B₁ Mapping by Bloch-Siegert Shift

Abstract

A novel method for B₁⁺ field mapping based on the Bloch-Siegert shift is presented. Unlike conventionally applied double-angle or other signal magnitude-based methods it encodes the B₁ information into signal phase, resulting in important advantages in terms of acquisition speed, accuracy and robustness. The Bloch Siegert frequency shift is caused by irradiating with an off-resonance RF pulse following conventional spin excitation. When applying the off-resonance RF in the kHz range, spin nutation can be neglected and the primarily observed effect is a spin precession frequency shift. This shift is proportional to the square of the RF field magnitude B₁². Adding gradient image encoding following the off-resonance pulse allows one to acquire spatially resolved B₁ maps. The frequency shift from the Bloch-Siegert effect gives a phase shift in the image that is proportional to B₁². The phase difference of two acquisitions, with the RF pulse applied at two frequencies symmetrically around the water resonance is used to eliminate undesired off-resonance effects due to B₀ inhomogeneity and chemical shift. In-vivo Bloch Siegert B₁ mapping with 25 seconds / slice is demonstrated to be quantitatively comparable to a 21 minute double-angle map. As such this method enables robust, high resolution B₁⁺ mapping in a clinically acceptable time frame.

INTRODUCTION

A wide variety of B₁ mapping methods have been developed to date, however no single one has emerged yet in widespread application. B₁ mapping is used in diverse applications in MR- including transmit gain adjustment to produce specific flip angle RF pulses, design of multi-transmit channel RF pulses (1-3), T₁ mapping and other quantitative MRI (4), and chemical shift imaging.

Generally, B₁ mapping methods fall into two classes: signal magnitude, or signal phase-based. The large majority of B₁ mapping methods depend on changes in signal magnitude based on RF flip angle. Existing methods in this category include fitting progressively increasing flip angles (5), stimulated echoes (6), image signal ratios (7-10), signal null at certain flip angles (11), and comparison of spin echo and stimulated echo signals (12).

These methods suffer from combinations of the following problems: T₁ dependence, long acquisition times-mainly from acquiring many images, and/or a long TR to mitigate the T₁ dependence, inability to use some of these methods with slice-selection, or in a multi-slice acquisition, inaccuracy over a large range of B₁ especially at low flip angles or flip angles close to 90° or 180°, and large RF power deposition in the case of B₁ mapping sequences based on large flip angles or reset pulses to mitigate the T₁ dependence.

There are far fewer phase-based B₁ mapping methods. One method by Morrell uses the phase accrued from a 2α - α flip angle sequence to determine B₁ (13). This method has the same long TR requirement as the signal magnitude-based sequences, although it is effective and more accurate over a larger range of flip angles than a double-angle signal magnitude-based B₁ map (14). A very different phase-based approach was proposed by J.Y. Park and M. Garwood, where they utilize the B₁-dependent phase produced by adiabatic hyperbolic secant half- and full-passage pulses (15). This method nicely eliminates the problems of T₁ and B₀ dependence, however SAR is a significantly limiting factor in applying this clinically at high field.

Here, we describe a novel phase-based B₁ mapping method based on the Bloch-Siegert shift(16). This Bloch-Siegert shift is utilized to create a |B₁|-dependent signal phase. The resulting B₁ mapping method is shown here to be robust to TR, T₁ relaxation, flip angle, chemical shift, background field inhomogeneity, and magnetization transfer. Because of this insensitivity, accurate Bloch-Siegert based B₁ maps can be acquired very quickly with a short TR.

THEORY

The term Bloch-Siegert shift has been used to describe the effect where the resonance frequency of a nucleus shifts when an off-resonance RF field is applied (16,17). This effect is an additional contribution to the static B₀ field that arises from the off-resonance component of the RF field. In the case where RF is applied either far enough off-resonance and/or with a pulse shape such that it does not cause spin excitation, the spins experience a change in precession frequency without excitation (18). The spin precession frequency shifts away from the off-resonance irradiation, and is dependent on the magnitude of the B₁ field, and the difference between the spin resonance and RF frequency ω_RF.

