(a) Acquisition timing diagram between (top) applied RF pulses (middle) crusher gradients $$$G_C$$$, and the crusher gradient-induced phase for the five pathways relevant to this 4-pulse experiment. (b) The RF phase cycling scheme used in this work modulates the phase of $$$E_3$$$ and $$$E_5$$$ by $$$\pi$$$ between k-space segments, but does not modulate the phase of $$$E_2$$$ and $$$E_4$$$. Here, $$$F^H$$$ represents the adjoint Fourier transform operation, and $$$\Phi^H_{E_e}$$$ adds the complex conjugate of the RF-induced phase to the $$$e^{th}$$$ pathway.

In vivo MR-CPU results from the brain of a healthy volunteer. Multi-coherence pathway images were reconstructed successfully with both Cartesian and radial k-space trajectories. Each image is windowed separately for display. The arrow indicates the presence of barely visible streaking artifacts in the radial image that are not present in the Cartesian image.

Fig1. Proposed VUDU sequence and reconstruction for GRE contrast. Using FLEET ordering, two shots of EPI are acquired successively for each slice, before proceeding to the next slice. Phase encoding polarity is alternated between the shots. Variable flip angle (vfa) excitation maximizes the signal. A fieldmap estimated from interim blip-up and -down reconstructions is incorporated into parallel imaging model to jointly reconstruct two shots with low-rank regularization to eliminate distortion. In SE/diffusion variant, 180° refocusing pulses succeed each excitation pulse.

Fig2. shows individual SENSE reconstructions for each shot of vfa-FLEET acquisition with GRE contrast. At TR_slice=80 msec, it took vfa-FLEET 160 msec to encode each slice, and 5.1 sec for the entire volume.

Horizontal lines help compare the geometric fidelity of distortion-free VUDU reconstruction relative to each shot. Yellow and blue arrows point to distortion artifacts in the sagittal views of SENSE reconstructions, which were eliminated in the VUDU result.

Figure 4. Axial spiral-in-out images of a healthy volunteer without (top row) and with (bottom row) Maxwell compensation, acquired at 0.55T. Substantial artifacts seen without compensation are suppressed with compensation. Parameters included: TR/TE_eff: 3200/~130 ms, FOV: 250 mm, slice thickness: 5 mm, slices: 11, matrix: 320, interleaves: 90, trajectory: self-retraced 7.2-ms spiral in-out, averages: 4 with T2-decay compensation (8 total), Maxwell compensation: 4.4 ms per echo spacing, acquisition time: 2.6 min.

Figure 2. Self-retraced spiral in-out waveform and associated Maxwell integrals illustrating compensation achieved by adapting trapezoidal waveforms (red arrow) and adding bipolar waveforms (green arrows). Without compensation, Maxwell integrals at times A and C are not equal and that at B is not zero, whereas values at A and C are equal and that at B is zero with compensation. A small bipolar is sometimes needed because gradient duration is a discrete variable, and so the exact change in Maxwell integral required is not achieved by only modifying the trapezoidal waveform.

Figure 5: LACE brain images of 5 human subjects in the presence of B₀ inhomogeneity induced by a paper clip (FoV 256x192x128 mm³ at 2x2x4 mm resolution). 3D gradient echo images show large areas of signal dropout near the paper clip (top row). LACE images recover signal in this area, but exhibit image deformations due to the extreme inhomogeneity (middle row). Multi-Coil generated LACE images show largely the same image quality than the ones acquired with standard gradient coils (lower row). No image distortion correction was applied.

Figure 1: LACE sequence. A) Sequence diagram. B) Phase graph. The sequence consists of two broadband excitation pulses separated by T_E/2. Signal is acquired at the time of the spin echo of the two RF pulses (red crosses in B), which in the steady-state comprises a combination of signal from spin and stimulated echoes. Crusher gradients symmetrically around the 2nd RF pulse and at the end of T_R ensure a consistent signal independent of the background B₀ field.

Interleaved FLAIR and DMI of human brain 75 min following the oral administration of [6,6’-²H₂]-glucose. DMI was acquired as a 13 x 9 x 11 matrix (YXZ) over a 260 x 180 x 220 mm³ FOV, whereas the FLAIR images were acquired as 14 slices and a 256 x 192 matrix over a 256 x 192 mm² FOV (TR/TI/TE = 8800/2200/90 ms). During the ~ 7 min FLAIR acquisition, the DMI data could be acquired twice (i.e. NA = 2). (A-C) FLAIR images spanning circa 40 mm, covering two axial planes from the 3D DMI dataset as shown in (A) and (C).

