Iterative multi-channel radio frequency pulse calibration with improving B1 field uniformity in high field MRI
© Hernandez et al.; licensee BioMed Central. 2015
Received: 17 November 2014
Accepted: 9 February 2015
Published: 21 February 2015
In high field MRI capable of multi-channel radio frequency (RF) transmission, B 1 shimming is a time-consuming job because conventional B 1 shimming techniques require B 1 mapping for each channel. After acquiring the complex-numbered B 1 field maps, the optimal amplitude and phase of the driving RF pulse are determined for each channel to maximize the B 1 field uniformity in conventional B 1 shimming. However, time-consuming B 1 shimming procedures at the pre-scan may not be tolerated in the clinical imaging in which patient throughput is one of the important factors.
To avoid the time-consuming B 1 mapping, the first spin echo and the stimulated echo were repeatedly acquired in the slice-selective stimulated echo sequence without imaging gradients. A cost function of the amplitudes and phases of the driving RF pulse for every channel was defined in a way that the ratio between the spin echo and stimulated echo amplitudes rapidly converged to √ 2. The amplitude and phase of the driving RF pulse were iteratively modified over the repeating RF pulse sequence so that the cost function was minimized.
From the finite-difference-time-domain (FDTD) electromagnetic field simulations with a human body model placed in a birdcage coil operating at 3 T, it was observed that the RF pulse calibration with iterative cost function minimization can give improvement of B1 field uniformity as well as flip-angle calibration. The experiments at 3 T also showed improvement of RF field uniformity in the phantom imaging studies.
Since the proposed RF pulse calibration is not based on B 1 mapping, the RF pulse calibration time could be much shorter than the B 1-mapping based methods. The proposed method is expected to be a practical substitute for the B 1-mapping-based B 1 shimming methods when long pre-scan time is not tolerable.
Radio frequency (RF) pulse calibration, also called flip angle calibration, is one of the calibration procedures which are performed in the pre-scan of MRI. The main objective of RF pulse calibration is to find the RF pulse amplitude that makes the desired flip angle, usually 90 degrees, over the region of interest. The RF pulse calibration time is usually negligible if the RF magnetic field is uniform over the imaging region. However, if the RF magnetic field, often called B 1 field, is highly inhomogeneous in the human body as in high field MRI, the RF pulse calibration may become troublesome since the flip angle is also inhomogeneous over the imaging region in the human body. B 1 shimming is the technique to improve the RF field homogeneity in high field MRI. To make B 1 shimming, the MRI system must be equipped with a multi-channel RF transmission system to drive a multi-channel transmit coil [1,2]. By driving the multi-channel transmit coil with optimal amplitude and phase, the RF field homogeneity can be greatly improved over the imaging region in high field MRI [3-5]. However, B1 shimming requires B 1 field mapping for each channel of the multi-channel transmit coil to determine the optimal amplitude and phase of the RF pulse at each channel. Although many fast B 1 mapping techniques have been developed [6-16], the extra scan time for B 1 mapping for every channel would not be acceptable in the clinical pre-scan.
We propose a fast RF pulse calibration technique that does not require time-consuming B 1 mapping to drive the multi-channel transmit coil with RF pulses of optimal amplitude and phase. For the RF pulse calibration, we use the stimulated echo pulse sequence consisting of three RF pulses of the same amplitude without applying any imaging gradients. We repeat the RF pulse sequence with changing the amplitude and phase of the driving RF voltage at each channel. The optimal amplitude and phase are found by minimizing the cost function, defined on the magnitudes of the first spin echo and the stimulated echo, during the idle time between the RF pulse sequence. With the cost function minimization, the RF pulse calibration can give us improvement of the RF field homogeneity as well as the flip angle calibration. We present finite-difference-time-domain (FDTD) simulation results along with the experimental results performed at 3 T MRI.
B1 field formed by multi-channel transmission
RF pulse calibration sequence
Iterative adjustment of the shimming parameters
The minimization has been performed by running the constrained nonlinear optimization algorithm, so called interior point algorithm. The minimization algorithm finds a solution with fewer iterations than other linear programing methods [18,19]. The built-in function in MATLAB (The Mathworks, Natick, USA), fmincon, has been used to implement the interior point algorithm.
Verification of the RF pulse calibration using a FDTD model
To verify the B 1 shimming tendency of the RF pulse calibration in the human body, the RF field generated by a high-pass birdcage coil in an adult human body model (Virtual family model, Duke ) has been computed. In the computation, a FDTD electromagnetic solver (SEMCAD X, Switzerland) has been used. The birdcage coil, with the diameter of 700 mm and the height of 820 mm, has 16 rungs and two excitation ports separated 90 degree apart. The birdcage coil has been tuned and matched at 123.5 MHz. The complex-numbered B 1 maps have been taken from the torso region of the human model which consists of 35 different tissues with their own electrical conductivity and permittivity. The voxel size for the B 1 maps was 3.57 × 3.57 × 5.46 mm3 on a FOV of 350 × 350 × 350 mm3 with a matrix size of 98 × 98 × 64. For the excitation of the birdcage coil at each port, a Gaussian pulse of the center frequency of 123.5 MHz and a bandwidth of 100 MHz was applied. The B 1 map of one channel was computed with driving the corresponding channel with a voltage source and setting the other channel idle, and vice versa for the B 1 map of the other channel. The two B 1 maps have been combined in the quadrature mode as an initial condition for the optimization. The flip angle map was then computed from the composite field.