Figure 1 shows the effective B₁ field in the RF rotating frame (B₁^eff) when the RF is applied off-resonance at frequency ω_RF. The frequency difference between spin precession and the RF frequency can be visualized as a constant magnetic field along z. In this rotating frame the B₁^eff field is constant, and is given by Eqn 1:

$$\gamma B_1^{\mathit{eff}}=\sqrt{{\omega }_{\mathit{RF}}^2+\gamma B_1^2}$$ [1]

For a large off resonance ω_RF >> γB₁ this results in the component ω_BS of the B₁^eff field vector which is a small constant field approximately along the main magnetic field axis. This additional field constitutes the Bloch-Siegert shift and results in the spin precession frequency shift coming from off-resonance RF irradiation.

Figure 1.

B₁ field in the rotating frame of the RF. The frame rotates at frequency ω₀ + ω_RF. In this frame, the B₁ field is static, where as the spins rotate at ω_RF. The Bloch-Siegert frequency shift ω_BS is a constant field in this rotating frame along the effective RF field vector γB₁^eff.

A simple analytical relationship for the Bloch-Siegert shift ω_BS can be derived from Figure 1. Under the assumption of large, relative off-resonance:

$${\omega }_{\mathit{RF}}⪢\gamma B_1$$ [2]

a trigonometric identity can by used to solve for ω_BS according to:

$${({\omega }_{\mathit{BS}}+{\omega }_{\mathit{RF}})}^2={\omega }_{\mathit{RF}}^2+{\left(\gamma B_1\right)}^2$$ [3]

$${\omega }_{\mathit{BS}}=\frac{{\left(\gamma B_1\right)}^2}{2{\omega }_{\mathit{RF}}}$$ [4]

This derivation is described in detail by Ramsey in a theoretical paper in Phys Rev. 1955 (17). This paper first describes the case dealt with here where a single non-resonant frequency is applied, and later deals more generally with irradiation at multiple non-resonant frequencies.

In practical application, the Bloch-Siegert shift has been used for determining the magnitude of a B₁ decoupling field in solid state spectroscopy (19,20). However to the best knowledge of the authors this has never been applied in MR imaging.

The Bloch-Siegert shift can be applied to B₁ field mapping as follows: An off-resonance RF pulse of frequency ω_RF is applied immediately after excitation in an imaging sequence. The RF pulse shape and frequency is chosen such that it does not excite spins in the sample. The frequency shift of spins during the off-resonant RF pulse results in a phase shift in the image that can be used to determine the spatial B₁ magnitude. The phase shift φ_BS due to the Bloch-Siegert shift is given by:

$${\phi }_{\mathit{BS}}={\int }_0^T{\omega }_{\mathit{BS}}\left(t\right)={\int }_0^T\frac{{\left(\gamma B_1\left(t\right)\right)}^2}{2{\omega }_{\mathit{RF}}\left(t\right)}\mathit{dt}$$ [5]

The expected phase shift can be calculated from Eqn. 5 for any arbitrary pulse B₁(t) with constant or time dependent frequency offset ω_RF(t).

The relationship between Bloch-Siegert phase shift and the peak B₁ of a generalized RF pulse is given by Eqn. 6:

$${\phi }_{\mathit{BS}}={B_{1,\text{peak}}}^2{\int }_0^T\frac{{\left(\gamma B_{1,\text{normalized}}\left(t\right)\right)}^2}{2{\omega }_{\mathit{RF}}\left(t\right)}\mathit{dt}={B_{1,\text{peak}}}^2\times K_{\mathit{BS}}$$ [6]

$$B_1\left(t\right)=B_{1,\text{peak}}\ast B_{1,\text{normalized}}\left(t\right)$$ [7]

K_BS is a constant that describes the phase shift (radians/gauss²) for a given RF pulse. For example: for a hard pulse, 4 kHz off resonance, K_BS = 14.23 radians/gauss²/msec. B_1,peak is the magnitude of the maximum point in the RF waveform B₁(t).

