3D Free‐breathing multichannel absolute B1+ Mapping in the human body at 7T

To introduce and investigate a method for free‐breathing three‐dimensional (3D) B1+ mapping of the human body at ultrahigh field (UHF), which can be used to generate homogenous flip angle (FA) distributions in the human body at UHF.


| INTRODUCTION
One of the major challenges at ultrahigh magnetic field (UHF) is the heterogeneous amplitude of the transmit (Tx) magnetic field (B + 1 ). It yields a spatially heterogeneous flip angle (FA) and, therefore, spatially varying contrast-limiting UHF applications. This issue has been addressed, among other solutions, using multitransmit coils in combination with several different parallel transmission (pTx) strategies. 1,2 Several studies have also demonstrated that pTx methods strongly improve signal-to-noise and contrast-to-noise ratios when targeting the human body. 3 Moreover, FA variations in the human body are typically more pronounced than in the human brain because of the larger and patient-dependent body size. Static pTx methods are often sufficient to achieve acceptable FA homogeneity for small two-dimensional (2D) regions of interest (ROIs) such as used for the prostate, 4 whereas the complexity of the pTx strategies needs to increase when large organs such as the liver 5 are targeted. Therefore, it is expected that an extension of the ROI to cover a larger 3D volume in the human body also requires more complex FA optimization strategies.
The knowledge of the underlying B + 1 maps of each single Tx channel is a prerequisite for any pTx optimization, independent of the target region. Such maps are either acquired for each subject at the beginning of each session or in case of universal pulses 6 during a set of training subjects, which then eliminates the need for subject-specific B + 1 mapping. Several different techniques for acquiring (absolute) B + 1 maps exist, among them are methods based on the Bloch-Siegert shift, 7 presaturation turbo fast low-angle shot, 8 dual refocusing echo acquisition (DREAM), 9,10 and actual flip angle imaging (AFI). 11 A straightforward approach to obtain individual B + 1 maps of each Tx channel consists of combining a single absolute B + 1 map obtained by one of the aforementioned methods [7][8][9]11 with a set of multiple Tx gradient echo (GRE) acquisitions, where, for example, only a single Tx channel is active per acquisition. 12 Similarly, absolute 2D B + 1 maps can also be acquired based on the B1TIAMO method. 13 For obtaining absolute B + 1 maps in the human body at 7T of multiple 2D slices or 3D volumes, however, the aforementioned methods are often limited by radiofrequency (RF) power demand, motion, and/or blood flow and their acquisition times might be too long for a breath-hold. Instead, a method for generating relative B + 1 estimations 14 of the N Tx Tx channels, initially introduced for the human brain, can be acquired without high power requirements based on GRE images with low FAs. This allows the acquisition of B + 1 maps of a single slice within a few seconds, that is, within a breathhold when applied to the body. However, a limitation of this method is that the amplitude of the maps is relative, if no additional absolute B + 1 map is acquired to calibrate these maps, and that the maps are biased by the square-root of the proton density. 14 Despite these limitations, the relative B + 1 mapping method has proven to be highly suitable for FA optimization in the human body at 7T, not only for B + 1 shimming purposes, 15,16 but also for slice-selective pTx methods such as spokes RF pulses. 5,17,18 For pTx techniques that optimize the FA within 3D volumes such as the whole liver or heart, however, B + 1 maps covering the 3D volume are required. Although the relative B + 1 mapping technique mentioned previously has been extended to multiple slices, 17,19 full 3D mapping cannot be achieved within a single breath-hold.
Therefore, we investigate in this work a method to acquire free-breathing, 3D absolute B + 1 maps in the human body at 7T. 20 This technique is based on a fast, low-power-demanding relative B + 1 mapping method, 14 as well as a radial phaseencoding (RPE) acquisition scheme, 21-23 which enables retrospective binning in respiratory motion states. This flexible 3D acquisition scheme is applied for two acquisitions: (1) a modified AFI calibration scan to acquire absolute B + 1 maps in a combined, single Tx configuration 24 ; and (2) small FA spoiled GRE acquisitions. We first use the GRE scans to derive relative B + 1 maps of the human body that are subsequently calibrated using the AFI scan resulting in estimated, absolute B + 1 maps of each channel and different respiratory motion states. We quantitatively evaluate the method first in a motion phantom scan and subsequently show the suitability of this technique to compute B + 1 maps in 11 volunteers. 2D Cartesian cine GRE scans, as well as 3D GRE scans with and without static phase-only B + 1 shims are used to qualitatively validate the resulting B + 1 maps.