Interleaved FLAIR MRI+DMI sequence. (A) ¹H pulse acquisition scheme. 7 slices are inverted consecutively followed by a fast spin-echo (FSE) acquisition (TR/TI/TE = 8800/2200/90 ms). The (B) ²H pulse acquisitions are placed in the dead time during TI and right after FSE with equal TR (= 314 ms). (E) Shows the gradients used during acquisition. Note the plot only shows the first half of FLAIR TR, where half of the slices (odd number slices) were excited. The pulse acquisition scheme is repeated on the even number slices in the second half of TR. 28 DMI acquisitions are achieved in one FLAIR TR.

Figure1: Diagrams of the proposed TDM-2s (B), TDM-2e (B) and TDM-3e EPI (C) sequences. The red gradient pulses alternately dephase and rephase the echoes to separate the k-space of two TDM slices, and gray gradients compensate for the phase dispersion induced by the slice-selection gradients. Numbers listed on or below the gradients signify the relative value of gradient area (i.e. zeroth moment) and corresponding subscripts denote that gradients those have same subscripts share the same relative unit standard.

Figure 2: Evaluation of signal leakage for two representative shifting factors of 2.0 rad/mm (A) and 4.8 rad/mm (B) in TDM-3e EPI sequence. To purely acquire the leaked signal of high spatial frequencies from one slice to the others, only one pair of excitation and refocusing RF pulses was enabled with the other two disabled in a single sequence cycle. The numbers in the bottom right of the images represent the corresponding enlargement factor.

Figure 2 (a)The representative 2D J-resolved spectrum from the spatial location marked by the red dot. Please noting the tilting feature of the spectrum due to the mixing chemical shift and J splittings along the spectral dimension. (b) 2D J-resolved spectrum with J-decoupled chemical shift dimension.

Figure 1 (a) 2D J-resolved xSPEN MRSI sequence performing multiple scans with increasing time (t₁) evolution to achieve the chemical shift dimension, while the J couplings are obtained by repeating the distortion-free echo-planar imaging-based acquisition of xSPEN in a turbo spin echo train evolution way. (b) 2D J-resolved xSPEN MRSI sequence with pure chemical shift dimension.

Figure 2 Comparison of spiral T2W water images of a right knee. Data were collected with difference spiral-in and spiral-out combinations. The ratio of SNR from left to right is 1: 1.22: 1.36 estimated inside the region shown by the yellow box.

Figure 3 Sagittal PDW and T2W images of a right knee. Cartesian reference images, spiral water-fat combined images and spiral water only images are shown from left to right. In T2W spiral imaging, the fat only image (not shown) was partially (18%) combined with the water only image to form the water-fat combined image in the middle column. Spiral in/out lengths are 8.5/17ms. The yellow arrows point to flow artifacts seen in the Cartesian images, which are mitigated in the spiral images.

Reformatted images of 3 representative patients using the following reconstruction frameworks: a) no motion correction (NMC), b) 2D iNAV translational correction (2D iNAV TC), c) v3D iNAV translational correction (v3D iNAV TC), d) 2D iNAV non-rigid motion compensation (2D iNAV NRMC) and e) the proposed v3D iNAV non-rigid motion compensation (v3D iNAV NRMC). Improvements when using v3D iNAV can be observed in all the cases, although in some cases (patient 1) these are minor.

In the first step of proposed autofocus-based virtual 3D iNAV non-rigid motion correction reconstruction framework, the FH and RL motion is estimated from the 2D iNAVs. RL and AP motion is estimated with autofocus approach, assuming linear relationship between the FH iNAV signal and AP movement of the heart. Respiratory binning using the FH motion estimated from the iNAVs is performed and beat-to-beat 3D translational respiratory motion is applied to each bin. 3D non-rigid motion is then estimated from respiratory-resolved bin images and used to produce motion-corrected datasets.

Figure 2. (a, e) TOF-MRA images, (b, f) TOF-MRA MIP-8 mm images, (c, g) SWI images, and (d, h) SWI mIP-8 mm images, from original and MB-accelerated acquisitions. No visible aliasing artifacts were observed with MB acceleration and overall image contrast was similar between original and MB-accelerated images. CBMs were well visualized in SWI mIP-8 mm images, as depicted by arrows.

Figure 4. SWI mIP-8 mm images focusing on four CMBs from two patient from original and MB accelerated acquisitions were shown. The profiles over a line (with 5.9 mm length) across the center of CMBs have similar patterns between the two acquisitions, while the minimum signal levels were slightly higher with MB acceleration, possibility due to an increased noise level.

