A field-monitoring-based approach for correcting eddy-current-induced artifacts of up to the 2^nd spatial order in Human-Connectome-Project-style multiband diffusion MRI experiment at 7T: a pilot study

Abstract

Over the recent years, significant advances in Spin-Echo (SE) Echo-Planar (EP) Diffusion MRI (dMRI) have enabled improved fiber tracking conspicuity in the human brain. At the same time, pushing the spatial resolution and using higher b-values inherently expose the acquired images to further eddy-current-induced distortion and blurring. Recently developed data-driven correction techniques, capable of significantly mitigating these defects, are included in the reconstruction pipelines developed for the Human Connectome Project (HCP) driven by the NIH BRAIN initiative. In this case, however, corrections are derived from the original diffusion-weighted (DW) magnitude images affected by distortion and blurring. Considering the complexity of k-space deviations in the presence of time varying high spatial order eddy currents, distortion and blurring may not be fully reversed when relying on magnitude DW images only. An alternative approach, consisting of iteratively reconstructing DW images based on the actual magnetic field spatiotemporal evolution measured with a magnetic field monitoring camera, has been successfully implemented at 3T in single band dMRI (Wilm et al., 2017, 2015). In this study, we aim to demonstrate the efficacy of this eddy current correction method in the challenging context of HCP-style multiband (MB=2) dMRI protocol.

The magnetic field evolution was measured during the EP-dMRI readout echo train with a field monitoring camera equipped with 16 ¹⁹F NMR probes. The time variation of 0^th, 1^st and 2^nd order spherical field harmonics were used to reconstruct DW images. Individual DW images reconstructed with and without field correction were compared. The impact of eddy current correction was evaluated by comparing the corresponding direction-averaged DW images and fractional anisotropy (FA) maps.

¹⁹F field monitoring data confirmed the existence of significant field deviations induced by the diffusion encoding gradients, with variations depending on diffusion gradient amplitude and direction. In DW images reconstructed with the field correction, residual aliasing artifacts were reduced or eliminated, and when high b-values were applied, better gray/white matter delineation and sharper gyri contours were observed, indicating reduced signal blurring. The improvement in image quality further contributed to sharper contours and better gray/white matter delineation in mean DW images and FA maps.

In conclusion, we demonstrate that up-to-2^nd-order-eddy-current-induced field perturbation in multiband, in-plane accelerated HCP-style dMRI acquisition at 7T can be corrected by integrating the measured field evolution in image reconstruction.

1. Introduction

The Human Connectome Project initiative of the National Institute for Health (NIH) pioneered significant advances during the recent years in imaging techniques aimed at mapping the functional and structural connectivity of the human brain, especially with functional MRI (fMRI) and diffusion MRI (dMRI) (Bookheimer et al., 2019; Glasser et al., 2016; Harms et al., 2018; Kochunov et al., 2015; Smith et al., 2013; Sotiropoulos et al., 2016, 2013; Ugurbil, 2014; Ugurbil et al., 2013; Van Essen et al., 2013, 2012; Van Essen and Ugurbil, 2012; Vu et al., 2017, 2015; Wu et al., 2019). In particular, these results have demonstrated the tremendous impact of increasing spatial resolution, and in the case of dMRI, of increasing the number of diffusion-encoding directions and using higher b-values. However, smaller voxels and increased b-values result in reduced signal to noise ratio (SNR), which can compromise subsequent analyses. Offering higher intrinsic SNR, scanners operating at Ultra High Magnetic field (≥7T) (UHF) have the potential to further push back these limits (Kraff et al., 2015; Ugurbil, 2014), albeit at the cost of significant challenges, including transmit B1 and B0 inhomogeneity as well as RF power limitations due to specific absorption rate (SAR) (Ugurbil et al., 2013; Van Essen et al., 2013, 2012; Van Essen and Ugurbil, 2012; Vu et al., 2017). Despite these challenges and the tradeoffs they impose, it has been shown, when merging dMRI at 7T with dMRI at 3T, dMRI at the higher resolution afforded at 7T provided some specific information for fiber track orientation and fiber crossing that were missing at lower spatial resolution at 3T, even though higher b-values were used at 3T (Sotiropoulos et al., 2016).

While dramatic improvements in gradient coil engineering and MR acquisition techniques (especially parallel imaging and simultaneous multiband (MB) excitation) have been critical towards improving dMRI (Sotiropoulos et al., 2013), advanced image reconstruction techniques played an equally pivotal role in enabling much greater fiber tracking conspicuity. This concerns particularly eddy-current-induced encoding errors in dMRI, yielding geometric distortions (shear, shrinkage, dilation, shift) that greatly vary between diffusion-encoding directions (Jezzard et al., 1998; Le Bihan et al., 2006). These errors could further result in inconsistency and blurring when calculating diffusion tensors that form the basis of fiber tracking computation (Mukherjee et al., 2008). These eddy-current-induced artifacts are largely mitigated in the standard HCP dMRI processing pipelines using an image-based data-driven approach known as FSL eddy (Andersson et al., 2017; Andersson and Skare, 2002). While remarkably efficient, these approaches consist of deriving correction parameters directly from magnitude dMRI images affected by distortion and blurring. Thus, directly measuring the magnetic field deviations and integrating this information in the reconstruction process in principle may achieve a more precise correction. This is particularly significant for complex field deviations resulting from eddy currents with higher spatial orders. The subsequent intricate image distortion and blurring may not be fully reversible using only a magnitude-image-based approach. Investigating this issue, however, requires the knowledge of the actual temporal field evolution.

