Data Stitching for Dynamic Field Monitoring With NMR Probes

ABSTRACT

Purpose

To propose a new method for characterizing sequences with higher resolution or readout length than allowed by standard field monitoring approaches.

Methods

Our proposed method was devised to characterize entire readout gradients by stitching multiple segment‐specific dynamic field measurements obtained across a matched number of consecutive TRs corresponding to a certain segmentation of the readout gradient. The utility of our proposed stitching method for high‐order dynamic field measurements was illustrated using 2D spiral sequences. It was first demonstrated at 10.5 T and then at 7 T using both simulated and experimental MRI data. At 10.5 T, two extreme spiral readout scenarios were considered where standard field monitoring did not work. Our method was then validated in humans at 7 T, where spiral sequences were employed for brain imaging. At 7 T, our method was further compared against gradient impulse response function (GIRF)‐based trajectory prediction.

Results

At 10.5 T, our stitching method outperformed the standard approach, producing plausible dynamic field measurements throughout entire readouts. At 7 T, it produced nearly identical measurements for one readout where standard field monitoring also worked; for another readout when standard field monitoring did not work, it still produced sensible field measurements, improving image reconstruction for both simulated and experimental MRI data.

Conclusion

Our proposed stitching method provides an effective means to characterize challenging imaging gradients using commercially available hardware and without assuming a linear gradient system, thereby having utility for many applications especially those aiming for ultrahigh‐resolution MRI at ultrahigh field.

1. Introduction

Ultrahigh‐field (UHF) magnetic resonance imaging (MRI) systems operating at 7 T and above have significant advantages over those operating at lower field strengths, providing enhanced signal‐to‐noise ratio (SNR) and improved tissue contrast [1, 2, 3]. However, UHF MRI faces its own challenges, including increased susceptibility to system imperfections such as eddy currents. Eddy currents, especially those associated with the image readout gradients, can become problematic when pursuing high‐resolution imaging, a major driver for UHF MRI. For high‐resolution imaging, the image readout often has to be accomplished with relatively long gradients that are also relatively large in amplitude. This can lead to increased eddy currents, which in turn can result in strong image artifacts when uncorrected. One effective way to characterize eddy currents (for their subsequent correction) is by dynamic field monitoring.

Dynamic field monitoring [4] using nuclear magnetic resonance (NMR) probes [5] has shown utility for various MRI applications [6, 7, 8, 9, 10], improving image quality in both Cartesian [8, 11] and non‐Cartesian acquisitions [9, 10, 12, 13, 14, 15]. This is due in large to its ability to measure time‐resolved high‐order dynamic field changes associated with the readout gradients within each repetition time (TR). These high‐order dynamic field measurements can be incorporated into image reconstruction based on the expanded signal model [4, 9, 12, 13, 14, 16] to correct for unwanted field perturbations, resulting in improved image quality with reduced artifacts.

However, the application of dynamic field monitoring to characterizing a long‐duration or ultrahigh‐resolution readout remains challenging [9, 14, 15]. This is due in large to the maximum effective measurement duration being limited by T ₂* decay within the probe [9, 14], or dephasing caused by strong gradients, or both. These limitations indicate that long‐duration or ultrahigh‐resolution readout gradients cannot be effectively characterized using current concurrent and prospective field monitoring approaches. These limitations can be addressed by several other proposed dynamic field monitoring methods, including continuous field monitoring with rapid re‐excitation of NMR probe sets [17]. However, continuous field monitoring requires specialized hardware including short‐lived NMR probes (with sub‐millisecond T ₂ values) and cannot be fulfilled using a standard commercially available field monitoring system that relies on long‐lived NMR probes (with T ₂ values on the order of tens of milliseconds).

Another way to characterize the challenging readout gradients is by predicting the associated dynamic field changes based on gradient impulse response function (GIRF) measurements. It is shown [18] that high‐order GIRF measurements can be obtained using NMR probes to characterize the dynamic performances of a gradient system. These GIRF measurements can then be used to predict the high‐order dynamic field changes for any given nominal gradient waveforms. It is also shown [19] that the GIRF‐predicted trajectories can be used to improve image reconstruction, reducing image artifacts observed when using nominal trajectories. However, the GIRF prediction is inherently based on the assumption of linear and time‐invariant (LTI) systems, which may not fully capture the nonlinearities or temporal variations present in certain imaging scenarios [20, 21].

In this work, we propose an additional method for monitoring long‐duration or ultrahigh‐resolution readouts. Our method is a novel data stitching method which combines data from multiple sub‐readout length segments of the readout trajectory and combines those segments to generate a full‐length trajectory measurement for each TR. The effectiveness of our proposed stitching method for measuring high‐order dynamic field changes was illustrated using 2D spiral sequences and Skope field cameras (Skope MRT, Zurich, Switzerland), all in the “prospective monitoring” fashion where dynamic field changes are measured in a separate calibration session [11]. Our proposed method was first demonstrated at 10.5 T using field measurements for two extreme scenarios, and then validated at 7 T using simulated and experimental MRI data. This was done by extending existing open‐source MR simulation and image reconstruction tools to address high‐order dynamic field changes based on the expanded signal model. For 10.5 T demonstration, our proposed stitching method was applied with a Skope clip‐on field camera to measure the dynamic field changes for two extreme readout scenarios where the standard field monitoring approach did not work. Our results showed that our proposed method provided plausible high‐order dynamic field measurements for a spiral readout as lengthy as ∼88 ms, as well as for another spiral readout targeting a resolution as high as 0.3 mm, while using fluorine‐19 probes (of 0.4 mm in radius and ∼23 ms in T ₂*). For 7 T validation, our proposed method was used with a Skope dynamic field camera to characterize two representative 2D spiral readouts applied to image the human brain using the commercial NOVA 32‐channel radiofrequency (RF) head coil. Now with high‐precision proton probes (of 0.4 mm in radius and ∼35 ms in T ₂*), our results showed that our proposed stitching method measured high‐order dynamic field changes with accuracy in both cases; it led to nearly identical measurements when characterizing a shorter, ∼29‐ms readout where the standard approach also worked; it still produced sensible measurements, leading to improved image reconstruction with reduced artifacts when characterizing a longer, ∼88‐ms readout where the standard approach did not work. As such, our proposed stitching method has potential to promote various imaging applications especially those at ultrahigh field targeting ultrahigh resolution and complement existing dynamic field measurement techniques.