| METHODS
Our method to compute multichannel 3D respiration-resolved, absolute B + 1 estimations relies on two separate acquisitions: an RPE-based, 3D respiration-resolved AFI (RPE-AFI) acquisition, 24 and a Tx channel-wise RPE-based 23,25 3D respiration-resolved-gradient echo (Tx-RPE-GRE) acquisition. An overview of the workflow is depicted in Figure 1A. Relative B + 1 maps are calculated from Tx-RPE-GRE and calibrated with RPE-AFI to obtain absolute B + 1 map estimations. To obtain a sufficiently high FA for the calibration, the RPE-AFI is measured with a B + 1 shim setting Φ eff , providing a locally high Tx efficiency in the frontal region of the heart. Calibration is then performed for ROIs in the heart with a FA > 40° (see the white ROI in Figure 1A).

| Radial phase encoding and self-navigation
Using an RPE-based acquisition, respiration-resolved images are obtained by acquiring the 3D k-space as illustrated in Figure 1B. k-Space is sampled on a Cartesian grid along the readout direction (k x ), whereas the two phase-encoding (PE) directions (k y , k z ) are sampled on a non-Cartesian, radial grid. After completing the N PE readouts along one radial line, the next radial line is rotated by a golden-angle increment of 111.24°. The resulting RPE trajectory covered the PE plane homogenously and allowed retrospective binning of the data into p = (1, . . . , N p ) respiratory motion states using self-navigation.
The N p undersampled respiration-resolved k-space data sets are subsequently reconstructed using nonuniform fast Fourier transformation (NUFFT) based on an iterative sensitivityencoding (SENSE) algorithm. 23,26,27 A respiratory motion surrogate for self-navigation is retrieved from the 1D projection in the head-feet direction for k y = k z = 0. 23 The temporal sampling intervals for self-navigation and the number of readouts per radial line are listed in Table 1 for the different acquisitions.

| 3D Multichannel Tx-RPE-GRE and reconstruction of relative B + 1 map
In the Tx-RPE-GRE acquisition, the RPE scheme is applied to a small tip angle GRE sequence, which consisted of N Tx + 2 repetitive RPE-GRE scans. During each scan, only a single Tx channel is active while the signal is received through all m = (1, . . . , N Rx ) Rx elements. 14,28 The active Tx channel number k = (1, . . . , N Tx ) was incremented through the scans. In addition to the N Tx scans, we acquired another scan with all N Tx channels and one with no Tx channel active for transmission. The latter scan is used for noise decorrelation of the receive channels used during image reconstruction.
The magnitude of the resulting 3D respiration-resolved image |I k,m,p (r) | of Tx channel k, Rx channel m, and respiratory phase p for each spatial position r was then given by the simplified signal equation: with the complex receive profile B − m,p (r), the complex transmission profile B + k,p (r), the proton density 0 (r) , and the spatially independent, complex scaling factor c including RF pulse, hardware, and reconstruction-related scaling factors. Consequently, the sum of all magnitude images This assumption introduced a bias into the resulting B + 1 maps that is proportional to the square root of the proton density and symbolized by the hat. Estimated, relative B + 1 magnitude maps were obtained for each Tx channel k and respiratory motion state p by weighting the expression (Equation 2) by relative image signal intensities Relative Tx phase maps k,p (r) of Tx channel k relative to one fixed Tx channel k f are calculated based on the complex images by: Here, * denotes the complex conjugate and arg is the phase of the complex value. The resulting estimated B + 1 maps were finally given by: is reconstructed during the actual imaging session using all acquired data without any binning. A second set of respiration-resolved B + 1 estimations B + k,p (r) with N p = 3 is obtained retrospectively after each session because of reconstruction time limitations.
The nonrespiration-resolved B + k (r) maps obtained with the default transmission phase ϕ 0 are used to compute two static phase-only B + 1 shim settings based on multiple manually drawn ROIs covering multiple slices. The first shim setting is computed for three transversal-slice ROIs covering the human heart, by following the heart-lung border, to obtain a homogenous B + 1 shim ϕ hom . The central slice S c is placed in the center of the heart, along the head-feet direction; the other two slices are placed above and below S c. The second shim setting is computed for a ROI eff with a diameter of 2 to 3 cm, in a single transversal slice to obtain an RF-efficient B + 1 shim ϕ eff in an ROI covering the anterior section of the heart and myocardium. The efficiency is computed as in Metzger et al 4 and aimed to maximize the constructive interference of the N Tx B + 1 maps in the target region. The phase setting ϕ hom is applied to achieve homogeneous FAs in subsequently acquired high-resolution 3D RPE-GRE acquisitions, as well as 2D Cartesian cine GRE scans; ϕ eff is applied for an RPE-AFI mapping as outlined below.