Figure 2: Axial, coronal and sagittal anatomical planes of the 3D $$$\zeta$$$-based acquisition. A,B,C) was reconstructed using the entire dataset of 1,000 heart beats while D,E,F) consists of the first 250 heart beats.

Figure 5: 3D MRI cross-sections in addition to segmented LCA, RCA and RCX as well as a segmented left ventricle, right ventricle and right atrium. A,C) was reconstructed using the entire dataset of 1,000 heart beats while B,D) is based on the first 250 heart beats.

Representative reconstructions at HR = 137 bpm and 126 bpm for trajectories without inter-block additional angles Ɛ (i.e. Ɛ = 0), random Ɛ (between 0 and 2π), and optimized Ɛ. The trajectories in k-space are depicted on the top right corner of each reconstruction. The arrows denote worst edge (blue) and vessel (red) conspicuities with Ɛ = 0. Improvements are noticeable with random Ɛ. Further edge improvement is observed with optimized Ɛ. bpm: beats per minute.

Framework to reduce effects of clustering. After a block of N spokes spanning T_RT, additional angles (εi) are played to reduce coherence during cardiac gating. The k-space from the first block corresponding to N = 64 spokes is shown with the blue lines denoting the trajectories. Within each block the angular increment for the trajectories is Δϑ allowing adequate k-space coverage for reconstruction of real-time series.

Figure 1. Sampling via CPD. Each $$$(k_{y},k_{z})$$$ point is acquired exactly once along the echo dimension, save for a fully sampled 24 by 8 central region. This allows full sampling of k-space with incoherent sampling at each TE while promoting temporal sparsity. For a single echo train (white arrows), successive echoes are acquired within a constrained k-space neighborhood to minimize eddy currents. This results in approximate $$$R=ETL$$$ acceleration. To obtain different acceleration rates, new sampling patterns are generated and set unioned with the existing pattern.

Figure 2. Sampling and reconstruction. (a) ME GRE images ($$$\mathbf{x}$$$) are multiplied by coil sensitivities ($$$\mathbf{S}$$$) and Fourier Transformed ($$$\mathbf{F}$$$). CPD masks ($$$\mathbf{M}$$$) are applied to produce the undersampled data array. (b) Singular Value Decomposition on 5000 signal evolutions with $$$T_{2}^{*}$$$ selected between $$$0.1$$$ and $$$2000$$$ ms generates a temporal basis. The $$$K$$$ principal components ($$$\mathbf{\phi}$$$) with the largest singular values are selected as a truncated basis. (c) Locally low rank regularization.

Fig 1 - SILVER optimizes a single parameter, the angular increment, α, in the window sizes that are included in the optimisation set, S (A). In this project a TURBINE acquisition scheme, (B), was used (fig modified from [4]), and the data were reconstructed using 2D non-Cartesian SENSE (C).

Fig 2 - Predicted sampling efficiency for different numbers of spokes per frame. SILVER optimised regions highlighted in gray.

Parameters estimated from LTE and STE spiral images. The mean diffusivity (MD) is higher in the free water than in the vials with microstructure. The microscopic isotropic diffusion coefficent (D_iso) is lower than MD in the microstructure. The fractional anisotropy (FA) is higher than the microscopic FA ($$$\mu$$$FA). The estimates of $$$\mu$$$FA in the free water is relatively high which is due to the fact there was only noise left for the higher b-value.

Sequence diagram for the free gradient waveform diffusion sequence with spiral readout.

Figure 1 - (a) Conventional EPI phase encoding scheme showing uniform density coverage of k-space. (b) Proposed variable density EPI phase encoding, with larger PE blips at the beginning of the readout (yellow lines), and smaller blips towards the end (blue lines). (c) Conventional PE showing an exponential signal decay envelope. (d) Variable density PE with linear signal decay envelope ($$$\alpha$$$=T2*).

Figure 4 - Example reconstructions and zoomed insets. (a,d,g): Zero-filled reconstruction of the 3/4PF sampling, (b,e,h): VC reconstruction of the 3/4PF sampling, (c,f,i): VC reconstruction of the vdPE sampling. Green arrows denote a feature that is sharp in the VC reconstructions, and blurry in the zero-filled. Red arrows denote a ringing artefact visible in both 3/4PF data, but is not present in the vdPE reconstruction.

