Precompensation for mutual coupling between array elements in parallel excitation
Cite this article as: Pang Y, Zhang X. Precompensation for mutual coupling between array elements in parallel excitation. Quant Imaging Med Surg 2011;1:4-10. DOI: 10.3978/j.issn.2223-4292.2011.11.02
Original Article
Precompensation for mutual coupling between array elements in parallel excitation
Yong Pang1, Xiaoliang Zhang1,2
1Department of Radiology and Biomedical Imaging, University of California San Francisco, San Francisco, CA, United States; 2UCSF/UC Berkeley Joint Graduate Group in Bioengineering, San Francisco & Berkeley, CA, United States
Corresponding to: Xiaoliang Zhang, PhD. Dept. of Radiology and Biomedical Imaging, University of California San Francisco, Byers Hall, Room 102, 1700 4th ST, San Francisco, CA94158-2330, USA. Tel: 1-415-514-4801. Email: xiaoliang.zhang@ucsf.edu.
Abstract
Parallel transmission or excitation has been suggested to perform multi-dimensional spatial selective excitation to shorten the pulse width using a coil array and the sensitivity information. The mutual coupling between array elements has been a critical technical issue in RF array designs, which can cause artifacts on the excitation profile, leading to degraded excitation performance and image quality. In this work, a precompensation method is proposed to address the mutual coupling effect in parallel transmission by introducing the mutual coupling coefficient matrix into the RF pulses design procedure of the parallel transmission. 90° RF pulses have been designed using both the original transmit SENSE method and the proposed precompensation method for RF arrays with non-negligible mutual coupling, and their excitation profiles are generated by simulating the Bloch equation. The results show that the mutual coupling effect can be effectively compensated by using the proposed method, yielding enhanced tolerance to insufficient mutual decoupling of RF arrays in parallel excitation, ultimately, providing improved performance and accuracy of parallel excitation.
Key words
Parallel transmission; mutual coupling; transmit SENSE; transceiver array; Bloch equation
Quant Imaging Med Surg 2011;1:4-10. DOI: 10.3978/j.issn.2223-4292.2011.11.02
Introduction
Multidimensional spatially selective RF pulses have been used in MRI to limit the electromagnetic signal emitted from the imaging object within arbitrarily shaped and spatially restricted areas (1-6). This approach requires homogeneous radiofrequency (RF) field to ensure the accuracy of the excitation profile, especially for spin echo imaging. This requirement has impeded the further development and application of multidimensional spatial RF pulses to ultrahigh field MRI (7 Tesla and beyond) (7-13) in which homogeneous RF field is difficult to be achieved (8,14-18) due to the high frequency wave effect in the conductive and high dielectric imaging object such as human body (19). To achieve homogeneous RF field distribution and shorten the pulse width, parallel transmission (20-28) is suggested to perform spatial selective excitation using a coil array and the sensitivity information of each element. The amplitude and phase of each element are independently controlled to manipulate the RF field distribution within imaging object to ultimately achieve B1 homogeneity (29,30). The parallel transmission can be used not only in small-tip-angle excitation, but also in large-tip-angle excitation and refocusing pulses at ultrahigh fields (31-33). Although the average and local specific absorption ratio (SAR) increase with the acceleration factor in parallel transmission (34), the SAR can be optimized using different strategies such as variable sampling rate or optimized k-space trajectories (21,35-38), providing feasible ways to make tradeoffs between the acceleration factor and the power deposition.
The mutual coupling has been a critical problem in RF coil array design (39,40), especially at ultrahigh fields where the imaging sample mediates the mutual coupling among the array elements (9,11,12,29,41-43). Comparing with the situation in parallel reception, this decoupling problem becomes more critical in parallel transmission, deteriorating the excitation accuracy and degrading the image quality. Although a variety of decoupling schemes have been developed to address the issue (12,14,29,40,42-46), insufficient decoupling among array elements is still a major problem hindering the development and application of parallel transmission.
