Motion-corrected 3D-EPTI with efficient 4D navigator acquisition for fast and robust whole-brain quantitative imaging

Abstract

Purpose:

To develop a motion estimation and correction method for motion-robust 3D quantitative imaging with 3D-EPTI.

Methods:

The 3D-EPTI technique was designed with additional 4D navigator acquisition (x-y-z-echoes) to achieve fast and motion-robust quantitative imaging of the human brain. The 4D-navigator is inserted into the relaxation-recovery deadtime of the sequence in every TR (~2s) to avoid extra scan time, and to provide continuous tracking of the 3D head motion and B₀-inhomogeneity changes. By utilizing an optimized spatiotemporal encoding combined with a partial-Fourier scheme, the navigator acquires a large central k-t data block for accurate motion estimation using only 4 small-flip-angle excitations and readouts, resulting in negligible signal-recovery reduction to the 3D-EPTI acquisition. By incorporating the estimated motion and B₀-inhomogeneity changes into the reconstruction, multi-contrast images can be recovered with reduced motion artifacts.

Results:

Simulation shows the cost to the SNR efficiency from the added navigator acquisitions is <1%. Both simulation and in-vivo retrospective experiments were conducted, that demonstrate the 4D navigator provided accurate estimation of the 3D motion and B₀-inhomogeneity changes, allowing effective reduction of image artifacts in quantitative maps. Finally, in-vivo prospective undersampling acquisition was performed with and without head motion, in which the motion corrupted data after correction show close image quality and consistent quantifications to the motion-free scan, providing reliable quantitative measurements even with head motion.

Conclusion:

The proposed 4D navigator acquisition provides reliable tracking of the head motion and B₀ change with negligible SNR cost, equips the 3D-EPTI technique for motion-robust and efficient quantitative imaging.

Introduction

Quantitative imaging provides more repeatable and direct measurements than conventional weighted imaging with less bias from system conditions and human interpretation, providing potential to further improve the accuracy and efficacy of clinical MRI (1). A variety of neurological diseases have been investigated using quantitative MRI for improved sensitivity and specificity, including epilepsy (2,3), brain tumor (4,5), multiple-sclerosis (6-8) and Alzheimer (9,10). Moreover, the change of tissue properties can be well measured by quantitative MRI over time and between groups of populations, providing a useful tool to gain further understanding of neurological diseases and brain developments. (11-13). However, since multiple contrast-weighted images are usually needed to fit the quantitative parameters, multi-parametric imaging requires much longer scan time than conventional contrast-weighted imaging, which leads to higher motion sensitivity and lower cost-effectiveness, preventing it from wide clinical use.

To improve the acquisition efficiency of multi-parametric MRI, many fast quantitative imaging techniques have been developed. MR fingerprinting (MRF) (14,15) is one of the most seminal approaches, that is able to acquire multiple quantitative parameters simultaneously using randomized pulse sequences sensitive to both T₁ and T₂ relaxation, instead of sequentially acquiring each one of them. The high acceleration of MRF acquisition relies on the use of spatiotemporal signal correlation governed by the compressed sensing theory (16); where spatial and temporal incoherence are created by randomized acquisition parameters and non-uniform sampling trajectories. MR multitasking (17) is another emerging approach for multi-parametric mapping that exploits the signal correlation in multidimensional data based on a low-rank tensor model (18,19) to achieve high undersampling. One notable feature of MR multitasking is that different motion states can also be modeled as a new dimension in the low-rank tensor approach, allowing robust cardiac quantitative imaging without electrocardiography control. Although these techniques have shown promising results for brain imaging with significantly reduced acquisition time compared with the conventional methods, relatively long acquisition time still remains a major technical challenge especially for high spatial resolution and imaging of more parameters. Many efforts have been made recently based on MRF to further improve its spatial resolution and reduce acquisition time including more dedicated non-Cartesian sampling such as 3D spiral and radial trajectories (2,20-22), and advanced reconstruction algorithms such as machine-learning based approaches (20,23).

Recently, we have developed a novel fast imaging approach, named Echo-Planar Time-resolved Imaging (EPTI) (24,25), that can resolve hundreds of distortion and blurring free images across a modified continuous echo-planar imaging (EPI) readout to track the signal evolution. The continuous data sampling with bipolar readout after each excitation provides high acquisition efficiency, and the densely acquired signals with strong spatiotemporal correlation enables the design of highly-accelerated encoding in the spatiotemporal domain (25,26). By exploiting both the temporal signal correlation and the spatial information from multi-channel receiver coils, the full k-t (frequency-echo) signals can be well recovered from the highly-undersampled EPTI data, resolving hundreds or thousands of distortion and blurring-free multi-contrast images. The recent extension of the EPTI approach to 3D acquisition (25,27,28) enables ultra-fast acquisition of multiple quantitative parameters at isotropic resolution under higher acceleration rates by taking advantage of the spatiotemporal correlation within and between the readouts with optimized encoding in the 4D k-t space (k_x-k_y-k_z-t). The 3D-EPTI method has been demonstrated to provide whole-brain T₁, T₂, and T₂* maps in only 3 minutes at 1-mm isotropic resolution, with high repeatability and accuracy in vivo (28).

