Figure 3 (a) 2D MRF derived M0/T1/T2 and MWF/ IEWF/FWF maps of a representative subject. (b) 3D MRF derived M0/T1/T2 and MWF/ IEWF/FWF maps of a representative subject (axial, sagittal and coronal view).

Figure 4 Myelin development curves in Genu and Splenium of Corpus Callosum and Left/Right precentral White Matter.

Figure 2. The scan-rescan within-subject coefficient of variance (wCV) of cortical thickness and relaxation times on cortical structures acquired with three-dimensional magnetic resonance fingerprinting. The scan-rescan wCVs of local cortical thickness, T1 value, and T2 value are overlaid on an inflated brain surface.

Figure 4. The scan-rescan within-subject coefficient of variance (wCV) of volume and relaxation times on subcortical structures acquired using three-dimensional magnetic resonance fingerprinting. The scan-rescan wCVs of subcortical volume, local T1 value, and local T2 value. Each subcortical structure is colored according to the regional wCV, and the brain surface is made transparent for the ease of visualization.

Figure 3. Matched MRF parameters in a lower arm. (a) Measured signal curve (blue) and matched dictionary element (red) in a voxel in the arm muscle. (b) Matched proton density map. (c) Matched T₁ map. (d) Matched T₂ map. Parameter maps were set to zero in the background.

Figure 1. Experimental setup. (a) 27 cm bore Halbach array with a 50 mT field at the center of the bore. (b) Custom built gradient and RF power amplifiers are used to drive the gradient and RF coils. The MRF sequence is run on a Magritek Kea2 spectrometer. (c) MRF flip angle pattern of 240 pulses, preceded by an inversion pulse, used for the MRF experiments.

A schematic overview of the learning-based optimization of the acquisition schedule (LOAS). MTC-MRF signals are synthesized using randomly initialized scan parameters, noise, and tissue parameters (Input) and fed to the fully connected neural network (FCNN). The FCNN outputs tissue parameter estimates (Output). A loss function is a mean square error between the ground-truths and estimated tissue parameters. The calculated loss was back-propagated with an ADAM optimizer to update scan parameters.

Optimized MRF schedules consisting of four scan parameters (B₁, Ω, Ts, and Td) with 40 dynamic scans from the LOAS, CRLB, IP strategies and PR, and Linear schedule. CRLB strategy generates an acquisition schedule by minimizing CRLB values of the MTC-MRF signal model. IP strategy generates an acquisition schedule using an IP optimization algorithm by maximizing signal difference between different tissue types. PR schedule was generated by increasing spectral and temporal incoherence between dynamic scans. PR schedule was the same as that used in our previous studies.

Figure 2: T1 map (red) and T2 map (blue) of an optimized sequence (top two rows) and the truncated human-designed sequence (bottom two rows). The leftmost four columns are simulations that contain undersampling and the background phase variations in 4 different possible directions. The rightmost column shows the maps from an actual in vivo scan using the corresponding sequences. The simulated and in vivo maps from the human-designed sequence yield apparent shading artifacts, but the maps from the optimized sequences are not affected.

Figure 3: In vivo T1 and T2 maps from multiple optimized scans, demonstrating reproducible results that are robust against undersampling and system variations. These maps do not show shading artifacts commonly observed in the maps from the human-designed sequence shown in Figure 2.

Figure 4 Representative T1 and T2 maps obtained using retrospective 4x acceleration in k-space and 4x in image space. The proposed method achieves better performance both quantitatively and qualitatively.

Figure 1 Method overview. Our method consists of a Graph Convolutional Network for k-space and a Quantification Network for image space for reconstruction from undersampled 3D MRF data.

Fig. 2. T₁, T₂, T₂^*, T_1⍴ and FF maps obtained from a single MRF acquisition with the proposed method (bottom row) compared to the reference maps (top row) in two representative subjects. Subject #2 presented previously diagnosed mild liver steatosis. A mild elevation in liver fat content can be observed in the FF MRF map, and confirmed with the reference method.

Fig. 4. Scatter plots showing correlation between MRF-derived T₁, T₂, T₂^*, T_1⍴ and FF and their corresponding reference values. Linear fits (grey lines) show slopes not significantly different from 1.0 (p>0.05) in the cases of T_1⍴ and FF quantification. Green dashed line denotes the identity line.