One technique to accurately characterizing the temporospatial magnetic field evolution utilizes multiprobe magnetic field monitoring (Barmet et al., 2008; De Zanche et al., 2008). The technique has been successfully applied to correct eddy-current-induced geometric distortions in single-shot single-band (SB) echo-planar imaging (EPI) (Wilm et al., 2015) and spiral dMRI (Wilm et al., 2017), with multiple repetitions and a b-value of 1000 s/mm². Compared to these studies, HCP dMRI acquisitions at 7T present further challenges, including the use of higher b-values (up to 2000 s/mm²), significantly smaller voxels (volume = 1.05x1.05x1.05 mm³) and a single average. All the three factors result in reduced SNR, with additional reconstruction constraints related to multiband (MB) excitation (also known as simultaneous multi-slice excitation) (Larkman et al., 2001; Moeller et al., 2010; Setsompop et al., 2012), potentially making it more difficult to appreciate the effect of field correction. In this work, we aim to demonstrate that a field-monitoring-based approach can correct for up-to-2^nd-order-eddy-current-induced artifacts in MB HCP-style dMRI acquisitions at 7T. Because of high computational demands for the reconstruction, this initial demonstration only includes a subset of the standard 7T HCP protocol (reduced number of slices and diffusion-encodings).

2. Theory

The expression of the dynamic field B(r,t), with r and t, spatial coordinates and time, respectively, can be expanded with N_L spatially varying spherical harmonics fl(r) (Barmet et al., 2008):

$$|\mathit{B}(\mathit{r},t)|={\Sigma }_{l=0}^{N_L-1}{c}_l(t)f_l(\mathit{r})+|{\mathit{B}}_{ref}(\mathit{r})|$$

Where |B_ref(r)| denotes the magnitude of the magnetic field at a given reference time point, after which the static field, including the effect of the shimming currents, will not change.

The MR signal S(t), at a given time during the readout window of the sequence, when neglecting longitudinal and transversal relaxation, dephasing and rephasing, diffusion, coil sensitivity, can be formalized as

$$S(t)\propto \int M_{xy}(\mathit{r})e^{-i}{\int }_0^t\int \gamma |B(\mathit{r},t^{\prime })|d{t}^{\prime }d\mathit{r},$$

where M_xy and γ denote transverse magnetization and the gyromagnetic ratio, respectively. Especially in the presence of system imperfections, such as eddy currents that are induced by the diffusion-encoding gradients, |B(r,t’)| can substantially deviate from the values predicted by nominal k-space trajectories as defined with ideal gradient waveform. Straight 2D Fourier Transform (FT), on the other hand, relies on Cartesian, regularly distributed k-space sampling. Therefore, ignoring k-space deviations results in image artifacts that have been extensively described (Jezzard et al., 1998; Le Bihan et al., 2006). When a more accurate estimation of actual |B(r,t’)| is known for each time point, as is the case with a magnetic field camera, eddy-current-induced field deviations can in principle be corrected for during image reconstruction. When |B(r,t’)| is modeled with spherical harmonics that do not exceed 1^st order terms (x, y, z), the induced k-space deviations can be described as temporal modulations of nominal spatial encoding gradient. In such case, one can use relatively straightforward regridding algorithms, such as non-uniform FourierTransform (NUFFT) for k-space sampling fulfilling Nyquist criteria (Beatty et al., 2005; Dutt and Rokhlin, 1993; Fessler and Sutton, 2003) to regenerate a regularly distributed k-space before applying FFT reconstruction. When considering non-Cartesian sampling and higher order spherical harmonics (up to the 2^nd order in the present study), however, the encoding matrix is no longer described by a Fourier transform. Thus, more sophisticated reconstruction strategies must be used. In this work, we focus on a CG-SENSE based reconstruction framework (Wilm et al., 2011).

3. Material and Methods

3.1. MR acquisition

Two control subjects, who signed a consent form approved by the University of Minnesota IRB, were imaged on a 7 Tesla Magnetom Siemens scanner (Siemens Healthineers, Erlangen, Germany), using a single-transmit and 32-receive channel RF head coil (Nova Medical, Wilmington, MA, USA). The dMRI sequence and related acquisition parameters, except for the number of slices, diffusion-encoding steps and simultaneously excited inter-slice distance, were similar to those of the 7T HCP dMRI protocol described in (Vu et al., 2015). Major parameters included: single-shot Spin-Echo (SE) Echo-Planar (EP) dMRI with a Stejskal-Tanner diffusion-weighting scheme, TR/TE = 7000 ms/71.2 ms, FoV = (210 × 210 mm²), in-plane resolution = (1.05 × 1.05 mm²), nominal bandwidth = 277.8 kHz, slice thickness = 1.05mm, MB factor = 2 with blipped-CAIPI (Setsompop et al., 2012), in-plane acceleration = 3. The sequence started with the acquisition of 66 lines of GRE AutoCalibration Signal (ACS) for each slice, followed by Single Band (SB) reference EPI signal acquired just prior to the actual diffusion-weighted (DW) acquisition. The diffusion gradient parameters included: ramp time = 700 μs, δ = 14420 us, Δ = 34350 μs, amplitude = 7.91, 32.39 and 45.67 mT/m for b-values of 60,1000, and 2000 s/mm², respectively. For proof of principle, a smaller number of slices (10 instead of 132) and fewer diffusion encodings (19 instead of 71+72=143) were used because of extensive computational times required in the initial implementation of the reconstruction pipeline. The inter-slice distance for simultaneous MB excitation was 21 mm, the 6 diffusion-encoding directions (for non-zero b-values) were defined as: [x,y,z] = [1 0 1], [−1 0 1], [0 1 1], [0 1 −1], [1 1 0], [−1 1 0] and all data were acquired using a single phase encoding polarity in the EPI sequence. The resulting acquisition time was 2:41 min for each run. Albeit only a subset of HCP dMRI acquisition is included in the study, the effectiveness of eddy current correction is not expected to be affected since field correction does not depend on number of diffusion-encoding directions or number of slices. Raw complex data were transferred to another server before applying the reconstruction strategies programmed in Matlab (The Mathworks, Natick, MA, USA).