Although the short scan time of 3D-EPTI reduces its sensitivity to involuntary subject motion when compared to conventional approaches, the image quality and accuracy of quantitative measurements can still be compromised if large motion occurs during the scan. This can be quite common in less compliant patients, even in a 3-minute scan, such as pediatric or patients with neurological conditions. To correct for the bulk motion in brain imaging, both prospective correction approaches that can track and update the pulse sequence in real time (29-34), and retrospective methods using self- or extra navigators (35-40) to track the head motion, have been developed and shown promising results. Compared to prospective correction methods, retrospective correction methods are normally less reliant on extra hardware, thus easier to implement. They also provide the potential to estimate the change in the field inhomogeneity (ΔB₀) due to the head movements (41), that can affect the quality of T₂* imaging, using multi-echo acquisition (42). However, retrospective motion correction methods may reduce the imaging efficiency if extra navigator acquisition is required, and may lead to limited accuracy of 3D motion correction (e.g., through plane motion) when compared to prospective approaches.

In this work, we equipped the 3D-EPTI with an efficient 4D navigator acquisition to achieve fast and motion-robust quantitative imaging with whole-brain coverage. The 4D navigator (x-y-z-echoes) is designed to estimate both the 3D rigid motion (6 degrees of freedom (DOFs)) and the B₀-inhomogeneity change (ΔB₀) caused by head movements in every TR. To avoid extra scan time, the navigator was acquired during the deadtime for magnetization recovery of the sequence. An optimized highly-undersampled spatiotemporal encoding combined with a partial-Fourier scheme was utilized to achieve large k-t space data coverage with only 4 small flip-angle (FA) excitations and readouts, which reduces the SNR cost of the navigator acquisition to less than 1% based on simulation analysis. By modeling the motion and ΔB₀ of every TR (~2s) in a motion-corrected 3D subspace reconstruction, multi-contrast images with reduced motion artifacts can be recovered for quantitative fitting. Both simulation and in-vivo experiments were performed using an inversion-recovery gradient-echo (IR-GE) EPTI sequence for simultaneous T₁ and T₂* mapping, that demonstrate the effectiveness of the proposed method for motion-robust quantitative imaging.

Theory

Review of 3D-EPTI acquisition

The IR-GE 3D-EPTI acquisition is illustrated in Fig. 1a (red window), where multiple excitation pulses are applied after the inversion pulse with 3D-EPTI readouts to track the T₁ recovery and T₂* decay. Each 3D-EPTI readout utilizes a continuous sampling to acquire multiple time points with different k_y-k_z encoding to cover a large 4D block in the k-t space (Fig. 1b, left panel). An optimized spatiotemporal CAIPI encoding scheme is employed, which was demonstrated in our previous studies to provide accurate image reconstruction under high undersampling factors (e.g., 80×) (28,43) by exploiting the strong temporal signal correlation across the EPTI readout and additional multi-channel coil information with a complementary pattern. In order to further accelerate the acquisition, 3D-EPTI acquires a radial-block pattern at each inversion time (TI) with less TRs instead of the full k-t space, which creates incoherent aliasing across TIs to allow image recovery based on compressed sensing theory (16) by exploiting the temporal correlation between these readouts. By combining the spatiotemporal CAIPI encoding and radial block sampling, high-quality quantitative imaging can be acquired at a high undersampling rate in the k-t space and reconstructed with a low-rank subspace reconstruction approach (19,28,43,44). For example, whole-brain quantitative imaging at 1-mm isotropic resolution can be acquired in 2 minutes, with a 4D block size of 8 × 10 × 210 × 48 (k_y × k_z × k_x × nEcho) and 45 TRs to form 2 radial-block blades at each TI (assuming TR = 2.6 s).

FIG. 1.

The graphic illustration of the IR-GE 3D-EPTI acquisition with 4D navigator. (a) The simplified sequence diagram and corresponding signal evolution as well as the block-wise sampling pattern of the IR-GE 3D-EPTI sequence with 4D navigator acquisition. The 4D navigator is acquired within the recovery time, which only takes about 250 ms with 4 excitations after the imaging scan (~1300 ms). (b) An optimized spatiotemporal encoding pattern is employed in the navigator acquisition for large k-t block sampling after each excitation, which has been used in the 3D-EPTI readout as well. In addition, a partial-Fourier scheme was used to acquire the navigator, to allow a larger coverage along k_y and k_z after reconstruction with less excitations (4 excitations in this example).