Phase-based methods usually require taking the difference of two scans to remove additional, undesired phase effects in the image. The difference in phase between the two scans gives the Bloch-Siegert phase shift, removing transmit excitation and receive phases, other sequence related phase, and the phase shift from off-resonance B₀. All these phase factors are the same in both scans. Acquiring two scans- one with the RF pulse at +ω_RF, and one at −ω_RF enables one to calculate B₁. Applying the off-resonance RF symmetrically around the water peak removes the B₀-inhomogeneity and chemical shift dependence of the Bloch-Siegert shift as well. For off-resonance spins precessing at frequency ω₀ + ω_B0, Eqn. 4 for the Bloch Siegert frequency shift becomes:

$${\omega }_{\mathit{BS}}=\frac{{\left(\gamma B_1\right)}^2}{2({\omega }_{\mathit{RF}}+{\omega }_{B0})}$$ [8]

By a 2^nd order Taylor expansion, assuming ω_B0 << ω_RF:

$${\omega }_{\mathit{BS}}=\frac{{\left(\gamma B_1\right)}^2}{2({\omega }_{\mathit{RF}}+{\omega }_{B0})}\approx \frac{{\left(\gamma B_1\right)}^2}{2{\omega }_{\mathit{RF}}}-\frac{{\left(\gamma B_1\right)}^2{\omega }_{B0}}{2{\omega }_{\mathit{RF}}^2}+O\left({\omega }_{B0}^2\right)$$ [9]

The Bloch-Siegert phase shift of a spin at B₀ offset of ω_B0 is given by:

$${\phi }_{\mathit{BS}}\approx {\int }_0^T\frac{{\left(\gamma B_1\left(t\right)\right)}^2}{2{\omega }_{\mathit{RF}}\left(t\right)}\mathit{dt}-{\int }_0^T\frac{{\left(\gamma B_1\left(t\right)\right)}^2{\omega }_{B0}}{2{\omega }_{\mathit{RF}}^2}\mathit{dt}+O\left({\omega }_{B0}^2\right)$$ [10]

The ω_B0 dependent term drops out when one takes the phase difference between two scans with the off-resonance pulse at symmetric +/− ω_RF frequencies. The result is a phase shift that is up to first order independent of off-resonance frequency.

The percentage error in B₁ calculated from the phase difference of two scans with off-resonance RF applied at +/− ω_RF, where there is a B₀ offset of ω_B0 is given by Eqn’s 11 and 12:

$$\text{error}\left({\phi }_{\mathit{BS}}\right)=\frac{{\int }_0^T\left(\frac{{\left(\gamma B_1\left(t\right)\right)}^2}{2({\omega }_{\mathit{RF}}\left(t\right)+{\omega }_{B0})}+\frac{{\left(\gamma B_1\left(t\right)\right)}^2}{2({\omega }_{\mathit{RF}}\left(t\right)-{\omega }_{B0})}\right)\mathit{dt}}{{\int }_0^T\frac{{\left(\gamma B_1\left(t\right)\right)}^2}{{\omega }_{\mathit{RF}}\left(t\right)}\mathit{dt}}$$ [11]

$$\text{error}\left(B_1\right)=100\%\times \sqrt{\frac{\text{error}\left({\phi }_{\mathit{BS}}\right)}{K_{\mathit{BS}}}}$$ [12]

This percentage error in B₁ calculation as a function of B₀ offset is shown in Figure 2. The error is shown for RF pulses at off-resonance frequencies 2, 4, and 8 kHz, over a range of +/− 1 kHz B₀ inhomogeneity.

Figure 2.

Percentage error in B₁ calculation as a function of B₀ offset over a range of 1 kHz. The error is calculated from Eqns. 11 and 12, for RF pulses at off-resonance frequencies of 2, 4, 8 kHz.

METHODS

The sequences in Figure 3 were implemented on a 3 Tesla GE DVMR scanner, (GE Healthcare, Milwaukee, WI, USA). 15 human subjects were studied in accordance with institutional review board guidelines for in-vivo research. All subjects provided informed consent. A basic gradient echo sequence was modified by including an off-resonance Fermi pulse immediately following excitation. A basic spin echo sequence was modified by including two Fermi pulses, applied around a refocusing pulse. All gradient echo images shown in this work were acquired with an 8 msec Fermi saturation pulse, and frequency offsets of ω_RF = +/− 4 kHz relative to water. All spin echo B₁ maps were acquired with two 6 msec Fermi saturation pulses, and frequency offsets of ω_RF = +/− 4 kHz relative to water. Figure 4 shows the 8 msec Fermi pulse, and its frequency excitation profile. A frequency profile with minimal on-resonance excitation is necessary to not excite spins in the sample.

Figure 3.

Gradient and spin echo sequences, modified for B₁ mapping. The gradient echo sequence has an 8 msec off-resonance Fermi pulse at off-resonance frequency ω_RF following excitation. The spin echo sequence has two 6 msec off-resonance Fermi pulses. The first pulse is at off-resonance frequency ω_RF and the second at −ω_RF .

