Figure 1 - R2’ maps of each healthy volunteer. 1-9 are from initial scans of each volunteer, 1R-9R are from repeat scans taken 1-2 weeks after the first scan. Avg represents combined average R2’ map of all maps in Session 1 and Session 2. ROI represents the regions of interest used to analyze R2’ values.

Figure 3 - R2’ and rCBF at baseline for Healthy control between initial scans for each volunteer and their mixed effects model output below (Session 1) and repeat scans for each volunteer taken a week or more from the initial scans and their mixed effects model output below (Session 2).

Figure 1. Schematic of the DE-MPRAGE approach showing the progression of M_z (solid blue line) during a cycle of TC=8004 ms. The first half of TC is readout with α_PD (gray area) and the second half is readout with α_T1 (white area). Vertical black lines denote center of k-space using linear k-space ordering. Dashed blue lines show the PD-weighted and T₁-weighted DEs. Dotted blue lines show from which volumes/maps each map is obtained.

Figure 2. Maps of T₁ and B₁⁺ derived through either a LUT-based approach (A), without an independent reference for the PD-w DE, S_PD, (B) and with an independent reference (C). Compared to C, the T₁ maps in A and B are overestimated while the B₁⁺ maps are underestimated.

Figure 1: Bloch simulation of θ(T₂, α) for φ_inc=2. a) 2D θ(T₂, α) map b) plots at constant flip angle α - θ(T₂, α=const.) , for α =10°,15° and 25° and c) plots at constant T2 - θ(T₂=const., α), for T2=35,45 and 55 ms.

Figure 4: STARE - human volunteer imaging. Upper images shows the acquired magnitude data, the imaginary part of a signal defined as imag(Mag.·e^iθ) and θ maps. The bottom images show the output T₂ and B₁ maps at the main cross sections (sagittal, transversal and coronal images).

Figure 1. Multitasking image reconstruction schematics for motion-resolved brain MRI.

Figure 5. In vivo demonstration of no motion (top), discrete motion experiment (bottom left) and periodic motion experiment (bottom right) with no motion handling, motion-removal, and motion-resolved, along with example images of identified motion states. The proposed motion-resolved solution provided the best image quality with sharper tissue structures and less blurring/ghosting artifacts.

Figure 1. The pulse sequence diagram of 3D EPTI. The signals of inversion recovery gradient echo (IR-GE) and variable flip angle gradient-echo-and-spin-echo (GRASE) are acquired using a spatiotemporal encoding in k-t domain, which encodes a block of the 3D k-t space that later forms a radial-blade after combining the data across different TRs. The radial-blades are with different angulation to create incoherence along time to help with time-resolving ~1350 images at TE increments of ~1ms. The time-resolved images are used to fit quantitative parameters of T1, T2, T2*, PD and B1+ maps.

Figure 5. Synthesized multi-contrast images using the 3-minute 1-mm protocol compared with contrast-weighted images acquired by clinical 3D sequences.

Figure 5. A set of representative results from a healthy subject using the proposed method. High-resolution T₁, T₂, PD maps at 1.0×1.0×2.0 mm³ resolution and metabolite distributions (NAA, Cr, Cho, …) maps at 2.0×3.0×3.0 mm³ resolution were obtained in a total 8-minute scan.

Figure 4. In vivo 3D high-resolution T₁ and T₂ maps obtained from a healthy subject with one extra minute scan time.

Figure 2: Illustration of a mid-brain slice of the presented acquisition in a healthy volunteer over all acquired contrasts. Thereby, the data is ordered by echo time with the first 48 images corresponding to the first TE=73ms. The data is shown before any preprocessing is performed.

Figure 1: Illustration of the sequence. (A) Multiple Echos, (B) Global inversion and slice shuffling strategy and the logarithmic acquisition and (D) the variation of diffusion properties per slice rather then per volume. (D) is adapted from Hutter et al, Chapter 9 in Topgaard 2020

Figure 1. R2* (sec-1) in each region of interest ; in PD patients and controls and between PD sub-groups (based on disease duration ; disease (PD - G1 <5 years; PD - G2, between 5 and 10 years; PD - G3, between 10 and 15 years and PD - G4> 15 years). The p-values were calculated using two samples t-tests. ***p≤0.0001 **p≤0.005, *p≤0.05.