4D navigator acquisition

At the end of each TR in the IR-GE EPTI acquisition, there is deadtime of around 500-1000 ms with no excitations/readouts to allow for recovery of the longitudinal magnetization (M_z) before the next TR. To avoid any increase in the acquisition time, the proposed 4D navigator is acquired during this recovery time (Fig. 1a, blue window). Moreover, the navigator is designed to have minimal effect on the desired M_z recovery process by: i) using the optimized temporal-variant spatiotemporal CAIPI encoding (Fig. 1b, left) to cover a large 4D block after each excitation, ii) acquiring with a partial-Fourier scheme along both k_y and k_z as shown in Fig. 1b (right) that allows a recovery of higher frequency signals with less excitations, iii) utilizing a smaller FA than what is used in the image acquisition to further reduce the impact of the extra excitations on M_z.

These optimizations of the 4D navigator not only reduce the cost of the signal recovery and SNR efficiency, but also make sure that the differences in the M_xy signal generated by these small-FA excitations at the end of the inversion process is relatively small, thus the 4D blocks acquired at different TIs with different k_y-k_z encodings can be combined along TI with reduced timepoints to reconstruct (as shown in Fig. 1, 4 TI-blocks are combined to form a navigator). To provide accurate estimation with less excitations, different block pattern schemes were tested through simulation (examples are shown in Supporting Fig. 1), showing that the proposed partial-Fourier scheme can provide accurate 3D motion estimation with much less excitations. In this study, only 4 excitations are utilized to acquire the 4D navigator acquisition, which takes up ~250 ms during the signal recovery period in each TR, allowing a k-t space coverage of 30 × 24 × 150 × 48 (k_y × k_z × k_x × t), corresponding to a resolution of ~7 × 7 × 1.5 mm³ and a 40 ms readout, for accurate motion and ΔB₀ estimation. This navigator acquisition with reduced number of excitations and smaller FA results in < 1% reduction of the signal recovery based on a simulation analysis that will be shown in the results section.

FIG. 4.

Motion estimation (a), reconstructed multi-contrast images (b), and the estimated quantitative maps before and after correction (c) in the simulation experiment (frequent random motion). The designed 4D-navigator acquisition provides accurate estimation for all the 6 motion parameters, and the motion artifacts in the reconstructed multi-contrast images are effectively reduced after motion correction. After motion correction, the error of all the quantitative parameters is significantly reduced (ME: mean error, MPE: mean percentage error), and multi-parametric maps without noticeable artifacts are obtained.

Motion and ΔB₀ estimation using 4D navigator

The framework of navigator reconstruction and motion/ΔB₀ estimation is illustrated in Fig. 2. First, a subspace reconstruction is used to reconstruct the undersampled 4D navigator data into multi-echo volumes for every TR with the following objective function:

$${\text{min}}_c\Vert UFSB\varphi c-y{\Vert }_2^2+\lambda R(c),$$ (1)

where ϕ is the temporal subspace bases generated based on the signal model by an extended phase graph (EPG)-based simulation, c is the coefficient maps of the subspace bases, B is the pre-calculated phase evolution (resulting from B₀ inhomogeneity) across different echoes, S is the coil sensitivity, F denotes the Fourier transform operator, U is the undersampling mask, and y is the acquired undersampled 4D navigator data. R(c) is the locally-low-rank (LLR) regularization applied on c, and λ is the control parameter. The pre-calculated B₀ and coil sensitivity maps are obtained from a fast k-t calibration scan. After solving c, the multi-echo images can be obtained by ϕc, with no image distortion. In addition to estimating motion parameters using the reconstructed images, the B₀ changes due to motion can also be estimated using the multi-echo phases. During motion, not only the B₀-inhomogeneity maps will translate/rotate, but the actual local B₀ values would also change (ΔB₀) due to the interaction of shimming field and head position. In order to accurately estimate the change of B₀, different ΔB₀s ranging from −50 Hz to 50 Hz (1 Hz sample spacing) are simulated in the subspace basis generation step, that has been demonstrated to provide accurate ΔB₀ estimation in the subspace reconstruction (24,45). The use of the subspace approach with prior information from the signal model for k-t reconstruction can dramatically reduce the number of unknowns in the optimization process, leading to reduced image artifacts and improved SNR. More details of the subspace reconstruction for EPTI data can be found in Ref (43). The missing k-space section in the partial-Fourier scheme is also recovered in the subspace reconstruction.

FIG. 2.

The framework of 3D rigid motion and B₀ change (ΔB₀) estimation using 4D navigators. First, multi-echo volumes are reconstructed by complex subspace reconstruction, and the reconstruction process is iterated 3 times to correct for the motion of the B₀ maps using the estimated motion parameters in the previous iteration. After reconstruction, the final rigid motion estimation can be obtained using the magnitude of volumes with FLIRT function. Finally, the image phase change of the multi-echo data are used to fit the ΔB₀ map of each TR, and the ΔB₀ is filtered by a spatially 3^rd-order polynomial function to remove artifacts and noise.

