Three Dimensional Radial Echo Planar Imaging for Functional MRI

Abstract

Purpose:

To demonstrate a novel 3D Radial Echo Planar Imaging (3D REPI) sequence for flexible, rapid and motion-robust sampling in functional MRI (fMRI)

Methods:

The 3D REPI method expands on the recently described golden angle rotated EPI TURBINE approach by exploiting the unused perpendicular direction in the EPI readout to form fast analogues of rotated stack of stars or spirals trajectories that cover all three dimensions of k-space. An iterative conjugate gradient algorithm with SENSE reconstruction and time-segmented non-uniform FFT was used for parallel imaging acceleration and to account for the effects of B₀ inhomogeneity. The golden angle rotation allowed for sliding window reconstruction schemes to be applied in brain BOLD fMRI experiments.

Results:

Combined whole brain visual and motor fMRI experiments were successfully carried out on a clinical 3T scanner at 2 mm isotropic and 1×1×2 mm³ resolutions using the 3D REPI design. Improved sampling characteristics and image quality were observed for twisted trajectories at the expense of prolonged readout times and off-resonance effects. The ability to correct for rigid motion correction was also demonstrated.

Conclusions:

3D REPI presents a flexible approach for segmented volumetric fMRI with motion correction and high in-plane spatial resolutions. Improved BOLD fMRI brain activation maps were obtained using a sliding window reconstruction.

INTRODUCTION

Functional Magnetic Resonance Imaging (fMRI) enables imaging of detailed spatial variations of blood dynamics through the entire brain. 3D volumetric acquisitions are particularly attractive in this context due to their capability for high spatial resolution and improved Signal-to-Noise Ratio (SNR) (1–3). 3D acquisitions also allow the use of parallel imaging acceleration along all three dimensions and are frequently used in rapid fMRI (4,5). Although rapid fMRI based on single-shot volumetric methods is promising, the high spatial resolutions desired in most fMRI experiments typically require the application of k-space segmentation due to gradient limitations (6,7). The most common rapid volumetric acquisition is segmented 3D EPI, however, other non-Cartesian variants such as multi-shot stack-of-spirals have received considerable attention as well (8,9).

Recently, a segmented volumetric radial EPI method termed TURBINE (Trajectory Using Radial Batched Internal Navigator Echoes) has been proposed for fMRI (10,11). This technique exploits the intrinsic self-navigation of radial sampling (12,13). Furthermore, the application of a continuous golden angle (GA) rotation between excitations enables the reconstruction of images from a variable number of shots with high sampling efficiency. Thus, image time series can be obtained from the same dataset at different temporal resolutions penalized by the severity of streaking artifact. Few shots can be used to provide estimates of more rapid physiological changes such as respiration and motion that can in turn be used to reconstruct better quality images with more shots to observe BOLD activation. The favorable aliasing characteristics of undersampled radial methods are hereby exploited and high temporal resolution in the image timeseries can be achieved (14). Another advantage of the radial nature of the TURBINE acquisition is that the in-plane dimension is sampled quickly by frequency encoding leading to lower distortion from off-resonance even for high in-plane resolutions.

In this work we present a highly flexible, segmented 3D sampling approach referred to as 3D Radial Echo Planar Imaging (3D REPI) that conceptionally combines TURBINE and two-dimensional radial EPI (15,16). 3D REPI trajectories are fast analogues of rotated stack-of-stars or spirals trajectories that exploit all three dimensions of k-space within each single shot (17,18). Compared to TURBINE imaging, this generally results in more benign aliasing patterns in undersampled fast imaging applications such as fMRI and leads to an increase in temporal stability of the signal. The 3D REPI trajectories are designed and applied in visual and motor task BOLD fMRI at 2 mm isotropic and 1×1×2 mm³ resolution on a 3T MRI scanner. Image quality and BOLD activation was further improved by using sliding window reconstruction schemes.

METHODS

Sampling and Gradient Design

The 3D REPI and the TURBINE acquisitions can be conceptualized by rotating a standard EPI trajectory by 90° along the readout axis such that the phase-encoding direction is along the k_z direction. In each successive excitation the readout train, referred to as ‘blade’, is rotated around the k_z-axis by the GA ≈ 111.25° to fill in 3D k-space. In 3D REPI the sampling efficiency is further increased by introducing an additional twist (θ) along the k_z direction producing a ‘twisted blade’ with a helical arrangement of the phase-encoding lines (Figure 1B–C). A single blade is hereby defined by three gradients: the readout gradient (G^read) defining in-plane sampling (in-plane resolution and field of view (FOV_xy)), the z phase-encoding gradient G^phase (Eq. 1) defining k_z sampling parameters (z resolution and FOV_z) and the gradient to perform the rotation between successive EPI readout lines (G^rot, Eq. 2).