3.2. Raw data extraction

During data acquisition, the MR signal is oversampled by the console at twice the nominal bandwidth. The first standard pre-processing step consists of down-sampling the raw data, thereby halving the output data size, preceded, in case of non-equidistant k-space sampling (in the present case this concerns ramp sampling at both edges of the EPI readout), by data interpolation toward a regular k-space grid based on a nominal k-space time evolution assuming ideal gradient waveforms. These assumptions, however, do not apply anymore when explicitly using actual, measured field evolution; therefore, data oversampling was preserved when performing CG-SENSE reconstruction, resulting in acquisition matrix sizes twice larger along the readout.

3.3. Dynamic Field Monitoring

16 ¹⁹F NMR probes with a standalone spectrometer (Skope, Zurich, Switzerland) were used to monitor the field evolution during the EPI readout. Field monitoring was conducted in a separate, dedicated session, using same sequence and protocol as during human scans, with the probes spatially distributed on a tridimensional scaffold positioned at the isocenter of the gradient coil along the Z axis. We denote this acquisition as “dynamic field monitoring”, to be distinguished from “concurrent field monitoring” (Kasper et al., 2017; Wilm et al., 2017, 2015), where field monitoring is performed simultaneously with the MR acquisition during a human scan, which is not part of the present work. The synchronization of the excitation and signal reading of the ¹⁹F probes with the ¹H MR sequence was obtained by inserting in the MR sequence a transitor-transitor logic (TTL) output right after the slice excitation RF pulse. Using the timing of the TTL input, the field monitoring spectrometer was programmed to trigger the ¹⁹F probes excitation after a delay carefully calculated to start the measurement of the ¹⁹F probes signal prior to the EP readout of the MR scanner. Every readout event of the probes lasts 50ms to cover one entire echo train of the EP readout, with a sampling bandwidth of 1MHz. The effective TR between two consecutive ¹⁹F excitations was 1200ms, allowing virtually full T1 relaxation of the probe ¹⁹F signal (Kasper et al., 2017). The acquisition scheme for dMRI and field measurement is displayed in Fig. 1.

Fig. 1.

Acquisition scheme for dMRI and field measurement using ¹⁹F NMR probes. The synchronization of the ¹⁹F NMR probes excitation and signal measurement with the MR console was obtained by inserting a TTLout in the EPI sequence right after the 90° RF excitation pulse, followed by an acquisition delay on the field monitoring spectrometer which was determined, based on the MR acquisition parameters, to start the signal measurement of the ¹⁹F probes right before the prewinding gradients of the Echo Planar sequence. The trigger received by the field camera system is denoted as TTLin.

Based on the measured ¹⁹F probe signal, the 0^th, 1^st and 2^nd order field terms were fitted by the field camera console and transferred to another server. The basis functions f_l and the noise standard deviation of the temporal coefficient k_l(t), assuming SNR = 10 for individual ¹⁹F probes, are listed in table 1. The noise standard deviation was derived from the actual position of the probes, using Eq.(8) from (Barmet et al., 2008).

Table 1.

Real-valued expansion of the spherical harmonics up to 2^nd order and their standard deviation of the coefficients

Spatial Order	Cartesian representation	SD of the coefficient
0	1	0.026 rad
1	x	0.476 rad/m
1	y	0.471 rad/m
1	z	0.514 rad/m
2	xy	3.858 rad/m2
2	zy	7.101 rad/m2
2	3z2- (x2 + y2 + z2)	6.861 rad/m2
2	xz	3.201 rad/m2
2	x2 – y2	3.132 rad/m2

3.4. B0-modulation and Blip-modulation measurement

On Siemens scanners, eddy-current-induced 0^th order temporal deviations are predicted according to the gradient waveforms of the MR sequence and converted into corresponding real time variation of the synthesized demodulating RF frequency, thereby cancelling the predicted undesired phase accumulation. As a result, complex raw data are corrected by the console before being written on disk. We denote this correction term as B0-modulation. Likewise, for Blipped-CAIPI MB acquisition, to compensate for the additional phase difference generated when neither slice is at isocenter (Setsompop et al., 2012), a constant phase is added to every other readout line of the EPI echo train. We denote this term as Blip-modulation. In this study, we followed the following steps to measure the combined effect of B0-modulation and Blip-modulation (these acquisitions were obtained without using the ¹⁹F probes):

1. An external RF synthesizer (PTS500, PROGRAMMED TEST SOURCES inc, Littleton, MA, USA), synchronized to the 10MHz clock of the MR console and programmed to generate a pure sinusoid waveform at the Larmor frequency reading on the MR console (297MHz), was used as the RF signal source.