Figure 2. R2* normalized (sec-1); in PD patients and controls and between PD sub-groups (based on disease duration ; disease (PD - G1 <5 years; PD - G2, between 5 and 10 years; PD - G3, between 10 and 15 years and PD - G4> 15 years). The p-values were calculated using two samples t-tests. ***p≤0.0001 **p≤0.005, *p≤0.05.

Figure 5. Real-time T₁ renal mapping of a live mouse upon injection of a Gd-DTPA bolus (0.1mmol/kg, mice weight = 25g). (a) SC IR GRE T₁ images reflecting an IR=1s, collected over the course of one hour. (b) Dynamic SC IR GRE T₁ maps collected over one hour. (c) T₁ FLAIR maps acquired before the dynamic SC IR GRE T₁ mapping. (d) Dynamic T₁ values extracted from both kidneys' cortex and medulla regions. The parameters of T₁-FLAIR T₁ mapping and SC-GRE T₁ mapping are the same as the ones used in Fig.4.

Figure 2. SC IR GRE and TGSE T₁ weighting and mapping experiments on a human brain. (a) Inversion-recovery weighted TGSE and SC GRE images. (b) T₁ maps afforded for both method. TGSE T₁ mapping parameters: 1.15×1.15×3mm³, TR = 6s, 2 averages, IR times =[0.04, 0.20, 0.60,1.20, 2.00, 3.00]s, 7 spin echo trains with 3 GRE echoes, total acquisition time=13mins. SC IR GRE parameters: 1.15×1.15×3mm³, Flip Angle excitation pulse (FA) = 10^o, TR = 10ms, 219 GRE readouts after the inversion pulse, total acquisition time = 2.2s. Reconstruction was as in Fig. 1d, with a K = 2 SVD subspace base.

Figure 3: (A) R₁-histograms for different FS levels (black: no FS) before (solid) and after (dash) correction using different correction methods; voxel-wise (b/a)-correction (left) and global-(b/a) correction using full (5pts) data set (middle) and reduced (2 pts) data set (right). (B) (i) Original and corrected R₁ maps. (ii) Variance of corrected R₁ map (SPIR FA=70^o) wrt no FS.

Figure 5: (A) T_1-histograms for a single slice (shown) for standard single slice IR-EPI (black line), MP2RAGE (orange) and MS-IR-EPI after correction (blue). Sagittal and coronal views from whole brain dataset also shown for MS-IR-EPI (top raw) and MP2RAGE (bottom). (B) T₁-values of histogram peak for data acquired with standard single slice IR-EPI, MS-IR-EPI with fat suppression (both same slice as the standard IR-EPI and whole brain) and whole brain MP2RAGE.

Figure 1: In vivo T₁^app, obtained with $$$\phi_0\in$$$[50°,117°,120°,144°], as a function of T₂. Dephasing across a voxel of 2π (a-b) and 6π (c-d) per TR are shown. (a,c) Numerical simulations. Fixed parameters are: T₁=1250ms, D=0.8µm²/ms, f_B1+=80% as measured in the transmit field map in the slice of interest. (b,d) Acquisitions and linear fitting for illustration purposes. The number of voxels included in each bin is depicted by the shaded background of each graph.

Figure 2: (a) Axial view from T₁ maps obtained with a dephasing per TR of 2π (columns 1, 3, 5 and 7) or 6π (columns 2, 4, 6 and 8) for each φ₀ (rows). These are presented before (i.e. T₁^app, columns 1 and 2) and after correction for imperfect spoiling with D=0.8µm²/ms and T₂ of either 35ms (columns 3 and 4), 45ms (columns 5 and 6) or 55ms (columns 7 and 8). Black and green boxes highlight areas particularly affected by changing or applying correction factors (c) Maps of σ, the voxel-wise standard deviation of T₁ across RF spoiling increments for a given condition (i.e. along columns in (a)).

R₁ maps corrected with UNICORT with (a) conventional sinc RF pulse in CP mode, and (b) with k-T points pulse.

Histograms (brain-masked) of uncorrected and UNICORT-corrected R₁ with (a) conventional sinc RF pulse in CP mode, and (b) with k-T points pulse.