Figure 1:

Top: Single blade k-space presentation (black) of 3D REPI trajectories rad0low (A), rad180low (B), rad540low (C) and spiral540low (D) for 2 mm isotropic resolution whole brain imaging with twist angles of 0°, 180°, 540° and 540°, respectively. Bottom: Single full blades of interleaved segmented 3D REPI trajectories rad180seg2 (E), spiral180seg2 (F) and spiral180seg3 (G) with N_seg= 2 and 3 for 1×1×2mm³ resolution whole brain imaging. The additional twist between segments was introduced to further distribute sampling in 3D k-space.

G^read (t): radial or spiral in − out gradient

$$\Delta k^{\mathit{\text{phase}}}=\gamma \int G^{\mathit{\text{phase}}}\left(t\right)\cdot dt=1/FO{V}_z$$ [1]

$$\Delta k^{rot}=\gamma \int G^{rot}\left(t\right)\cdot dt=2\cdot \text{sin}\left(\frac{d\theta }{2}\right)\cdot k_{max}$$ [2]

t: time; k_max: maximum extend of k_xy space line

Δk^phase: k_z space increment between z phase encodes

Δk^rot: k space increment between consecutive lines at k_max

dθ: incremental rotation angle between consequetive lines

In a variation of this trajectory design the radial readout gradient (G^read) is modified to produce an in-out spiral trajectory (Figure 1D) to improve k_x-k_y sampling efficiency. The spiral algorithm is based on the WHIRL design with less twist around the k-space origin to yield increased efficiency over standard spiral trajectories for higher numbers of interleaves (19). The in-out WHIRL gradients are adjusted for 3D REPI to move through the center of k-space at a constant velocity as opposed to going to zero as in a standard spiral sampling.

For acquisitions with increased resolution in which the design described above would lead to extended readout length, interleaved segmentation in the k_z direction is applied (see Figure 1). For a given segmentation factor (N_seg), blades are designed that sample only every other N_seg k_z phase-encode. These blade segments are played out during consecutive shots in an interleaved manner to fill the missing k_z planes using additional z phase-encoding gradients (G_seg). A rotation along k_z is introduced between segments so that the total rotation α^tot for each segment is described by Eq 3:

$${\alpha }^{tot}=GA\cdot n_{\mathit{\text{blade}}}+\left(\frac{\pi }{n_{seg}}+\pi \right)\cdot n_{seg}$$ [3]

with n_blade = 0…(N_blades − 1) and n_seg = 0…(N_seg − 1)

In 3D REPI acquisitions, undersampling can be realized by either leaving out k_z phase-encodes within blades (k_z undersampling) or by using a reduced number of blades (k_x-k_y undersampling), or both. The segmentation of the blade into multiple shots loosens the restrictions on its design as arbitrary angles between excitations can be selected without any penalty in sampling efficiency. A rotation scheme was implemented that evenly spreads the N_Seg segments in the rotational plane thereby increasing the incoherence along the k_z direction (Figure 1). The rotated interleaved segmentation of 3D REPI blades leads to highly incoherent constructs that will nevertheless be referred to as ‘blades’ for reasons of clarity. However, they may also be viewed as k_z undersampling schemes with alternating k_z sampling, particularly if the rotation between segments matches the GA rotation between shots in the acquisition.

In this study three 3D REPI trajectories with varying degrees of k_x-k_y twist, rad0low, rad180low and rad540low with a 0°, 180° and 540° rotation along k_z over the entire blade, respectively, as well as one trajectory with a spiral design spiral540low (540° rotation) were generated for 2×2×2 mm³ resolution whole brain fMRI (21×21×14.4 cm³). Trajectories were designed to sample all of the 72 k_z phase-encodes. The radial gradient design (|G_read|) for all three radial trajectories was kept the same. The corresponding k-space representations and gradient waveforms are shown in Figure 1. The readout length of the basic planar rad0low design was ~ 53.7 ms. With increasing degree of twist the duration was prolonged considerably to 55.2 ms (~103%) and 59.4ms (~111%) for rad180low and rad540low due to the need for larger G_rot blips and again to 68ms (~127%) for the twisted spiral readout gradient. Even in the case of rad540low the rotation angle between consecutive lines remained relatively low at 7.5°. A further increase of the rotation or the implementation of alternating rotation schemes to reduce coherence was deemed impractical due to the further prolongation of the readout and thereby increase in sampling inefficiency.

In addition, three trajectories with a 180° rotation for segmented fMRI at 1×1×2 mm³ resolution (21×21×14.4 cm³) were generated (rad180seg2, spiral180seg2 and spiral180seg3) using the 3D REPI segmentation approach described above. Rad180seg2 (radial) and spiral180seg2 (spiral) were designed for an N_seg = 2 segmentation scheme. With otherwise equal parameters, the introduction of the spiral twist led to the increase in readout duration from 43 ms to 58 ms for each segment. To avoid the extended readout duration a spiral180seg3 (spiral) was generated for N_seg = 3 resulting in 40 ms long segments.

All of the 3D REPI trajectories used in this work were generated using ramp-sampled trapezoidal or spiral gradients at a 2.5 μs dwell time, a slew rate of 130 T/m/sec, and maximal gradient power of 30 mT/m. Gradient waveforms were generated in Matlab (The Mathworks, Natick, MA) and read into the pulse sequence during scanning.