Figure 4.

Normalized B₁(t) and corresponding frequency excitation profile for an 8 msec Fermi pulse, and ω_RF = 4 kHz.

For the 8 msec 4 kHz off resonance Fermi pulse used in the gradient echo experiments described here, K_BS = 74.01 radians/gauss². For the 6 msec 4 kHz off resonance Fermi pulse used in the spin echo experiments described here, K_BS = 55.26 radians/gauss². The spin echo sequence contains two 6 msec Fermi pulses for a total K_BS for the sequence of 110.52 radians/gauss². The relationship between phase shift and B_1,peak is shown in Figure 5 for the 8 msec Fermi pulse. Also shown is a comparison between the phase shift predicted by the analytical expression in Eqn. 6 and the phase shift predicted by numerical Bloch simulation of this off-resonance pulse.

Figure 5.

Phase shift φ_BS vs. |B₁| for an 8 msec Fermi pulse at 4 kHz. Simulated by the analytical expression of Eqn. 6, and numerical Bloch simulation.

The Fermi RF pulse is used regularly for magnetization transfer preparation- which has similar RF pulse requirements as our case here (21,22). The relationship between phase shift and B_1,peak can be calculated similarly for any arbitrary RF pulse. Figure 6 shows a comparison of K_BS for four choices of RF pulses: the hard pulse, Fermi, and adiabatic sech/tanh, and tanh/tan pulses (23). Also shown is a comparison of the width of the frequency band that contains 99% percent of spin excitation for these pulses.

Figure 6.

Comparison of four RF pulses, all of 8 msec pulse length, at 4 kHz off-resonance, relative to water. The hard pulse, Fermi, adiabatic hyperbolic secant (with a time varying frequency sweep ω_RF(t) of +/−2kHz around 4 kHz), and the adiabatic tanh/tan pulse (with a time varying frequency sweep ω_RF(t) of +/−20kHz around 4 kHz). K_BS (radians/gauss²) is calculated for these four pulses, as well as the frequency range that contains 99% of spin excitation. This Fermi pulse is used for all subsequent experiments shown here.

RESULTS

Gradient echo Bloch-Siegert B₁ maps and double angle maps were acquired from a silicon oil phantom, and a saline phantom with three inner subcompartments filled with milk to assess sensitivity of this method to chemical shift and to magnetization transfer. A GE birdcage transmit/receive head coil was used for RF transmission and reception.

Figure 7a shows a double angle B₁ map of the silicon oil phantom. The two gradient echo images were acquired with TE = 10 msec, TR = 5 sec, flip angles α = 60°, 2α =120°, slice thickness 1 cm, in plane resolution 128×128. The flip angle map for the 60° image was calculated by (24):

$$B_1^{\text{flip angle}}=\text{arccos}\left(\frac{S_{2\alpha }}{2S_{\alpha }}\right)$$ [13]

where S_2α and S_α are the signal magnitudes of the 2x and 1x flip angle images. The B₁ map calculated for the 60° flip angle RF pulse is shown here for comparison with the Bloch-Siegert B₁ maps. Figure 7b shows two Bloch-Siegert B₁ maps taken with TE = 15 msec, and TR of 70 and 2000 msec, which demonstrate lack of TR-dependence. Figure 7c shows the percent difference between the double angle map and the 70 msec TR Bloch-Siegert map. These match to within 2%.

Figure 7.

a. Double angle B₁ map, calculated from two scans acquired with a 3.2 msec sinc pulse having flip angles of α = 60°, 2α = 120°, TE = 10 msec, TR = 5 sec. Slice thickness = 1 cm, 128×128 resolution. b. Gradient echo Bloch-Siegert B₁ map, acquired with TE = 15 msec, TR = 70 msec (left), 2 sec. (right), 8 msec, +/−4 kHz Fermi pulse. c. Error between the two methods: Double Angle map / Bloch-Siegert map * 100% d. B₁ maps acquired with the amplifier output at 0.33, 0.5, 0.75, 1.0, 1.5 * B_1,peak, where B_1,peak = 0.073 gauss B₁ field produced at the center of the slice. The B₁ maps are displayed rescaled to 0.073 gauss for comparison. e. Bloch-Siegert B₁ maps of a saline phantom with three milk compartments acquired with the 8 msec Fermi pulse at off-resonance frequencies of 2, 4, 6, and 8 kHz relative to the water resonance.