In this work, a precompensation method is proposed to address the mutual coupling effect in transmit SENSE by introducing the mutual coupling coefficient matrix into the RF pulses design procedure of the transmit SENSE. Studies show that by using this precompensation technique, the mutual coupling effect on the excitation pattern can be compensated by using the corrected RF pulses as long as the mutual coupling between array elements is not high enough to cause a clear split of the element resonance peak, or in a weakly coupling case. This precompensation technique provides a valuable approach to performance optimization of transmit SENSE or parallel excitation using multichannel RF transmit arrays with non-negligible mutual coupling between array elements.
Theory and methods
The transmit SENSE uses coil array to excite the spins to achieve the desired profile. For an R-element array, the desired excitation pattern can be described by the superposition of all the individual pulse profiles weighted by the corresponding sensitivity profiles, which is described as below:
where Pdes(x) is the desired pattern, Sn(x) and Pn(x) are the complex sensitivity profile and the pulse profile of the nth coil, respectively. The profile Pn(x) of each coil can be expressed as:
where M0 is the initial magnetization, B1,n(t) denotes the RF pulse of the nth element of the array. G(t) and S(k(t)) are the accompanying gradient and the spatial frequency sampling function respectively. k(t) is the k-space trajectory defined by the gradient function G(t). By defining
the Eq.[2] can be rewritten as
Then, the mutual coupling between the array elements is introduced into the calculating procedure. Assuming the mutual coupling coefficient between the mth coil and the nth coil is cm,n, the excitation pattern of the mth coil becomes:
Thus, the desired excitation pattern Pdes(x) can be expressed as the superposition of all the individual patterns weighted by the sensitivity patterns:
where Sm(x) is the sensitivity of the mth coil. Thus, from Eq.[4] and (6) the Eq.[1] can be rewritten as:
or
where S* n (x) is defined as
Eq.[8] is similar to the central equation of transmit SENSE. The difference is the sensitivity pattern S*n (x) equals the sum of all the individual sensitivity patterns multiplied by the corresponding mutual coupling coefficient. This corresponds to the compensation for the mutual coupling effect in the excitation procedure. The following steps for designing the pulses are the same as that in transmit SENSE: the spatial coordinate x can be discretized to vectors first, and the Pdes(x), Pn(x) and S*n (x) can be rewritten as vectors; then these three vectors can be transformed to k-space style by convolution and by choosing proper k-space trajectory and the full size variable Pfull(x) and S*full(x) can be obtained; finally, the individual excitation pattern Pn(x) under the effect of mutual coupling can be calculated by solving the inverse problem and each individual RF pulse can be obtained by the k-space analysis method. The flowchart of the improved transmit SENSE with precompensation method is shown in Figure 1.
To investigate the feasibility and the effectiveness of the proposed method, a simple example of transmit SENSE is simulated by solving the Bloch equation. Excitation pulses were designed using transmit SENSE and the precompensation method respectively for comparison. In both methods, the same spiral trajectory with 12 turns was used. The max value of k-space extension was 0.5 cycle/cm. The desired excitation pattern was a cylinder with 10 cm diameter, whose 2D profile is shown in Figure 2A. The desired pattern was excited using a 4-element array with the reduction factor of 2. The sensitivity patterns of each element are shown in Figure 2B-E. The mutual coupling coefficient matrix between the elements is shown in Figure 3. The proposed precompensation method was applied to design the excitation pulses for implementing the transmit SENSE using the RF arrays with nonnegligible mutual coupling between elements.
Figure 1. Flowchart of the RF pulse design procedure using the precompensation method in parallel excitation with multichannel transmit array.
Figure 2. (A) Desired excitation profile; (B-E) intrinsic sensitivity pattern of each array element.
Figure 3. Mutual coupling coefficients between array elements.