Simulations of Sampling Characteristics

Point spread function (PSF) simulations were performed using trajectories rad0low, rad180low, rad540low and spiral540low (20 iterations, N_blades= 4). Sidelobe-to-peak ratios (SPR) were determined according to Eq. 4:

$$SPR,ma{x}_{i\ne j}\left|\frac{PSF\left(i,j\right)}{PSF\left(i,i\right)}\right|$$ [4]

Additionally, simulated 3D REPI fMRI time series of continuously GA rotated sampling schemes were generated using trajectories rad0low, rad180low, rad540low and spiral540low. The k-space datasets were synthesized from an input brain image via Non-Uniform Fast Fourier Transform (NUFFT) and used for an iterative reconstruction at N_blades = 10, 20, 21, 34, 40 and 60. See below for more details on the reconstruction. No noise was added prior to reconstruction in order to only simulate the fluctuating aliasing pattern inherent to an undersampled GA rotated sampling scheme. Both “temporal SNR” (tSNR) maps and average brain values were used to quantify the degree of signal fluctuation.

Data Acquisition

In vivo MRI scans were performed on three healthy adult volunteers. Participants were recruited and scanned under informed consent using a protocol approved by the joint Institutional Review Board by the Queens Medical Center and the University of Hawaii. All measurements were performed on a Siemens MAGNETON Prisma 3T (Erlangen, Germany) scanner equipped with a 52‐channel head coil. The fMRI protocol included: Sensitivity and Field map Estimation: Two Cartesian gradient-echo scans were performed for the 2×2×2 m³ and 1×1×2 mm³ resolution 3D REPI measurements. The parameters for low/high resolution were approximately a 2min/4min scan time, 64×64/128×128 pixel resolution, 21 cm FOV, 15° FA, 72 2 mm slices, TR of 28 ms, and TE’s of 5 and 6 ms; Calibration scan: A 20 s calibration scan to correct gradient and timing imperfections was performed prior to data acquisition in analogy to previous described procedures (20), see Supporting Information (SI) for more information; Functional MRI Acquisition: 3D REPI fMRI data were acquired using the trajectories for the two different resolutions. The 3D REPI pulse sequence used in this work is based on a standard 3D spoiled gradient echo sequence in which the conventional readout train is replaced by the 3D REPI trajectory. A fat saturation pulse and a slab selective (14.4 cm) excitation pulse (496 ms) were applied. The flip angles ranged between 18–22° reflecting the Ernst angle for a T₁ of 1 s. The TEs and TRs were in the range of 29–36/22–31 ms and 77–92/64–82 ms for low/high resolution, respectively depending on the lengths of the readout; T₂*-weighted reference scan: A 3D REPI reference scan was acquired with imaging parameters matched to the fMRI scan, but lower flip angles (8°−10°) and fewer blades (100/200 blades low/high resolution). The reference scan took between 8 s and 40 s. fMRI paradigm: The fMRI task was designed to produce visual activation using the Cogent 2000 toolbox (Cogent 2000 developed by the Cogent 2000 team at the FIL and the ICN and Cogent Graphics developed by John Romaya at the LON at the Welcome Department of Imaging Neuroscience). The tasks for 2 mm isotropic and 1×1×2 mm³ resolutions consisted of six and eight blocks of 20 s flickering checkerboard separated by 20 s resting periods leading to a total duration for the paradigm of 4:20 min and 5:40 min, respectively. The subjects were also asked to perform a finger-thumb opposition task during the visual stimulus to produce motor activation as well.

Image Reconstruction and fMRI Analysis

All image reconstruction and fMRI processing was performed offline using Matlab. Images were reconstructed using a time-segmented iterative conjugate gradient NUFFT SENSE algorithm that accounts for parallel imaging acceleration as well as the zero order effects of B₀ inhomogeneity (21,22). The reconstruction code was developed using the freely available Michigan Image Reconstruction Toolbox (MIRT) (https://web.eecs.umich.edu/~fessler/code/). The coil sensitivity and B₀ maps were derived from the gradient echo scans using methods by Walsh et al. (23) and Funai et al. (24). Prior to reconstruction, k-space trajectories were adjusted using the calibration data according to the method described in the SI (see SI.Figure S1&2). Multi-coil k-space data were compressed to eight virtual coils via principal component analysis (25). Trajectories were parsed into 12 time-segments for the inhomogeneity correction.