| 3D RPE-AFI
An RPE-GRE acquisition scheme was modified to acquire two interleaved repetition times (TRs; RPE-AFI), 24 which enables the computation of absolute, respiration-resolved B + 1 maps according to the AFI approach. 11 The RPE-AFI data is acquired in vivo with B + 1 shim setting ϕ ef . Each readout of the RPE k-space trajectory is consecutively sampled twice with different TR (ratio n = TR 2 ∕TR 1 ) in an interleaved fashion, which results in N p respiration-resolved image data sets A 1,p (r) and A 2,p (r). The FA p (r) for each motion state p and spatial position r is computed following Yarnykh. 11 Before the FA calculation, A 1,p (r) and A 2,p (r) is median filtered within a three-voxel neighborhood. The obtained FA p (r) in degree is converted to absolute B + 1 maps, termed B + AFI p (r) , which are given in μT or related to unit power in μT/ √ kW.

| Reconstruction of unbiased and estimated, absolute multichannel B + 1 maps
Unbiased, respiration-resolved, absolute B + 1 maps of each Tx channel are obtained following Van de Moortele et al, 12 and by combining the RPE-AFI with the images obtained by the Tx-RPE-GRE acquisition. This approach, however, requires a sufficiently high FA of >20° throughout the body, which is not achievable in the center of the body with our set-up because of RF power limitations.
To circumvent this, a different approach is used as already suggested in Van de Moortele et al 14 for brain applications by calculating a single scaling factor λ based on the RPE-AFI acquisition in a manually drawn ROI λ with a sufficiently high FA of >40° (as shown in Figure 1A). .
To achieve this calibration, the same efficient B + 1 shim ϕ eff is retrospectively applied to the B + k,p (r) maps. The scaling factor is subsequently applied to the relative B + k,p (r) maps (Equation 4) to yield estimated, absolute B + 1 maps, termed B + , k,p (r) in the following:

| Experiments
All scans were obtained on a 7T system (Magnetom 7T; Siemens Healthcare, Erlangen, Germany) equipped with a pTx system and 8 × 1 kW amplifiers (Stolberg AG, Stolberg, Germany). The phantom study was performed using an in-house-built 8 Tx/8 Rx transceiver head coil. The in vivo measurements were performed with a commercial body coil array (MRI Tools, Berlin, Germany), consisting of 32 transceiver elements (eight dipoles and 24 loops) that are driven in an 8 Tx/32 Rx channel mode. The body coil has a field-of-view (FOV)/excitation of approximately 240 mm along the head-feet direction. It consists of an anterior and a posterior half with fixed, solid housings. The anterior and posterior halves have four parallel aligned blocks with four elements each: one dipole and three loop elements. The three loop elements are distributed along the head-feet direction and each loop element covers approximately one-third of the dipole. In the Tx case, the blocks of one dipole and three loop elements are combined with fixed phases to form one Tx channel, respectively. The body coil was certified by a notified body to comply with the local specific absorption rate (SAR) limits in a firstlevel controlled mode of 20 W/kg (IEC 60601-2-33) that were ensured by limiting the RF power for each Tx channel to the body coil. The conversion from RF power to a local SAR was estimated based on electromagnetic simulations with 10 million random-phase settings. The worst-case shim combined with an RF power of 11.8 W applied to each Tx channel resulted in a 10 g-averaged peak spatial SAR of 11.1 W/kg; thus, it left an additional safety margin factor of 1.8. Although such limits are then independent of the applied Tx phase setting, the approach provides rather conservative power limits.