Example of mono-planar T-Hex scheme. Red and yellow dots mark those points of the hexagonal grid which are covered by two subsequent shots. Green lines in the background show that all points of the hexagonal grid lie on nodes of a finer, rectilinear lattice, from which the shift in the 1st phase-encoding (PE) direction of each EPI shot can be derived. Subsequent shots exhibit multiples of the initial shift c, modulo the PE step size d. This shift also determines the necessary echo-time shift ΔTE_N = shift_N/d · TAQ_line, where TAQ_line denotes the acquisition time of one k-space line.

Images acquired with T-Hex EPI as depicted in Fig.1. The whole brain is covered with 0.7x0.7x2mm³ resolution in 4.3s, TE = 20ms.

Results from run B. 1) Time course of raw data, mean over ten exemplarily chosen, activated motor cortex voxel. Gray lines mark right hand tapping, dotted line marks pause (no tapping). 2) Spectrum of (1). 3) Spectrum of 12 exemplarily chosen voxel in CSF. 4) and 5) Output from cardiac and respiratory monitoring.

T-Hex spiral used in run A. Upper panel: k-space time course of one shot. Lower panel: Cross-section through T-Hex stack, colour encoding different shots (left) and acquisition time (center). Parametric view of one shot, colour encoding again acquisition time (right).

Figure 1. Demonstration of VCC-ssEPI compared to conventional ssEPI. With an 8Tx array and an 8.7ms 3-spoke pTx pulse, the VCC-ssEPI jointly achieved a relatively homogeneous flip angle distribution and the target VCC phase optimized by the 32Rx array, showed no obvious SNR degradation due to flip angle homogeneity, and achieved same SENSE g-factor with x6 acceleration as the conventional ssEPI with x3 acceleration.

Figure 2. Demonstration of VCC-msEPI compared to shuttered msEPI, showing the ideal excitation patterns, achievable excitation patterns from pTx pulse design, and the 1/g factor map from different excitation strategies. Off-target excitation between the bands cannot be minimized with limited pulse duration and RF power limit, and the shuttered msEPI showed degraded 1/g map and thus reduced SNR compared to VCC msEPI.

Generation of elliptical shells trajectory. Each spiral is confined to the surface of an ellipsoid of revolution about the Z axis. Ellipsoid i is defined by axes Kzmax_i and Kxymax_i. The dimensions of the voronoi patch are dkr*dkθ, as shown. For a given set of Kzmax and Kxymax, dkr is determined by the local geometry of the elliptical shells, and the spiral pitch dkθ is adjusted to produce a voronoi patch of the desired area for the local sampling density (see text).

PCASL difference images from the two trajectories shown in Figure 2, as well as a fully sampled segmented stack of spiral acquisition.

Figure 5: In-vivo 3D ¹H-MRSI SPSP liver data of one volunteer. A) Transverse, coronal and sagittal MR image of the liver overlaid with the ¹H-MRSI grid. Spectra of three different voxels indicated in panel A are shown in the green (B­-SPSP water, E-SPSP choline), orange (C­-SPSP water, F-SPSP choline) and blue (D-SPSP water, G-SPSP choline) frames below.

Figure 3: Coronal image of the spherical phantom (d=10cm) (A) and the liver (E) with a normal excitation pulse, but without slice selection, and with the spectral-spatial pulse (B and F), showing the transversal slice excited by the spectral-spatial pulse. Panel D shows a normal coronal image of the body with coronal slice selection as a reference. Line profiles through the images acquired with the spectral-spatial pulse (blue lines in B and F) in the phantom (C) and in the liver (G).

Figure 4: Metabolites maps, RMSE on image support, and example spectra from subspace reconstructions of fully sampled , uniformly undersampled (R = 2), and undersampled with the proposed trajectory (R = 2) on a spectroscopy phantom containing physiological concentrations of the major brain metabolites. The proposed trajectory yields similar spectra and metabolite maps to the fully sampled acquisition and achieves ~2x reduction in RMSE across the metabolites in comparison to uniform undersampling.

Figure 1: Schematic view of (a) the fully sampled 3D-spiral MRSI trajectory and (b) our proposed randomly undersampled trajectory. For demonstration purposes, we assume 1 temporal interleaf. In (a), the same angular interleaf and $$$k_z$$$ point is sampled at each timepoint in a TR. The proposed (b) trajectory samples random angular interleaves and $$$k_z$$$ points during each TR and can be accelerated by reducing the number of TR’s. Our proposed trajectory takes advantage of the 4D-encoding space by spreading incoherent aliasing across spatial and spectral dimensions.