2. Methods

2.1. Data Stitching for Dynamic Field Monitoring

Our proposed data stitching method (Figure 1) was devised to provide two modes: (1) constant‐segment stitching mode and (2) variable‐segment stitching mode. In either mode, the entire readout gradient was characterized by stitching multiple segment‐specific dynamic field measurements obtained across a matched number of consecutive TRs corresponding to a certain segmentation of the readout gradient. In mode 1, segments of the same duration were measured from TR to TR, with the number of segments being determined based on the mono‐exponential signal T ₂* decay model. In mode 2, segments of variable durations were measured from TR to TR, with the number of segments being determined based on the intra‐voxel dephasing model [22] taking into account the physical properties of the field probes in use; this was done by ensuring that for all segments the maximum phase angle, ${\alpha }_i$, would be smaller than the value as dictated by the intra‐voxel dephasing model such that the residual signal retained would be higher than a prescribed threshold, that is, ${\alpha }_i=r·k_i<\sin {\mathrm{c}}^{-1}(\delta ),i=1,2,\dots ,N_{\mathrm{seg}}$, where $\delta$ is the residual signal threshold, N _seg the number of segments, r the probe radius, and k _i the k‐value of the i‐th segment spanning from time t _i−1 to time t _i , which is given by $k_i=\gamma {\int }_{t_{i-1}}^{t_i}g(\tau )\mathrm{d}\tau$ with $\gamma$ denoting the gyromagnetic ratio of the probe sample, and $g(t)$ the readout gradient.

FIGURE 1.

Schematic of our proposed data stitching method for characterizing dynamic field changes with segmented measurements. Shown is an example four‐segment field measurement for each of the two possible modes: (1) constant‐segment stitching (top) where segments of the same duration are measured from TR to TR, and (2) variable‐segment stitching (bottom) where segments of variable durations are measured from TR to TR. In both cases, the entire readout gradient (G) is characterized within four consecutive TRs, each with a TR‐specific trigger that triggers field monitoring of a single segment. Field monitoring (F) is performed over a constant recording window (shown in red), long enough to accommodate the maximum segment duration. TR‐specific effective data segments (shown in green) are extracted and stitched together to form a complete time course of field dynamics associated with the readout gradient.

In both modes, field monitoring per TR was performed over a constant recording window, long enough to accommodate the maximum segment duration, resulting in Skope output of TR‐specific measurements of high‐order k coefficients. The Skope output was used to create complete time courses of high‐order k or phase coefficients [4] for subsequent image reconstruction by (1) extracting TR‐specific effective data segments, (2) calculating time derivatives through differential approximation to derive corresponding TR‐specific high‐order gradient or dynamic coefficients [4], (3) stitching to form complete time courses of high‐order gradient coefficients associated with readout gradients, (4) smoothing around segment boundaries to minimize discontinuities observed at transition points, and (5) integrating in time to form the complete time courses of corresponding high‐order k coefficients. For any given segment boundary, the smoothing in step 4 was done by fitting a weighted quadratic polynomial to gradient coefficients within a time window around the boundary with the weights being determined by associated probes' mean signal.

To demonstrate the utility of our proposed method, we developed a Skope‐compatible 2D spiral gradient‐echo pulse sequence using the Pulseq framework [23]. The 2D spiral sequence was implemented to enable dynamic field monitoring in both constant‐ and variable‐segment stitching modes, with TR‐specific transistor‐transistor logic (TTL) triggers properly inserted to trigger the field measurements of individual segments from TR to TR. The sequence was implemented to also support field monitoring using the standard approach, that is, to characterize the entire readout gradient within a single TR. In all cases, time‐optimal spiral gradient waveforms were designed for readout by using the optimal control algorithm [24].

2.2. Image Reconstruction

For image reconstruction with high‐order field dynamics, we extended MRIReco.jl [25], an MRI reconstruction framework written in Julia [26] already implemented to support coil sensitivities and static off‐resonances [27]. Our extension mainly involved incorporating field dynamics up to third‐order spherical harmonic terms to enable image reconstruction based on the expanded signal model [9, 13, 15]. Here image reconstruction was formulated as a regularized least‐squares optimization problem [28]:

$$\widehat{m}=\underset{m}{\arg \min }{\Vert s-\mathit{Em}\Vert }_2^2+\lambda {\Vert m\Vert }_2^2,$$ (1)

where m is the image to be reconstructed, s the multi‐coil signal, E the encoding matrix based on the expanded signal model, and λ the regularization parameter. The reconstruction problem in Equation (1) was solved using the conjugate gradient (CG) algorithm [29] implemented in the Julia package RegularizedLeastSquares.jl. For improved computation efficiency, we utilized GPU‐enabled operations to speed up the evaluation of the expanded signal model. We also implemented functionality in MRIReco.jl to estimate and correct the synchronization delay between the field measurement and MRI data using a model‐based approach [30]. All image reconstructions were performed on a server and accelerated using a single NVIDIA GeForce RTX 3090 GPU (with 24 GB RAM). Unless noted otherwise, image reconstruction was fulfilled using 20 CG iterations and λ = 1e⁻⁹.