The image registration approach previously proposed for TURBINE fMRI was applied to correct for rigid body motion using six degrees of freedom (10). In a first step, the fMRI time series was reconstructed at high temporal resolution using a low number of blades to determine motion parameters. A sliding window scheme with N_blades= 6 and step-size n_step= 3 was applied to filter out high frequency fluctuations. The three-dimensional motion parameters were then extracted by co-registration of the crude image series using the first image of the series as reference volume. Parameters were temporally interpolated to give individual rotation matrices R_i and translation vectors T_i for every blade of the acquisition. In a second reconstruction step, these motion parameters were used to correct for rigid head motion in the reconstruction of images with higher blade numbers (i.e. N_blades= 20–40) depending on the desired fMRI temporal resolution and tolerable level of aliasing artifact. The k-space trajectory input as well as the raw k-space signal were modified according to the Fourier rotation and shift theorems prior to reconstruction, respectively, where s_i’(k(t)) is the corrected signal for a single blade and k(t) the corresponding k-space trajectory (Eq. 5).

$$s_i\text{'}\left(k\left(t\right)\right)=s_i\left(R_i\cdot k\left(t\right)\right)\cdot e^{-i{R}_i\cdot k\left(t\right)\cdot T_i},i=1\dots N_{\mathit{\text{blades}}}$$ [5]

Different sliding window schemes were applied in the reconstruction of the fMRI time series for improved temporal resolution and image quality. Fixed window sizes of 6–40 blades were used in combination with a step size of 3–10 blades depending on the acquisition. The first 80 excitations of the time course were omitted to ensure a steady state condition. The images were then reconstructed as described above and co-registered. Activation map processing was performed using a general linear model with a canonical hemodynamic response function with first and second order temporal trends removed. No spatial smoothing, masking, or corrections for multiple comparisons or autocorrelation were performed.

In order to test the efficacy of the sliding window reconstruction, a Receiver Operating Characteristic (ROC) curve analysis was carried out on the t-score maps obtained from the statistical analysis described above. False positive and true positive ratios were determined in step sizes of 0.01 for the t-values for each case. The differentiation between false positive and true positive was based on a predefined mask generated from the t-score maps themselves. Therefore, t-score thresholds were conservatively selected, and true positive mask smoothed and constrained to the brain region. Due to the potential of inter-measurement inconsistencies in the definition of true positive masks, the use of ROC curve analyses was limited to the performance evaluation of the different reconstruction schemes within single datasets.

RESULTS

PSF Simulations

The two major innovations of 3D REPI are the introduction of a rotation between consecutive lines along the k_z phase-encoding direction and the introduction of an in-out spiral type design for in plane sampling. The rationale was to cover larger areas of k-space with each single blade to increase incoherence in the aliasing pattern in undersampled image acquisitions that can be exploited for accelerated imaging. This notion was probed by comparing PSF simulations for a GA acquisition of the three radial trajectories rad0low, rad180low and rad540low and one spiral trajectory spiral540low. Significant differences between the rad0low and the twisted trajectories were observed (shown for N_blades = 4 in Figure 2). In the case of rad0low, aliasing exclusively occurred in the k_x-k_y plane in form of a streaking pattern consistent with what is seen for undersampling in standard radial and TURBINE imaging. The introduction of twist leads to signal intensity being distributed away from the central image plane resulting in more benign aliasing pattern covering the entire x-y-z volume that was reflected by a lower SPR in all cases. This effect can be observed even at very low twist angles and increases with larger degrees of rotation (SI.Figure S3). The replacement of the radial lines by a spiral design during the in-plane sections of the trajectory further distributed the aliasing energy. The full sets of PSF simulations along with additional information are shown in the SI.Figure S3.

Figure 2:

Point spread function simulations of 3D REPI trajectories rad0low, rad180low, rad540low and spiral540low with twist angles of 0°, 180°, 540° and 540°, respectively. Illustrations show the central plane of the simulation using N_blades= 4 for each trajectory. SPR ratios are indicated in white for each case. Complete sets of PSF simulations are shown in the SI.Figure S3.

Effects of Undersampling and B₀ Inhomogeneity

A series of brain images were obtained using the 3D REPI trajectories to examine the effects of undersampling and B₀ inhomogeneity. Presented are T₂*-weighted images with blade numbers N_blades = 3, 10, 40, 200 for the 3D REPI acquisitions at 2 mm isotropic resolution (see Figure 3) and with N_blades = 30, 40 and 200 for those at 1×1×2 mm³ resolution (see Figure 4). At high sampling (200 blades) good image quality was obtained for both the lower and higher resolution acquisitions. For the 2 mm isotropic resolution images, only minor aliasing artifacts were observable at blade numbers 40 and above for all three trajectories rad0low, rad180low and rad540low and only minor variations such as the amount of off-resonance, and slight differences in contrast were noticeable, which were attributed to the changes in readout length. The differences in the brain images as a result of varying degrees of twist in these trajectories were particularly apparent at high undersampling for which aliasing largely affects image quality. For blade numbers of 3 and 10 the streaky appearance of the rad0low images was reduced in images rad180low and rad540low. A quantitative comparison of the difference maps between N_blades= 200 and N_blades= 40 indicated a better rendering of brain images with increasing twist angles (see bottom row of Figure 3 and SI.Figure S4). The adaption of spiral readout led to additional improvements of aliasing artifacts in the undersampled images, however, the extended readout duration also resulted in stronger signal dropout and distortion (indicated by red circle in Figure 3). The acquisition time for a single brain volume using 40 blades was 3.4 s. The application of a B₀-informed time-segmented reconstruction led to visible reduction of off-resonance related artifacts (see Figure 3 & 4 and SI.Figure S5). However, a slight banding artifact along z was apparent in the upper slices of high-resolution brain images from the time-segmented reconstruction.