2. A 50Ω impedance cable carrying the RF output signal was used (instead of the standard receive cable used in normal operation) to feed one of the 32 channels of the receiver board of the MR console, this channel being denoted as tRC for testing Receive Channel. Starting with a very small amplitude, the voltage of the RF synthesizer output was gradually increased until the corresponding signal showing on the free induction decay (FID) display of the MR console reached a reasonable amplitude while staying largely below the receiver ADC saturation level. It was determined that in our configuration a 1 Volt amplitude at the RF synthesizer output satisfied these criteria. Several receive channels were tested for comparison: no phase variations and no noticeable differences in SNR were observed between the corresponding data measured by the MR console. In the reported results, channel 2 was arbitrarily used as tRC.

3. The same diffusion sequence and protocol used in vivo were run with the MR system and the RF synthesizer set at the same frequency (297MHz). In both cases, this setup allowed the combined B0- and Blip-modulation to become the only source of temporal phase variation (ignoring noise components) of the complex data written on channel tRC.

4. After acquisition, the raw data was exported to an external server as described in section 3.2. Only the signal from channel tRC was extracted for further processing. No filter or denoising algorithm was applied. The conjugate phase of the tRC complex data was directly applied to the 32-channel complex raw k-space data obtained during actual dMRI scans, prior to ¹⁹F-probe-based field correction.

As is the case with the ¹⁹F-probes field monitoring, the B0 modulation needs being measured over the entire dMRI sequence, from beginning to end, to capture the whole B0 modulation history. It should be noted that this eddy current compensation B0 modulation recording technique can be run as a standalone experiment, without the ¹⁹F probes, and regardless of whether or not a ¹H RF coil and phantom are used. At the same time, it may be advantageous to use the very same technique during a simultaneous ¹⁹F field monitoring session and/or during an actual simultaneous ¹H acquisition, to the cost, in the latter case, of losing the ¹H signal of one receive channel (out of 32 in our case).

Note, however, that one should not remove the Blip-modulation term for MB slice-GRAPPA (sGRAPPA) (Setsompop et al., 2012) and MB one-shot SENSE reconstruction. B0-modulation was not removed either. In our CG-SENSE implementation, designing the encoding matrix required explicitly pre-defining field evolution and slice position, therefore the Blip-modulation term needed to be removed from the data before reconstruction. B0 modulation needed to be removed from the raw data to perform full field correction using measured field evolution.

3.5. Comparing B0-modulation with measured 0^th order field evolution

To compare the B0-modulation automatically applied by the scanner with the 0^th order field evolution measured by the field camera, B0- and Blip-modulation have to first be separated and identified. In MB acquisition, the phase of the combined B0- and Blip-modulation imposed by the scanner, denoted as φ_{total, MB}, can be written as:

$${\phi }_{\text{total},\text{MB}}={\phi }_{\text{EC},\text{EPI}}+{\phi }_{\text{EC},\text{diff}}+{\phi }_{\text{MB}},$$

where φ_{EC, EPI} and φ_{EC, diff} are meant to compensate the predicted 0^th order field deviations, due to EPI-and-diffusion-gradient-waveform-induced eddy currents, with φ_MB being the Blip-modulation term. During the SB reference EPI acquisition, obtained at the beginning of the MB dMRI sequence, the CAIPI encoding gradient blip was still applied, with the combined B0- and Blip-modulation phase described by:

$${\phi }_{\text{total},\text{SBref}}={\phi }_{\text{EC},\text{EPI}}+{\phi }_{\text{MB}.}$$

Measuring φ_{EC, EPI} on its own was obtained by simply running a SB acquisition with the same parameters as the SB reference EPI obtained at the beginning of a MB dMRI acquisition, but without Blipped-CAIPI encoding, as in SB acquisition the system only applies the B0-modulation term (ignoring for simplicity a global phase offset for off-center slices). The Blip-modulation term φ_MB was then derived by subtracting the measured φ_{EC, EPI} term from the measured φ_{total, SBref} term. The B0-modulation term due to EPI-and-diffusion-gradients-induced eddy currents, represented by φ_{EC, diff} + φ_{EC, EPI}, can be obtained by subtracting φ_MB and φ_{EC, EPI}, from φ_{total, MB}. This B0-modulation term could then be compared with the 0^th order field evolution measured with the field camera.

Here we measured φ_EC,EPI with a separate SB acquisition for the demonstration purpose. In the cases where the summation of φ_EC,EPI and φ_EC,diff rather than φ_EC,EPI alone is of interest, the B0-modulation term can be alternatively measured by running the same MB acquisition but switching off the blipencoding if the sequence allows for this operation.

3.6. sGRAPPA reconstruction

For sGRAPPA, the signals of two simultaneously excited slices were first unfolded using SB EPI reference data, as previously described (Setsompop et al., 2012), followed by in-plane GRAPPA reconstruction using GRE-acquired ACS lines, the last step consisting in SENSE1 signal combination between receive coils (S. N. Sotiropoulos et al., 2013). Field deviations explicitly described with spherical harmonics up to the 2^nd order cannot be accounted for with the sGRAPPA formalism in its standard form, thus sGRAPPA reconstruction was only performed without field correction.