2.3. Demonstration at 10.5 T

To demonstrate the usefulness of our proposed data stitching method, we conducted field measurements at 10.5 T. Two extreme 2D spiral readout scenarios (Figure 2) were considered: (1) a long‐duration readout and (2) a short readout targeting ultrahigh resolution. In scenario 1, the readout gradient was designed to image at 1‐mm isotropic resolution with full k‐space sampling, resulting in a long readout of ∼88 ms. In scenario 2, the readout gradient was designed to achieve 0.3‐mm isotropic resolution with 30‐fold k‐space under‐sampling, leading to a short readout of ∼21 ms but a maximum gradient moment of as high as ∼1 mT·s/m. In both scenarios the nominal field of view (FOV) was set to 150 × 150 mm², and TR to 500 ms.

FIGURE 2.

Pulse sequences at 10.5 T. Shown are the 2D spiral sequences used to demonstrate the utility of our proposed stitching method, (a) one designed to have a long readout (∼88 ms) to fully sample the k‐space with 1‐mm in‐plane resolution, and (b) another to have a short readout (∼21 ms) to under‐sample by 30‐fold the k‐space with 0.3‐mm ultrahigh in‐plane resolution. Both sequences were developed in the Pulseq framework to image a field of view (FOV) of 150 × 150 mm². The long readout of the first sequence was characterized using the constant‐segment stitching mode where field dynamics were measured with four segments assuming that T ₂* decay was the dominant source of probe signal loss, whereas the short readout of the second sequence using the variable‐segment stitching mode where field dynamics were measured using 36 segments assuming that dephasing was the dominant source of probe signal loss, with the number of segments being determined using a signal dephasing model taking into account the physical size of field probes. For comparison, the standard field monitoring approach was also applied to characterize the entire readout gradient within a single TR. All field monitoring was conducted using a Skope clip‐on field camera with 16 field probes.

For scenario 1 with T ₂* decay being a dominating limiting factor, the readout gradient was characterized in the constant‐segment mode. The segmentation was determined such that each segment would not exceed 22 ms in length (a quarter of the total readout and within one T ₂* decay time of the field probes used), resulting in a total of four segments with the same duration. For scenario 2 with signal dephasing being the main limiting factor, the readout gradient was characterized in the variable‐segment mode. The segmentation was determined by setting $\delta =0.41$ (the residual signal threshold prescribed to ensure each segment would maintain at least 41% of the initial probe signal assuming no T ₂* decay), and $r=0.4$ mm (the probe radius), leading to a total of 36 segments of variable durations.

For both scenarios, the readout gradients were characterized on a Siemens 10.5 T plus MR scanner (Siemens, Erlangen, Germany) equipped with whole‐body gradients (capable of 70 mT/m maximum amplitude and 200 T/m/s maximum slew rate). Dynamic field monitoring was conducted using a clip‐on field camera (Skope MRT, Zurich, Switzerland), with 16 fluorine‐19 NMR probes optimally placed in a scaffold. For comparison, dynamic field measurements were also obtained using the standard field monitoring approach.

2.4. Demonstration at 7 T

We also demonstrated and validated our proposed data stitching method at 7 T. To this end, two representative 2D spiral readout schemes (Figure 3) were considered: (1) a short readout and (2) a long readout, both with fourfold k‐space undersampling (R = 4). In scheme 1, the readout gradient was designed to image at 1‐mm isotropic resolution, resulting in a relatively short readout of ∼29 ms for which the standard field monitoring approach was expected to work. In scheme 2, the readout gradient was designed to accomplish higher 0.5‐mm isotropic resolution, giving rise to a relatively long readout of ∼88 ms for which the standard field monitoring approach was expected to fail. Other relevant imaging parameters were kept constant for both readout schemes, including FOV = 200 × 200 mm², slice thickness = 2 mm, flip angle = 90°, TE = 5 ms, TR = 500 ms, bandwidth = 1 MHz, and a fat‐saturation flip angle of 110°.

FIGURE 3.

Pulse sequences at 7 T. Shown are the two single‐shot 2D spiral sequences used to validate our proposed stitching method, (a) one designed to have a short readout (∼29 ms) with 1‐mm in‐plane resolution, and (b) another to have a long readout (∼88 ms) with 0.5‐mm in‐plane resolution, both with fourfold k‐space undersampling. Both sequences were developed in the Pulseq framework to image an FOV of 200 × 200 mm². The short readout of the first sequence was characterized using the constant‐segment stitching mode where field dynamics were measured with four segments, whereas the long readout of the second sequence used the variable‐segment stitching mode where field dynamics were measured using 187 segments. For comparison, the standard field monitoring approach was also applied to characterize the entire readout gradient within a single TR. All field monitoring was conducted using a Skope dynamic field camera with 16 field probes.

For scheme 1, the readout gradient was characterized in the constant‐segment mode using four segments with the same duration. For scheme 2, the readout gradient was characterized in the variable‐segment mode where the segmentation was determined using the intra‐voxel signal dephasing model, leading to a total of 187 segments of variable durations.

For both schemes, the readout gradients were characterized on a MAGNETOM Terra 7 T MR scanner (Siemens Healthineers, Forchheim, Germany) equipped with the same whole‐body gradients as our 10.5 T scanner. Dynamic field monitoring was performed using a Dynamic Field Camera (Skope MRT, Zurich, Switzerland) with optimal integration of 16 high‐precision proton NMR probes. For comparison, dynamic field measurements were also obtained using the standard field monitoring approach.