Figure 4

T₂ map generated from T₂-prepared volumes shown in figure 3. T₂ values show good contrast between gray matter and white matter structures. T₂ estimation may be compromised in the inferior portion of the cerebellum which may be due to B₁ inhomogeneity.

Figure 3

Orthogonal views of T₂-prepared images obtained from a healthy subject show good contrast and increasing T₂ weighting as a function of T₂-prep time. Fair signal homogeneity can be observed till the basal area of the brain with a slight signal drop in the cerebellum. High level of detail can be observed in the cerebellum and corpus callosum in the coronal views as benefit from sub-millimetric resolution. Signal-shift artifacts originating from cerebrospinal fluid (arrows) can be observed and will be investigated.

Figure 4: (A) The relative deviation of MS-IR-EPI and MP2RAGE T₁ measurements at 7T with respect to single slice IR-EPI T₁ measurements. T₁-value measures averaged across 6 (T₁-spheres) and 4 (T₂-spheres) measurements. Note that T₁ values for the T₁_3 sphere are an average across voxels within a single measurement. (B) Coefficient of variation (CoV) showing the repeatability of T₁ measures for methods at 7T. Note that the CoV for T₁_3 sphere was computed over the last 4 measurements.

Figure 5: Plots of R₁ (s^-1) obtained using MS-IR-EPI at 3T and 7T versus the NiCl₂ (left) and MnCl₂ (right) nominal concentration (mM^-1). Dashed lines represent linear regression fit.

Figure 3: 0.6 mm isotropic resolution image obtained by voxel-wise signal response curve matching. The inset image shows more pronounced cortical detail to appreciate the potential of the method for high-resolution mapping.

Figure 2: One-slice comparison of T₂ maps produced by: (A) SSE technique, (B) MESE with mono-exponential signal modelling, (C) MESE with dictionary based EMC modelling method.

Figure 3. Maps of NAA, Cho, Cr, and mIns at different TIs obtained by the proposed method.

Figure 4. Representative spectra at different TIs from (a) low-resolution IR-MRSI (16x16) that were acquired using phase encoding gradients for spatial encoding and (b) the proposed high-resolution IR-MRSI (64x64), where the blue lines are the reconstructed spectra and the red lines are the fitted spectra.

Figure 1: RAMSES pulse sequence diagram and parameter estimation scheme. With a Cartesian acquisition scheme, each k-space line is sampled during TR₁ and TR₂ with a mono- and multi-gradient echo, respectively. RF spoiling is employed by incrementing pulse phase φ while gradient spoiling takes place after data acquisition in read-only direction. Rewinder gradients are played in both phase directions.

Figure 3: Estimated T1 and T2* mean and standard error values of the phantoms (gelatin and Gd-DOPA solutions) for RAMSES and their relative ground truth estimated via Inversion Recovery for T1 and multi-echo gradient-echo for T2*. Similar T1 values for Gd-DOTA solutions are found in Shen et al.¹⁰ although solvent and temperature were different (human blood at 37°C against water at room temperature).

Fig 4: Synthesized time series after subspace-constrained reconstruction with intensity-coded magnitude and color-coded phase. Frame rate equals acquisition rate (8s sweep duration).

Fig 5: Parameter maps obtained after pixelwise fitting of subspace-constrained reconstruction.

Figure 4. The MWF/QSM maps of 8 adjacent slices from one prospectively undersampled datasets with R=6 and the fully-sampled dataset.

Figure 3. The profile plots corresponding to the black lines in the QSM maps of the fully-sampled data and the TDLLS reconstructed data from 9 subjects (R=6). The blue lines and green lines in the plots refer to the signal variations of the fully-sampled data and the TDLLS reconstructed data, respectively. High agreements are observed between the signal of TDLLS reconstructed data and that of the fully-sampled data.

Figure 4. SWI, B0 and QSM processing schematic. Echo 1 phase was removed from echo 2-6 complex data in order to facilitate phase alignment across flip angles, prior to complex averaging. Complex phase difference data for both flip angles (α = 3° & 24°) were averaged for echoes 2-6. Echo 6 data alone was unwrapped, filtered and processed to create SWI, and echoes 2-6 data were processed to generate QSM. For B0 processing, all data was resampled to 2mm isotropic prior to phase rotation and averaging, then phase unwrapped and fit to a linear function (Δθ vs ΔTE) to map B0.