Figure 1: Extended formulation unifying three parallel imaging aspects: (i) in-plane PE acceleration, (ii) SMS acceleration and (iii) lipid-water separation. The steps show how an EPI image (far right) is equivalent to an SMS of water and lipid “slices” (I_w and I_lip) and to an in-plane PE acceleration (I_{lip&w #2} vs. I_w+I_{lip shifted}). The formulation can be extended to any number of slices and fat/water images.

Figure 5: Resting-state fMRI. a),b) Examples of simultaneously acquired slices. Left to right: standard reconstruction, water image after lipid separation, and a fat suppressed image. Arrows mark artifacts from the lipids. (c) tSNR on three orthogonal planes. SNR and tSNR in main text where estimated from marked regions. SAR was 33% without fat-suppression and 97% with fat-suppression (reference amplitude of 240 V for a 1 ms 180° hard pulse). Scan parameters: in-plane accelerations ×3, SMS ×2, FOV=220×220 mm², resolution = 1.7×1.7 mm², slice thickness = 1.7 mm, TR/TE = 1500/22 ms.

FIG. 3. Mean DWI maps of a sample slice created from 6 different diffusion-encoding directions (b = 1000 s/mm²), acquired with acceleration factors R = 2-5, and varying field map resolutions.

FIG. 4. Noise SD maps for acceleration factors of R = 2-5, and isotropic field map resolutions of 3 mm, 2 mm, and 1.5 mm. Maps created by calculating the SD of 100 b0 image replicas and scaled inversely by the square root of R. Numbers below maps indicate the mean/maximum noise SD of brain and skull components. All values shown are truncated and are to be multiplied by a factor of 10^-6 to show the full values.

Figure 2: Image reconstructions. a) Low WC parameters R=4x4, b) Reference image, c) Very High WC parameters R=4x4

Table 2: Conventional vs Insert gradient reconstruction results

Figure 1. The acentric Cartesian spiral pattern in PE-SPE plane, with matrix size 128 x 64, 75% partial Fourier in both directions.

Figure 2. The upper row are eight short axis slices at the end of systole; the lower row are the corresponding eight slices at the end of diastole. The distance between two adjacent slices shown is 8.4 mm (four slice thickness).

Figure 1. Representative images from a patient, including T2w with fat suppression (FS), T1w with contrast, MK and MD based on DKI with 5b-values (200, 400, 800, 1500, 2000).

Table 1. The b-value combinations and simulated acquisition time used in this study.

one-slice images of the 3D-T2*-FFE.A:Coronal image of lumbosacral plexus.The areaof interest in the nerve and muscle. B: Conventional 3D-T2*-FFE with SENSE factor of 2.C-G: 3D-T2*-FFE with CS factors of 2, 3, 4,5 and 6, respectively. Data were collected from a healthy volunteer (male, 24 years old).

The scan parameters of 3D-T2*-FFE with SENSE factor of 2, 3D-T2*-FFE with CS factors of 2, 3, 4,5 and 6, respectively.

Fig. 5. Comparison of quantitative measurement (FA maps) between ssEPI and turboPROP.

Fig. 4. Demonstration of of geometric distortion artifacts, which are observed in the trace images from ssEPI but minimized in turboPROP.

Figure 3. The correlation between pairs of phasors was calculated for the initial set of N phasors (1). The phasors with the smallest correlation was added to the "input optimal set" (2). The sum of correlations squared was calculated between the remaining $$$(N-i)$$$ phasors, and the phasors in the "input optimal set", for a total of $$$(N-i)$$$ β values. The phasor with the smallest $$$β$$$ value was then added to the "output optimal set" (3). The ”output optimal set” became the new input, and steps 2 and 3 were repeated until the final optimal set contained the desired number of phasors (4).

Figure 5. Brain images reconstructed from the simulated phasor patterns. Image reconstruction was performed using 128 encoding patterns in a 128x128 matrix. The overall image resolution is improved by applying a higher Bloch-Siegert pulse amplitude (C vs. B).

Fig. 1a) Multi-shot approach of FREE 1b) is a single-shot approach. First double spin-echo pair has the greatest R-difference. Subsequent π pulse pairs have a difference of exactly ∆R incrementally adding phase at each echo acquired. 1c) Multi-shot version of FREE, in which all (odd and even) echoes are acquired. All pulses, except for the first, have R_base + ∆R, where R_base is any adiabatic R value. Further shots reduce the R value of the first pulse (R_o) by integer values of ∆R. The k-space matrix is created by concatenating the data columns (shot number) with rows as echo number.