2.4.1. Reconstruction Using Simulated MRI Data

We started by demonstrating the usefulness of our proposed stitching method through image reconstruction using simulated MRI signals. Noise‐free MR signals were calculated by extending KomaMRI.jl [31], an open‐source framework for MRI simulations also written in Julia compatible with any sequence developed in Pulseq. Here KomaMRI.jl was extended to enable (1) MR simulation with high‐order field dynamics (by incorporating dynamic field changes up to third‐order spherical harmonic terms into the calculation of the effective magnetic field in the z direction), and (2) multi‐coil signal simulation for parallel imaging (by taking into account multiple coil sensitivity maps). In either readout scheme, MR signal was simulated by considering up to third‐order dynamic field measurements associated with the corresponding readout gradient obtained using our proposed stitching method. In both cases, MR signal was simulated for a single TR from a representative axial slice (located at the gradient isocenter) of a digital brain phantom dictated by proton density (Figure S1) and assuming no transverse magnetization relaxation throughout the sequence. To simulate effects of static off‐resonances for a more realistic situation, a 2D quadratic U‐shaped ΔB ₀ map (Figure S1) was synthesized to have a maximum value of 150 Hz and a minimum value of 14 Hz across the brain region.

In both schemes, multi‐coil signal simulation was carried out assuming uniform transmit B ₁ across the FOV and using coil sensitivity maps (Figure S1) of the commercial Nova 32‐channel RF coil estimated using ESPIRiT [32] based on multi‐echo gradient echo (GRE) acquisition in a spherical phantom. All maps including proton density, ΔB ₀ and coil sensitivities were sampled at 0.1‐mm in‐plane resolution (higher than the nominal image resolution) to better simulate partial volume and intra‐voxel dephasing effects in the subsequent image reconstruction. All MR simulations were performed on a server and accelerated using a single NVIDIA GeForce RTX 3090 GPU.

Simulated complex‐valued MR signals were further contaminated by adding Gaussian noise to both real and imaginary parts to synthesize noisy complex‐valued MR signal to mimic a more realistic situation. Noisy synthetic MR signal was then used to reconstruct the image using our expanded MRIReco.jl and using up to third‐order field dynamics measured with our proposed stitching method. The reconstruction performances were evaluated by calculating quality assessment metrics including Normalized Root Mean Square Error (NRMSE) and Structural Similarity Index (SSIM) values all in reference to proton density serving as the gold standard. The image reconstruction results were compared to those reconstructed using the same synthetic data but using nominal gradient waveforms and using up to third‐order field dynamics obtained with the standard field monitoring approach.

2.4.2. Validation Using Experimental MRI Data

We then validated our proposed data stitching method by conducting human experiments on the same Terra scanner as field measurement. The commercial NOVA 8‐channel transmit 32‐channel receive head RF coil operating in its Circularly Polarized (CP) mode was used for RF transmission and signal reception. A healthy adult who signed an informed consent form approved by local IRB was scanned using the same two readout schemes as for reconstruction with simulated data.

For image reconstruction, fully‐sampled multi‐echo 2D GRE images were acquired to estimate coil‐sensitivity and ΔB ₀ maps (Figure S2). For either readout scheme, multi‐echo GRE images were collected with matched in‐plane resolution, FOV and slice thickness, other relevant imaging parameters being: 6 echoes, TE₁ = 3.06 ms, ΔTE = 1.02 ms, and TR = 25 ms. Coil sensitivity maps were estimated from the first echo using ESPIRiT [32] implemented in MRIReco.jl, whereas the ΔB ₀ map was estimated from all echoes using MRIFieldmaps.jl [33], a Julia package for regularized field mapping.

Image reconstructions were performed using our expanded MRIReco.jl and using up to third‐order field dynamics measured with our proposed stitching method. The result was compared to that obtained with the same data but using up to third‐order field dynamics measured with the standard field monitoring approach. For both reconstructions, the eddy current compensation applied to the raw data by the scanner to counteract eddy current b ₀ (i.e., the zeroth‐order spherical harmonic term) was reversed as in previous studies [10, 34]. This was done by simulating eddy current b ₀ based on the nominal gradient waveforms using the same multi‐exponential predictive model as used by the scanner. Simulation of eddy current b ₀ was fulfilled using the code publicly available at https://github.com/praveenivp/SpiralReco. For comparison, image reconstruction was also conducted using the nominal gradient waveforms.

Moreover, all reconstructions were carried out with synchronization delay correction. This was accomplished using two steps, with step 1 aiming to estimate the synchronization delay (τ) and step 2 to reconstruct images with estimated synchronization delay. In step 1, the delay was estimated using an iterative procedure with a jump factor of 6 and a minimum Δτ of 1 ns. During each iteration, the reconstruction problem in Equation (1) was solved using the CG algorithm. In step 2, the estimated delay was used to synchronize dynamic field measurements with the MR data through interpolation, and final images were reconstructed by solving the same reconstruction problem in Equation (1).

2.4.3. Comparison With GIRF‐Based Prediction

To further demonstrate the utility of our proposed stitching method, we compared against GIRF‐based prediction. For both spiral readouts under consideration, associated GIRF‐based prediction of high‐order field dynamics was obtained by frequency‐domain multiplication of the nominal readout gradient waveforms with the measured GIRFs [19]. GIRF measurements were performed similarly as described by Vannesjo et al. [18] using a sequence developed in Pulseq. Briefly, GIRFs corresponding to three input channels (i.e., Gx, Gy, Gz) and 16 output channels (i.e., up to 3rd order spherical harmonics) were obtained by applying a set of different yet complementary gradient input pulses in each input channel and measuring the output high‐order field dynamics with the Dynamic Field Camera. GIRFs were then calculated through frequency‐domain division of the measured output by the known input and using least‐squares combination of data from all input pulses. For accurate GIRF calibration, a set of 12 triangular gradient input pulses (rising at a slew rate of 180 T/m/s and with time‐to‐peak ranging from 50 to 160 μs in steps of 10 μs) were played out per input gradient channel with a 2‐s TR and 25 averages, leading to a total measurement time of 30 min.

3. Results

3.1. Demonstration at 10.5 T

When characterizing the long readout gradient, the use of our proposed method eliminated discontinuities associated with T ₂* signal loss, generating a plausible gradient waveform and a sensible trajectory across the entire k‐space (Figure 4). In contrast, the k‐space trajectory measured using the standard approach became corrupted toward the end of the readout. For the ultrahigh resolution short readout, similar results were observed, demonstrating efficacy for eliminating discontinuities associated with gradient‐induced probe dephasing. Likewise, when comparing dynamic field measurements for other spherical harmonic terms (Figure 5), the use of our proposed method resulted in more sensible time courses than using the standard approach.