Figure 1. Acquisition of multi-echo SPGR complex data allows for the generation of multi-parametric maps.

Fig. 3 A sagittal view of T₁, PD* , MT_sat and T₂* maps using the data acquired with the CP mode and PTx pulses along with the corresponding B₁⁺ scale map. The TR is 45 ms for both MTw scans. The nominal MT flip angle is 260° for PTx image and 320° for CP. Both MTsat maps have low CNR due to the insufficient MT saturation, especially in the Cerebellum. The PTx B₁⁺ scale map shows improved excitation in the Cerebellum compared to the CP map. The PTx T₁ map has higher values than the CP T₁ map and robust voxel estimates throughout the brain.

Fig. 1 Sagittal, coronal and axial view of T₁w, PDw and MTw images acquired using CP mode and PTx pulses. The last column shows the MTw scan with prolonged TR and the same nominal MT flip angle as the CP mode. The acquisition times are listed for each scan. All three MTw scans share the same CP mode MT pulse with different nominal saturation flip angles and TRs in order to match the SAR limits, listed respectively. The ones with a higher FA show slightly better soft tissue contrast.

Figure 3: Trans-axial slice of a reconstruction of a real brain tumor data set. (top left) IFFT of data from 1 st echo. (top middle) Han filtered IFFT. (top right) T1 1H image used as anatomical prior. (bottom left) iterative reconstruction of Na signal using anatomical Bowsher prior and signal from 2 echos (β_f = 0.01). (bottom middle) jointly reconstructed decay image Γ (β_Γ = 0.03).

Figure 1: Results of 3D reconstructions of simulated dual echo Na MR data. Reconstruction of first noise realization, mean, bias and standard deviations imagesof f and Γ. (top left) unfiltered and filtered IFFT of data. (bottom left) simulated ground truth images. (right) Reconstructions of f and Γ for different levels of regularization.

Figure 1. A diagram of the stimulated multi-echo-train EPI sequence. This sequence is based on a diffusion-weighted stimulated echo, and employs multiple EPI echo-train readouts at and after the peak of the stimulated echo. Each echo train corresponds to a different effective TE. A collection of the echo trains can be used to calculate T2*. G_ss, G_diff, G_TM are the slice-selection, diffusion-weighted, and spoiling gradients, respectively. ET denotes echo train.

Figure 2. (a) Brain images acquired with the stimulated multi-echo-train EPI sequence in Figure 1 from a healthy subject using three TMs (first row), three TEs (second row), and three b-values (last row). (b) T1, T2*, and ADC maps obtained from the corresponding row of images in (a). The numerical scales are shown on the right with the units indicated on top of each color map.

Comparison of directly acquired image quality. A) Non-CS Tri-TSE and B) CS Tri-TSE images are shown with PD-, T2-, and T1-weighted acquisitions from left to right.

Whole-brain histogram comparison. The CS-Tri-TSE images have less vulnerability to flow ghosting artifacts, which probably lead to tighter PD, T1, and T2 histograms (CS in blue and non-CS in gray).

Figure 4: Reconstructed parameter maps and BLAKJac-estimated frequency-domain plots of variances of the noise (bottom row); left: Original sequence; right: Optimized sequence. In the images, narrow windowing has been applied to visualize the noise. Vertical axis of the graphs is the noise variance, arbitrary units, but same scale between the two graphs. The graphs show the noise-enhancement for the high phase-encoding values in the Original sequence, which is seen in image as high-spatial-frequency noise in the corresponding images.

Figure 2: Flip-angle sequence (blue) and phase-encode values (orange) for the four evaluated sequences

Figure 2 – Intercept (β) and slope (R₂*^’) of R₂* FA dependence obtained from linear fitting according to Eq. 1. The same axial slices are shown as in Figure 1. The spatial variability in the slope (β) highlights specific, predominantly white matter structures, such as the superior cerebellar fibres, brachium conjunctivum and corpus callosum.

Figure 3 – Simulations of R₂* variation with respect to FA, residency time and f_MW. A: R₂* as a function of FA together with linear fits according to Eq. 1 for a fixed f_MW of 16%, or a fixed residency time of 100ms. B: Variability of slopes and intercepts across investigated conditions (residency time = 100-500ms, f_MW = 2-20%). The intercept R₂*^’ shows higher sensitivity to f_MW (12.6%), but effectively no dependence on residency time (0.74% variance across range investigated). The slope was most sensitive to the f_MW (~55%), but additionally depended on residency time (~13%).