Figure 3:

Two selected slices of 2×2×2 mm³ 3D REPI brain images using varying degree of undersampling (rows 1–4) for trajectories rad0low, rad180low and rad540low with increasing twist angle in the blade design as well as spiral540low. The number of blades used for image reconstruction were N_blades = 3, 10, 40 and 200. TE and TR were matched for all trajectories (36 ms and 100 ms) and flip angle was set to 8° to increase contrast. Images were windowed identically. Also shown are images reconstructed with N_blades = 200 but without the use of time-segmented B₀ correction (row 5). The red circle highlights an area of signal dropout due to off-resonance, which is reduced by the time-segmented reconstruction. Difference maps between magnitude images with N_blades = 200 and 40 for each trajectory are shown in row 6.

Figure 4:

Selected sagittal, transversal, and coronal slices of 1×1×2 mm³ 3D REPI brain images for trajectories rad180seg2 (left), spiral180seg2 (middle), and spiral180seg3 (right) using varying degree of undersampling. The number of blades used for image reconstruction and acquisition time (TA) are indicated below the images. The first column of spiral180seg2 images was reconstructed with N_blades = 200 but without the use of time-segmented B₀ correction. The blue arrows highlight areas of signal dropout due to off-resonance, which is reduced by the time-segmented reconstruction. The red arrow indicates residual streaking artifact due to undersampling.

T₂*-weighted brain images obtained with the segmented 3D REPI trajectories rad180seg2, spiral180seg2, and spiral180seg3 at different undersampling factors are presented in Figure 4. At high sampling, the key structural features of the brain are well resolved such that white and grey matter are clearly distinguishable for most parts of the brain. At lower blade numbers with acquisition times of a few seconds, images become significantly blurrier and residual streaking artifacts are visible (indicated by red arrows).

Temporal Fluctuation of Aliasing in Image Time Series

The use of the GA radial fMRI approach in general produces a temporally varying aliasing pattern in the undersampled time series. In order to investigate sampling effects on the signal stability in 3D REPI fMRI, a series of tSNR measurements and simulations of the aliasing fluctuations were performed using trajectories rad0low, rad180low, rad540low and spiral540low (see Figure 5 and SI.Figure S6&7). Average tSNR brain values and tSNR maps are shown for N_blades = 10, 20, 40 and 60 (for N_blades = 21, 34 see SI.Figure S6). As expected, average tSNR values increased with higher N_blades consistent with the lower degree of aliasing and improved thermal SNR in the brain scans. Besides this general trend, significant differences between the four 3D REPI trajectories were observed. Average tSNR values increasingly improved with larger N_blades for the twisted trajectories with up to 17% increase for rad180low and spiral540low at N_blades = 40 and 18% for spiral540low at N_blades = 60 (see Figure 5). Thereby, the optimal twist angle seemingly depended on N_blades used in the reconstruction, which was supported by simulations of aliasing fluctuations on radial trajectories caused solely by the rotating GA acquisition (see SI.Figure S7). In the simulated data, the differences in signal stability showed a similar trend for the different trajectories but was even more pronounced (up to 47% increase). Normalization of the tSNR values to account for the increase in acquisition time further reduced and in the case of N_blades = 10 even overturned the benefit of using the twisted and spiral trajectories (see Figure 5, bottom right). However, a 16% increase remained for rad180low at N_blades = 40 even when penalized by the increase in acquisition time.

Figure 5:

tSNR maps (top) from acquired brain datasets for 3D REPI trajectories rad0low (A), rad180low (B), rad540low (C) and spiral540low (D) as well as two bar diagrams of tSNR values averaged over the entire brain volume (bottom left) and normalized averages (bottom right). tSNR maps are presented for N_blades = 40. Average tSNR values and normalized average tSNR values are shown for N_blades = 10, 20, 40 and 60.

Task-based Functional MRI

Combined visual and motor task-based fMRI experiments were carried out using trajectories rad0low, rad180low, rad540low and spiral540low at 2 mm isotropic resolution and trajectories rad180seg2, spiral180seg2 and spiral180seg3 at 1×1×2 mm³ resolution on healthy subjects. Selected BOLD activation maps obtained from standard and sliding-window reconstructions of rad0low and rad540low as well as rad180seg2, spiral180seg2 and spiral180seg3 are shown in Figures 6–9 (additional slices of activation maps are depicted in the SI.Figure S8–14). In general, detailed activation patterns in areas of the motor and visual cortexes were obtained that largely followed gray matter pattern of the reference T2*-weighted brain images for all cases. The limited number of subjects did not allow for secondary analysis or detailed quantitative comparison, but qualitative consistency throughout the datasets was observed. Stronger activation was observed for the lower resolution acquisitions (see Figure 7, right) which was mainly attributed to the lower levels of SNR for the high-resolution acquisitions.