Phantom is a NMR tube with ~15 cm water doped with copper sulfate. Structure was created in the phantom by purposefully creating a flip angle range. Comparison of the GRE projection and FREE reconstruction. The x-axis represents nutation frequency which has positional dependence due to the surface coil’s B₁ gradient. The plane of surface coil is located on the right where is the largest. Linearity of the B₁ gradient decreases with distance from the coil. Good agreement between GRE and FREE reconstructions is achieved except at the deeper location.

Figure 1: RAS-Q T₁T₂ pulse sequence acquisition scheme. Four images are acquired in the same diastolic phases within 4 consecutive heartbeats (t). Each image is acquired with a different flip angle (α = [10°, 50°, 90°, 130°]) after ten linear startup pulses (ST). All further sequence parameters are kept constant (T_R/T_E: 2.96/1.48ms, CS-SENSE: 3). Image acquisition is performed during breath-hold in ≤4s.

Figure 2: Magnetization curves for different T₁/T₂ ratios. Graphs show normalized magnetization evolution over flip angles from 10°-130° for 9 different tubes of the T1MES phantom.¹⁵ Measured mean pixel intensity (black, dashed curves) is compared to theoretical values of RAS-Q T₁T₂ (red curve) and the transient bSSFP function (blue, dotted curves). Results are depicted for heartrate 60bpm. Measured RAS-Q T₁T₂ pixel intensities demonstrate a close alignment to expected theoretical values over different T₁/T₂ ratios and heartrates.

Figure 3. Axial views of the reference GRE magnitude, EPI and ERASE images for a single subject. The solid red lines indicate the manually drawn masks as a guide for comparison of image quality. Signal loss and image degradation in prefrontal cortex of the normal-orientation scans (white arrows) are reduced in tilted scans (blue arrows and yellow arrows).

Figure 2. Measured B0 maps at normal and tilted head orientations at 3T and 7T. Black arrows indicate B0 inhomogeneity near the prefrontal region. In head-tilted scan (c-d, g-h), B0 field distribution is spread more indicating that local gradient is smaller than the normal orientation scan (a-b, e-f).

Figure 5. Brain MP-SSFP images with 1.5-mm isotropic resolution. Images acquired with α_std = 6º, optimal flip angle and even phase (A) provided stronger image contrasts between gray and white matter as compared to those with α_std=20º, optimal flip angle and odd phase (B), but as predicted in simulation and phantom experiments, the noise level is noticeably higher in the images acquired with α_std=6º.

Figure 3. Brain MP-SSFP images acquired with α_std=6º (A) and 20º (B). With α_std=6º, strong image contrasts between gray and white matters were detected, which is consistent in even and odd RF phase images. With α_std=20º, odd RF phase provided stronger image contrasts in brain tissues than even RF phase. Although SNR increased along with an increase of N_MP, image contrasts were consistent in each RF pulse setting.

Figure 3: The estimated displacements. The black lines indicate the estimated displacements for the experiments with (a) a simple pendulum, (b) coupled pendula, (c) a spherical pendulum, and (d) coupled spherical pendula. For the 2D acquisitions in (c) and (d), the $$$x$$$- and $$$y$$$-displacements are plotted separately. The red line is the reference line as determined in Fig. 2.

Figure 1: (a) In conventional MRI, a different line in k-space is sampled every repetition. (b) In spectro-dynamic MRI, one k-space line is repeated $$$N_\textrm{rep}$$$ times, reducing the time interval between the acquisition of the same data point in k-space. (c) Schematic representations of the four dynamical systems used for our experiments. (d) The experimental setup with two pendula, each containing a gel-filled vial (red arrow), which are connected with a spring (light blue arrow).

Figure 4: Vocal fold oscillation in the coronal plane reconstructed into 4 slices and 12 Frames resulting in a temporal resolution Δt = 890μs (f₀ = 92Hz). Although motion of the vocal folds is visible, no full contact can be observed. The vocal fold oscillations cause the EGG electrodes to vibrate on the skin, which can be seen on the edges of each frame.

Figure 1: Sequence diagram of the 2.5D SPIRE method. Rapidly switched phase encoding gradients immediately follow $$$G_\mathrm{SS}$$$ and slice rephasing is performed simultaneously with the frequency encoding in slice direction (dark grey areas indicate equal gradient moments). PE gradients are rewound and a spoiler is applied with opposite sign to the readout gradient to reduce switching when ramping to $$$G_\mathrm{SS}$$$ at the beginning of the next acquisition block. Dotted lines indicate the gradient shapes for the largest phase encoding moments.

Figure 1: Coronal slice of a dedicated rubber phantom acquired at 15 mT/m gradient strength (A, B) and 24 mT/m (C, D). Images A and C were acquired with the modified approach including the low-strength gradients.