After the initial navigator reconstruction, 3D rigid motion parameters (6 DOFs) of every TR can be estimated from the low-resolution volumes using FLIRT (46,47). To estimate the value changes of the B₀ field (ΔB₀), the navigator reconstruction is iterated to correct the motion (translation and rotation) of the pre-calculated B₀ maps based on the estimated motion parameters in the previous iteration as shown in Fig. 2. This also improves the reconstruction performance since the motion-corrected pre-calculated B₀ map is closer to the field of the acquired data. After several iterations (3 times in this work, after which the estimation is stable), the final multi-echo low-resolution volumes are reconstructed for motion and ΔB₀ estimation for every TR. The phase changes of the multi-echo volumes are first calculated by subtracting the phase from the first TR, and then temporal linear fitting is applied across TEs per TR to obtain the raw ΔB₀ map. Finally, a spatially 3^rd order polynomial fitting is applied to the raw ΔB₀ maps to remove potential image artifacts and improve the SNR, by assuming the ΔB₀ should be spatially smooth since it should be caused by the interaction of shimming and head position.

Motion-corrected subspace reconstruction

Using the estimated motion and ΔB₀ parameters from the 4D navigators, a motion-and-phase corrected 3D subspace reconstruction is implemented to recover multi-contrast volumes acquired by the IR-GE 3D-EPTI sequence with reduced motion artifacts:

$${\text{min}}_c\Vert U_{n}FS{B}_{n}T\varphi c-y_n{\Vert }_2^2+\lambda R(c).$$ (2)

Here, T is the rigid motion transformation operators (48), that transforms the multi-contrast volumes into N different motion states (N should be the number of TRs) based on the estimated parameters, and B_n is the updated phase evolution for the n-th motion state using the estimated ΔB₀s.

By modeling the motion and ΔB₀ of every TR in the 3D subspace reconstruction, the motion artifacts in the reconstructed multi-contrast images can be effectively reduced. Quantitative parameters including T₁, T₂*, proton density (PD) and B₁⁺ maps can then be estimated by dictionary matching.

Methods

All in-vivo data were acquired with a consented institutionally approved protocol on a Siemens Prisma 3T scanner with a 32-channel head receiver coil (Siemens Healthineers, Erlangen, Germany) on healthy volunteers (N = 3).

Simulation evaluation

To analyze the SNR cost of the navigator acquisition, an EPG-based numerical simulation was performed. The mean magnitude of all the signals are calculated at steady state (after 8 excitations, when the M_z before inversion becomes steady) under different scenarios: no navigator acquisition, navigator acquisition with FA = 30° (same as data acquisition), navigator acquisition with FA = 10°, and navigator acquisition with FA = 10° and 50 ms longer TR. Since the acquisition of navigator will only affect the T₁ recovery, different T₁ values (500-3000 ms) were simulated with constant T₂ of 65 ms and T₂* of 50 ms. All of the acquisition parameters used in the simulation are the same as in the in-vivo experiment that will be described later.

An image simulation experiment was also performed to evaluate the rigid motion estimation and correction prior to undertaking the in-vivo experiments. IR-GE EPTI data were generated using a set of pre-acquired T₁, T₂*, PD, B₀ and B₁⁺ maps of the brain using EPTI, and two motion types were simulated by applying motion transformations to different TRs, including random motion and sudden motion (within ±8 mm / degrees). 2-mm isotropic datasets were simulated, with a matrix size of 110 × 88 × 70 × 48 × 24 (k_y × k_z × k_x × nEcho × nTI), and the last 4 TIs are the navigator acquisition. The FA for GE excitations was 30°, and 10° for navigators, echo spacing (ESP) = 0.7 ms, TR = 2.1 s, and 21 TRs were simulated to form a 2 radial-block line acquisition. The simulated data were undersampled using the 3D-EPTI spatiotemporal sampling pattern (block size = 10 × 8, k_y × k_z), and 32-channel data are generated with added noise in the k-t space (SNR = 20 based on the L2 norm between k-space signal and noise). The 4D navigator data were also generated for each TR using the 4-block pattern as shown in Fig. 2. Note that only the rotation/translation of B₀ was simulated in this experiment without value changes to evaluate the rigid motion estimation and correction. The motion estimation, reconstructed images and quantitative maps were compared with the gold-standard parameters and maps used to simulate the datasets.