Figure 4: Left: Maps of 2D normalized spectra of subvoxel T1-MD values along with the corresponding marginal probability density functions (i.e., 1D normalized spectra) of subvoxel T1 values (top row) and subvoxel MD values (left column) in a healthy volunteer. Spectral components specific to WM (green), GM (red), subcortical GM (yellow), myelinated WM fibers (magenta), and CSF (blue) can be observed both on the T1-D spectra as well as on the corresponding marginal distributions. Right: Corresponding maps of the estimated apparent inversion efficiency η and non-attenuated signal.

Figure 5: Maps of signal fractions corresponding to the principal T1-MD spectral components delineated with color-coded boundaries in Fig. 4: Short-T1 WM (component 1) - magenta; WM (component 2) - green; GM (component 3) - red; Basal Ganglia (component 4) - yellow; and CSF (component 5) - blue. Matching axial slices in three healthy volunteers show similar anatomical features corresponding to these spectral domains.

(a). BUDA-SAGE sequence diagram. Each scan can provide 3-echoes (one gradient echo, one mixed gradient-and spin echo, and one spin echo). Multiple scans can provide additional contrasts by changing the TEs of the sequence.(b). BUDA-SAGE reconstruction pipeline. (a) We conduct sliding window SENSE reconstruction for blip-up shots and blip-down shots, then put them into topup to estimate B0 field map. We incorporate B0 field map into MUSSELS to do BUDA reconstruction for all echoes. (c). The framework and training paradigm of the Self2Self model.

Whole-brain, distortion-free quantitative T₂ and T₂^* maps at 1×1×2 mm³ resolution were obtained using Bloch dictionary matching using the multi-contrast images. We use 8-shot, 3-groups data (acquisition time: 140s=40s/group+5s dummy) as a reference. We provide the maps based on the reconstruction method of BUDA, BUDA+S2s, BUDA+supervisedNN with a subset of 2-groups, 4-shot data (acquisition time: 47s=20s/group + 5s dummy). BUDA+S2S with 2-groups, 4-shot data obtained comparable maps respect to those from 3-groups, 8-shot data.

In-vivo MR-STAT reconstruction times for a matrix size of 224 × 224 (1 mm² in-plane resolution) using various implementations of the reconstruction algorithm.

In-vivo parameter maps reconstructed using MR-STAT. The data was acquired from a healthy volunteer on a 3T MR system using a Cartesian, gradient-spoiled acquisition with varying flip angles. The total scan time was 9.9 s. The reconstruction time on the GPU was 2 minutes whereas before, using the same reconstruction algorithm, the reconstruction would take 3 hours using 96 CPU's on a computing cluster.

Figure 3: MTSat, PD, R1, and R2* maps obtained from GRAPPAx2 and compressed sensing reconstructions with acceleration factors 2, 4, 8.

Figure 2: Magnitude images of the first echo obtained from the T1-weighted (T1w), PD-weighted, and MT-weighted multi-echo GRE acquisitions in comparison of the different acceleration techniques: GRAPPAx2 and compressed sensing (CS) reconstructions with acceleration factors 2, 4, and 8.

Figure 2: Overview of determined T1-relaxation times for different underlying background matrices, for various NM models with and without metal ions. Values are calculated as the mean over T1 times inside a circular ROI (~80 voxels) of a plane through the tubes. Standard deviations in the order of approximately 50ms for the longest relaxation times.

Figure 1: Experimental procedure. A: Phantom with tubes placed in 3d-printed sample holder inside a plastic bucket and temperature monitoring system around it. B: Inversion-Recovery-TSE curves. C: Spin-echo decay curves. All curves represent single voxel data sets.

Figure 1. Phantom T1-maps derived from the different sequences: IR sequence (left column), MP2RAGE (center column), compressed sensing MP2RAGE (right column). The upper and lower rows show the results from the 20- and 64-channel head RF receive coils, respectively.