Figure 1: Reconstruction errors obtained for each sequence and each pattern, as well as an example of noised fingerprint. The signal annulations in the qRF-MRF sequence made the ratio impracticable. Direct match on 2D-based dictionaries, 10 000 signals each.

Figure 4: Results obtained with the GESFIDSE (TE=60ms) concatenation pattern. Vf estimates on animal data with the different dictionaries generated, as well as examples of the geometries. Regression-based reconstruction on 3D-based dictionary, 15 000 signals each.

Figure 1. (A) Sequence diagram. (B) Spiral-projection spatiotemporal encoding with left) the original tiny-golden-angle (TGA) scheme and right) the proposed tiny-golden-angle-shuffling (TGAS) scheme. (C) and (D) the k-space coverage of the first 3 TRs for acquisition groups G_1-16, G_17-32 and G_33-48, where through-plane rotation was implemented around x-, y- and z-axis respectively to achieve multi-axis rotation for better incoherence.

Figure 2. (A) The flow chart of subspace reconstruction. Five subspace bases were extracted from the MRF dictionary and used to reconstruct the coefficient maps (at 1×, 2×, 2×, 10×, and 10× scalings respectively for better visualization). The coefficient maps are then used to generate the MRF time-series images and dictionary template matching performed to obtain T₁, T₂, and PD maps. (B) Comparison between sliding-window iNUFFT and subspace reconstructions, where T₁ & T₂ maps from 1-mm isotropic acquisitions at acceleration factors R=1 & 3 are shown.

The MRS-FP sequence pattern used with the 3 different fitting parts for relaxation inhomogeneity and k_CK.

(a) Two step fitting procedure of the Phantom for validation. (b) 3 step procedure for in vivo data

Figure 2 shows the representative MRF fitting using phantom and in vivo experiment.

Figure 3 SNR evaluation for 5 measured metabolites in MRS-FP experiment. Scanning time can be shortened up to 2min without compensation of measurement reliability

Figure 3: Reconstructed water relaxation (T1w, T2w), amide exchange rate (Ksw) and volume fraction (fs) and semi-solid exchange rate (Kssw) and volume fractions (fss) from an in vivo healthy subject imaged with the clinical CEST-MRF pulse sequence.

Figure 1: Pulse sequence diagram for the proposed MRF-CEST sequence for one time step. A gaussian-shaped pulse train saturates the amide proton which then exchange with the water protons. The reduction in the water signal is measured with an EPI readout

Figure 3. GRE (A) and SE (B) images from HEPI and T2 FLAIR (C) as reference of the patient brain acquired on the same scanner. D, E, F are the permeability maps, G, H, I are the vessel radius maps and J, K, L are the rCBV maps in the GRE (D, G, J), SE (E,H,K) and combined GRE-SE (F, I, L) images.

Figure 4. Comparison of signals from voxels in NWM, NGM and tumor tissues from GRE (A,B,C respectively) and SE (D,E,F, respectively) images with the signals obtained from the individual GRE and SE dictionary atoms ( red ) and that from the respective GRE and SE of the combined dictionary atoms ( yellow ) with maximum correlation

Figure 1. Overview of the MR vascular fingerprinting technique. A pulse sequence sensitive to the vascular parameters of interest is utilized for both imaging and MR physics simulations. Physiological ranges of SO₂, CBV, and vessel radii are used to simulate the MR signal in a virtual voxel with each combination of those parameters. After the images are acquired, the time-course signal evolution of each voxel is compared to all dictionary entries. The closest match between the fingerprint and dictionary allows for the extraction of the underlying parameters for quantitative mapping.

Figure 5. Mean RMSE of vascular parameters predicted from matching algorithm and the signals true underlying parameter values at five SNRs and with five echo train lengths. The RMSE for each parameter was calculated by taking 10 random parameter combinations and finding the RMSE at each SNR/TE combination. This was repeated 1000 times resulting in 10,000 total RMSE values for each SNR/TE combination tested. The means and standard deviations were calculated and plotted as the dots and error bars in the graphs.

Fig 1. (A) The original MRF framework. (B) Our approach.

Fig 2. Low-resolution (left) and high-resolution (right) T1 and T2 maps of the same subject.