3.7. CG-SENSE reconstruction

Unlike sGRAPPA, CG-SENSE reconstruction enables the use of algebraically defined non-Fourier encoding (Pruessmann et al., 2001; Wilm et al., 2011), represented here by the ¹⁹F-measured encoding field evolution. CG-SENSE reconstruction, on the other hand, requires receive coil sensitivity maps. For comparison, three different methods were used to generate the sensitivity maps:

1. sACS: For each receive channel, the GRE ACS lines were multiplied by a Gaussian filter, followed by zero-filling along phase encoding direction and 2D Fourier transform. To generate normalized sensitivity maps, these complex images were divided by the root sum of squares (rSoS) of the magnitude images across all channels.

2. sSBref: Aiming to account for the geometric mismatch between GRE and EPI acquisition that may introduce artifacts in SENSE-based reconstruction, a GRAPPA reconstruction of the Single Band EPI reference (SBref) scan was first obtained using the GRE-acquired ACS lines. A Gaussian filter was applied in the k-space domain right after GRAPPA unfolding followed by Fourier transform. As with the previous approach, normalized sensitivities were obtained by dividing the complex images by the rSoS of the magnitude images across all channels.

3. ESPIRiT: An eigenvalue decomposition was used to generate the sensitivity profiles using ACS lines as described in (Uecker et al., 2014).

Here, we did not perform field monitoring or field correction on the GRE ACS or SBref data. Ramp sampling was handled using interpolation-based k-space regridding. Only smoothed images were required for the sensitivity profiles, without the need for conspicuous details of brain structures, and we did not observe reconstruction issues imputable to eddy-current-induced errors that occurred during ramp sampling in GRE readout and SB EPI.

Prior to CG-SENSE reconstruction, the fitted field coefficients from the field camera were downsampled to coincide with the dwell times and echo spacing of MR imaging sampling. During the reconstruction process, 15 CG-SENSE iterations were always included. When sensitivity maps were obtained with sSBref or sACS, the normalization of the sensitivity profiles was performed after the CG loops to preserve the SNR of the final images (Sodickson and McKenzie, 2001). Examples of sensitivity profile magnitude generated by the three methods are shown in Fig. 2, for 8 out of the 32 receive channels.

Fig. 2.

Magnitude sensitivity maps for 8 out of the 32 Rx channels generated with three different methods. Top: sACS, Middle: sSBref, Bottom: ESPIRIT.

For each of the three methods, two CG-SENSE reconstructions were performed, with and without including the field evolution terms (0^th, 1^st and 2^nd order) measured with the field camera.

3.8. Three-reference lines versus measured field correction

When the ¹⁹F-measured field correction was not applied, a three-reference-lines Nyquist ghost correction (Heid, 1997) as well as ramp sampling correction were performed before sGRAPPA and CG-SENSE reconstruction. For CG-SENSE, the encoding matrix was defined as the nominal k-space trajectory, including EPI (kx and ky) and blipped-CAIPI (kz) encoding. When applying the field correction with CG-SENSE, the encoding matrix was defined by the ¹⁹F-measured field evolution.

3.9. Mean DW and FA maps

In all reconstructions, MP-PCA-based denoising (Does et al., 2019; Veraart et al., 2016) was applied to the final images with the sliding window size of [5x5], in order to further reduce the noise in the reconstructed images for further processing. Mean DW images were then obtained, as described in (Wilm et al., 2017, 2011), by averaging the reconstructed DW images without coregistraton obtained along the six diffusionencoding directions, for b = 2000 s/mm² , which is most subjective to eddy current from diffusion gradient. Fractional anisotropy (FA) maps were calculated using all acquisitions (b = 0, 1000, and 2000 s/mm²) (Kingsley, 2006) to provide a comprehensive estimation of the effectiveness of eddy current correction.

The entire reconstruction pipeline was programmed in Matlab 2016a (Mathworks, USA) and executed on a linux server (simultaneously shared with other users) (CPU: AMD Opteron(tm) Processor 6140, 8 cores, cache size: 512 KB, CPU MHz: 2600). Due to the large memory required to load the full encoding matrix during CG process, no parallel computation was used, yielding a total computational time of 1 minute per excitation (two slices) in the current implementation.

3.10. Eddy current correction using scanner imposed B0 modulation and measured k0

To examine whether the field camera measured k0 describes the field evolution more accurately compared to the scanner-imposed B0 modulation, we reconstructed the images with CG-SENSE scheme retaining scanner-imposed B0 modulation rather than replacing it with the measured k0. Other reconstruction parameters, including sensitivity maps, 1^st and 2^nd order field data were the same for both strategies. The DW images and mean DW images reconstructed with each strategy were compared.

4. Results

4.1. 1^st and 2^nd order measured field evolution

Fig. 3 shows, during the EPI echo readout train, the measured evolution of the three 1^st order (k_x, k_y and k_z) and three of the five 2^nd order (k_xy, k_zy and k_2z^2-x^2-y^2) field terms. As expected, no difference was observed (see Fig. 3A) in the measured field evolution when changing across the different pairs of simultaneously excited slices while applying a same diffusion-encoding gradient. By contrast, deviations of the field evolution were readily observed for all terms when applying different diffusion-encoding gradients while keeping everything else the same, as shown in Fig. 3B for b = 2000 s/mm².

Fig. 3.