Figure 4. Evaluation of brain T1 relaxometry as a function of sequence and RF coil. Top row: Comparison of T1 estimation with 3D sequences versus IR measured in cortical (left panel) and subcortical (right panel) regions. Bottom row: Correlations between T1 estimates from MP2RAGE and csMP2RAGE (64ch coil) from cortical (left panel) and subcortical (right panel) regions.

Fig. 3 Cortical distribution of the gyral-sulcal asymmetry index 2(G-S)/(G+S).

Fig. 4 Cortical distribution of the left-right asymmetry index 2(L-R)/(L+R).

Microstructural gradients in the striatum show aging-related changes.

(A) R1 functions along the main axes of the caudate (left) and putamen (right), averaged across 20 young adults and 18 older adults. Shaded area = ±1 SEM.

(B) Interhemispheric asymmetry is shown for 3 axes of the caudate and putamen, averaged across young and older adults. Asymmetry is defined as within-subject mean difference (MAE) between the left-hemisphere and right-hemisphere 1/R1 functions [ms]. Shaded area = ±1 STD.

Different qMRI parameters show distinct spatial and aging-related changes.

(A) Representative axial slices of R1, MTV and R2* mappings, showing sensitivity to myelin, non-water content and iron concentration, respectively. (B) Spatial variability profiles of the different qMRI parameters along the anterior-posterior (left), ventral-dorsal (middle) and medial-lateral (right) axes of the putamen. Averaged across young (N=17) and older adults (N=16). Shaded area is ± 1 SEM.

Fig. 4 Each parameter map derived from QPM of the brain of a representative subject (24-year-old man). The upper row represents k_FS maps, second row k_SF maps, third row K maps, and the bottom row T₁ maps for typical slice sections.

Fig. 5 A 75-year-old female with glioblastoma WHO grade V. Each parameter map shows variation in contrast in the abnormal region. In MR spectroscopy, the choline and lipid/lactate signals showed a high rate of increase.

Figure 2. Dictionary design used in this study: (top row) dictionary step sizes illustrated in a T1-T2 plane, (lower rows) representative images generated from different dictionaries (the representative spherical VOI placement is shown in green). Since datasets for each subject are inherently aligned in MR fingerprinting, each VOI was copied and pasted across all datasets. Note that the images obtained from different dictionaries are difficult to distinguish visually.

Figure 4. Effect of the dictionary step size on GLCM features: (a) ICCs for GLCM features (rows) extracted with different dictionary step sizes (columns), (b) inter-dictionary percent relative change of the features. A higher magnification of the figure is shown on the right. Features vulnerable to the dictionary size were the maximum probability, joint energy, joint entropy, sum entropy, difference entropy, inverse variance, inverse difference, and inverse difference moment.

Figure 3: R2, normalized to average global white matter R2, as a function of white matter fiber orientation. R2 was acquired using multiple single echo spin echo (SE) sequences (violet curve), a multi-echo SE sequence (green curve), multiple single echo turbo spin echo (TSE) sequences (blue curve) and a dual-echo TSE sequence (orange curve).

Figure 1: R2 maps of a volunteer acquired using multiple single echo spin echo (SE) sequences (a), a multi-echo SE sequence (b), multiple single echo turbo spin echo (TSE) sequences (c) and a dual-echo TSE sequence (d).

Figure 2: Left: Exponential fits to ROIs in caudate (green), splenium (red) and lateral ventricle (blue). S(0) represents the intensity of the DE after inversion and partial convergence at readout of k-space center. Center: Maps of extrapolated RAGE intensity and T₁ after coregistration of RAGE2 volumes. Right: Whole brain histogram of fitted T₁ values at 3T.

Figure 3: Comparison of T₁ obtained by DE MP-RAGE (left) with those obtained by VFA at constant B₁=8.16uT (right). Scatterplot of 2800 pixels revealed slightly lower T₁ by VFA (0.925±0.005). The pseudo-color overlay indicates slightly larger noise in the unbiased DE MP-RAGE maps.

Figure 3: The change in hue of the T₁ maps (pseudocolor scale 600ms to 2200ms) and the whole-brain T₁ histograms show the small, but discernable shift to lower T1 estimates from constant duration (left), constant B_1peak (middle), to constant rmsB1 (right).