Zone analysis demonstrated on MRF T1 map in a right temporal GBM

Boxplots of significant pre and post contrast texture features from NET regions showing near vs far zones in METs and GBMs

Figure 2. Mean and standard deviation of MRF T1 and T2 values of gray matter in selected Brodmann areas. Paired t-test was performed between Brodmann areas 8 and the other areas. p* < 0.05

Figure 5. Correlation analyses between T1 and T2. Spearman’s correlation analysis was performed in each BA. Green: p* < 0.05, red: p > 0.05

Figure 3 MRF dictionary matching accuracy between classical monoexponential Bloch equations (left box), Magin et al model (middle box), and extended Bloch equations (right box) in cortical aeras 7A, 7P, 7PC, 5L, 5M, 5Ci, and hIP3 was compared using a) dot product of the actual and best matching MRF signals, and b) mean squared error of MRF residuals. Note that outliers more than three median absolute deviations (MAD) are removed.

Figure 4 Distribution of time-fractional order parameter α values was compared across ten cortical areas of interest; a) areas 2, 4, and 6, b) areas 7A, 7P, 7PC, 5M, 5L, 5Ci, and hIP3.

Violin plots with medians for T1 and T2 values of NAC GM, NAC WM, and tumour regions from repeated MRF and established T1 VFA and T2 MESE relaxometry. MRF repeat violins (red/blue) are almost indistinguishable, indicating MRF measurements are highly repeatable. MRF values are consistently lower than established techniques (green).

Table 2: Summary of Spearman’s Rho correlation testing and Bland-Altman statistics for: VFA vs. MRF T1, MESE vs. MRF T2 and repeated MRF measurements of both T1 and T2.

Figure 1: Representative images acquired using tailored magnetic resonance fingerprinting (TMRF) which provides qualitative and quantitative data simultaneously within ~4 minutes. This includes T1 weighted, T1 fluid attenuated inversion recovery (T1 FLAIR), T2 weighted, short tau inversion recovery (STIR), water and fat images. Quantitative data include T1 and T2 maps. All images were acquired on in vivo healthy human brain on a 3T GE 750w scanner. The reconstructed qualitative images were denoised using DL. The maps were generated using DRONE method.

Figure 3: Signal to noise ratio (SNR) for the four contrasts (T1 weighted, T1 fluid attenuated inversion recovery (T1 FLAIR), T2 weighted, and short tau inversion recovery (STIR)) over a period of 4 days. All scans were performed on same in vivo healthy human subject on a 3T GE 750w scanner. The white matter (WM) and grey matter (GM) was segmented semi automatically using 3D slicer to get the (a) WM SNR and (b) GM SNR where different color represents different contrasts. The SNRs were similar for all the four days.

Figure 2. A comparison of average DARTEL-normalized T1 and T2 maps of all healthy volunteers reconstructed by using low-density and high-density dictionaries. Consistencies were evident in most brain parenchyma.

Figure 1. Example of T1 map overlaid with the volume of interests selected from Freesurfer’s segmentation results.

Mixture maps (margins cropped) of the WM, GM and a CSF related compartments for the in-vivo brain using different MC-MRF algorithms.

Estimated T1/T2 values (milliseconds) for in-vivo WM, GM compartments using MC-MRF algorithms compared to the 1.5T literature values in [11]* and [12]⁺.

Figure 4 Estimated volume fraction maps and RF fields for one subject scanned 7 times. The subject was repositioned after every scan, possibly resulting in slightly different slice locations, volume estimations and $$$B_1^-$$$ field estimations, although visual differences are minimal this hindered quantitative comparison on a voxel basis. Low rank reconstruction(rank 6) was used, in subsequent SPIJN processing $$$\mu=0.2$$$ was applied. Tissues were identified based on relaxation times. The acquitisition scheme from [4] was used.

Figure 3 Boxplots of estimated $$$T_1$$$, $$$T_2$$$ and relative proton densities over 7 scans per subject. $$$T_1$$$ and $$$T_2$$$ values show descrete estimations due to the used dictionary grid (5% relative step size). Proton densities were calculated relative to gray matter. Literature values for WM relative to GM are between 84% and 90%, for CSF 116% and 128%. Relaxation times for WM are consistent with literature[15], GM shows slightly lower times than expected, potentially caused by partial volume effects in GM areas.