Results
The conventional transmit SENSE method was applied to design the excitation pulses for parallel excitation with the 4-element transmit array in which non-negligible mutual coupling between array elements exists. Based on these pulses, the excitation pattern of each array element was generated and plotted, as illustrated in Figure 4.(A)-(D). The resulting excitation patterns were also calculated. When the pulses were designed based on conventional transmit SENSE, the artifacts in the resulting excitation pattern is unable to be cancelled by each other. This leads to the deteriorated excitation pattern with the residual aliasing artifacts, as shown in Figure 4.(E). It is expected that the distortion of excitation pattern will become worse when the electromagnetic coupling between array elements increases.
With the use of the proposed precompensation method, the specific RF pulses were designed by taking the mutual coupling coefficients into calculation for each array element. By using these RF pulses, the mutual coupling between the elements can be compensated. The artifacts in the excitation pattern of each element (Figure 4.(F)-(I)) can be potentially cancelled by each other through superposition, resulting in reduced artifacts in the resulting excitation pattern, as shown in Figure 4.(J). The improved parallel excitation performance using the proposed method over the conventional transmit SENSE indicates that the mutual coupling effect of the imperfectly designed transmit array can be efficiently corrected by the precompensation technique.
Figure 4. The excitation profiles of a 4-element coil array with non-negligible mutual coupling between array elements: (A-D) individual excitation pattern of each element using conventional transmit SENSE; (E) the resulting excitation pattern from 4 elements, showing that the aliasing in excitation profile of each element is unable to be cancelled, leading to considerable artifacts; (F-I) individual excitation pattern of each element using the proposed precompensation method; (J) the resulting excitation pattern, showing that the artifacts caused by the mutual coupling of array elements are significantly reduced due to the artifact cancellation of each element profile, yielding an improved excitation profile.
Discussion
In this work, the mutual coupling coefficients between array elements have been taken into the pulses design procedure of transmit SENSE. The sensitivity patterns of all the elements are multiplied by the corresponding mutual coupling coefficient and then added together to form new sensitivity patterns. The central equation of the superposition of all the individual patterns multiplied by the sensitivity pattern is modified although the pulse design procedure is the same as that in the conventional transmit SENSE. Thus, each individual pattern can be obtained by solving the same inverse problem in transmit SENSE, and each individual RF pulse can be calculated according to the k-space analysis method.
The results of the transmit SENSE studies with a 4-element coil array by simulating the Bloch equation have demonstrated the proposed precompensation method is feasible to diminish the artifacts caused by the mutual coupling between the elements, making the parallel excitation method more tolerant to mutual coupling in RF transmit arrays, ultimately improving the quality of excitation. This is very helpful for parallel excitation because current decouple methods are unable to thoroughly eliminate the mutual coupling in RF transmit arrays. Combining this precompensation method and conventional decouple schemes together for multi-channel excitation has potential to decrease excitation artifacts and improve the excitation profile accuracy. Although this method is validated by using transmit SENSE in this work, it can also be applied to other parallel excitation methods such as the spatial domain method.
Acknowledgment
This work was partially supported by NIH grants EB004453, EB008699, EB007588-03S1 and P41EB013598, and a QB3 Research Award.
References
  • Pauly JM, Nishimura DG, Macovski A. Introduction to: A k-space analysis of small-tip-angle excitation. J Magn Reson 2011. [Epub ahead of print].
  • Pauly JM, Nishimura D, Macovski A. A linear class of large-tip-angle selective excitation pulses. J Magn Reson 1989;82:571-87.
  • Hardy CJ, Cline HE. Spatial localization in 2 dimensions using NMR designer pulses. J Magn Reson 1989;82:647-54.