Retrospective in-vivo motion experiment

In order to quantitatively evaluate the proposed motion estimation and correction in-vivo, motion-free IR-GE 3D-EPTI datasets at 3 different head positions were acquired with independent pre-calibration scans, and these datasets were subsampled and combined together afterwards to mimic a motion-corrupted acquisition with 3 different motion states. The key acquisition parameters were: FOV = 224 × 180 × 150 mm³, 1.5-mm isotropic resolution, matrix size = 150 × 120 × 100 × 48 × 24 (k_y × k_z × k_x × nEcho × nTI), the last 4 TIs were navigator acquisition with FA = 10°, FA of GE = 30°, ESP = 0.7 ms, TE range of each readout = 1.3 – 34.2 ms, TR = 2.1 s, 57 TRs were acquired to form 4 radial-block lines and the acquisition time of each dataset was 2 minutes. The block size of the spatiotemporal CAIPI encoding was 10 × 8 (k_y × k_z), corresponding to a 80× undersampling in the k-t space, and 57 blocks were acquired for each TI with a 4-line golden angle radial block-wise pattern that provides another 4× acceleration, resulting in an overall undersampling rate of 320× in the k-t space. The k-t calibration scan was acquired to estimate the B₀ and coil sensitivity maps for each dataset using a GE sequence with bipolar readout, where data were acquired with the same FOV and echo spacing as the imaging scan. Other acquisition parameters were: matrix size = 42 × 32 × 150 × 7 (k_y × k_z × k_x × nEcho), TR = 22 ms. The k-space center (12 × 12) was fully-sampled and the rest of k-space was undersampled along k_y and k_z by a factor of 2 × 2, resulting in a total acquisition time of ~10s. GRAPPA (49) was used to reconstruct the missing data points in the k-t calibration data, where the central fully-sampled calibration data were used to calibrate the GRAPPA kernels.

The motion-corrupted data were synthesized by combining the 1-18 TRs of the 1^st dataset, 18-38 TRs of the 2^nd dataset, and 39-57 TRs of the 3^rd dataset. The 4D navigators were also extracted from the corresponding TRs of the 3 datasets to estimate the 3D rigid motion and ΔB₀ of each TR. In addition to reconstructing the synthesized motion-corrupted data using the proposed motion-corrected subspace reconstruction with estimated parameters, datasets at the 3 head positions were also reconstructed to obtain reference motion parameters and ΔB₀s, and the quantitative maps of the 1^st position is used as reference.

Prospective in-vivo motion experiment

A prospective motion correction experiment was conducted in healthy subjects (N=3) to evaluate the performance of the motion correction in vivo. The acquisition parameters were the same as the retrospective motion acquisitions. During the 2-minute 3D-EPTI scan, volunteers were asked to move head randomly. Before the motion scan, a scan with stationary head position was also acquired as a motion-free reference for comparison. K-t calibration data were acquired using the same parameters as in the previous retrospective scan, resulting in a 10 s calibration scan. The reconstructed quantitative maps including T₁ and T₂* were compared between the stationary case, the motion-corrupted case without correction, and motion + ΔB₀ corrected case. A region-of-interest (ROI) analysis was also performed to compare the quantitative values between the stationary and the motion-corrected data across 159 auto-segmented brain ROIs.

Image reconstruction and processing

In this work, the subspace reconstruction was used for both navigator and image reconstruction. For the navigator reconstruction, the subspace bases were generated using principal component analysis (PCA) from the simulated signals with different T₂* decays and ΔB₀s, ranging from 5 ms to 400 ms and −50 Hz to 50 Hz. Six bases were used that can approximate the simulated signal evolutions with an error < 1%. For image reconstruction, 8 bases were extracted from the simulated IR-GE signal evolutions (error < 0.2%) with the EPG method, with a wide range of quantitative parameters: : T₁ from 400 ms to 5000 ms, T₂* from 5 ms to 500 ms, B₁⁺ factor from 0.75 to 1.25. The subspace reconstruction was solved by the alternating direction method of multipliers (ADMM) algorithm (50), and a maximum number of iterations = 100 was set as the stop criterion, with a lambda of 0.01 that was used in the previous study (43). The dictionary for quantitative parameter fitting was generated with the same parameter range in the basis generation of the IR-GE sequence. After dictionary matching, T₁, T₂*, PD, B₁⁺ can be obtained, the estimated B₁⁺ maps were fitted spatially by a 2^nd-order polynomial function to remove residual artifacts, since the B₁⁺ field should be smooth in the spatial domain.

The 3D rigid motion between navigators was estimated by FLIRT (46,47) using the echo-averaged volumes, to obtain motion parameters (6 DOFs) for each TR. Freesurfer (51) was used to auto-segment 159 ROIs using the synthesized T₁-weighted image of the motion-free data for the ROI analysis in the prospective in-vivo experiment, including cortical, subcortical, white matter and cerebellum regions after removing ROIs smaller than 200 voxels. Before segmentation, the different image volumes acquired from stationary and motion scans were co-registered by FLIRT, and the skull was removed by BET (52). All of the image reconstruction and post-processing were performed in MATLAB on a Linux workstation (CPU: Intel Xeon, 3.00GHz, 24 Cores; RAM: 512 GB; GPU: Quadro RTX 5000, 16 GB memory).