Figure 1: Sketch of the partial saturations of the bound pool imposed by the RF pulse over flip angle, relative to the free pool (blue). The vertical scale is not known and thus arbitrary. Note the different behavior at constant duration (grey) and B_1peak (purple). The green arrow at 15° indicates the lower saturation of the bound pool for the three cases, showing that inverse MT toward the free pool is strongest for constant rmsB1 (red).

RMS misfit maps, computed as percentage of the maximum signal amplitude, for maps of the slice in each inversion case when fit to a (A-C) monoexponential or (D-F) biexponential recovery model. A Nyquist (n/2) ghost is clear in the anterior region stemming from the EPI readout as well as an elliptical region of B₀ inhomogeneity above the sinuses in A and D. Data from this region was omitted in analysis.

T₁ measurements yielded from a monoexponential fit to IR data in each ROI labeled in Figs. 1A and 1C and three selected gray matter ROIs. Saturation data in the genu of corpus callosum, minor forceps, and caudate are omitted because B₀ inhomogeneity above the sinuses prevented reliable analysis.

Figure 4. Reconstructed brain T₁ maps from data acquired with 3D IR-radFLASH technique at 1.0 mm isotropic resolution. Data were reconstructed with the algorithm shown in Figure 1b at temporal resolutions of 8.7ms, 26.1ms and 39.15ms. The 1.00 mm isotropic T₁ maps are presented in axial, coronal and sagittal orientations. The high resolution preserves the brain anatomical details in the T₁ map. Whole brain data were acquired under 5 minutes.

Figure 2. Computer simulations of the effect of the temporal resolution on T₁ error for a range of T₁ values. The simulations were based on sampling the recovery curve over 3 seconds, thus for each temporal resolution a different number of TI points (indicated by N in the plot) was used to fit the data. Data were simulated by adding noise corresponding to 32dB and using 100 noise realizations.

Figure 1. (A) Single-shot OLED sequence for overlapping-echo imaging. The four excitation pulses have a same flip angle α=30° and the refocusing pulse with a flip angle of β=180°. G₁, G₂, G₃ and G₄ are echo-shifting gradients for OLED encoding. (B) Framework of the proposed parallel reconstruction and motion correction and estimation for T₂ mapping. Five-level U-Net is used for nonlinear mapping in these three learning tasks. LPC: Linear phase correction. MoCo: Motion correction.

Figure 5. (A) T₂ mapping results of representative slices with continuous motion for subjects 1. (B) Mean T₂ value curves from 4 ROIs (marked with red circles) of the 9 measurements in (A). The first image was selected as reference for coregistration. (C) The velocity field of the 9 measurements in (A) and representative example of motion vector field (highlighted with red dotted line) reconstructed.

Figure 1 Single-shot double-slice SMS-OLED T₂ mapping sequence. The RF pulses α_a1 and α_a2 are used to excite slice a, and α_b1 and α_b2 are used to excite slice b. The RF pulse β can be a multi-band hybrid 180° refocusing pulse that causes magnetization vectors of both slices a and b to be inverted simultaneously. Four echo-shifting gradients G₁, G₂, G₃, and G₄ are used to shift the four main echoes from the center of k-space, and G_cr indicates crusher gradients along three directions.

Figure 2 The magnitude images and T₂ maps of rat head obtained with SMS-OLED under different slice-to-slice gaps, in comparison with reference T₂ maps. (a) 4 mm gap; (b) 6 mm gap; (c) 8 mm gap; (d) 10 mm gap.

Figure 3. Example MWF maps obtained from T₂-weighted contrasts acquired with different k-space sampling schemes or with retrospective undersampling of the ACS region (uACS) and reconstructed with conventional and joint-CAIPI (J-CAIPI). Residual aliasing artifacts in CAIPI reconstructions with integrated ACS heavily compromise image quality of retrieved MWF maps. Such artifacts are mitigated in J-CAIPI reconstructions but still present if k-space shifts across echoes are not employed (blue arrows). MWF std in corpus callosum (CC) decreases in J-CAIPI reconstructions.

Figure 1. k-space sampling strategies investigated in this study. (A) CAIPI 3x2⁽¹⁾ (acquired with an external reference scan for calibrating the reconstruction kernels). (B) CAIPI 3x3⁽¹⁾ on an elliptical Cartesian grid with an integrated autocalibration signal (ACS) region and (C) with additional shifts across echoes for complementary k-space coverage. (D, E) Same as in (B) and (C), respectively, but with retrospective undersampling of the ACS region with a CAIPI 2x2⁽¹⁾ pattern. Acquisition times (TAs) are given for a 1.6 mm³ isotropic whole-brain scan.