  • Hardy CJ, Cline HE. Broadband nuclear magnetic resonance pulses with two-dimensional spatial selectivity. J Appl Phys 1989;66:1513-6.[LinkOut]
  • Yuan J, Zhao TC, Tang Y, et al. Reduced field-of-view single-shot fast spin echo imaging using two-dimensional spatially selective radiofrequency pulses. J Magn Reson Imaging 2010;32:242-8.[LinkOut]
  • Yuan J, Madore B, Panych LP. Spatially varying fat-water excitation using short 2DRF pulses. Magn Reson Med 2010;63:1092-7.[LinkOut]
  • Lei H, Zhu XH, Zhang XL, et al. In vivo 31P magnetic resonance spectroscopy of human brain at 7 T: an initial experience. Magn Reson Med 2003;49:199-205.[LinkOut]
  • Vaughan JT, Garwood M, Collins CM, et al. 7T vs. 4T: RF power, homogeneity, and signal-to-noise comparison in head images. Magn Reson Med 2001;46:24-30.[LinkOut]
  • Wiggins GC, Potthast A, Triantafyllou C, et al. Eight-channel phased array coil and detunable TEM volume coil for 7 T brain imaging. Magn Reson Med 2005;54:235-40.[LinkOut]
  • Yacoub E, Van De Moortele PF, Shmuel A, et al. Signal and noise characteristics of Hahn SE and GE BOLD fMRI at 7 T in humans. Neuroimage 2005;24:738-50.[LinkOut]
  • Wu B, Wang C, Krug R, et al. 7T human spine imaging arrays with adjustable inductive decoupling. IEEE Trans Biomed Eng 2010;57:397- 403.[LinkOut]
  • Li Y, Xie Z, Pang Y, et al. ICE decoupling technique for RF coil array designs. Med Phys 2011;38:4086-93.[LinkOut]
  • Pang Y, Zhang X, Xie Z, et al. Common-Mode Differential-Mode (CMDM) Method for Double-Nuclear MR Signal Excitation and Reception at Ultrahigh Fields. IEEE Trans Med Imaging 2011;30:1965-73.[LinkOut]
  • Zhang X, Ugurbil K, Chen W. Microstrip RF surface coil design for extremely high-field MRI and spectroscopy. Magn Reson Med 2001;46:443-50.[LinkOut]
  • Zhang X, Ugurbil K, Sainati R, et al. An inverted-microstrip resonator for human head proton MR imaging at 7 tesla. IEEE Trans Biomed Eng 2005;52:495-504.[LinkOut]
  • Ibrahim TS, Lee R, Baertlein BA, et al. Effect of RF coil excitation on field inhomogeneity at ultra high fields: a field optimized TEM resonator. Magn Reson Imaging 2001;19:1339-47.[LinkOut]
  • Collins CM, Yang QX, Wang JH, et al. Different excitation and reception distributions with a single-loop transmit-receive surface coil near a headsized spherical phantom at 300 MHz. Magn Reson Med 2002;47:1026-8.[LinkOut]
  • Zhang X, Ugurbil K, Chen W. A microstrip transmission line volume coil for human head MR imaging at 4T. J Magn Reson 2003;161:242-51.[LinkOut]
  • Yang QX, Wang J, Zhang X, et al. Analysis of wave behavior in lossy dielectric samples at high field. Magn Reson Med 2002;47:982-9.[LinkOut]
  • Katscher U, Bornert P, Leussler C, et al. Transmit SENSE. Magn Reson Med 2003;49:144-50.[LinkOut]
  • Zhu Y. Parallel excitation with an array of transmit coils. Magn Reson Med 2004;51:775-84.[LinkOut]
  • Grissom W, Yip CY, Zhang Z, et al. Spatial domain method for the design of RF pulses in multicoil parallel excitation. Magn Reson Med 2006;56:620-9.[LinkOut]
  • Katscher U, Bornert P. Parallel RF transmission in MRI. NMR Biomed 2006;19:393-400.[LinkOut]
  • Katscher U, Börnert P, van den Brink JS. Theoretical and numerical aspects of transmit SENSE. IEEE Trans Med Imaging 2004;23:520-5.[LinkOut]
  • Lee D, Lustig M, Grissom WA, wt al. Time-optimal design for multidimensional and parallel transmit variable-rate selective excitation. Magn Reson Med 2009;61:1471-9.[LinkOut]
  • Ma C, Xu D, King KF, et al. Joint design of spoke trajectories and RF pulses for parallel excitation. Magn Reson Med 2010. [Epub ahead of print].
