Machine learning-based modeling of physical systems has attracted significant interest in recent years. Based solely on the underlying physical equations and initial and boundary conditions, these new approaches allow to approximate, for example, the complex flow of blood in the case of fluid dynamics. Physics-informed neural networks offer certain advantages compared to conventional computational fluid dynamics methods as they avoid the need for discretized meshes and allow to readily solve inverse problems and integrate additional data into the algorithms. Today, the majority of published reports on learning-based flow modeling relies on fully-connected neural networks. However, many different network architectures are introduced into deep learning each year, each with specific benefits for certain applications. In this paper, we present the first comprehensive comparison of various state-of-the-art networks and evaluate their performance in terms of computational cost and accuracy relative to numerical references. We found that while fully-connected networks offer an attractive balance between training time and accuracy, more elaborate architectures (e.g., Deep Galerkin Method) generated superior results. Moreover, we observed high accuracy in simple cylindrical geometries, but slightly poorer estimates in complex aneurysms. This paper provides quantitative guidance for practitioners interested in complex flow modeling using physics-based deep learning.

Purpose: In this study, we demonstrate the first combination of 3D FID proton MRSI and spatial encoding via concentric‐ring trajectories (CRTs) at 3T. FID‐MRSI has many benefits including high detection sensitivity, in particular for J‐coupled metabolites (e.g., glutamate/glutamine). This makes it highly attractive, not only for clinical, but also for, potentially, functional MRSI. However, this requires excellent reliability and temporal stability. We have, therefore, augmented this 3D‐FID‐MRSI sequence with single‐echo, imaging‐based volumetric navigators (se‐vNavs) for real‐time motion/shim‐correction (SHMOCO), which is 2× quicker than the original double‐echo navigators (de‐vNavs), hence allowing more efficient integration also in short‐TR sequences.Methods: The tracking accuracy (position and B₀‐field) of our proposed se‐vNavs was compared to the original de‐vNavs in phantoms (rest and translation) and in vivo (voluntary head rotation). Finally, the intra‐session stability of a 5:40 min 3D‐FID‐MRSI scan was evaluated with SHMOCO and no correction (NOCO) in 5 resting subjects. Intra/inter‐subject coefficients of variation (CV) and intra‐class correlations (ICC) over the whole 3D volume and in selected regions of interest ROI were assessed.Results: Phantom and in vivo scans showed highly consistent tracking performance for se‐vNavs compared to the original de‐vNavs, but lower frequency drift. Up to ~30% better intra‐subject CVs were obtained for SHMOCO (P < 0.05), with values of 9.3/6.9/6.5/7.8% over the full VOI for Glx/tNAA/tCho/m‐Ins ratios to tCr. ICCs were good‐to‐high (91% for Glx/tCr in motor cortex), whereas the inter‐subject variability was ~11–19%.Conclusion: Real‐time motion/shim corrected 3D‐FID‐MRSI with time‐efficient CRT‐sampling at 3T allows reliable, high‐resolution metabolic imaging that is fast enough for clinical use and even, potentially, for functional MRSI.

Purpose: Proton MR spectroscopic imaging (MRSI) benefits from B₀ ≥ 7T and multichannel receive coils, promising substantial resolution improvements. However, MRSI acquisition with high spatial resolution requires efficient acceleration and coil combination. To speed up the already‐fast sampling via concentric rings, we implemented additional, non‐Cartesian, hybrid through‐time/through‐k‐space (tt/tk)‐generalized autocalibrating partially parallel acquisition (GRAPPA). A new multipurpose interleaved calibration scan (interleaved MUSICAL) acquires reference data for both coil combination and PI. This renders the reconstruction process (especially PI) less sensitive to instabilities.Methods: Six healthy volunteers were scanned at 7T. Three calibration datasets for coil combination and PI were recorded: a) iMUSICAL, b) static MUSICAL as prescan, c) moved MUSICAL as prescan with misaligned head position. The coil combination performance, including motion sensitivity, of iMUSICAL was compared to MUSICAL for single‐slice free induction decay (FID)‐MRSI. Through‐time/through‐k‐space‐GRAPPA with constant/variable‐density undersampling was evaluated on the same data, comparing the three calibration datasets. Additionally, the proposed method was successfully applied to 3D whole‐brain FID‐MRSI.Results: Using iMUSICAL for coil combination yielded the highest signal‐to‐noise ratio (SNR) (+9%) and lowest Cramer‐Rao lower bounds (CRLBs) (‐6%) compared to both MUSICAL approaches, with similar metabolic map quality. Also, excellent mean g‐factors of 1.07 and low residual lipid aliasing were obtained when using iMUSICAL as calibration data for two‐fold, variable‐density undersampling, while significantly degraded metabolic maps were obtained using the misaligned MUSICAL calibration data.Conclusion: Through‐time/through‐k‐space‐GRAPPA can accelerate already time‐efficient non‐Cartesian spatial‐spectral 2D/3D‐MRSI encoding even further. Particularly promising results have been achieved using iMUSICAL as a robust, interleaved multipurpose calibration for MRSI reconstruction, without extra calibration prescan.