FIGURE 4.

Comparing gradient measurements using our proposed stitching method versus the standard field monitoring approach at 10.5 T. Shown are gradient waveforms measured using our stitching method and their differences from what was measured using the standard approach, along with respective k‐space spiral trajectories, for the long readout (top row) and ultrahigh resolution short readout (bottom row). In both cases, segments are color coded for improved visualization. For both readout scenarios, note that our proposed stitching method effectively corrected the errors observed with the standard approach, leading to a more sensible trajectory without erroneous k‐space traversal.

FIGURE 5.

Comparing measurements of other spherical harmonic terms (up to second order) using our proposed stitching method versus the standard field monitoring approach at 10.5 T. Shown are measurements using our stitching method and their respective differences from what was measured using the standard approach for the long readout (left) and ultrahigh resolution short readout (right). For each term in both readout scenarios, note that the use of our proposed stitching method effectively avoided the large fluctuations observed with the standard approach especially toward the end of the readout, resulting in a more plausible field measurement throughout the entire readout.

3.2. Demonstration at 7 T

Our stitching method yielded nearly identical gradient measurements (Figure 6) when characterizing the short, ∼29‐ms readout where the standard approach worked nicely giving rise to the same k‐space spiral trajectory. It also produced sensible gradient measurements when characterizing the long, ∼88‐ms readout where the standard approach did not work, leading to a k‐space trajectory starting to degrade toward the end of the readout. Similar results were observed when comparing measurements of other spherical harmonic terms (Figure 7).

FIGURE 6.

Comparing gradient measurements using our proposed stitching method versus the standard field monitoring approach at 7 T. Shown are gradient waveforms measured using our stitching method and their differences from what was measured using the standard approach, along with respective k‐space spiral trajectories, for the short readout (top row) and long readout (bottom row). In both cases, segments are color‐coded for improved visualization. Note that our stitching method led to nearly identical spiral trajectories when characterizing the shorter ∼29 ms readout where the standard approach worked nicely and that it still produced sensible measurements when characterizing the longer, ∼88 ms readout where the standard approach did not work.

FIGURE 7.

Comparing measurements of other spherical harmonic terms (up to third order) using our proposed stitching method versus the standard field monitoring approach at 7 T. Shown are measurements using our stitching method and their respective differences from what was measured using the standard approach for the short readout (left) and long readout (right). Note that our stitching method led to nearly identical dynamic field measurements when characterizing the shorter ∼29 ms readout where the standard approach worked nicely and that it still produced sensible measurements when characterizing the longer, ∼88 ms readout where the standard approach appeared to result in large fluctuations toward the end of the readout.

Correspondingly, for the short readout, our proposed method resulted in nearly identical image reconstruction to when using the standard approach (Figure 8). It however led to improved reconstruction with reduced artifacts for the long readout where the use of the standard approach resulted in erroneous field measurements giving rise to degraded reconstruction. Quantitatively, when comparing to the standard approach, our proposed method reduced the NRMSE by ∼43% (0.04 vs. 0.07 for the standard approach) and increased the SSIM by ∼40% (0.88 vs. 0.63 for the standard approach). Similar results were observed for image reconstruction using experimentally acquired human data (Figure 9).

FIGURE 8.

Image reconstruction at 7 T using simulated MR data. Shown are image reconstructions for the short 1‐mm (a) and long 0.5‐mm (b) readout scenarios, when using nominal readout gradients (Nominal), up to third‐order field dynamics measured with our stitching method (Stitched), and those with the standard field monitoring approach (Standard). In each readout scenario, the same MR signal simulated by expanding KomaMRI.jl using experimentally measured coil sensitivities of the commercial Nova 32‐channel receive RF coil was used for all three reconstructions. All reconstructions were fulfilled by expanding MRIReco.jl to allow reconstruction with high‐order field dynamics. The image reconstruction problem was formulated as regularized least squares and was solved iteratively using the CG algorithm. Normalized root mean square error (NRMSE) and Structural Similarity Index (SSIM) values calculated relative to proton density serving as the reference are also reported for quantitative comparison. Note that, although producing comparable results to the standard approach for the short 1‐mm readout as expected, our stitching method led to the best reconstruction quality for the long 0.5‐mm readout, producing images visually identical to the reference and effectively eliminating artifacts observed for reconstruction using nominal readout gradients or field dynamics measured with the standard approach.

FIGURE 9.

Image reconstruction at 7 T using experimental MR data. Shown are image reconstructions for the short 1‐mm and long 0.5‐mm readout scenarios, when using nominal readout gradients (Nominal), up to third‐order field dynamics measured with our stitching method (Stitched), and those with the standard field monitoring approach (Standard), along with zoom‐in images of a representative brain region (as indicated by a box). In each readout scenario, same MR data acquired in a healthy adult using the commercial Nova 8‐channel transmit 32‐channel receive coil were used for all three reconstructions. Coil sensitivity and ΔB ₀ maps were estimated based on fully‐sampled multi‐echo GRE. For all data collection, the Nova coil was used in its circularly polarized mode to mimic a single‐channel transmit setup. All reconstructions were fulfilled by expanding MRIReco.jl to allow reconstruction with high‐order field dynamics. The image reconstruction problem was formulated as regularized least squares and was solved iteratively using the conjugate gradient with the synchronization delay between field dynamic measurements and MRI data being determined using a model‐based method. Note how our stitching method led to improved reconstruction with reduced blurring and striping artifacts especially at 0.5‐mm resolution where the use of the standard approach resulted in erroneous field measurements giving rise to worsened reconstruction (as evident by comparing the zoom‐in images in red boxes).