Figure 7d shows Bloch-Siegert B₁ maps as a function of peak B₁ power. Four Bloch-Siegert B₁ maps were acquired with B_1,peak = 0.11, 0.073, 0.055, 0.037, 0.024 gauss. B_1,peak was controlled by scaling the exciter output by 1.5, 1.0, 0.75, 0.5, 0.33. The B₁ maps are scaled by these factors for easier comparison.

Figure 7e shows Bloch-Siegert maps of the saline/milk phantom acquired with the 8 msec Fermi pulse at off-resonance frequencies of 2, 4, 6, and 8 Hz relative to the water resonance. No effect of chemical shift or magnetization transfer is evident in the milk or water compartments.

The B₁ maps in Figure 7d and e were acquired with TR = 70 msec. Total scanning times were 21.3 min. for the double angle map, and 18 sec. for the Bloch-Siegert maps.

This was repeated in-vivo in the brain, sagittal orientation, with a GE birdcage transmit/receive head coil (Figure 8). There is a small difference in the magnitude images with the off-resonance pulse (Figure 8a, b.) and without the off-resonance pulse (Figure 8c). This is likely the result of magnetization transfer, however this does not cause any obvious artifacts in the B₁ map. The double angle map in Figure 8d overestimates the B₁ field in the CSF, resulting from the known T₁ dependence of this method and the less than optimal TR of 3 seconds. T₁ dependence is not evident in the Bloch Siegert B₁ map of Figure 8e.

Figure 8.

a, b. Magnitude gradient echo images with 8 msec off-resonance Fermi pulse, ω_RF = +/− 4 kHz. c. Same image acquisition, without the off-resonance pulse. d. Double angle B₁ map, 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 3 sec. Flip angles α = 45° 2α = 90°. e. Bloch Siegert map calculated from the phase difference between images a. and b. The peak B₁ of the Bloch-Siegert map was twice the peak B₁ used in the double angle map. Resolution 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 100 msec, off resonance pulse: 8 msec Fermi, ω_RF = +/− 4 kHz.

Additional gradient echo double angle and Bloch-Siegert B₁ maps acquired in vivo in a human leg, sagittal orientation, using a GE birdcage transmit/receive knee coil are presented in Figure 9. No effects are evident in the Bloch-Siegert B₁ map from either magnetization transfer or chemical shift from lipids.

Figure 9.

a. Double angle B₁ map, resolution 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 5 sec. Flip angles α = 60° 2α = 120°. b. Gradient echo Bloch-Siegert map, resolution 128×128, slice thickness = 0.5 mm, TE = 12 msec, TR = 100 msec, off resonance pulse: 8 msec Fermi, ω_RF = +/− 4 kHz.

Figure 10 shows spin echo images and corresponding spin echo Bloch-Siegert B₁ maps acquired in vivo in two subjects in the shoulder (10a), and four in the abdomen (10b,c). A GE DVMR whole-body transmit coil was used for the shoulder images. The abdomen B₁ maps were acquired on a GE Signa Excite HDx system using the body transmit coil. Signal reception was done with the body transmit/receive coil for the shoulder, and a local 8-channel receive array (GE) for the abdomen. All images were acquired without breath holding. These images show no discontinuity in the B₁ maps between water and lipids. The abdomen B₁ maps have artifacts along the phase-encoding direction from breathing and blood flow through large vessels, but not to an extent that significantly impacts the B₁ maps.

Figure 10.

Spin echo Bloch-Siegert B₁ maps, acquired with two 6 msec, +/− 4 kHz off-resonance Fermi pulses, applied symmetrically around a 3.2 msec sinc refocusing pulse. The Fermi pulses had the same peak B₁ as the excitation pulse. TE = 28 msec, TR = 200 msec, resolution = 128×128, slice thickness = 1 cm. a. Shoulder, two subjects, taken with GE DVMR whole body transmit/receive coil. b. Abdomen, axial orientation two subjects, taken with whole body transmit, GE 8-channel torso receive array. c. Abdomen, sagittal and coronal orientations.