To validate the respiration-resolved B + 1 maps, a cylindrical motion phantom (radius = 12.5 cm, height = 12.0 cm) filled with water, 2% agaroses, 0.2% sodium chloride, 0.1% copper sulfate (which corresponds to σ phantom = 0.4s∕m, ε r = 80) was used that performed a translational sinusoidal-like motion along the bore axis with a peak-to-peak amplitude of 3 cm and a frequency of 0.1 Hz. To perform this motion, the phantom was placed on a wagon driven by a piston that was attached to a flywheel. The rotation of the flywheel was controlled by a cord that was wound on the flywheel. This cord was unwound by a step motor located in the operator room. Tx-RPE-GRE and RPE-AFI data sets were acquired during the translational movement of the phantom, referred to as "dynamic" acquisition. For comparison, RPE-AFI and Tx-RPE-GRE data were acquired for two extreme motion states of the phantom mimicking an inhale and exhale state, referred to as "static" acquisition. Sequence parameters are listed in Table 1. RPE-AFI and Tx-RPE-GRE data were low-pass-filtered before NUFFT reconstruction. For binning, self-navigation was used to reconstruct data into three different respiratory motion states using an iterative SENSE algorithm. 23 All subjects underwent the same protocol, which started with the coil's default B + 1 shim and no additional Tx phase. The default shim is set by the manufacturer as a trade-off between B + 1 power efficiency, SAR efficiency, and avoidance of voids throughout the entire ascending aorta, descending aorta, and the heart. This default shim is used only as a starting point because the maps and the resulting excitation pattern vary within subjects. In this configuration, a Tx-RPE-GRE was acquired under free-breathing; for comparison, a Cartesian multichannel GRE sequence (2D-Tx-GRE) was applied to obtain three equidistant transversal 2D slices without cardiac gating within one breath-hold. Additionally, a high-resolution RPEbased anatomical GRE acquisition (RPE-GRE) was obtained with default B + 1 shim. After calculation of ϕ eff based on the B + k,p (r)maps generated by Tx-RPE-GRE reconstructed with N p = 1 and Equation 4, an RPE-AFI was obtained with phase setting ϕ eff . Here, TR 1 = 10ms, TR 2 = 50ms was used, thus at the lower end within the range recommended by Yarnykh, 11 which reduced acquisition time and allowed a k-space center update of 0.48 seconds needed for sampling the selfnavigation signal. Additionally, B + 1 mapping was performed under a deep-breathing condition in two healthy subjects (S10 and S11). In these two cases, the data were reconstructed into N p = 5 respiratory motion states, which required doubling the acquisition time of both RPE-AFI and Tx-RPE-GRE with otherwise same acquisition parameters. Thus, p = 5 indicates the end inspiration motion state for deep breathing; p = 3 indicates the end inspiration motion state for shallow breathing. All RPE acquisitions were carried out with a rectangular pulse with a pulse duration of 0.5 ms.

| Image reconstruction
The Tx-RPE-GRE-based data were reconstructed during the in vivo data acquisition on a separate computer (12 central processing units (CPUs) with 2.1 GHz and 128 GB of random-access memory (RAM)). To reconstruct nonrespirationresolved RPE-GRE data, which have been used to calculate the B + k (r) maps used online during the same scanning session, a NUFFT was applied. 26 The respiration-resolved data sets were reconstructed after the scanning session on a separate reconstruction computer with 24 CPUs and 256 GB RAM. Undersampled RPE data was reconstructed for N p = 3 respiration-resolved states using a NUFFT iterative SENSE reconstruction. 27 Respiratory binning was performed using a self-navigation approach 23 and a sliding window with a 20% overlap for each side of the bin. The 3D RPE-GRE sequence obtained for the shimming demonstration was reconstructed using iterative SENSE reconstruction, resulting in 3D images in four different respiratory motion states. Subsequently, a single set of high-resolution, respiratory motion-corrected RPE-GRE images I MOCO was obtained based on the motion fields from the four states. To this end, nonrigid motion fields were estimated using NIFTYREG 29 according to an algorithm outlined in Cruz et al 21 and Kolbitsch et al. 30

| Data analysis
Quantitative evaluation was performed for an ROI computing the mean efficiency and the coefficient of variation (CV) following Metzger et al 4 and Schmitter et al. 28 The mean efficiency was defined as  31 The CV was defined as with standard deviation SD. Moreover, pixel-wise differences between B + 1 estimations were computed to quantify the accuracy of the proposed B + 1 mapping approach. The difference between static and dynamic phantom experiments was analyzed based on the MOS of static and dynamic B All results were masked based on thresholded low-pass filtered magnitude images with a kernel size of five voxels. For Tx-RPE-GRE, the SOM of Tx channels was used.