Fig. 1. 3D UTE-MRF sequence diagram ⁵. (a) shows the pattern of flip angles in an MRF unit. It varies among every TR. A delay time of 2000 ms between two repetitions is used. (b) shows the sequence during a TR. UTE is the first (ultrashort) echo time.

Fig. 3. 3D UTE-MRF dual echo results of a healthy volunteer (Subject 1). A: Real part of the signal curves in both WM and GM for the dual-echo images. Frame 62 is chosen as the optimum frame for myelin imaging. B: Different frame images for different contrast. (a-d) are echo 1 from frame 58, 62, 68 and 74. (e-f) are echo 2 from frame 58, 62, 68, and 74. (i-l) are echo difference from frame 58, 62, 68, and 74. (j) shows that at frame 62, the long T2 tissue is suppressed.

Whole-brain 1mm iso T₁/T₂/PD/ViSTa and MWF maps in three orthogonal views.

Figure 1. (A) Sequence diagram of 3D ViSTA-MRF. (B) extended phase graph (EPG) simulation of the first ViSTa signal. The myelin-water signal with short-T₁ is preserved in the ViSTa signal while the white-matter (WM), gray-matter (GM) and CSF are suppressed, which enables direct myelin-water imaging. (C)Simulated signal curves of myelin-water, WM, GM and CSF for the ViSTa-MRF sequence. FA: flip angle.

Optimization result acquired with PG on Hybrid-State model. Targeted relative CRB values after minimization rCRB(m0s)=1.1 · 10^5, rCRB(T1)=2.0 · 104 and rCRB(T2f)=3.26 ·104. Biophysical parameters included in the CRB computation are proton density=1, m0s=0.1, T1=1.6 sec, T2f=65 msec, R=30, T2s=60 µsec, B0 and B1. Relative CRB is defined as rCRB(T1)=CRB(T1)Texp/TRT12

Hybrid-State equations solved by PG for cycle of 4 seconds. Each signal is normalized by its mean magnitude for visualization. The oscillations are aligned with RF pulses. Representation of such a signal by piece-wise polynomials needs higher orders which quickly blows up the number of unknowns to solve the BVP. PG can increase order of accuracy without increasing the number of unknowns by putting more effort to locally defined simple problems.

Figure 4: In vivo quantitative maps of (a) $$$f$$$, (b) $$$T_1^s$$$ and (c) $$$T_2^s$$$ from a single axial slice through the brain at the level of the lateral ventricles. The fast compartment ($$$T_1^f$$$ and $$$T_2^f$$$) was fixed to literature values for the fitting process. Note that the anterior brain is corrupted by $$$B_0$$$ artifact arising from metal in the volunteer's face mask.

Figure 2: (a) Spin dynamics of the slow (blue) and fast (red) compartment on the Bloch sphere. Note that the magnetization of each compartment is normalized by their respective fractions for visual clarity. (b) Numerically optimized $$$\vartheta$$$ pattern over time. (c) Fisher information over time. The optimized sequence prefers two distinct information dense periods per $$$T_{cyc}$$$.

Table 2: Mean and standard deviation (SD) of signal to noise ratio (SNR) for (a) white matter (WM) and (b) grey matter (GM). The SNR was calculated for all the three methods – GS, MRF and TMRF (columns) and for all the four contrasts (rows). Initially, WM and GM were segmented and then SNR was calculated using 3D slicer software. SNR was measured using “difference image” method, where the same brain images were acquired twice with identical conditions. The SNR for GS>TMRF>MRF for WM and GM for all the contrasts.

Figure 1: Qualitative healthy brain images obtained using gold standard method (first row), magnetic resonance fingerprinting (MRF) (second row) and tailored MRF (TMRF) (third row). The color axis bar for each image is different. Each column represents different contrasts along with the representative grey matter and white matter segmentation (last column) using 3D slicer. Images obtained using MRF method were synthetically generated and have flow artifacts as shown in the yellow circle.

(top) We utilize a singular value decomposition (SVD) based k-space compression method. Image series $$$x$$$ can be compressed with SVD. (bottom) in the iterative reconstruction, the undersampling mask $$$P$$$ is replaced by $$$U_R^H P U_R $$$ with a size of R times R for a compressed k-space, instead of computing vary large data matrices. Therefore, the iterative reconstruction is performed on a compressed k-space.