Results

Figure 3 shows the effect on the SNR of the sequence from adding in the proposed navigator, using a numerical simulation analysis of the mean magnitude signals for different T₁s. The navigator acquisition with FA = 30° shows reduced amplitude up to ~7% (red line) compared with the case without navigator acquisition (blue line) for T₁ = 3 s, whereas for tissues with shorter T₁s the amplitude reduction is less due to the faster recovery. Using a smaller FA of 10° for navigator acquisition (yellow line), the loss of amplitude is further reduced to less than 1% even for T₁ of 3 s. Such reduction of signal amplitude is corresponding to a very small loss in SNR efficiency for 3D-EPTI, which is less than 1%. By increasing the TR by 50 ms, the reduction in amplitude due to the navigator acquisition (FA = 10°) can be fully compensated, where a slightly higher amplitude than the case without the navigator acquisition is achieved for all T₁ values (purple line). The simulation evaluation results of the proposed 4D navigator acquisition for motion and B₀ estimation are provided in Supporting Figure S1 and S2.

FIG. 3.

EPG-based simulation analysis of the signal reduction caused by adding a 4-block navigator acquisition during the T₁-recovery period of the IR-GE 3D-EPTI sequence. The normalized amplitude of the averaged imaging signals is calculated for four cases: i) no navigator, ii) navigator acquisition with FA = 30°, iii) navigator acquisition with FA = 10°, iv) navigator with FA = 10° and 50 ms longer TR. The plot shows that the reduction of the signal amplitude by adding navigator with FA = 10° is less than 1% for all simulated T₁ values of the tissue. By increasing the TR of 50 ms, the loss of SNR can be fully compensated with slightly higher signal amplitude.

Figure 4 shows the results from the motion estimation and image correction simulation experiment with random motion (Fig. 4). The 3D rigid motion estimation using the 4D navigator provides accurate motion parameters with low errors. For the random motion case (Fig. 4a), the estimation errors were: translation = 0.10 ± 0.07 mm (mean error ± standard deviation), rotation = 0.09 ± 0.05°. The example reconstructed images at different TIs are shown in Fig. 4 b, where images without correction suffer from severe blurring and artifacts, and the motion-corrected images show much less artifacts with lower errors. The consistent and small errors across TIs after correction indicate the consistent correction performance of different TIs, due to the robustness of the golden-angle radial-block sampling to rotations as well as the use of joint subspace reconstruction. The proposed motion correction also improves the accuracy of quantitative mapping in the simulation test, as shown in Fig. 4c with example results from the random motion case. The severe artifacts and large errors (mean errors, MEs, or mean percentage errors, MPEs, are listed) due to motion in the T₁, T₂*, PD and B₁⁺ maps are significantly reduced in the motion-corrected data. Figure 5 and Supporting Information Table S1 show more simulated motion cases using realistic motion parameters obtained from previous patient scans (14 cases, motion traces of 4 example cases are presented in Fig. 5). The mean errors of T₁ (30.3 ± 0.5 ms) and T₂* (2.8 ± 0.1 ms) after correction are consistent and relatively low for all the simulated motion scenarios, further demonstrating the effectiveness of the rigid motion correction.

FIG. 5.

Motion simulation using realistic motion parameters obtained from previous patient scans. 14 cases were simulated and motion traces of 4 example cases are presented in the figure.

The results of retrospective in-vivo motion experiment are shown in Fig. 6-8. In Fig. 6, example reconstructed navigator images are presented in three orthogonal views. Both the averaged image magnitude of all echoes and the raw ΔB₀ maps (before spatial fitting) are shown, in which head rotations and spatially varying B₀ changes can be observed between the two navigators acquired at two different motion states. Figure 7a shows the estimated 3D motion parameters from the 4D navigators for the synthesized motion-corrupted data together with the reference parameters obtained from the dataset at each of the three head positions. Close estimation between the navigator and reference are presented, with an error of 0.02 ± 0.02 mm for translation and 0.05 ± 0.05° for rotation, demonstrating the accuracy of rigid motion estimation of the 4D navigator for in-vivo acquisition. Figure 7b shows the estimated ΔB₀ of the 30^th and 50^th TR relative to the 1^st TR after spatial polynomial fitting (3^rd order). The estimations using 4D navigator and reference (using the k-t calibration scan at each head position) of different motion states are compared, which show close values with small differences. These results indicate that the 4D navigator can provide accurate tracking of B₀ changes due to head movements, for use to incorporate into the image reconstruction to avoid the associate image artifacts. The comparison of the quantitative maps including T₁ and T₂*, fitted from motion-free data (1^st head position), motion-corrupted data without correction, rigid-motion corrected data, and motion + ΔB₀ corrected data, are shown in Fig. 8. Without correction, the quantitative maps show detrimental artifacts with large MPEs, where T₂* map shows more obvious artifacts than T₁ indicating it is more sensitive to motion in the IR-GE acquisition. After rigid motion correction, the artifacts in the quantitative maps are markedly reduced with much lower MPE. By further correcting for the ΔB₀ in the reconstruction using estimates from the navigators, the image artifacts and errors are further reduced, especially for the T₂* map as indicated by the zoomed-in areas in the figure (yellow window), providing much more accurate quantifications even with large head motions (up to 15° in this data). The MPE after correction is very close to the baseline error between motion-free datasets acquired at different head positions, which is 8.8% for T₁ and 14.5% for T₂*.