Figure 6:

Selected transversal slices of the BOLD maps of a healthy subject showing activation in the temporal lobe and sensorimotor region of the brain (2 mm isotropic resolution). Maps are obtained A) with the sliding window (N_blades= 40, n_step= 10) or B) regular reconstruction (N_blades= 40, n_step= 40) using trajectories rad0low (TR = 77 ms) and rad540low (TR = 85 ms). A task block design (checkerboard and simultaneous finger tapping) was used as fMRI paradigm (20 s stimulus and 20 s resting period). No spatial smoothing was applied, and activation maps were overlaid onto the corresponding T2*-weighted 3D REPI images. The ROC curvess for both image time series as well as an up sampled image time series matching the sampling of the sliding window image series (blue) are presented in the middle column.

Figure 9:

Selected brain slices of BOLD activation maps obtained from a visual/motor task fMRI experiment (5:40 min). Maps were generated at 1×1×2 mm³ resolution from a whole brain 3D REPI image series (rad180seg2, TR = 69 ms) reconstructed using a sliding window scheme (N_blades= 40 and n_step= 10). No spatial smoothing was applied, and activation maps were overlaid onto the corresponding T2*-weighted 3D REPI images.

Figure 7:

Selected brain slices of BOLD activation maps obtained from a simultaneous visual/motor task fMRI experiment (4:20 min). Maps were generated at 2 mm isotropic resolution from a whole brain 3D REPI image series (rad540low, TR = 85 ms) reconstructed using a sliding window scheme (N_blades= 40 and n_step= 10). No spatial smoothing was applied, and activation maps were overlaid onto the corresponding T2*-weighted 3D REPI images.

The application of sliding window reconstruction consistently produced higher t-scores than the standard block-wise reconstruction in the analyses of fMRI data which was partially contributed to the increase of sampling points. A more valid comparison based on ROC analysis also showed a significant gain in sensitivity and specificity for the sliding window time series throughout all experiments (see Figure 6,8) as indicated by the ROC curves.

Figure 8:

Selected slices of the BOLD activation maps at 1×1×2 mm³ resolution showing activation in the temporal lobe and sensorimotor region of the brain. Maps are obtained with the sliding window or regular reconstruction using segmented 3D REPI with trajectories radial180seg2 (TR = 69 ms, N_blades= 40, n_step= 10 or N_blades= 40, n_step= 40, respectively; top left), spiral180seg2 (TR = 82 ms, N_blades= 40, n_step= 10 or N_blades= 40, n_step= 40, respectively; top middle) and spiral180seg3 (TR = 64 ms, N_blades= 30, n_step= 5 or N_blades= 30, n_step= 30, respectively; top right). A task block design (checkerboard and simultaneous finger tapping) was used as fMRI paradigm (20 s stimulus and 20 s resting period). No spatial smoothing was applied. The ROC curves for all three acquisitions for the sliding window and regular image time series as well as an up-sampled image time series matching the sampling of the sliding window image series (blue) are presented in the graphs below the corresponding Bold activation maps.

The performance of the rigid motion correction was tested in an fMRI experiment with deliberate head motion (see Figure 10). Therefore, the corresponding image time series was reconstructed at high temporal resolution using a sliding window scheme (N_blades = 6, n_step=3, TR = 85 ms). After the extraction of motion parameters (see Figure 10 right, black) and the adjustment of k-space data and trajectory, the newly reconstructed image series showed significantly less motion artifacts and motion parameters were strongly reduced (see Figure 10 right, red). However, residual motion particularly in form of translation could still be observed in the sub voxel range likely due to a general underestimation of the displacements as a result of temporal averaging over the reconstruction windows ~0.5 s. Simulations on the motion tracking abilities of trajectories rad0low, rad180low, rad540low and spiral540low with N_blades = 6, n_step= 3 and N_blades = 10, n_step= 5 demonstrated the importance of balancing temporal resolution and image quality (see SI.Figure S15&16). At lower N_blades, maximum displacements were generally tracked more accurately at the expense of introducing unwarranted high frequency fluctuations.

Figure 10:

Results from rigid head motion correction. Right: interpolated motion data pre- and post-correction (black and red) with deliberate head rotation at ~0.5 Hz (block-wise: i) no motion, ii) left-right, iii) up-down, iv) random; rad540low, 2 mm isotropic resolution, 6 blades, sliding window: step size n_step= 3). Left: BOLD activation maps (N_blades= 40, n_step= 40) obtained with and without motion correction.