Measured field evolution during the EPI echo readout train, comparing: (A) five different selective slice excitation positions (blue, red, yellow, violet and green curves) with same diffusion-encoding gradient, or (B) three different diffusion-encoding gradients (yellow, violet and green curves) with same slice-selective excitation, with b = 2000 s/mm². Upper left (A and B): k_y as a function of k_x. Lower left (A and B): k_z as a function of time. Upper, Middle and Lower Right (A and B): k_xy, k_zy, and k_2z^2-x^2-y^2, respectively, as a function of time. The nominal trajectories of ky-kx and kz are plotted as gray dots. An insert in the upper right corner of each upper left chart (A and B) shows a zoomed-in view of the lower right corner of the plot for better visualization. In chart (A), additional inserts in the Upper, Middle and Lower charts show a zoomed-in 2.4ms segment of the plots for better visualization.

4.2. B0-modulation versus measured k0

The results of the multi-step procedure to measure the scanner-imposed B0-modulation and Blip-modulation phase terms, and the comparison with the measured k0 term evolution are detailed in Fig. 4A. The global phase term φ_total,MB is shown in Fig. 4A as well as its three components (φ_diff, φ_EPI and φ_MB) derived from scans with a test receiver channel fed with an RF synthesizer, for b = 2000 s/mm² with G = [0 1 1]. The impact of EPI readout and diffusion-encoding gradients is further detailed in Fig. 4B for b = 0 s/mm² and, with two different diffusion gradient directions, for b = 2000 s/mm². The first row of Fig. 4B shows the global term φ_total,MB removed from the raw data, while the second and third rows show the sum of the EPI and Diffusion related terms, as imposed by the scanner (φ_EPI + φ_diff), versus the applied correction terms as derived from the field monitoring camera results (φ_EPIȲ + φ_diffȲ), respectively. The temporal evolution of (φ_EPI + φ_diff) and (φ_EPIȲ + φ_diffȲ) is plotted in Fig. 4C by unwrapping the second and third rows from Fig. 4B and organizing the results in the correct temporal order. Differences between scanner-imposed B0-modulation and measured k0 are readily visible. In addition to the difference in the degree of phase excursion across the EPI readout, the measured k0 showed larger phase difference between the adjacent readout lines.

Fig. 4.

Comparison between the scanner imposed B0-modulatlon and the 0^th order field (k0) evolution as measured with the field monitoring camera. (A) Leftmost plot: scanner-imposed φ_total,MB followed by the 3 sub-components φ_EPI , φ_diff and φ_MB, shown in the next three plots to the right, for b = 2000 s/mm² and G = [0 1 1]. (B) Upper row: scanner-imposed φ_total,MB for, from left to right, b = 0 and 2000 mm/s² with G = [−1 0 1], and b = 2000 mm/s² with G = [1 1 0], Middle row: subset [φ_diff + φ_EPI] of scanner-imposed modulation for the same b-values and diffusion-gradient directions. Lower row: [φ_diff′ + φ_EPI′] phase correction term, corresponding to the measured k0 evolution, for the same b-values and diffusion-gradient directions. (C) Time evolution of measured (red line) and scanner-imposed (gray line) k0 during the readout for the same b-values and diffusion-gradient directions as from (B). All results are expressed in radians.

4.3. Impact of measured-field correction on image reconstruction.

Fig. 5 shows the DW images of two simultaneously excited slices obtained with five different reconstruction schemes, without or with measured-field correction, as shown in the first two or in the last three columns, respectively, with either b = 60 s/mm² or b = 2000 s/mm². 7 reconstructions were performed: sGRAPPA without measured-field correction, CG-SENSE without measured-field correction with three different sensitivity maps, and CG-SENSE with measured-field correction also with three sensitivity maps. However, results for CG-SENSE without measured-field correction are only shown for sACS sensitivity maps (2^nd column in Fig. 5 and Fig. 6) as no noticeable difference was observed when using either of the two other maps.

Fig. 5.

Two simultaneously excited slices reconstructed with different approaches, including (from left to right) slice-GRAPPA, CG-SENSE without field correction, CG-SENSE with field correction using sensitivity maps generated from ACS, SBref and ESPIRiT approaches. The arrows indicate areas in the images where improvement after field correction can be appreciated. Red arrow: aliasing artifacts observed from sGRAPPA reconstruction that vanished after field correction. Yellow arrows: artifacts observed from CG-SENSE recon without field correction that vanished after field correction. Green arrows: sharper contrast and tissue edges could be observed after field correction.

Fig. 6.

Mean DW images (b = 2000 s/mm²) and FA maps of two simultaneously excited slices averaged across 6 diffusion-encoding gradients, from different reconstruction approaches. The green boxes overlaid on the mean DW images indicate areas where significantly reduced signal blurring is observed when field correction is applied in the reconstruction, resulting in improved tissue contrast and sharper brain edges.

For DW images acquired with a very small diffusion weighting of b = 60 s/mm², (1^st and 3^rd row), CG-SENSE without measured-field correction tended to introduce some residual aliasing artifacts (yellow arrow) that were absent with sGRAPPA (1^st column). However, when CG-SENSE reconstruction was applied with measured-field correction (columns 3 to 5), not only did these artifacts disappear, but other artifacts observed with sGRAPPA (red arrow) also vanished in the reconstruction. As is commonly observed in DW SE-EPI, when large diffusion weighting was applied (b = 2000 s/mm², 2^nd and 4^th row), with subsequent SNR reduction and the attenuation of CSF signal with hyperintensity, aliasing residual artifacts became less easy to identify.

