Design and numerical evaluation of a volume coil array for parallel MR imaging at ultrahigh fields
Original Article

Design and numerical evaluation of a volume coil array for parallel MR imaging at ultrahigh fields

Yong Pang1, Ernest W.H. Wong2, Baiying Yu3, Xiaoliang Zhang1,4,5

1Department of Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, CA, USA; 2Agilent Technologies, Santa Clara, CA, USA; 3Magwale, Palo Alto, CA, USA; 4UC Berkeley/UCSF Joint Graduate Group in Bioengineering, San Francisco & Berkeley, CA, USA; 5California Institute for Quantitative Biosciences (QB3), San Francisco, CA, USA

Corresponding to: Xiaoliang Zhang, PhD. Department of Radiology and Biomedical Imaging, University of California San Francisco, Byers Hall, Room 102D, 1700 4th ST, San Francisco, CA 94158-2330, USA. Email:

Abstract: In this work, we propose and investigate a volume coil array design method using different types of birdcage coils for MR imaging. Unlike the conventional radiofrequency (RF) coil arrays of which the array elements are surface coils, the proposed volume coil array consists of a set of independent volume coils including a conventional birdcage coil, a transverse birdcage coil, and a helix birdcage coil. The magnetic fluxes of these three birdcage coils are intrinsically cancelled, yielding a highly decoupled volume coil array. In contrast to conventional non-array type volume coils, the volume coil array would be beneficial in improving MR signal-to-noise ratio (SNR) and also gain the capability of implementing parallel imaging. The volume coil array is evaluated at the ultrahigh field of 7T using FDTD numerical simulations, and the g-factor map at different acceleration rates was also calculated to investigate its parallel imaging performance.

Keywords: Volume coil array; birdcage coil; transverse birdcage coil; helix birdcage coil; signal-to-noise ratio (SNR); g-factor map; parallel imaging

Submitted Jan 15, 2014. Accepted for publication Feb 26, 2014.

doi: 10.3978/j.issn.2223-4292.2014.02.07


Radiofrequency (RF) coil arrays with a set of surface coils (1-7) become more popular in MR imaging as they can provide improved signal-to-noise ratio and the capability of performing parallel imaging (8-30). Compared with surface coils, RF volume coils, such as birdcage coils (31), are able to generate homogenous magnetic fields (B1) and potentially uniform MR images (17,32-36,37-53). In recent years it has been demonstrated that multiple tuned volume coils for multiple nuclear MR applications (54) can be designed by integrating different type of birdcage coils which are intrinsically decoupled due to the cancellation of their magnetic flux. In this work, we propose and investigate a single tuned proton volume coil array based on that design concept using combination of different typed birdcage coils for improving SNR (31) and also for implementing parallel imaging (55-59) and parallel transmission (60-65) to accelerate imaging. To demonstrate the design concept, a 3-channel volume coil array was designed, which consists of a conventional birdcage coil, a transverse birdcage coil, and a helix birdcage coil. All the three coils were intrinsically decoupled and tuned to 298 MHz which is corresponding to proton frequency at 7T. By taking advantage of the intrinsic decoupling feature, this volume coil array can be designed without using any decoupling circuitry between array elements. The performance of the volume coil array is evaluated using FDTD numerical simulation (39,66-69) in terms of the RF field distribution and mutual coupling. The parallel imaging performance of the 3-element volume coil array was also evaluated by calculating the g-factor map (56) at different acceleration rates for SENSE reconstruction.


The structure of the proposed multichannel volume coil array is shown in Figure 1. The inner coil is a 16-strut low-pass helix birdcage coil with 3 cm ID, the middle coil is a 16-strut birdcage coil with 3.8 cm ID, while the outer coil is a conventional birdcage coil with 4.5 cm ID. The coils were all built using copper tape and the coil length was 4 cm. Capacitors were place on each strut and used to tune the resonant frequency to 298 MHz. The coaxial feed port was modeled as a voltage source with 50 Ohm impedance. The software XFDTD6.4 (Remcom Inc., State College, PA, USA) was used to model this 3-channel birdcage coil array and evaluate the magnetic field distribution. The Yee cell size was 0.5 mm on both the transverse plane and longitudinal direction which was small enough for satisfying the accuracy requirement of the FDTD calculation. The boundary condition was set as Perfectly Matching Layers (PML). To ensure the calculation stability and accurate performance of the PML absorbing boundaries, in each direction 20 Yee cells of free space padding were placed between the PML boundary and the conducting materials. The Gauss waveform was used to sweep frequency to determine the proper capacitance value for each volume coil working at 298.2 MHz, and the stop criteria were that the calculation converged to –30 dB. Then, after obtaining the capacitance, the sinusoid waveform was used to calculate the RF field distributions and the stop criteria were set as the calculation converged to –30 dB.

Figure 1 The 3-channel volume coil array consists of 3 different birdcage coils: (A) Conventional birdcage coil (outer); (B) Transverse Birdcage coil (middle); and (C) Helix birdcage coil (inner); (D) The volume coil array.