DISCUSSION

The 3D REPI method presents a versatile radial sampling concept for fast MRI and has potential for a variety of imaging modalities ranging from diffusion imaging to thermometry (26,27). This study focused on its utilization in whole brain fMRI in combination with a GA rotation scheme. Key features of the 3D REPI trajectory design are the twist along k_z within blades and the spiral twist within the k_x-k_y plane. As proof of concept, 3D REPI radial designs with 0, 180, 540 degrees of rotation along the k_z axis as well as a spiral version were presented. Larger twists in the blades produced a more even distribution of aliasing in the PSF simulations and improved image quality in undersampled images as shown in Figures. 2 and 3. tSNR analyses and simulations on aliasing fluctuations in the GA time series further supported the general observation of improved sampling characteristics for the twisted and spiral 3D REPI trajectory variations that resulted in an increase in signal stability in GA image time series. A dependency on the number of blades used to reconstruct the individual images were hereby observed, and no single optimum for all values of N_blades could be determined (see Figure 5 and SI.Figure S6&7). The improvements of twisted 3D REPI were in line with recent observations made comparing stack-of-stars and rotated stack-of-stars acquisitions (17,18). In the case of 3D REPI, however, increasing the twist of the blade led to prolonged readout durations which is associated with increasing sensitivity towards off-resonance, motion and physiological noise. Therefore, the high degree of rotation proposed for stack-of-stars sampling was deemed impractical for 3D REPI. Nevertheless, even for the trajectories presented in this paper with a relatively small twist angle, the tSNR efficiency at high undersampling was lower than for 3D REPI without twist. Only at N_blades > 20 did the improvements in signal stability begin to outweigh the increase in TR (see Figure 5). Sampling at larger N_blades is also the most relevant for the majority of imaging applications, however, the importance of balancing readout length and twist angle to achieve an optimal performance in 3D REPI is demonstrated. This was also particularly true for the spiral design, for which the extended in-plane sampling added significantly to the length of the readout trajectories. Although segmentation or k_z undersampling could be used to mitigate prolonged readout lengths, the spiral 3D REPI design may be more beneficial for imaging a subregion of the brain for which fewer z-phase encodes are needed.

Whole brain 2 mm isotropic resolution 3D REPI images with good image quality were obtained and as few as 10 blades were sufficient to reconstruct decent quality images. Imaging at higher resolution was achieved by applying additional interleaved segmentation along the k_z direction of the blades in analogy to segmented EPI. Segmentation along k_z also allows for large rotations between segments for highly incoherent sampling making 3D REPI particularly attractive to imaging at higher resolution. Based on this k_z segmented sampling scheme we were able to obtain 1×1×2 mm³ resolution over the whole brain using two or three segments along k_z at the expense of increasing the acquisition time for a single blade respectively. These novel 3D REPI trajectories were successfully applied in BOLD fMRI experiments which produced detailed activation maps of the visual and motor cortexes at 2 mm isotropic and 1×1×2 mm³ resolution. The limited scope of this study, however, did not allow for a direct comparison of fMRI performance of the different trajectory designs.

Other key features of GA 3D REPI are the inherent robustness to motion due to the continuous acquisition of the k-space center and the ability to incorporate retrospective motion correction in the reconstruction at a sub temporal resolution timescale as demonstrated previously for TURBINE imaging and to a lesser extent in this study (see Figure 10). For fMRI this has potential particularly for experimental settings or patient groups in which methods of constraining the head motion are not feasible and severe motion readily occurs during the data acquisition.

The flexibility of retrospectively grouping or even reordering of k-space data is a strength of the continuous GA approach for temporal applications such as fMRI. However, as a consequence each image in the time series is sampled with a uniquely rotated k-space trajectory contributing to signal fluctuations within each pixel. For high degrees of undersampling in particular, alternating aliasing contributes largely to the signal variation making it more difficult to characterize the underlying activation pattern in fMRI. The sliding window reconstruction scheme helped to address this by effectively temporally filtering of high frequency fluctuations, as indicated by the improvements in fMRI results (see Figures. 6 and 8). However, the high degree of autocorrelation in the resulting image time series is a matter of concern as straight forward statistical analysis of the fMRI data using established approaches becomes problematic and inflated t-scores are obtained. A more careful statistical modeling of autocorrelation via autocorrelation regression or the reduction of degrees of freedom may give more reliable t-scores (28,29). Alternatively, more deliberate temporal filtering strategies such as UNaliasing by Fourier-encoding the Overlaps using the temporal Dimension (UNFOLD) (30,31) or asymmetric backward-looking k-space weighted image contrast (KWIC) filter (32) could be applied to reduce the amount of autocorrelation incorporated into the image time series. In general, more sophisticated approaches that make use of temporal-spatial correlations could be implemented to more effectively exploit the benign aliasing characteristics of the 3D REPI sampling (34,35). However, the iterative 3D SENSE reconstruction used in this work was associated with large computational effort of up to ~24 hours of offline reconstructions on a workstation (12 cores, 256 GB memory) in Matlab for a 1×1×2 mm³ resolution fMRI time series. This high computational demand presents a major disadvantage of the 3D REPI approach as described in this work and was a limiting factor for the development of more comprehensive image reconstruction algorithms.

As an alternative approach, a pseudo GA rotation scheme could be applied that would repeat itself after a predefined number of blades to avoid temporal fluctuation of aliasing (33). This would still allow subset reconstruction at high temporal resolution to perform motion correction as proposed but would also increase the temporal coherence in the dataset.