  • Yip CY, Grissom WA, Fessler JA, et al. Joint design of trajectory and RF pulses for parallel excitation. Magn Reson Med 2007;58:598-604.[LinkOut]
  • Zhang Z, Yip CY, Grissom W, et al. Reduction of transmitter B1 inhomogeneity with transmit SENSE slice-select pulses. Magn Reson Med 2007;57:842-7.[LinkOut]
  • Adriany G, Van de Moortele PF, Wiesinger F, et al. Transmit and receive transmission line arrays for 7 Tesla parallel imaging. Magn Reson Med 2005;53:434-45.[LinkOut]
  • Wu B, Wang C, Lu J, et al. Multi-Channel Microstrip Transceiver Arrays Using Harmonics for High Field MR Imaging in Humans. IEEE Trans Med Imaging 2011. [Epub ahead of print].
  • Grissom WA, Yip CY, Wright SM, et al. Additive angle method for fast large-tip-angle RF pulse design in parallel excitation. Magn Reson Med 2008;59:779-87.[LinkOut]
  • Setsompop K, Alagappan V, Zelinski AC, et al. High-flip-angle sliceselective parallel RF transmission with 8 channels at 7 T. J Magn Reson 2008;195:76-84.[LinkOut]
  • Xu D, King KF, Zhu Y, et al. A noniterative method to design large-tip-angle multidimensional spatially-selective radio frequency pulses for parallel transmission. Magn Reson Med 2007;58:326-34.[LinkOut]
  • Zelinski AC, Angelone LM, Goyal VK, et al. Specific absorption rate studies of the parallel transmission of inner-volume excitations at 7T. J Magn Reson Imaging 2008;28:1005-18.[LinkOut]
  • Homann H, Graesslin I, Nehrke K, et al. Specific absorption rate reduction in parallel transmission by k-space adaptive radiofrequency pulse design. Magn Reson Med 2010. [Epub ahead of print].
  • Liu Y, Feng K, McDougall MP, et al. Reducing SAR in parallel excitation using variable-density spirals: a simulation-based study. Magn Reson Imaging 2008;26:1122-32.[LinkOut]
  • Liu Y, Ji JX. Minimal-SAR RF pulse optimization for parallel transmission in MRI. Conf Proc IEEE Eng Med Biol Soc 2008;2008:5774-7.
  • Wu X, Akgün C, Vaughan JT, et al. Adapted RF pulse design for SAR reduction in parallel excitation with experimental verification at 9.4T. J Magn Reson 2010. [Epub ahead of print].
  • Roemer PB, Edelstein WA, Hayes CE, et al. The NMR phased array. Magn Reson Med 1990;16:192-225.[LinkOut]
  • Lee RF, Giaquinto RO, Hardy CJ. Coupling and decoupling theory and its application to the MRI phased array. Magn Reson Med 2002;48:203-13.[LinkOut]
  • Wu B, Wang C, Kelley DA, et al. Shielded microstrip array for 7T human MR imaging. IEEE Trans Med Imaging 2010;29:179-84.[LinkOut]
  • Gilbert KM, Curtis AT, Gati JS, et al. Transmit/receive radiofrequency coil with individually shielded elements. Magn Reson Med 2010;64:1640-51.[LinkOut]
  • Zhang X, Ugurbil K, Sainati R, et al. An inverted-microstrip resonator for human head proton MR imaging at 7 tesla. IEEE Trans Biomed Eng 2005;52:495-504.[LinkOut]
  • Setsompop K, Wald LL, Alagappan V, et al. Parallel RF transmission with eight channels at 3 Tesla. Magn Reson Med 2006;56:1163-71.[LinkOut]
  • Chu X, Yang X, Liu Y, et al. Ultra-low output impedance RF power amplifier for parallel excitation. Magn Reson Med 2009;61:952-61.[LinkOut]
  • Vossen M, Teeuwisse W, Reijnierse M, et al. A radiofrequency coil configuration for imaging the human vertebral column at 7 T. J Magn Reson 2011;208:291-7.[LinkOut]

Refbacks

  • There are currently no refbacks.