DISCUSSION

The Bloch-Siegert shift gives a fast, accurate, robust, and conceptually straightforward method for measuring B₁ field maps. The Bloch-Siegert shift provides a detectable phase shift to use for B₁ mapping, providing one uses a long enough off-resonance RF pulse with amplitudes compatible with clinical applications. The associated increase in echo time can be afforded for most in-vivo applications. In general, phase sensitive B₁ mapping methods have a significant advantage over signal magnitude based methods in scan time and accuracy over a wide dynamic range of flip angles (14). The Bloch-Siegert method in particular is shown here to be insensitive to T₁, TR, chemical shift, magnetization transfer, and inhomogeneous B₀ within a range reasonably expected in vivo.

This method will work with a large variety of off-resonance pulse shapes. The optimal pulse shape for this method would be one that maximizes the integral in Eqn. 5, but does not directly excite spins in the sample. Several pulse shapes were considered- the hard pulse, adiabatic hyperbolic secant, Gaussian, as well as the Fermi pulse. The latter offered a good choice in terms of maximizing the integral of Eqn. 5, and minimizing on-resonance excitation.

The Bloch-Siegert phase shift produced by a single off-resonance RF pulse is B₀ dependent. However, the phase difference between two scans with the off-resonance pulse at approximately symmetric frequencies around the on-resonance water peak, is independent of B₀ for ω_B0 << ω_RF. One would choose the RF off-resonance frequency ω_RF to satisfy this condition, as well as to avoid on-resonance excitation. The off-resonance frequency ω_RF of 4 kHz was chosen for this pulse based on the criteria that the pulse excite <1% of spins within a ±1 kHz range around the center resonance frequency.

The off-resonance Fermi pulse used here to produce the Bloch-Siegert shift is similar to off-resonance RF pulses typically used in a magnetization transfer sequence. There is a magnitude difference between in-vivo images acquired with and without the off-resonance RF pulse that is likely due to magnetization transfer, flow, and motion. There is a small asymmetry in the magnitude of the two images with the off-resonance pulse on either side of the water peak (25). However, no phase contribution from the magnetization transfer is evident in any of the in-vivo experiments, or the milk compartment phantom experiments.

Because of the insensitivity of this method to relaxation and TR, one would likely use as short a TR as possible. The SNR of a Bloch-Siegert B₁ map is dependent on the base SNR of the two acquired images, and the phase shift between the images. Scan time in most cases will be limited at lower field by a tradeoff between imaging time and SNR, and at high field (≥ 3 Tesla) by clinical SAR limits.

The Bloch-Siegert phase shift scales with the integrated area of B₁², as does SAR. For the gradient echo sequence: All imaging demonstrated here in vivo including acquisitions with TR of 50 msec was within all SAR limits as measured by conventional scanner power monitoring. At 3 Tesla, with a TR of 35 msec, and peak B₁ of 0.2 gauss, we skirt the short term (10 second) SAR limits. However, our in-vivo experiments gave more than adequate signal to noise with peak B₁ = 0.07 gauss and TR of 50 msec. This was well within the long-term SAR limits for continuous scanning. At higher field strengths, one can extend the TR. The spin echo sequence presented here was more SAR intensive, but could be run continuously with a body transmit coil with a peak Fermi pulse B₁ of 0.1 gauss with a TR of 200 msec.

Even at longer TR the time advantage of this method is maintained. This method is fully compatible with EPI, spiral readout, or other imaging acceleration methods, which can additionally reduce scan time and/or SAR.

The Bloch-Siegert shift was used in this work to measure the magnitude of the B₁⁺ field, needed in a large number of MR applications. A subclass of these applications may also benefit from knowledge of the phase of the B₁⁺ field, or of the receive B₁⁻ sensitivity. While the B₁⁺ phase and the B₁⁻ profile can not be determined directly from the Bloch-Siegert shift, they may be obtained using information collected in the Bloch-Siegert B₁⁺ mapping scans. For example, in a manner similar to the one described by Wang et al. (26), the B₁⁻ profile can be obtained using a fast third acquisition with the contrast between tissues minimized, and the B₁⁺ map from the Bloch-Siegert shift. B₁ phase is conventionally determined from the phase difference between images where each coil transmits individually. One could similarly take the phase difference between images used for Bloch-Siegert B₁ maps where each coil is used individually for excitation. It may be the case that acquiring B₁ magnitude from the Bloch-Siegert shift, and B₁ receive from a second scan is a beneficial method for parallel transmit applications as well.