CONCLUSIONS

3D REPI applies the TURBINE imaging concept to a more general readout trajectory design by introducing twist within each blade and thereby fully exploiting all three k-space dimensions within each single shot. This leads to less coherent aliasing in undersampled images and ultimately can be exploited to reduce the temporal signal fluctuations caused by the continuous GA rotation in image time series, a crucial aspect for fMRI applications. The application of temporal filtering via sliding window reconstruction schemes further reduces the temporal instabilities of the signal and whole brain BOLD fMRI experiments can be carried out on a 3T scanner at 1×1×2 mm resolution.

Supplementary Material

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SI.Figure S1: Comparison between measured (red), delay-corrected (blue) and input (black) readout trajectories showing plots of differences (top), overlaid k-space trajectories (bottom left) and corresponding gradient waveforms (bottom right) as well as determined gradient delays for each radial spoke along k_z in the case of rad540low (with and without defining a pre-estimate of 5 μs of delay, top right).

SI.Figure S2: Uncorrected brain images (left), images with gradient delay correction using a calibration scan (middle) and images using the measured k-space trajectory as input in the reconstruction (right).

SI.Figure S3: Results from PSF simulations for trajectories rad0low, rad180low, rad540low, and spiral540low (top) and rad180seg2, spiral180seg2 and spiral180seg3 (bottom) as well as for 3D REPI trajectories with a twist of 45° and 90° that are not discussed in detail in the manuscript (middle). Full set of PSF along with SPR values are given for rad0low, rad180low, rad540low, and spiral540low (top).

SI.Figure S4: Quantitative comparison of difference maps of 3D REPI brain images shown in Figure 3. Selected slices of the difference maps (N₄₀-N₂₀₀) are shown on the top for trajectories rad0low, rad180low, rad540low and spiral540low along with the corresponding histograms of the difference values within the brain region (top right). On the top left, the standard deviation of the difference values in the brain region is plotted for all six possible difference map combinations from Figure 3 (N_N(blade)-N₂₀₀, with N(blade)= 3, 5, 7, 10, 20 and 40). The bottom shows the corresponding standard deviation plot and histograms after normalizing the difference values by the relative trajectory length using rad0low as reference.

SI.Figure S5: Comparison of distortion in 3D REPI brain images using Cartesian FLASH images as reference (bright outline). The effect of B₀-informed time-segmented reconstruction on image distortion is shown for rad540low (top). Selected transversal, coronal and sagittal slices of brain images obtained with trajectories rad180seg2, spiral180seg2 and spiral180seg3 using the time-segmented reconstruction are shown on the bottom. The prolonged readout length of spiral180seg2 leads to increased distortion in the images when compared to the rad180seg2 or spiral180seg3.

SI.Figure S6: Results on the temporal SNR in measured brain image time series using different 3D REPI trajectories depicted as bar diagram and 2D plot. Average tSNR values are plotted for N_blades= 10, 20, 40, 60 and Fibonacci numbers 21 and 34 for trajectories rad0low, rad180low, rad540low and spiral540low. Data were derived from single acquisitions using the fMRI sequence protocols for each trajectory.

SI.Figure S7: Simulations on aliasing fluctuations as a result of the GA approach on the image time series. Simulated tSNR maps for N_blades= 10, 20, and 40 are shown for rad0low, rad180low, and rad540low (left). Aliasing fluctuations were quantified using the tSNR definition. ‘Average tSNR’ values were also obtained from simulations on a range of 3D REPI trajectories with twist angles from 0–540° and a step size of 45°. The corresponding bar diagram is shown on the top right demonstrating a dependency on the twist angle for different N_blades values.

SI.Figure S8–14: Selected slices of BOLD activation maps for all seven trajectories rad0low, rad180low, rad540low, spiral540low at 2 mm isotropic resolution as well as rad180seg2, spiral180seg2 and spiral180seg3 at 1×1×2 mm³ resolution. The BOLD activation maps shown were obtained with a sliding window reconstruction scheme (see Figures for details).

SI.Figure S15: Simulation to test motion tracking ability of rad0low, rad180low, rad540low, and spiral540low using a sliding window reconstruction scheme of N_blades= 6 and n_step= 3. (A) Comparison of all six motion parameters during the simulated time course of the input (black) and the output obtained with rad540low (red). (B) Differences between input and output for all four trajectories. (C) Standard deviation of the differences for the rotation parameters for all four trajectories. (D) Standard deviation of the differences for the translation parameters for all four trajectories.

SI.Figure S16: Simulation to test motion tracking ability of rad0low, rad180low, rad540low, and spiral540low using a sliding window reconstruction scheme of N_blades= 10 and n_step= 5. (A) Comparison of all six motion parameters during the simulated time course of the input (black) and the output obtained with rad540low (red). (B) Differences between input and output for all four trajectories. (C) Standard deviation of the differences for the rotation parameters for all four trajectories. (D) Standard deviation of the differences for the translation parameters for all four trajectories.