Figure 3. The T2 map results reconstructed by different methods. Note: 1D Cartesian with partial Fourier sampling pattern (R=6) were adopted in this experiment. The T2 map RLNEs of ALOHA, MORASA, and the proposed method are 0.1370, 0.1309, and 0.1113.

Figure 1. Reconstruction results of different methods for 2D imaging. Note: The relative $$$\ell_2$$$ norm error (RLNE) of $$$\ell_1$$$-SPIRiT, AC-LORAKS, STDLR-SPIRiT, and proposed method are 0.0866, 0.0759, 0.0735, and 0.0614, respectively.

Figure 5: Lifespan changes in T2 in females (red) and males (blue). The y-axes are different, although all cover a range of 30 ms. In early age, T2 decline relates to myelination and iron accumulation. In late life, T2 increases largely due to tissue loss, often exceeding the T2 values of childhood, except in iron-rich regions like putamen and globus pallidus. The green lines are 2^nd order polynomial fits (T2 =A*age² + B*age + C). R-squared values are shown.

Figure 4: Coefficients of variation (CoV) for scan-rescan T2 measurement using Bloch fitting. The CoVs are remarkably low and also include some errors due to segmentation. For example, the amygdala has the worst performance at 1.4%, likely due to its small size affecting segmentation. These results indicate a high level of consistency between T2 maps acquired over multiple days. This degree of repeatability is possible because the exact sequence is modelled, accounting for actual flip angles used in each voxel.

Figure 4: T2 map for a volunteer brain measured using MESE and the proposed method. T2 values measured using the proposed method for white matter (white dashed ROI, T2 = 60±11), grey matter (red dashed ROI, T2 = 78±9.7), and CSF (black dashed ROI, T2 = 401±186) were close to those measured using MESE (T2 = 62±2.5, 73±2.8, and 354±70). However, artifacts were observed in the lateral ventricle in the proposed method. Since the sequence uses an unbalanced gradient moment, CSF pulsation may cause the artifacts.

Figure 1: Pulse sequence diagram used in this study. Three-echo DESS sequence acquires FISP (S⁺₁ and S⁺₂) and PSIF (S¹_-) echoes. The two FISP echoes with different TEs enables B0 map estimation which is used to demodulate B0 phase components of S⁺₁ and S^-₁. RF excitation is performed with a quadratic increase of transmitting phase to encode T2 information into the phase of the signal. Calibration acquisition using positive and negative readout gradient without phase-encoding is incorporated to remove eddy current-induced phase error.

Figure 1. The reconstructed $$$T_{1\rho}$$$-weighted images at $$$TSL=1$$$ ms with locking field amplitude w=500 Hz using the SCOPE method and the L+S method for net acceleration factor R=3 and 4, respectively.

Figure 2. The reconstructed $$$T_{1\rho}$$$-weighted images at $$$TSL=40$$$ ms with locking field amplitude w=5000 Hz using the SCOPE method and the L+S method for net acceleration factor R=3 and 4, respectively.

Figure 3: Comparison of T₁ maps obtained with standard fitting (top) and the proposed method (bottom) for all three evolution fields. One can clearly see the lesion in the low field T₁ maps. The proposed method is able to reduce noise in all T₁ maps and enables a clear distinction of the lesion.

Figure 2: Reference T₁ maps (top) and reconstruction results for simple non-linear least squares fitting (standard, bottom left) compared with the proposed model-based reconstruction and fitting algorithm (bottom right).

Figure 1. Left) A transverse slice from a 3D dataset as a function of increasing inversion times (note that the CSF appears hypointense due to saturation, TR<<T₁). Right) A T₁ map is generated by fitting a mono-exponential inversion recovery relaxation curve to the images. The T₁ of grey and white matter are measured to be 330 ± 26 ms and 242 ± 41, respectively.

Figure 5. The relaxation parameters measured in this work are compared to ex-vivo values reported in the literature (8), with generally good agreement between the two with some differences in the muscle T₁ and bone marrow T₂.