When compared to GIRF‐based prediction, our proposed stitching method resulted in nearly identical k‐space trajectories (Figure 10). However, it led to a different time course for the zeroth‐order field term (k ₀), presenting a global trend of drifting over time.

FIGURE 10.

Comparison with gradient impulse response function (GIRF)‐based prediction at 7 T: Field dynamics. Shown are zeroth‐order terms (k ₀) and k‐space trajectories obtained for the short (top row) and long (bottom row) 2D spiral readouts using GIRF‐based prediction (green) versus our proposed stitching method (orange). GIRF measurements were obtained following the recipe described in Vannesjo et al. to characterize 16 output channels (i.e., up to 3rd order spherical harmonics) for each of the three input channels (i.e., Gx, Gy, Gz). For both spiral readouts under consideration, GIRF‐based prediction of high‐order field dynamics was calculated using the GIRF measurements and the corresponding nominal readout gradient waveforms. Note that although producing nearly identical k‐space trajectories to GIRF‐based prediction, our proposed method led to a different k ₀ time course.

4. Discussion

In this study, we proposed and demonstrated a data stitching method for dynamic field monitoring, suitable for characterizing challenging readout gradients that are lengthy, targeting high resolution, or both. Our proposed stitching method was validated based on high‐order image reconstruction using both simulated and experimental MR data. Our results (Figures 4, 5, 6, 7, 8, 9) show that our proposed stitching method can be used to characterize readout gradients with accuracy especially when imaging at higher spatial resolution where the standard field monitoring approach does not work.

For a proof of principle, we implemented our proposed stitching method to have two modes: the constant‐segment mode and the variable‐segment mode. The constant‐segment mode assumes that T ₂* relaxation is the dominant mechanism underlying the probe signal decay, therefore more suitable for low‐resolution, long readouts where the probe signal decay due to gradient‐induced intra‐probe dephasing is negligible. By contrast, the variable‐segment mode assumes that gradient‐induced dephasing is the dominant mechanism underlying the probe signal decay, therefore more suitable for high‐resolution, short readouts where the probe signal decay due to T ₂* relaxation is negligible. For readouts commonly used in neuroimaging, T ₂* relaxation and intra‐probe dephasing contribute to the probe signal decay. The variable‐segment mode may be more convenient because it does not require tremendous trial and error as in the constant‐segment mode when identifying the minimum segments needed. However, to compensate for additional signal decay due to T ₂* relaxation especially in the first segment which tends to be the longest among all, it is recommended that a more conservative residual signal threshold be used to retain more residual signal from intra‐probe dephasing. For improved robustness and accuracy in predicting probe signal decay, our variable‐segment mode can readily be extended to a unified mode that also takes into account T ₂* relaxation in determining segmentation.

At 10.5 T, we considered two extreme readouts: a long ∼88‐ms spiral and another short ∼28‐ms spiral targeting ultrahigh resolution of 0.3 mm. This was meant to demonstrate the efficacy of the two modes we implemented for our proposed stitching method when attempting to address the effect of T ₂* relaxation or intra‐probe dephasing on probe signal decay. Both modes were demonstrated effective in characterizing their designated challenging readout spiral, leading to sensible high‐order dynamic field measurements when compared to the standard field monitoring approach.

To further validate our proposed data stitching method, we performed human experiments at 7 T. This was done by considering two spiral readout schemes: a low‐resolution readout that could also be measured with the standard field monitoring approach and another high‐resolution readout that could not. The rationale behind choosing these two readouts is that it is equally important to show that (1) our method would result in the same dynamic field measurement as does the standard approach when dealing with an “easy” readout gradient, as well as (2) our method extends to work in the case where the standard approach cannot be used.

Although sufficient to demonstrate the advantages of our proposed stitching method over the standard field monitoring approach in characterizing challenging readout gradients, our image reconstruction with stitched high‐order field dynamics (Figure 9) presented residual artifacts (e.g., blurring) especially for the 0.5‐mm in‐plane resolution. These residual artifacts were likely due to lack of correction for T ₂* signal decay and/or insufficient correction for field inhomogeneities, given the long readout duration (∼88 ms). Another source of residual artifacts was measurement error arising from the discontinuities observed at segment boundaries. Part of our future work is to investigate how to improve the measurement accuracy for our stitching method and to refine our image reconstruction by incorporating the T ₂* signal decay into the expanded signal model [35] and by solving the inverse problem with more advanced, time‐segmented and frequency‐segmented algorithms [36, 37] for improved correction of field inhomogeneities.

When comparing to GIRF‐based prediction (Figure 10), we observed non‐negligible differences in the zeroth‐order field terms (i.e., k ₀). Particularly, for the long 0.5‐mm spiral readout, the global drift observed with our proposed stitching method, featured by a sudden change in the slope of k ₀ occurring around the middle of the readout and similar to what was captured using the standard field monitoring approach, was missing in the GIRF‐based prediction. Similar discrepancies in k ₀ field terms were reported in a previous study [20] when comparing GIRF‐based prediction versus actual field monitoring in characterizing a 2D single‐shot spiral readout at 0.8‐mm in‐plane resolution at 7 T. Further examining image reconstruction (Figure S3) revealed that GIRF‐based prediction resulted in degraded reconstruction with images artifacts (e.g., shading artifacts observed for both spiral readouts and additional ringing artifacts observed for the long 0.5‐mm readout) and that these image artifacts were effectively reproduced using our stitched field dynamics but without k ₀ field correction. These results suggest that the zeroth‐order field term predicted by GIRF can be inaccurate, so caution should be exercised when using GIRF‐predicted field dynamics for image reconstruction.