| RESULTS
In this section we show the acquisition and reconstruction of respiration-resolved 3D absolute B + 1 estimations of a moving phantom and the human thorax at 7T for 11 subjects with a wide range of BMIs and body dimensions. The figures illustrate the changes compared with previous techniques applied in the body: the extension from 2D to 3D, the ability to provide respiration-resolved maps, and the change from relative to absolute maps. The validity of the B + 1 maps is shown by a static phase-only B + 1 shim and successive cine GRE acquisitions.
(3% ± 6%) in the exhale position and a mean difference B + 1 = 1.2 ± 2.9 μT/ √ kW (3 ± 6%) in the inhale position. Background voxels were excluded from the analysis. Figure 3 illustrates the measured B + ,λ k,p of subject S4 in transversal and sagittal view for Tx channel k = 1, 3 ( Figure 3A,B). Differences in B + ,λ k,p between exhale and inhale of up to 15% and between nonrespiration-resolved and exhale/ inhale of up to 10% and 7%,respectively, have been found. Figure 4A shows channel-wise 2D Cartesian and 3D nonrespiration-resolved RPE B + ,λ k,p maps for each Tx channel in a transversal view of the isocenter in subject S8. All 3D B + ,λ k,p maps show comparable results in terms of magnitude and phase distribution compared with the 2D reference images; none of the channels shows motion artifacts. Consistent results were found for all subjects. Quantitative comparison was carried out with line plots for cross sections through the heart of the central slice for Tx channel k = 2, 4 ( Figure  4B,C) for phase and magnitude of 2D Cartesian (red) and 3D RPE-based B + ,λ k,p (black). Figure 5 illustrates the 3D absolute B + ,AFI p maps (RPE-AFI) acquired with shim setting Φ eff and absolute B + ,λ k maps acquired with shim setting Φ 0 that have been combined retrospectively with shim setting Φ eff . There is an excellent match between both maps in the heart region, thus demonstrating the validity of combining relative and absolute maps and to calculate the calibration factor λ used to compute the absolute B + ,λ k maps. The resulting CV and efficiency η for all volunteers are shown in Figure 6, with values calculated in a region covering three transversal slices of the heart as can be seen in Figure 7. Across all subjects, the variations in the ROI could be substantially reduced from CV pre = 42.5% ±6.2% to CV post = 20.6% ± 2.0% for Φ hom . The mean efficiency was improved from η pre = 53.2% ±11.2% to η post = 90.0% ±7.5% for Φ eff . Figure 7 depicts a qualitative comparison of B + ,λ k maps and RPE-GRE images obtained for two different shim settings for one coronal and three transversal views. Figure 7A shows the results using the default phase setting Φ 0 , resulting in signal cancellations in the human heart. Importantly, the B + 1 maps qualitatively match the experimental RPE-GRE images and predict the underlying B + 1 artifacts denoted by the yellow arrows. Figure 7B shows the results after the homogeneous B + 1 shim setting Φ hom . The CV in these acquisitions was reduced from 42.9% (Φ 0 ) to 19.8% (Φ hom ), which is reflected by the improved homogeneity.
In Figure 8 magnitude and phase distribution for Tx channel 1 are illustrated in three different respiratory motion states p for exhale, inhale, and the nonrespiration-resolved reconstruction for subject S10 performing deep breathing in Figure 9. No motion artifacts are visible in the respirationresolved images, and a clear difference between the B + ,λ k distributions for the exhale and inhale motion state is visible. The spatial displacement of the right hemidiaphragm between inhale and exhale was approximately 30 mm.