Figure 3: Coronal slice of a wrist acquired at 15 mT/m gradient strength (A, B) and 24 mT/m (C, D). Images A and C were acquired with the modified approach including the low-strength gradients.

Figure 2: Example coronal slices and a 3D volume rendering in the abdominal region. a) prior obtained CT, b) Deep Learning reconstructed ZTE, c) ZTE calcifications (red) overlaid on the contrast enhanced water map MRI (LAVA-Flex based), d) 3D volume rendering showing the ZTE calcifications (cyan).

Figure 4: Example coronal slices and a 3D volume rendering in the head/neck region. a) prior obtained CT with indicated (red arrow) calcification, b) Deep Learning reconstructed ZTE, c) ZTE calcifications (red) overlaid on the contrast enhanced water map MRI (LAVA-Flex based), d) 3D volume rendering showing the ZTE calcifications (cyan).

Fig. 3: Coronal (first row) and sagittal view (third row) of PETRA (Acc=1) and csPETRA (Acc>1) images. Yellow numbers show the Acc factor used for the SPI acquisition. Second and fourth rows show difference images subtracted with Acc=1 images (far left images) of coronal and sagittal views, respectively.

Table 1: Examples of SPI acquisition times w.r.t. the parameters $$$\text{BR}$$$, $$$\text{TE}$$$, and $$$T_\text{enc}$$$ with the corresponding maximum gradient amplitude (|G|). Default parameters were: $$$\text{BR}$$$=512, $$$\text{TE}$$$=50 µs, $$$T_\text{enc}$$$=500 us, TR=2 ms, when they were not used as the sweep parameter.

Fig.4: Comparison of SER with other methods for eleven slices - the top row shows vendor-provided gold standard spin-echo (SE), a turbo SE with an ETL of 7 and a GRAPPA factor of 6, a half-Fourier acquisition single-shot TSE (HASTE) at echo times (TE) shown in red font. The corresponding acquisition times (T_acq) are shown in yellow font and were recorded from the vendor’s user interface. The bottom row shows the corresponding images at TEs close to 80ms allowed by the vendor. SER images acquired using pypulseq at similar slice locations, do not suffer from saturation or blurring artifacts.

Fig. 5: Single echo reconstruction (SER) imaging performance a) SER provides the fastest acquisition time for the four methods, depends on echo time (TE) rather than repetition time (TR) and phase encoding steps, and is faster than TSE + GRAPPA by an order of magnitude; b) SER delivers the lowest RF power to the phantom among the methods, due to the one-time use of the 90⁰ and 180⁰ pulse; c) SER is the most silent scan with the least peripheral nerve stimulation (PNS) percentage due to the one-time use of the readout gradient

Figure 1. Schematic of the proposed receive loop geometry and circuitry. (a) Simulation setup for one of the four modulatable receive loops placed circumferentially around a cylindrical phantom. (b) Circuit diagram of the receive loop with tuning and matching capacitors as well as six adjustable varactor diodes (each in a range between 2 and 20pF) placed on the long sides of the loop, which are used to modulate receive sensitivity profiles B₁^-.

Figure 4. Sensitivity modulation during readout (RO) of k-space lines. k-space configuration weightings for (a) linear ramp, (b) 8 and (c) 64 sinusoidal oscillations between C1 and C2 along each RO line. The latter is equivalent to switching between C1 and C2 for each ADC sample. (d), (e), (f) G-factors for the respective sensitivity switching patterns. (g) Maximum g-factor for sinusoidal sensitivity switching versus number of oscillations, compared to static sensitivity sets of C1, C2 and combined C1 & C2.

Figure 4. Representative resolution phantom images reconstructed from retroactively under-sampled k-spaces corresponding to FGRE, x-Centric and FE Sectoral. AF were 7, 10 and 14. FGRE SNR was 20, x-Centric SNR was 28 and Sectoral SNR was 25. The FE Sectoral images show much less image distortions at all three AF compared to FGRE and x-Centric.

Figure 1. Depicts three different k-space under-sampling patterns corresponding to AF=10, used for each wash-out image retroactively in wash-out or SNR attenuation direction.

Figure 1. Excited volume from one-sided zoomed imaging excitation and optimized b) ΔB0 field. The Hyperboloid excitation volume does not take advantage of the don't care regions introduced by the alias deselection mask.