FIG. 6.

The example magnitude images and raw ΔB₀ maps (before spatial fitting) reconstructed from the 4D navigators of in-vivo datasets. Head motion between the two navigators can be observed from the presented views, and spatially smooth ΔB₀ up to ±20 Hz was estimated using the multi-echo images from the navigator.

FIG. 8.

The comparison of quantitative T₁ and T₂* maps in the retrospective in-vivo experiment, estimated from motion-free reference data, motion-corrupted data without correction, rigid motion corrected data, and motion + ΔB₀ corrected data. After rigid motion correction, most of the artifacts are removed in the T₁ map with close image quality to the reference, but there is still residual artifacts in the T₂* map as highlighted in the zoomed-in region. ΔB₀ correction further reduces the mean percentage error (MPE) and residual image artifacts, especially for the T₂* map.

FIG. 7.

Motion and ΔB₀ estimation in the retrospective in-vivo experiment. (a) The estimated motion parameters using 4D navigators compared with the reference estimation using high-resolution volumes. (b) Comparison of the estimated B₀ changes relative to the first TR at two different head positions using the proposed navigator and reference acquisition. Based on the results, accurate estimation for both motion and ΔB₀ are obtained using the 4D navigators.

Figure 9 shows the results from the prospective motion experiment. The tracking of 3D motion at every TR (2.1 s, 57 TRs in total) during the 2-minute scan is shown in Fig. 9a, with both small and large motion changes. Figure 9b shows the estimated B₀ changes in 5 example TRs due to head movements. The reconstructed quantitative maps (T₁, T₂*, PD) obtained from the stationary case (motion-free reference), the motion case without correction, and the motion + ΔB₀ corrected data are presented in Fig. 9c. The motion case without correction shows strong blurring and artifacts in the quantitative maps, with most of these artifacts removed after applying the proposed correction method, providing close image quality to the stationary case for all the quantitative parameters. To better visualize the image quality of the whole brain after the correction, 3 orthogonal views of the T₁ and T₂* maps are shown in Fig. 9d. The quantitative values after correction are compared with the stationary case in 159 auto-segmented ROIs across the whole-brain in 3 healthy subjects shown in Fig. 10. The motion parameters of the scan for subject 2 and 3 are plotted in Fig. 10b, with distinct head movement frequencies. The ROI analysis shows high correlation between the quantitative parameters from the stationary scan and the motion corrected case, with Pearson’s correlation coefficients (PCCs) of 0.994 for T₁ and 0.975 for T₂*. The Bland-Alman plots show a small bias of 0.164% for T₁ (P < 0.0001, limits of agreement from −3.64% to 3.97%), and small bias of 2.96% for T₂* (P < 0.0001. limits of agreement from −9.81% to 15.79%), which are consistent and comparable to the previous repeatability test of 3D-EPTI without motion (28).

FIG. 9.

Results of the prospective in-vivo experiment. (a) Estimated motion parameters during the 2-minute scan. (b) Estimated B₀ changes from different TRs. (c) Reconstructed T₁, T₂*, and PD maps from the stationary case, motion case without correction, and motion + ΔB₀ corrected data. The proposed motion correction effectively removes the motion artifacts in the 3D-EPTI acquisition, providing high-quality quantitative maps close to the scan without motion. (d) The 3 orthogonal views of quantitative maps obtained from the motion corrupted data after correction.

FIG. 10.

(a) ROI analysis of T₁ and T₂* quantification (159 ROIs, N=3 subjects) from the stationary scan and motion scan after correction, including scatter plots of the two scans (top), and the Bland-Altman plots of the quantitative parameters (bottom). (b) Motion traces of the scan for subject 2 and 3.

Discussion and Conclusions

This work presents a motion correction technique for 3D-EPTI using an efficient 4D navigator acquisition with motion-corrected subspace reconstruction. Continuous and accurate tracking of 3D head motion and B₀ change at every TR (~2 s) are provided by the 4D navigator, at a cost to the SNR efficiency of less than 1%. The estimated motion and ΔB₀ parameters are modeled and incorporated into the 3D subspace reconstruction, allowing fast and motion-robust quantitative neuroimaging using 3D-EPTI.