| DISCUSSION
The presented respiration-resolved, absolute multichannel B + 1 mapping method is based on a relative B + 1 mapping method, 14 providing proton-density relative 2D B + 1 maps in the human head. That technique has also been applied to the human body at UHF to derive relative 2D B + 1 maps within a single slice or multiple slices to calculate B + 1 shimming solutions. Furthermore, it has been applied to optimize the B + 1 field at 7T within various organs in the human body including the aorta and the kidney, as well as the human heart. 15,16,32 In addition, such a method has been used to calculate and apply multispoke pulses in the human heart and the liver at 7T, 5,33,34 as well as at 10.5T. 18 The present method extends this aforementioned technique with three modifications: (1) by extending it to 3D mapping in the human body, (2) by providing respiration-resolved maps, and (3) by enhancing the 3D AFI technique to allow for generating respirationresolved absolute B + 1 maps in the human body. The latter is used for calibration of the channel-wise maps. 3D mapping of the Tx field is highly beneficial when B + 1 shim solutions or pTx pulses are calculated for an entire 3D volume of interest. The resulting maps provide the flexibility to either optimize the B + 1 field for a single slice or multiple slices in (multislice) 2D imaging or for the entire volume in 3D imaging. 1 The ability to obtain B + 1 maps with calibrated magnitude is important for many applications, as it allows us to adjust the absolute FA value. In this work, relative maps obtained from the Tx-RPE-GRE acquisition were combined with an RPE-AFI acquisition that provides respiration-resolved B + 1 maps. Because this method uses GRE acquisitions obtained in the linear, small FA regime to calculate the relative B + 1 maps, the technique does not require high power levels. Nevertheless, the gradient of the individual B + 1 profiles from the body surface towards the center of the body makes it challenging to stay within the linear regime close to the coil, while still providing sufficient SNR in the more distant body regions. On the one hand, we observed decreased SNR in the posterior part of the heart in some volunteers. On the other hand, T 1 effects may bias the resulting B + 1 maps close to the skin, particularly when short TR values are being used to keep the scan time short as is the case for cardiac B + 1 mapping. This effect can be seen in the 3D map in Figure 4 that used a 25% higher FA compared with the 2D acquisition. Although the T 1 bias could be avoided by replacing the method with alternative techniques 35,36 that provide T 1 unbiased relative B + 1 maps, such methods may increase the acquisition time multifold. Furthermore, a general challenge that is associated with the body size is Corresponding respiratory motion-compensated high-resolution RPE-GRE images I MOCO are illustrated below for matching coronal and transversal slices obtained with Φ 0 , with CV = 42.7% and η = 42.6%. B, Estimation of B + 1 shim setting Φ hom optimized for homogeneity in the ROI with CV = 19.5% and efficiency η = 51.7% for coronal and transversal view, as well as corresponding slices for I MOCO obtained with Φ hom . The yellow arrows denote the signal dropouts in (A) obtained with Φ 0 that are recovered in (B) by applying Φ hom . Corresponding images are taken from subject S3. MOS, magnitude of the sum; RPE-GRE, radial phase-encoding-gradient echo given by regions of low FA in which the AFI method does not yield reliable values. This problem could be avoided by acquiring two or more AFI maps with different shim settings so that at each point within the region at least one of the shim settings provides sufficient B + 1 . The latter option is also exploited by the TIAMO method. 37 In principle, a similar technique, as proposed in Van de Moortele et al 12 for the human brain, could be extended to the human body. In that approach, individual, absolute B + 1 maps of each Tx channel are obtained by weighting relative Tx channel maps with one absolute B + 1 map acquired by transmitting with all Tx channels combined with a given B + 1 shim setting. This approach, however, was not feasible because it requires a well-defined FA map, ie, a FA > 20° throughout the entire 3D volume. In this work, a well-defined FA map could not be achieved in the center of the body given the power limits of the coil. We refrained from extending the duration of the rectangular RF pulse length because initial investigations showed altered FA values.
The AFI method could be replaced by other, less SAR demanding methods such as the DREAM technique, 9 which can provide very fast (ie, subsecond) absolute B + 1 maps of the human body. Furthermore, the method has also been used to show respiration-induced B + 1 changes in the human body at 3T. 38 However, the DREAM mapping technique is very sensitive to flow-induced artifacts, 39 which has also been confirmed by our own experiments, and it has a limited dynamic FA range. 9 Less flow/motion sensitivity has been observed by AFI. To estimate a potential FA error in the left ventricle and the myocardium (ie, within the ROI used for FA calibration), separate experiments in a flow phantom were conducted at 7T with a constant flow velocity of 55 cm/s, which corresponds to maximum intracardiac blood velocities 40 (see Supporting Information Figure S1). An average FA error of 15% was found compared with flow-off conditions. Furthermore, the impact of myocardial motion was estimated by extended phase graphs, which resulted in an estimated maximum error of <5%. The Bloch-Siegert shift mapping F I G U R E 8 RPE-GRE image in two respiratory states (exhale/inhale) with the corresponding MOS of estimated, absolute B + 1 distribution for subject S4 for B + 1 shim setting Φ hom . The yellow dashed line indicates the exhale position of the right hemidiaphragm. The solid white line denotes the position of line plot data. Images correspond to two cross sections taken from a three-dimensional volume. MOS, magnitude of the sum; RPE-GRE, radial phase-encoding-gradient echo technique, however, could not be applied in the body at 7T because of SAR constraints.