To demonstrate the broader utility of our proposed data stitching method beyond spiral imaging, we conducted additional experiments at 7 T using 2D single‐shot echo‐planar imaging (EPI) sequences. Specifically, two readouts (Figure S4) were considered: (1) a short readout (∼40 ms in length) targeting 1‐mm in‐plane resolution with fourfold k‐space undersampling, and (2) a long readout (∼89 ms in length) targeting 0.5‐mm in‐plane resolution with fivefold k‐space undersampling and 7/8 partial Fourier. The short readout was measured in the constant‐segment mode with four segments, whereas the long readout in the variable‐segment mode with 142 segments. The results were compared to what was attainable with the standard field monitoring approach. Like in the 2D spiral case, our stitching method yielded nearly identical EPI trajectories to the standard approach when characterizing the short readout; however, it outperformed the standard approach when characterizing the long readout, producing more sensible measurements (Figure S5). Correspondingly, image reconstruction using experimental human MR data (Figure S6) showed that our stitching method led to visually identical reconstruction for the short 1‐mm readout where the standard approach worked as well, but it gave rise to improved reconstruction with reduced image artifacts for the long 0.5‐mm readout where the standard approach started to result in erroneous field measurements. These results suggest that our proposed data stitching method holds promise for most high‐resolution functional and diffusion MRI studies where EPI readouts are used for data acquisition.

Moreover, we performed additional human experiments at 7 T targeting off‐isocenter slices to highlight the utility of our proposed stitching method in the presence of stronger effects of higher order fields. Using both 2D single‐shot spiral and EPI readouts, an off‐isocenter slice was imaged by moving the patient table ∼5 cm inward after a nearby slice was imaged at the isocenter. Both off‐isocenter and isocenter slices were reconstructed using the same field characterization with our proposed method versus with the standard field monitoring approach. Our results (Figure S7) showed that for both spiral and EPI readouts, the standard approach resulted in more pronounced artifacts in the off‐isocenter slice than in the isocenter slice; in contrast, our data stitching method effectively minimized image artifacts, improving image quality equally well for both isocenter and off‐isocenter slices.

For simplicity without loss of generality, we validated our proposed stitching method only by imaging a single slice with 2D sequences. Our stitching method is readily applicable for imaging a single volume when using a 3D pulse sequence such as a sequential or a simultaneous multi‐slice single‐shot 2D sequence, or a stack of spirals sequence. In these cases, the readout gradients can be characterized with the “prospective monitoring” scheme as adopted in the current study, and the measured high‐order dynamic field changes can be used to inform the image reconstruction.

A drawback of our proposed stitching method is its time overhead. When used in the “prospective monitoring” fashion to capture repeatable field dynamics in separate calibration sessions, our stitching method should be used in what we call the “interleaved” scheme to reduce the risk of merging segments of different thermal states. Given a scan or protocol, the “interleaved” scheme works by repeating the scan N _seg times (where N _seg is the number of segments needed to measure each readout gradient) and only characterizing the n‐th segment of every single readout event throughout the entire scan during the n‐th repetition. At the end of each repetition, a long inter‐session delay can be waited to cool the gradient system down. If the inter‐session delay waited is long enough that the gradient system returns to its same cold state as right before the first repetition starts, every single readout event throughout the entire scan will be characterized by merging segments of same thermal states. This however is achieved at the cost of time, with the total calibration time given by T _total = N _seg(T _scan + T _delay), where T _scan is the actual image scan time and T _delay the inter‐session delay waited in between repetitions.

For a scan with many duplicates of same readout gradients (e.g., using a multi‐slice 2D sequence), we note that our proposed stitching method may also be used in what we call the “concurrent” scheme for improved time efficiency. The “concurrent” scheme works by characterizing the readout gradients without repeating the entire scan or protocol, but at the cost of reduced temporal resolution. The temporal resolution is reduced by a factor of N _seg, meaning that an entire readout gradient can only be characterized once every N _seg TR's (assuming the TR used is longer than the Skope minimum allowed TR imposed to allow sufficient probe signal recovery from TR to TR). The “concurrent” scheme when combined with a clip‐on field camera can be used in the “concurrent monitoring” fashion to measure field dynamics while collecting image data. However, the reduction in temporal resolution may have implications when attempting to capture field perturbations due to thermal drift or physiology or both throughout the entire scan aimed at collection of time series data like in fMRI [10, 14] and diffusion [12, 15]. How the “concurrent” scheme may be optimized to promote time series data acquisition and how its reduced temporal resolution would affect image reconstruction warrant future investigation.

Vannesjo et al. [38] demonstrated how data stitching could be used to enable field camera measurements of gradient and shim impulse responses with optimized sensitivity using frequency sweeps. The data stitching used in that work was similar to ours when applied in its “constant‐segment” mode. However, in that work, the authors aimed to characterize a frequency swept input pulse that was lengthy in duration (∼10 s) using specialized field probes with much shorter T ₁ and T ₂ values (∼3 ms), so they re‐excited probes multiple times within each application of the input pulse to measure multiple segments of field responses. By contrast, we aim to characterize an imaging readout gradient which usually is much shorter (< 100 ms) using commercial field probes with much longer T ₁ and T ₂ values, so we only excite the probes once per application of the readout gradient. Moreover, we propose the “variable‐segment” mode for improved time efficiency. It remains to be investigated how our proposed “variable‐segment” mode can be extended to shim system characterization using frequency sweeps and commercial field probes.

5. Conclusion

We have proposed and validated a novel data stitching method for dynamic field monitoring using NMR probes. Our proposed stitching method is shown capable of making quality high‐order dynamic field measurements even for challenging readout gradients. Our proposed stitching method was demonstrated with field measurements at 10.5 T and validated using both simulated and experimental MRI data at 7 T. As such, our proposed stitching method provides an effective means to characterize challenging imaging gradients using commercially available hardware and without assuming a linear gradient system, thereby holding a promise to many imaging applications especially those at ultrahigh field in pursuit of ultrahigh resolution while representing a complement to existing dynamic field monitoring techniques.