3D in vivo result, acquired using a stack of spiral MRF. Severe artifacts resisted in the backprojection method, while they were effectively reduced with the proposed method.

Fig.2 Reconstructed maps of T1, T2 and PD, using the 5% sampled noiseless data. The acquisition length is $$$L=400$$$.

Fig.1 Illustration of the structure of the lifted matrix $$${\cal T}(\mathbf{x})$$$: The rows of the matrix are 3-D neighborhoods of the gradient-weighted $$$k$$$-space samples.

Figure 2: (Top) T₁, T₂, and T₁ρ in a healthy volunteer using our 2D MRF sequence during one breath hold. (Bottom) T₁, T₂, and T₁ρ in a healthy volunteer using our 2D MRF sequence during free breathing.

Figure 3: Whole pancreas mean T₁, T₂, and T₁ρ relaxation times for healthy controls (blue) and patients with CP (orange) using the 2D MRF sequence

Fig.3 T1, T2, T2* and FF maps for one representative subject obtained with (long cardiac acquisition window) MRF with no motion correction (NMC), with motion correction (proposed LRMC) and the corresponding conventional methods (MOLLI, T2-GraSE, 8-echo GRE for T2* and 6-echo GRE for FF). Residual artefacts (predominantly blurring) are present with NMC and are reduced with LRMC, achieving comparable quality to conventional single-parameter mapping methods.

Fig.1 Diagram for the proposed T1, T2, T2* and FF cardiac MRF. a) ECG-triggered data is acquired with varying preparation pulses; b) low rank subspace is estimated from the MRF dictionary; c) long acquisition window data is binned into multiple cardiac phases; d) cardiac resolved images are reconstructed with LRI-HDPROST; e) motion is estimated with free-form deformations; f) LRMC is performed producing a set of motion corrected singular values for all echoes; g) T1 and T2 is estimated via MRF dictionary matching, T2* and FF are estimated via a water/fat separation algorithm.

Figure 3: Resulting T1 and T2 maps from the reference sequences (MOLLI and T2-prep bSSFP), uncorrected MRF maps and motion corrected MRF maps. The red square is a zoomed view on the papillary muscle to highlight the improvement in image sharpness due to motion correction.

Figure 1: Presented framework for cMRF. 1. Raw data is acquired with described parameters. 2.a) Cine images are reconstructed from raw data. b) Non-rigid motion fields are determined from cine data. 3.a) Motion correction is applied during image reconstruction of MRF images. b) Dictionary matching is applied to obtain parametric maps. 4. Final T1 and T2 maps of the heart.

Fig. 4: Short axis view of T₁, T₂ and T_1ρ maps in a healthy subject (subject 1) with a heart rate of 64.3 bpm and a standard deviation of 4.4 bpm. Maps for T₁, T₂ and T_1ρ are shown that are reconstructed using dictionaries generated from EPG simulations and the neural network. The mean relative errors for the myocardium are 1.7%, 4.8% and 5.1% for T₁, T₂ and T_1ρ respectively.

Fig. 2: Comparison plots of predicted cardiac MRF signal evolutions by the feedforward neural network (blue) against those simulated using EPGs (red). Fingerprints are plotted using both methods for healthy (left column, T₁ = 1100 ms, T₂ = 50 ms and T_1ρ = 60 ms) and diseased (right column, T₁ = 1400 ms, T₂ = 65 ms and T_1ρ = 80 ms) myocardium for 3 different RR sequences (50 ± 5 bpm, 60 ± 6 bpm, 75 ± 3.75 bpm).

Figure 1: Schematic overview of the MRF-EPI sequence. a) Baseline images for four different measurements showing contrast variations throughout the MRF acquisition. Gray dashed lines point to the parameters used for acquiring the image. The red and green circles indicate the locations of the fingerprints shown in c). b) Flip angle (α) (34 to 84 degree) and echo time (TE) (28 to 89 ms) pattern of the MRF-EPI sequence. c) Signal evolution for 2 different fingerprints in the cartilage of a healthy subject, with the corresponding range of the complete dictionary (gray shading).

Figure 5: In vivo T1 and T2* maps for one slice of MRF (a) and reference scans (MOLLI and multi GRE) (b). c) multiple MRF maps illustrating full medial and lateral coverage with the proposed whole-knee technique.