RF pulse calibration experiment at 3 T
RF pulse calibration experiments have been performed at a 3 T MRI system capable of two channel RF transmission. A head birdcage coil with the diameter of 290 mm and the height of 270 mm has been used for both transmission and reception at the imaging experiment of a water-filled phantom. The phantom consists of two identical cylinders with the diameter of 58 mm and the height of 180 mm. To make inhomogeneous RF field distribution in the phantom of a small size, asymmetric electrical conductivity has been made at the two bottles. One bottle was filled with 0.2 S/m NaCl solution with the other bottle filled with 1.8 S/m NaCl solution. The relative electrical permittivity of the solution was 81 for both bottles. The spin–lattice relaxation time of the solution at both bottles was about 500 ms.
The RF pulse in the calibration sequence was sinc-shaped with the pulse width of 2.6 ms and the bandwidth of 1.5 KHz. The timing t 1 and t 2 were 6 ms and 7 ms, respectively. The repetition time was 500 ms and the slice thickness was 10 mm. A MATLAB script function was made to acquire the spin and stimulated echo signals and to compute the next shimming parameters through the minimization. The next shimming parameters were used to update the driving RF pulse for each channel. The iteration was repeated until the minimization converged to the thresholds.
Results and discussion
The B 1 uniformity computed from the simulated flip angle maps and the magnitude ratio and phase difference in excitation
RF pulse calibration
B 1 shimming
RF pulse calibration
B 1 shimming
a 1/a 2
The B 1 uniformity computed from the experimental flip angle maps and the magnitude ratio and phase difference in excitation
RF pulse calibration
B 1 shimming
RF pulse calibration
B 1 shimming
a 1/a 2
RF pulse calibration output at 10 trials of the experiment
RF pulse calibration output
No. of iterations
a 1 /a 2
Due to some difficulties in spectrometer programming, the RF pulse calibration experiments have been performed ignoring the T1 effects. That is, after setting the new RF voltages for the next cycle of iteration, the spin and stimulated echoes were acquired after repeating a few RF pulse sequences to saturate the T1 effects. If the spin and stimulated echoes are acquired at the very next cycle of the RF pulse sequence with short TR, the amplitude of the spin and stimulated echoes will be affected by the T1 effects as well as the RF voltage changes. The T1 effects on the RF pulse calibration should be investigated to use the RF pulse calibration with short TR. Since the computation time for one iteration is an order of ms, the computation time would not be a hurdle to implement the RF pulse calibration in a short TR configuration.
Since the number of iterations is an order of a few tens in most cases, the number of pulse repetitions in the RF pulse calibration is much smaller than is required in B 1 mapping. In B 1 mapping, a number of phase encodings are necessary for each channel and for magnitude and phase mapping, respectively. Therefore, the scan time for the RF pulse calibration would be much shorter than is for the B 1 mapping as long as similar TRs are employed in both cases. The present study is limited to two-channel excitation, but, the general principle of the present study can be applied to multi-channel excitation with the number of channels higher than two. In ultra-high field MRI with the main field strength higher than 7 T, eight-channel RF transmission or more is now used to overcome the B 1 inhomogeneity [21,22]. As the number of transmission channels increases for more efficient B 1 shimming, B 1 mapping time for every channel also increases. Therefore, long B 1 mapping time may become a big hurdle in applying B 1 shimming to clinical studies. Although many fast B 1 mapping techniques have been proposed to reduce the scan time of multi-channel B 1 mapping, implementing the multi-channel B 1 mapping in the pre-scan frame would be troublesome. It is expected that the proposed method can be also used for B 1 shimming in high field MRI with the number of transmission channels higher than two. The proposed method has a limitation that B 1 shimming at a region of interest (ROI) inside the entire slice is not possible since the spin echo and stimulated echo signals are acquired from the entire slice. In contrast, the conventional B 1 shimming can be applied to a small region of interest by taking the fields only at the ROI into consideration for the optimization.
A new method for fast RF pulse calibration with B 1 shimming capability has been proposed. Since the proposed RF pulse calibration is not based on time-consuming B 1 mapping, the RF pulse calibration time could be much shorter than the B 1-mapping based methods. The proposed method is expected to be a practical substitute for the B 1-mapping based B 1 shimming methods when long pre-scan time is not tolerable.
This work was supported in part by the National Research Foundation (NRF) of Korea funded by the Korean government (No: NRF-2013-R1A2A2A03006812) and in part by Samsung Electronics in Korea.
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