Conflicts of Interest

Cameron Cushing is an employee of Skope MRT. Jing An is an employee of Siemens Shenzhen Magnetic Resonance Ltd.

Supporting information

Figure S1: MR signal simulation at 7 T. Shown are (a) synthetic proton density, (b) off‐resonance (i.e., ΔB ₀) maps, and (c) coil sensitivity maps used to simulate MR signal for the short 1‐mm and long 0.5‐mm readout schemes. In both cases, MR signals were simulated with up to third‐order dynamic field changes by expanding KomaMRI.jl, for which the field dynamics measured using our stitching method were used and uniform transmit B ₁ was assumed. The proton density map was created by extracting a representative axial slice from a brain phantom, whereas the ΔB ₀ map was designed to have a quadratic U‐shape across the FOV. Coil sensitivity maps of the commercial Nova 32‐channel RF coil were considered and estimated using ESPIRiT based on multi‐echo GRE acquisition in a spherical phantom. All maps were sampled at 0.1‐mm resolution (higher than corresponding image resolution).

Figure S2: In vivo ΔB ₀ mapping at 7 T. Shown are (a) raw phase images for each of the six echoes and (b) corresponding off‐resonance (ΔB ₀) map estimated from all six echoes using MRIFieldmaps.jl. Fully‐sampled six‐echo 2D GRE images were acquired of the slice at isocenter with TE₁/ΔTE/TR = 3.06/1.02/25 ms. Note that large off‐resonances (> 100 Hz in amplitude) were observed in the vicinity of air‐tissue interfaces.

Figure S3: Comparison with gradient impulse response function (GIRF)‐based prediction at 7 T: image reconstruction using experimental MR data. Shown are image reconstructions for the same short 1‐mm (top) and long 0.5‐mm (bottom) readout scenarios as in Figure 10, when using up to third‐order field dynamics predicted with GIRF measurements (GIRF) versus measured using our stitching method without (Stitched, w/o k ₀) and with k ₀ correction (Stitched). Image reconstruction was fulfilled using the same MR data as for Figure 9. For both spiral readout scenarios, note that our proposed stitching method outperformed GIRF‐based prediction and that the shading artifacts observed with the GIRF‐based prediction were well reproduced using our stitched field dynamics but without k ₀ correction.

Figure S4: Demonstrating our proposed stitching method for 2D EPI at 7 T: pulse sequences. Shown are two 2D EPI sequences considered here: (a) a short readout (∼40 ms in length, targeting 1‐mm in‐plane resolution with fourfold k‐space undersampling and ∼23‐ms TE), and (b) a long readout (∼89 ms in length, targeting 0.5‐mm in‐plane resolution with fivefold k‐space undersampling, 7/8 partial Fourier and ∼41‐ms TE). Both sequences were developed in the Pulseq framework to image an FOV of 200 × 200 mm². The short readout of the first sequence was characterized using the constant‐segment stitching mode where field dynamics were measured with four segments, whereas the long readout of the second sequence using the variable‐segment stitching mode where field dynamics were measured using 142 segments. For comparison, the standard field monitoring approach was also applied to characterize the entire readout gradient within a single TR. All field monitoring was conducted using a Skope dynamic field camera with 16 field probes.

Figure S5: Demonstrating our proposed stitching method for 2D EPI at 7 T: comparing gradient measurements. Shown are gradient waveforms measured using our stitching method and their differences from what was measured using the standard approach, along with respective k‐space EPI trajectories, for the short readout (top row) and long readout (bottom row). In both cases, segments are color coded for improved visualization. Note that our stitching method led to nearly identical EPI trajectories when characterizing the shorter ∼40 ms readout where the standard approach worked nicely and that it still produced sensible measurements when characterizing the longer, ∼89 ms readout where the standard approach did not work.

Figure S6: Demonstrating our proposed stitching method for 2D EPI at 7 T: image reconstruction using experimental MR data. Shown are image reconstructions for the short 1‐mm and long 0.5‐mm readout scenarios, when using nominal readout gradients (Nominal), up to third‐order field dynamics measured with our stitching method (Stitched), and those with the standard field monitoring approach (Standard), along with zoom‐in images of a representative brain region (as indicated by a box). In each readout scenario, same human MR data were used for all three reconstructions. MR data were collected using the same coil setup and image reconstruction fulfilled following the same workflow as in the 2D spiral case. Note that like with 2D spiral, our stitching method led to improved reconstruction with reduced image artifacts especially at 0.5‐mm resolution where the use of the standard approach resulted in degraded reconstruction (as evident by comparing the zoom‐in images in red boxes).

Figure S7: Comparing image reconstructions at isocenter versus off‐isocenter. Shown are image reconstructions for the 0.5‐mm spiral and EPI readouts at 7 T, when using up to third‐order field dynamics measured with the standard field monitoring approach (Standard) and those with our stitching method (Stitched), along with zoom‐in images of a representative brain region (as indicated by a box). The off‐isocenter slice shown was imaged by moving the patient table ∼5 cm inward after acquiring a nearby slice at the isocenter. Note that the standard field monitoring approach resulted in more pronounced artifacts at off‐isocenter than at the isocenter and that our data stitching method effectively minimized image artifacts, yielding reasonable image quality at both isocenter and off isocenter locations.

Zhang J., Zhang Z., Zuo Z., et al., “Data Stitching for Dynamic Field Monitoring With NMR Probes,” Magnetic Resonance in Medicine 95, no. 4 (2026): 1944–1958, 10.1002/mrm.70164.

Data Availability Statement

The Matlab code for data stitching, and Julia code for sequence simulation and image reconstruction are available at https://github.com/BennyZhang-Codes/DataStitching (hash: 744b2ab). Matlab code is also made available at https://github.com/XiaopingWu2020/pulseq-sequences/tree/main for Pulseq sequence development and at https://github.com/XiaopingWu2020/girf-calc/tree/main for GIRF calculation and prediction.