The proposed 4D navigator acquisition is designed with several optimizations to achieve high efficiency. The optimized spatiotemporal acquisition not only provides data at multiple echoes to estimate the field change, but also enables a large k-space coverage after each excitation. Comparing to multi-echo GRE acquisition, the continuous readouts require less RF excitations and thus reduce the impact of navigator acquisition on signal recovery. Moreover, the proposed 4D EPTI navigator eliminates the image distortion in conventional EPI readouts, providing distortion-free B₀ change maps to avoid any mismatch with the imaging data. The use of a smaller FA in the navigator acquisition ensures minimal cost in SNR efficiency of less than 1% while providing sufficient SNR in the low resolution navigator to accurately estimate motion parameters and B₀ changes. An asymmetric partial Fourier scheme is employed in the navigator acquisition to allow a larger coverage with only 4 excitations. Supporting Figure S1 and S2 shows the designed partial Fourier scheme with 4 excitations can provide accurate estimation of motion and B₀ change with close accuracy to the 9 excitation case, which can also be useful in the design of other types of navigators. The ability of the proposed 4D navigator to accurately track motion and ΔB₀ was demonstrated for the IR-GE 3D-EPTI sequence in this study (Fig. 4, 7 and S2), and it can also be easily applied to other sequences to provide efficient motion navigation.

Both in-plane and through-plane motions were well-corrected for in 3D-EPTI by modeling the motion and ΔB₀ changes in the subspace reconstruction. Effective correction through motion-corrected subspace reconstruction has been validated, providing clean images with much more accurate quantitative measurements in the presence of motion. T₂* shows more artifacts and bias than T₁ when motion occurs, as well as more residual artifacts after rigid motion correction (Fig. 8). The underlying reason can be attributed to, i) ΔB₀ caused phase variations between acquired signals at different TEs, ii) the underlying value of T₂* may change at different head positions due to its B₀-orientation dependent nature that has been shown in previous studies, such as in (53). The correction of ΔB₀ was demonstrated to further improve the T₂* estimate (Fig. 8), and provides close image quality to the stationary case in the prospective motion experiment (Fig. 9). The T₂* value change due to its B₀-orientation dependance was not modeled in the reconstruction, which can cause variation with different head positions. We have calculated the baseline MPE of T₂* between two motion-free datasets with different head positions is around 14.5%, and a MPE of 15.7% was obtained after correction which is very close to the baseline. Based on the ROI analysis (Fig. 10), the bias and variation between two scans (stationary scan vs. motion scan) after motion correction are at the same level as the previous scan-rescan repeatability test of 3D-EPTI without intra-scan head motion (28), demonstrating the robustness to motion of the motion-corrected 3D-EPTI for quantitative mapping.

The radial-block acquisition of 3D-EPTI may also be designed in a way to allow a self-navigation acquisition, by acquiring a central block in every TR at a different TI (so there is no redundancy/repeat in the encoding). The major challenge of such self-navigated acquisition is that the significant contrast difference between the navigators from different TIs will affect the accuracy of motion estimation, and the resolution would also be lower. So we chose to design the efficient 4D navigator acquisition to ensure the estimation accuracy with minimized SNR cost. In this proof-of-concept implementation, the proposed navigator acquisition and motion-corrected reconstruction were applied to the IR-GE sequence for motion-robust T₁, T₂*, PD, and B₁⁺ mapping. They can be easily extended and applied to other sequences, such as the GRASE 3D-EPTI acquisition (28,54), to measure more quantitative parameters of interest with robustness to motion. The motion-robustness and fast acquisition provided by the motion-corrected 3D-EPTI may facilitate the use of multi-parametric MRI for more efficient and accurate brain exams and longitudinal monitoring. Future study of the motion-corrected 3D-EPTI technique with more subjects and also disease populations will be conducted to further validate the technique. Data corruption caused by motion during data sampling is not considered in this work, which can be addressed by applying data rejection and quality control strategies based on the image amplitude and artifacts level. In addition to the application in fast clinical exam, the use of the proposed method for generating high resolution quantitative imaging of the brain robustly will also be explored, to provide higher acquisition efficiency and preserve detailed structures by removing motion artifacts.

Supplementary Material

supinfo

FIG. S1. Evaluation of the motion estimation using different block patterns in the 4D navigator by simulation tests with a random motion. The mean estimation errors of translation and rotation (6 DOFs) are listed of the example patterns with different number of blocks. The proposed asymmetric partial-Fourier pattern (Case 3) provides good estimation close to the 9-block acquisition (Case 6), but with only 4 blocks, corresponding to much less time and excitations for the 4D navigator acquisition.

Table S1. The mean errors of T₁ and T₂* quantification after correction of the 14 simulated cases in the motion simulation test using realistic motion parameters.

FIG. S2. Simulation evaluation of the B₀ change estimation using a 9-block and a 4-block 4D navigator. The realistic B₀ change map estimated in-vivo is used in this simulation. The 4-block navigator achieves small error (small standard deviation of the difference map) close to the 9-block case, indicating its ability to monitor B₀ field change with high efficiency and accuracy.