Figure 2. MR-fingerprinting reconstructed images and T1, T2 quantitative maps for variable number of radial spokes per time point in a healthy volunteer.

Figure 3. Boxplots of T1 and T2 values within the prostate for acquisitions with various number of spokes per time point. #spk: number of radial spokes per temporal frame.

Figure 4: (A) Reference cartesian Dixon scan and (B) water/fat resolved MRF. Abdominal water/fat separated FISP-MRF results show proton density and T1/T2 parameter maps for both fat and water separately. A mask was applied to the parameter maps to only show regions of sufficient proton signal. The proton density images compare well between MRF and the classical Dixon sequence, with inflow effects being present in the MRF scan leading to bright vessels.

Figure 1: FISP-MRF sequence with interleaved in- and out-of-phase echo times for water/fat separation at 0.75T. For each flip angle, an out-of-phase image is acquired first with an echo time of 4.6 ms followed by an in-phase image with 9.21 ms echo time (N.B.: the water/fat shift at 0.75T is approximately 108 Hz). For acquisition, a 12 ms Archimedean spiral readout with 7 interleaves and 2mm nominal resolution was used. For each time point only one spiral interleave was acquired, leading to a 7-fold undersampled acquisition

Table-1: Results from the conventional MRF and the proposed method (i.e. MRF with different clustering methods)

Figure-1: Reconstructed T1/T2 Property Maps from the Reference MRF Method and Clustering

Figure 1: Overview of the MR Fingerprinting Pipeline.

The pipeline consists of acquisition (blue), dictionary generation (green), and property map creation (orange). At each stage of the pipeline there are many design choices that can be implemented, some of which are listed here. Each of these choices can influence the accuracy and precision of the resulting property maps. The design choices analyzed in this effort are highlighted in yellow (same across methods) and red (variable across methods).

Figure 3: Simulated phantom reconstructed property maps for each method compared to the true values.

Qualitatively, the T1 and T2 maps generated with each method are in good agreement with the true values in the digital phantom. Spiral artifacts can be seen in the background where there is no signal, appearing stronger near the edges of the field of view where they begin to infiltrate the reconstructed maps within each circle.

Reconstructed coefficient images for each of the 6 HSFP experiments. The trajectories used for the images (i,ii,iii) are not reordered, whereas those used for (iv,v,vi) are reordered. From the analysis in Fig.2 we expect the images (ii,iii) be severely impacted by eddy currents.

Representative nonlinear least-square fit results based on the coefficient images in Fig. 3 ii (top row) and v (bottom row).

Figure 3: a) FA and b) TR sequences at initiation and after optimisation for multi-component MRF. Optimisation was performed for tissue parameters {$$$T_{1}^{a}$$$, $$$T_{2}^{a}$$$, $$$M_{0}^{a}$$$} = {700ms, 60ms, 0.3} and {$$$T_{1}^{b}$$$, $$$T_{2}^{b}$$$, $$$M_{0}^{b}$$$} = {1100ms, 102ms, 0.3} with the constraints mentioned in the Methods section. Different initialisation of the optimisation problem returned the same result.

Figure 5: Relative CRB values were calculated using the multi-component Fisher matrix for a conventional MRF sequence (row 1) and an optimised sequence (row 2). The difference is shown in row 3 by subtracting the second row from the first. The rCRB is defined as $$$\text{rCRB} = \frac{\text{CRB}}{\sigma^2 \theta^2}$$$ where θ represents T₁^a, T₂^a or M₀^a. Tissue parameters for one tissue (superscript a) were fixed at T₁^a = 800 ms, T₂^a = 80 ms, while T₁^b and T₂^b for the second tissue (superscript b) vary. In the centre red dot the 2 tissues are exactly the same, resulting in a singularity.

T1 and T2 reconstructions from TR images with and without off-resonance correction.

Phase comparison between GAN correction and classical MRF with the ground truth reconstructions for different TRs.

Comparison of MRF-derived parametric maps for imaging during free-breathing FB. Top row=gridding recon; bottom row=GRASP. From left to right: PD, T1, and T2 maps.

Effect of reconstruction algorithm on standard deviation of calculated T1 and T2 values.