Figure 3. Sagital slice of excitation (a,b,c) and rFOV aliasing pattern (d,e,f) from Linear gradient optimized and linear gradients plus multicoil shim optimized rFOV excitation. (a,d) Linear gradients can select an off-axis slab between aliases with a sufficiency large rFOV. (b,e) Tighter rFOVs cannot be achieved with linear gradients only.(c,f) Multicoil shim array in conjunction with linear gradients achieves tighter rFOV.

Figure 3. The learned trajectories by different methods. The initialization is an under-sampled radial sampling pattern.

Figure 1. The gradient w.r.t. $$$\boldsymbol{x}$$$. We denote auto-differentiation of NUFFT as auto-diff, exact NDFT as exact, and our approximation method as approx. Three calculation methods achieve similar results.

Figure 1: Block diagram of an MRI RF-receiver

Figure 2: Block diagram of a five stages CIC filter combined with a compensation filter

Figure 3: Representative images from a patient with a large left sided sporadic VS imaged using a single low-dose (LD) interleaved high-temporal (HT) (frame duration of Dt = 1.46 s) and high-spatial resolution (Dt = 6.04 s) DCE-MRI acquisition on a 1.5 T Philips scanner. Kinetic maps derived using the HT segments alone (LDHT, left column) or the LEGATOS method are shown. Note the increased vascularity around the tumor capsule, visible on both the high-spatial T2W DRIVE acquisition (voxel size = 0.5 x 0.5 x 0.5mm3) and LEGATOS derived vp parameter maps (*).

Figure 4: Comparison of LEGATOS derived v_p and K^trans estimates from the in vivo single-injection low-dose DTR Study against tissue derived parameters

(A) Inter-tumor scatterplot comparison of LEGATOS derived mean tumor v_p estimates against mean CD31 % microvessel surface area (SA).

(B) Inter-tumor scatterplot analysis of LEGATOS derived mean tumor K^trans (min^-1) against mean CD31 % microvessel surface area (SA).

(C) Representative imaging and histology from a patient with a growing highly vascular VS (top row) and a comparatively less vascular static VS (bottom row) are shown.

Figure 4. Shows the comparison of b0 images acquired by SLR versus adiabatic refocusing pulses. The B1+ insensitivity of the adiabatic TR-FOCI pulse mitigates the B1+ inhomogeneity leading to retrieval of spin-echo signal at the temporal lobe and cerebellum. The first column shows the relative FA map indicating the low B1+ areas and the last column shows the relative SNR map. The SNR map indicates that in the B1+ starved areas of the brain SNR is improved up to 10 times. The TR value (30000 ms) was kept identical between the two measurements so that signal intensities could be comparable.

Figure 3. (a) shows the localizer view of the phantom with the location of the acquired slice. (b) shows the slice profile images of the SLR refocusing pulse versus TR-FOCI refocusing pulse with different scale factors for the power of the pulse. With the scale factor of one, the pulse is applied with the power of 9 T, which is derived from the simulations as the minimum value required for the adiabaticity of the pulse. (c), (d), and (e) show the slice profile across the superior, center, and the inferior regions of the slice.

Fig.1: RF-encoding simulated with unique spectral peaks assigned to 5 voxel ‘locations’ (coloured regions). A) Encoding scheme applied to each voxel at each encoding step, $$$m=1…5$$$. Amplitude was weighted randomly between 0.8 and 1 and phase modulated between 0 and 180$$$^{\circ}$$$. B) Receive sensitivities (shown for two coils), which are combined with (A) to generate weighted signals at each channel for each encoding step, $$$m$$$. Signals are concatenated over M=5 steps. C) Inversion of the system matrix, $$$\bf S$$$, reveals reconstructed signals from each voxel.

Fig. 4: Data acquired from two voxels (voxel 1=blue; voxel 2=orange) in a phantom (A) using proposed RF-encoded technique with an increasing number of encoding steps, M. (B) Combined signal (not unfolded) from all receive coils shows shot-to-shot variation in phase from (0°,30°,60°,90°,120°) modulation on voxel 2 using the dual-band pulses. (C) Reconstructed data using RF-encoding (steps M=2-5) are shown below coil-encoding only (M=1). The spectral SNR and effective g-factor values are stated next to each encoding.

Figure 1: Sequence diagram of the UTE se-quence with the rabbit feigning (RF) pulse shape. Note that the gradients in the lower part require fast switching capabilities and a small amount of time travel. Allergy advice: sequence may contain traces of nuts.

Figure 3: POTS reconstructed image of the EASTER-EGG sequence being presented to the CNN (or $$$CNN$$$ or CNN). Rabbit detection is completely impossible for a human being, but the CNN (or $$$CNN$$$ or CNN) was able to ignore it in less than 4 h.