T ¹H, and 121–125 MHz for 7T ³¹P imaging. Additional consideration should be given to the size of the primary coil. Based on EM simulation, we found the optimum coil size of the primary loop size is approximately 68% of the diameter of the secondary loop size.

6. Conclusion

We present a novel concentric-loops coil design and optimization strategy to achieve stronger $B_1^{+}$, $B_1^{-}$ and higher SNR compared to a single-loop coil as confirmed by EM simulation, bench tests and MRI/MRS experimental results for three nuclei imaging at different field strengths. In addition, moderate to significant noise reduction using the concentric-loops coil was predicted then confirmed in all MRI/MRS experimental results, which further boost SNR. This novel coil design can be adapted for broad MRI and MRS imaging applications with significantly improved coil sensitivity and imaging performance as compared to the traditional single-loop coil.

Supplementary Material

1

Supplemental Figure S1. (A) Separate secondary (8cm diameter) and primary (5.5 cm diameter) loops allows us to adjust the self-resonance frequency of the secondary loop (f_s) independently. (B) After adjusting f_s, the primary and secondary loops are stacked together as the concentric-loops coil for MRSI/MRI study at 10.5T ¹⁷O (60.6 MHz) and 1.5T ¹H (63.8 MHz). (C) The single-loop control coil (8cm diameter). (D) The imaging setup with a coil beneath a cylindrical phantom filled with 50mM NaCl.

Supplemental Figure S2. The control 8-cm diameter loop coil and the concentric-loops coil for MRSI/MRI study at 7T ³¹P (120.7 MHz). The coils are fabricated on the PCB boards and capacitors are connected through vias on the bottom side of the PCB boards.

Supplemental Figure S3. Electrical loss within a cubic phantom NaCl phantom for control and concentric loop condition at 60.6 MHz (10.5T ¹⁷O). Both conditions show a similar level of loss within the sample.