Clear differences in brain structure conspicuity were observed with b = 2000 s/mm² when including the measured field correction in CG-SENSE reconstruction, with an overall increase in brain structure sharpness. White/gray matter delineation was better preserved. In several locations, a clearer contrast was restituted between a darker background in sulci (corresponding to CSF) and brighter tissue signal at the edge of gyri, the contour of which were blurred in mean DW images without correction.

Similar observations regarding overall sharpness, gray/white matter delineation and restitution of dark sulci background, when applying the measured field correction, can be made in Fig. 6 on the mean DW images obtained for another pair of simultaneously excited slices with b = 2000 s/mm². In FA maps shown in the same figure and for the same pair of slices, when the measured field correction was included in the reconstruction, higher contrast-to-noise ratio and improved continuity of the major white matter tracts are observed. Since the improvement of the quality of FA maps was mostly observed within the brain, this was expected to be an effect of reduced blurring.

4.4. Impact of sensitivity maps

Using different sensitivity maps for CG-SENSE reconstruction did not result in noticeable differences within the brain in the final reconstructed images, regardless of whether or not the measured field correction was applied. The signals in the skull and skin region were further suppressed when using sSBref sensitivity maps. The geometric mismatch between GRE and EPI acquisitions did not result in obvious quality degradation in the reconstructed images, although it should be noted that the limited slab coverage in the current study (48.3mm coverage along the Z axis) did not encompass areas with large ΔB0 distortions.

4.5. Impact of 0^th order field

Fig. 7 shows the reconstructed DW images (b = 60, 2000 s/mm²) and mean DW images from the two simultaneously excited slices using either the measured k0 evolution (column 1, 3) or the scanner-imposed B0 modulation (column 2, 4). DW images with b-value of 60 s/mm² showed no difference in image quality between the two reconstruction strategies. For DW images with b-value of 2000 s/mm², using the field camera measured k0 evolution provided superior results in terms of signal deblurring, reflected by sharper brain edges and better delineation between gray and white matter.

Fig. 7.

Two simultaneously excited slices reconstructed with measured k0 (column 1,3) and scanner imposed B0 modulation (column 2,4), shown with DW images (b= 60, 2000 top 3 rows) and mean DW images (bottom 2 rows). Brain areas with a visible improvement of signal deblurring when using the measured k0 are highlighted with green boxes with zoomed images underneath for a better visualization.

5. Discussion

This study is motivated by the long-term goal of achieving very high fiber tracking accuracy in the human brain based on dMRI in the context of HCP-style protocols, with the specific target of demonstrating eddy current correction in multiband, high-resolution DW images. In this study, first, following the HCP dMRI protocol, we demonstrated successful field monitoring to measure up-to-2^nd-order field deviation induced by eddy currents; second, we implemented the reconstruction scheme to perform field correction to achieve signal deblurring; finally, the eddy current correction based on field monitoring significantly improved the quality of diffusion parametric maps. In addition, we observe in this study that scanner-imposed B0 eddy current correction terms need to be removed to achieve full field correction using the measured field evolution.

5.1. Impact of measured field correction on image reconstruction.

This approach was implemented on a Siemens 7T MRI system, using 16 ¹⁹F probes and a stand-alone spectrometer to measure the field evolution during single-shot HCP-style dMRI acquisition. The data measured with the ¹⁹F probes were fitted up to the 2^nd order spherical harmonics. Using MR signal expression based on MR physics and CG-SENSE reconstruction, our results confirm (see Figs. 5 & 6) that eddy-current-induced artifacts can be successfully corrected after integrating the measured field evolution, reflected by largely reduced blurring in reconstructed DW images. When more diffusionencoding steps are included, further improvement in the fidelity of diffusion parametric maps with field correction is expected based on the result of cleaner FA maps with higher contrast-to-noise ratio. Consistent with prior reports (Wilm et al., 2015), the field evolution dramatically differed between diffusion-encoding directions, while no significant variations were observed when comparing different pairs of excited slices keeping everything else the same. Regarding the 0^th order compensation, the readily visible difference between the B0 modulation imposed by the scanner and that measured with the ¹⁹F probes indicate that the former should be removed from the data and replaced with the conjugate of the latter.

5.2. Reconstruction strategies

Regarding background noise propagation in the context of multiband and GRAPPA acceleration, no noticeable differences were observed between sGRAPPA and CG-SENSE reconstruction, so long as sensitivity maps were appropriately defined (attempts with sensitivity maps obtained differently than through the steps described in the method section resulted in increased levels of noise – data not shown). Similar findings were reported by others using a conventional SENSE approach for MB reconstruction (Zahneisen et al., 2015). Two factors in particular should be considered when choosing a strategy to define the sensitivity profiles:

1. The ESPIRiT framework requires a far longer computational time to obtain the sensitivity maps, especially considering the large k-space matrix size in HCP-style protocols (200 x 200 x 32 per slice for 32 channels). It also relies on manually setting subject-specific and slice-specific eigenvalue thresholds for signal and noise, whereas, by contrast, sACS and sSBref approaches are fast and can be automated.

2. ESPIRiT, on the other hand, provides the smoothest sensitivity profiles and yields the lowest sensitivity to bright CSF signal in low b-value DW images.