Purpose: Inhomogeneities in the static magnetic field (B₀) deteriorate MRSI data quality by lowering the spectral resolution and SNR. MRSI with low spatial resolution is also prone to lipid bleeding. These problems are increasingly problematic at ultra‐high fields. An approach to tackling these challenges independent of B₀‐shim hardware is to increase the spatial resolution. Therefore, we investigated the effect of improved spatial resolution on spectral quality and quantification at 4 field strengths.Methods: Whole‐brain MRSI data was simulated for 3 spatial resolutions and 4 B₀s based on experimentally acquired MRI data and simulated free induction decay signals of metabolites and lipids. To compare the spectral quality and quantification, we derived SNR normalized to the voxel size (nSNR), linewidth and metabolite concentration ratios, their Cramer‐Rao‐lower‐bounds (CRLBs), and the absolute percentage error (APE) of estimated concentrations compared to the gold standard for the whole‐brain and 8 brain regions.Results: At 7T, we found up to a 3.4‐fold improved nSNR (in the frontal lobe) and a 2.8‐fold reduced linewidth (in the temporal lobe) for 1 cm³ versus 0.25 cm³ resolution. This effect was much more pronounced at higher and less homogenous B₀ (1.6‐fold improved nSNR and 1.8‐fold improved linewidth in the parietal lobe at 3T). This had direct implications for quantification: the volume of reliably quantified spectra increased with resolution by 1.2‐fold and 1.5‐fold (when thresholded by CRLBs or APE, respectively).Conclusion: MRSI data quality benefits from increased spatial resolution particularly at higher B₀, and leads to more reliable metabolite quantification. In conjunction with the development of better B₀ shimming hardware, this will enable robust whole‐brain MRSI at ultra‐high field.

Purpose: To assess the performance, in the presence of scanner instabilities, of three dynamic correction methods which integrate ∆B₀ mapping into the chemical exchange saturation transfer (CEST) measurement and three established static ∆B₀‐correction approaches.Methods: A homogeneous phantom and five healthy volunteers were scanned with a CEST sequence at 7 T. The in vivo measurements were performed twice: first with unaltered system frequency and again applying frequency shifts during the CEST acquisition. In all cases, retrospective voxel‐wise ∆B₀‐correction was performed using one intrinsic and two extrinsic [prescans with dual‐echo gradient‐echo and water saturation shift referencing (WASSR)] static approaches. These were compared with two intrinsic [using phase data directly generated by single‐echo or double‐echo GRE (gradient‐echo) CEST readout (CEST‐GRE‐2TE)] and one extrinsic [phase from interleaved dual‐echo EPI (echo planar imaging) navigator (NAV‐EPI‐2TE)] dynamic ∆B₀‐correction approaches [allowing correction of each Z‐spectral point before magnetization transfer ratio asymmetry (MTR_asym) analysis].Results: All three dynamic methods successfully mapped the induced drift. The intrinsic approaches were affected by the CEST labeling near water (∆ω < |0.3| ppm). The MTR_asym contrast was distorted by the frequency drift in the brain by up to 0.21%/Hz when static ∆B₀‐corrections were applied, whereas the dynamic ∆B₀ corrections reduced this to <0.01%/Hz without the need of external scans. The CEST‐GRE‐2TE and NAV‐EPI‐2TE resulted in highly consistent MTR_asym values with/without drift for all subjects.Conclusion: Reliable correction of scanner instabilities is essential to establish clinical CEST MRI. The three dynamic approaches presented improved the ∆B₀‐correction performance significantly in the presence of frequency drift compared to established static methods. Among them, the self‐corrected CEST‐GRE‐2TE was the most accurate and straightforward to implement.

Purpose: A properly characterized macromolecular (MM) contribution is essential for accurate metabolite quantification in FID‐MRSI. MM information can be included into the fitting model as a single component or parameterized and included over several individual MM resonances, which adds flexibility when pathologic changes are present but is prone to potential overfitting. This study investigates the effects of different MM models on MRSI reproducibility.Methods: Clinically feasible, high‐resolution FID‐MRSI data were collected in ~5 min at 7 Tesla from 10 healthy volunteers and quantified via LCModel (version 6.3) with 3 basis sets, each with a different approach for how the MM signal was handled: averaged measured whole spectrum (full MM), 9 parameterized components (param MM) with soft constraints to avoid overparameterization, or without any MM information included in the fitting prior knowledge. The test–retest reproducibility of MRSI scans was assessed voxel‐wise using metabolite coefficients of variation and intraclass correlation coefficients and compared between the basis sets. Correlations of concentration estimates were investigated for the param MM fitting model.Results: The full MM model provided the most reproducible quantification of total NAA, total Cho, myo‐inositol, and glutamate + glutamine ratios to total Cr (coefficients of variations ≤ 8%, intraclass correlation coefficients ≥ 0.76). Using the param MM model resulted in slightly lower reproducibility (up to +3% higher coefficients of variations, up to −0.1 decreased intraclass correlation coefficients). The quantification of the parameterized macromolecules did not affect quantification of the overlapping metabolites.Conclusion: Clinically feasible FID‐MRSI with an experimentally acquired MM spectrum included in prior knowledge provides highly reproducible quantification for the most common neurometabolites in healthy volunteers. Parameterization of the MM spectrum may be preferred as a compromise between quantification accuracy and reproducibility when the MM content is expected to be pathologically altered.