To demonstrate the parallel imaging performance of the proposed 3-element volume coil array, the g-factor maps at different acceleration rates were calculated and plotted based on the RF field distribution calculated from the FDTD simulation by using the equation below (56):


where ρ is the index of voxel in the FOV, S is the reduced Fourier encoding, ψ is the noise correlation matrix between channels. The g-factor is strongly depends on the voxel position and is related to the signal to noise ratio (SNR):


where R is the acceleration rate, showing that the SNR of the accelerated image is inversely proportional to the g-factor.


The simulated B1 field distribution is shown in Figure 2. The 1st row is the results of the conventional birdcage; the 2nd row is the results of the transverse birdcage coil, while the 3rd row is the helix birdcage coil. The left column results are the B1 field distribution of each coil when combined together as a birdcage coil array, while the right column results are the B1 distribution of each individual coil. It is clearly shown that, the B1 field distribution of each birdcage coil within the volume coil is almost the same as that of the individual coil, demonstrating excellent isolation between the three channels. The Blue arrows in the figures denote the direction of the magnetic field flux density. In a conventional birdcage coil, the B1 direction are along one direction within the whole coil; in a transverse birdcage coil, the B1 direction of the two half is opposed to each other; while in the helix birdcage coil, the B1 direction in one slice is the same, but along longitudinal direction the B1 direction varies from 0° to 360°, therefore its net magnetic flux is zero. Thus the flux from one coil to the others is theoretically zero, leading to excellent decoupling between each pair of birdcage coils.

Figure 2 Left column, B1 pattern of each volume coil when put in the 3-channel birdcage coil array; Right column, B1 pattern of each individual volume coil when stand alone. 1st row, The B1 pattern of the conventional birdcage coil; 2nd row, B1 pattern of the transverse birdcage coil; 3rd row, B1 pattern of the helix birdcage coil. The B1 pattern of the birdcage coil in the array is the same as that of an individual coil with same type, demonstrating the excellent decoupling performance between the 3 birdcage coils within the 3-channel birdcage coil array. The blue arrow denotes the magnetic flux direction in the birdcage coils. The green arrows in the Helix birdcage coil denote that the magnetic flux direction in transverse plane are identical, but varies along the longitudinal axis, therefore the net flux is zero.

Figure 3 shows the sensitivity maps and phase maps on transverse plane of the three volume coil elements when fed individually. This transverse plane is the central slice. Each element shows different B1 distribution, leading to different sensitivity maps which can be used for parallel imaging. Figure 4 shows the g-factor maps for 1D SENSE reconstruction at different acceleration rates: R =1.2, 1.5, 1.7, 2.0, 2.3 and 2.5. The acceleration rate and the corresponding average g-factor are shown on the top of each g-map. It is demonstrated that with the increase of the acceleration the average g-factor increases (Figure 5). At acceleration rate of 2, the g-factor is around 1.5, which is practically good for performing parallel imaging for this 3-element coil array.

Figure 3 The transverse sensitivity maps of each array element at the central slice: (A) Conventional birdcage coil; (B) Transverse birdcage coil; (C) Helix birdcage coil. The phase maps of the B1 field of each array element: (D) Conventional birdcage coil; (E) Transverse birdcage coil; (F) Helix birdcage coil.
Figure 4 G-factor maps for 1D SENSE reconstruction at acceleration rate R =1.2, 1.5, 1.7, 2, 2.3 and 2.5. At reduction factor of 2, the g-factor is approximately 1.5, which is adequate for this 3-element coil array.
Figure 5 The average g-factor varies with the acceleration rate from (1.2 to 3).

Discussion and conclusions

In this work, a novel volume coil array design using different types of birdcage coils is proposed for MR imaging. The resonant elements of this volume coil array are a conventional birdcage coil, a transverse birdcage coil and a helix birdcage coil. The field behavior and the parallel imaging performance of the volume coil array have been investigated using numerical simulations and SENSE parallel imaging algorithm. The studies verify the theoretical expectation on electromagnetic decoupling performance of these birdcage coil elements, demonstrating the feasibility of this volume coil array design technique. From the results it can be seen that the three birdcage coils are deeply decoupled from each other due to their unique magnetic flux directions resulting in the net magnetic flux cancellation in both the transverse birdcage coil and the helix birdcage coil. In this design method with intrinsic decoupling feature, there is no dedicated decoupling circuits needed, making the volume coil array design simple and practical. Each element of a volume coil array has bigger imaging coverage than that of conventional surface coil arrays, which may potentially lead to a better g-factor and ultimately improved parallel imaging performance, particularly in imaging with large field-of-view (FOV). Compared with conventional non-array volume coils, the volume coil array is expected to provide increased SNR in MR imaging. Typical magnetic field distribution of surface coil arrays is not uniform over the FOV, showing strong gradient behavior with much higher signal intensity in the peripheral area and weak signal in the center region. With the volume coil array, more uniform SNR distribution can be expected across a large volume.


This work was partially supported by NIH grants EB004453, EB008699, K99EB015487 and P41EB013598, a QB3 Research Award, a Springer Med Fund Award, and a National Natural Science Foundation of China Grant (51228702).

Disclosure: The authors declare no conflict of interest.


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Cite this article as: Pang Y, Wong EWH, Yu B, Zhang X. Design and numerical evaluation of a volume coil array for parallel MR imaging at ultrahigh fields. Quant Imaging Med Surg 2014;4(1):50-56. doi: 10.3978/j.issn.2223-4292.2014.02.07

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