It appeared that some residual aliasing artifacts were more pronounced in sGRAPPA reconstruction, whereas some others were noticed in CG-SENSE reconstruction without field correction. However, when applying CG-SENSE with field correction, these artifacts were all reduced or eliminated, which may indicate that CG-SENSE reconstruction outperforms sGRAPPA for aliasing reduction when the actual encoding matrix is known, whereas sGRAPPA may benefit from more robust multiband un-aliasing when field deviations are not known.

In our acquisitions, denoising was performed with MP-PCA (Does et al., 2019; Veraart et al., 2016) due to its straightforward implementation without requiring tuning of the threshold parameter, since this parameter is automatically determined from the noise distribution in the reconstructed images. In contrast, a regularized CG-SENSE approach typically requires empirical tuning of the relevant thresholding parameter through exhaustive search. For the non-Fourier encoding matrices used in this study, such an exhaustive search quickly becomes computationally prohibitive.

In its current implementation, the duration of the reconstruction process for a full HCP dMRI protocol could result in a significant burden. However, more advanced hardware can significantly accelerate the reconstruction. For example, when tested on a different and a more advanced linux server (Intel(R) Xeon(R) CPU E5-2697 v4 @ 2.30GHz18 cores, cache size 46080 KB, CPU MHz: 3600), despite of the latter being simultaneously shared by multiple users, the computation time dropped to 25 seconds per excitation (2 slices). Using graphic processing units (GPUs) on a dedicated workstation could further increase the reconstruction speed.

5.3. Comparison of scanner imposed B0 modulation and measured k0

The discrepancy between the scanner imposed B0 modulation and the k0 evolution measured with field monitoring may be explained in part by differences in hardware characteristics between the time when the scanner was calibrated and the corresponding B0 modulation coefficients determined, and the time when our experiments were conducted. Such putative drift in hardware characteristics across time may result in less accurate B0 modulation by the scanner for 0^th order eddy current correction. In practice, probe based field monitoring is expected to accurately capture the actual field deviations induced by eddy current, which is further confirmed by the improvement in the quality of the images reconstructed using measured k0 compared to scanner-imposed B0 modulation (Fig. 7).

5.4. Limitations.

In this study we did not utilize 3^rd order basis functions, limiting data fitting to the 2^nd order, for two reasons. Firstly, 3^rd order field terms include 16 basis functions, therefore requiring that the signal amplitude of all 16 probes remains well above the noise level until the end of the 50ms SE-EPI readout. This is a fairly long duration considering the average lifetime of the ¹⁹F probes on our 7T system, and we could not guarantee that none of the probes would experience excessive signal losses when reaching 50ms. Fitting up to the 2^nd order fields (defined with 9 basis functions), however, only requires the signal of 9 probes being above noise level, which was always achieved. Secondly, fitting 3^rd order basis functions ideally requires a spherical distribution of the 16 probes to maintain reasonable noise standard deviation in fitting coefficients. While easily done on a scaffold for dynamic field monitoring, this is not achievable during a human scanning session within the geometric constraints of our head RF coil setup. Considering that the methods developed and implemented in the current work are intended to pave the way for concurrent monitoring of in vivo acquisitions in future studies, we focused on experimental conditions that could be modified for that purpose with ease.

In principle, measured B0 maps can be included in the reconstruction framework to jointly correct for local-susceptibility-induced distortions (Wilm et al., 2015). The goal of the present study, however, was to address distortion and blurring that specifically affect DW images as well as their dependence on diffusion-encoding amplitude and direction. By comparison, susceptibility-induced local B0 distortions, approximated as static components, are not monitored by the field camera, and it was deemed preferable to not risk confusing eddy current related image alterations and their correction with the additional correction of unrelated local geometric distortions. It should be mentioned that, although sSBref and sACS derived sensitivity maps were satisfactory within a 10-slice subset of HCP-style protocol, the latter did not reach the inferior part of the brain where local susceptibility are more pronounced. When reaching slices at a lower level along the z axis, sSBref and ESPIRiT approaches are expected to be more robust to the corresponding stronger distortions in EPI images; this will have to be assessed experimentally.

When used during in-vivo experiments, the field camera can also detect magnetic field variations induced by physiological activity. This component was not considered in this work because our RF coil setup did not allow for easy integration at the time of the study. This implementation requires further investigation on an optimal placement of the probes with the presence of geometric constraints and avoiding local eddy currents in some conducting structures of the receive coils, which is beyond the scope of current study.

5.5. Perspective

With only six DW images and b-values of 60, 1000 and 2000 s/mm² it was not possible to generate detailed fiber track results. However, the successful field-monitoring-based eddy current correction demonstrated in this work, in HCP-style DW images at 7T, provides the rationale to expand computational resources towards much larger data size and to retrofit the head RF coil with ¹⁹F NMR probes in order to collect full HCP protocol data at 7T with concurrent field monitoring. With a longer acquisition time due to a larger number of diffusion-encoding steps, motion artifacts could potentially become an additional source of errors that could be addressed sequentially, using registration based approaches after field correction and denoising, or in a larger reconstruction framework integrating eddy-current-and-motion-induced encoding deviations. These future efforts will be dedicated towards a comprehensive comparison of the effectiveness of eddy current correction between magnitude-image-based strategies and fieldmonitoring-based strategies for high resolution dMRI at 7T.