Figure 1. Workflow for both 2D MRF and proposed 3D MRF reconstruction.

Table 1. Post-processing times for each step during 3D MRF reconstruction (seconds). The times for SVD, NUFFT, coil combination and pattern matching are presented for one slice.

Fig 3: Multi-resolution MRF results in the 2x2 pixel squares of the resolution phantom. The first column shows the ground truth T₁ and T₂ maps. The second column shows the result of acquiring low-resolution data and simply zero-padding the images; significant blurring is evident. The third column shows the result of acquiring 33% of the data with the high-resolution spiral trajectory. The fourth column shows the result of acquiring 50% of the data with the high-resolution spiral trajectory. The fourth column shows the result of acquiring all data with the high-resolution spiral.

Fig 1:(a) Flowchart for the proposed method. High-resolution data (red) and low-resolution data (black) are acquired and reconstructed to generate high-resolution timeseries images. A low rank reconstruction method is used to obtain property maps. (b) Spiral sampling scheme for 33% high-resolution data, where spiral 1 is the low-resolution spiral and spiral 2 is the high-resolution spiral. (c) Resolution phantom. Each cluster includes 4 squares with different T₁ and T₂ values, and range in size from 1x1 to 6x6 pixels. The white arrow denotes the 2x2 pixel cluster used in Figs 2-3.

Reconstructed T₁ and T₂ maps from MRF experiments using different acquisition parameters at acquisition length N = 400. (a) Reconstructed T₁ maps and relative error maps. (b) Reconstructed T₂ maps and relative error maps. Compared to the conventional MRF experiment design, the proposed spline-based design improves the T₂ accuracy by about a factor of 2, while improving T₂ accuracy. It provides a better reconstruction performance than the state-of-the-art approach, i.e., Optimized-II, but with a two-order magnitude improvement in computation speed (as shown in Figure 2).

Data acquisition parameters and the resulting magnetization evolutions from different MRF experiments. (a) Conventional MRF experiment; (b) Optimized-I MRF experiment; (c) Optimized-II MRF experiment; and (d) Proposed MRF experiment. Note that with a spline-based parametric constraint, the magnetization evolutions from the proposed approach exhibit a similar behavior to that from Optimized-II, but with a two-order magnitude improvement in the computational speed (as shown in Figure 2).

Figure 1: The T1 (A) and T2 (B) maps of the 4D XCAT phantom of 10 respiratory phases estimated from the triggered 4D-MRF acquisition method with 10 repetitions in the presence of irregular breathing. Dashed white lines are added to facilitate the visualization of respiratory motion.

Figure 2: The different image quality indexes measured in T1 maps. The A-F corresponds to overall T1 value error, liver T1 value error, tumor T1 value error, tumor T1 contrast, tumor T1 SNR, and liver T1 SNR respectively.

Figure 1: (A) One of the eight interleaves of the proposed seiffert spiral (B) All eight interleaves of the seiffert spiral (C) 120 random interleaves of the fully sampled acquisition (D) Flip angle modulation segment that is repeated every 800 TRs.

Figure 4: T₁ (top) and T₂ (bottom) relaxation maps obtained with the proposed 3D MRF sequence in the brain of a healthy volunteer.

Diagram of reconstruction algorithm. The algorithm has 2 main components: the non-linear curve fitting component for R₂* estimation, and the pattern matching component for T₁ and T₂ estimation.

R₂* quantification results in the ISMRM/NIST phantom. (a) The reference R₂* map collected with a 6-echo GRE sequence. (b) The R₂* map created from the composite half-lobe rosette MRF images. (c) A linear regression between the measured reference values and rosette MRF values. (d) A table of the R₂* values measured in the ISMRM/NIST phantom.

Figure 4: (a) T₁ map of T₁ array and (b) T₂ map of T₂ array generated using OMEGA. The units are in ms. The boxplots of min and max for each spheres in (c) T₁ spheres and (d) T₂ spheres are plotted. The red triangles are the GS values measured using the spin-echo method. The black squares are the data generated using OMEGA.

Figure 2: (a) Flip angle (FA) and (b) repetition time (TR) design in OMEGA. The design is identical to the previous MRF design in literature. (c) is the RF magnitude plot of the first 13 pulses implemented using Pulseq. The first pulse is the inversion pulse.