Therefore, the approach of calibrating the relative respiration-resolved B + 1 maps was employed in this work. Despite its benefits, the method has limitations. As reflected in Equation 2, the resulting maps are biased by the square-root of the proton density. The impact on the resulting B + 1 maps, however, is expected to induce only minor tissue-dependent variations of a few percentages. Furthermore, the technique is biased by the assumption used to obtain Equation 2 (ie, the SOM of the receive signal equals the SOM of the Tx signal), which is particularly the case for the present coil, where groups of four coil elements were combined to a single Tx element. According to electromagnetic field simulations obtained with the Duke model 41 and performed for the applied 8 Tx/32 Rx body-coil configuration, this assumption introduces an error of 10% on average throughout the thorax. The error could be reduced to 5% if the RF coil could be driven with 32 Tx and 32 Rx channels, as shown in Supporting Information Figure S2. Nevertheless, despite those limitations, a high similarity was found in qualitative comparisons between the excitation patterns and the resulting images, which is in strong agreement with previous work where the same technique was applied slice selectively in 2D. 5,15 The resulting absolute B + 1 maps obtained by the proposed method enabled successful B + 1 phase shimming as has been shown for cardiac imaging. The shim allowed for acquiring 2D cine GRE acquisitions (see Supporting Information Figure S3) in different views under breath-hold, as well as 3D respiration-resolved and respiration-corrected RPEbased GRE imaging of the entire thorax obtained under free-breathing, and in both cases, the image quality was substantially improved compared with the default shim. The magnitude of the absolute B + 1 maps was used to calibrate the nominal FA for each sequence accordingly. In two subjects, we observed phase singularities in the B + 1 maps of Tx channel 1, which was used as the reference channel. Based on calculating the phase difference, this effect translated into the B + 1 maps of the other seven Tx channels. Although this effect could be avoided by changing the reference channel (see Supporting Information Figure S4), we did not observe any impact on the resulting B + 1 phase shim magnitude; therefore, channel 1 was set as the reference Tx channel.
Our initial results found that a shim setting calculated on B + 1 maps in a respiratory state p performs better than a shim calculated on nonrespiration-resolved B + 1 maps for images acquired in motion state p. Furthermore, it seems that for shallow breathing patterns such differences in B + 1 and CV are rather minor 42 ; thus, a respiration-state-resolved reconstruction may not be needed. However, our initial results indicate that the effect becomes stronger when deep breathing F I G U R E 9 Estimated, absolute B + 1 magnitude and phase distribution for transmit channel 1 in three different respiratory motion states: p for exhale (P = 1), inhale (P = 5), and the nonrespirationresolved reconstruction for subject S10. No motion artifacts are visible in the respiration-resolved images, and a clear difference between the B + ,λ k distribution for exhale and inhale motion state is visible. The deep-breathing difference of the position of the right hemidiaphragm between inhale and exhale was approximately 30 mm is performed, which is in agreement with a recent study. 43 However, more-detailed investigations are necessary to be able to provide a more comprehensive description of the underlying effects.
Both the scan time and the reconstruction time are limitations of this method. Although a nonrespiration-resolved reconstruction requires 2 minutes, and therefore has been used during the session, the retrospective binning and reconstruction of three phases requires 15 minutes to reconstruct, which would have further prolonged the MR examination. Importantly, image acquisition times of 3 minutes and 24 seconds for the Tx-RPE-GRE and 6 minutes for the RPE-AFI are too long, particularly for future patient studies. With an increasing number of Tx channels, 44,45 the image acquisition needs to be accelerated to reduce total scan times, which could be achieved by decreasing the spatial resolution, increasing the undersampling factor, or introducing different k-space sampling strategies. 46 However, such steps might affect the quality of respiration-resolved B + 1 maps. For brain studies, so-called universal pulses have been proposed, 6 which calculate pTx RF pulses based on training data sets in several subjects that are successfully applied to subjects not included in the training pool. Although applying this approach straightforwardly to the body might be challenging because of variable body sizes, this step, combined with a minimum of information on B + 1 and/ or anatomy of the present subject, 47 may achieve the desired result at a minimum of additional calibration time.
Therefore, the present work provides a valuable basis for performing 3D imaging of the human body without signal dropouts and lays the foundation for future developments necessary for body imaging at 7T.