Quantitative MRI by nonlinear inversion of the Bloch equations.

PURPOSE: Development of a generic model-based reconstruction framework for multiparametric quantitative MRI that can be used with data from different pulse sequences. METHODS: Generic nonlinear model-based reconstruction for quantitative MRI estimates parametric maps directly from the acquired k-space by numerical optimization. This requires numerically accurate and efficient methods to solve the Bloch equations and their partial derivatives. In this work, we combine direct sensitivity analysis and pre-computed state-transition matrices into a generic framework for calibrationless model-based reconstruction that can be applied to different pulse sequences. As a proof-of-concept, the method is implemented and validated for quantitative T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ mapping with single-shot inversion-recovery (IR) FLASH and IR bSSFP sequences in simulations, phantoms, and the human brain. RESULTS: The direct sensitivity analysis enables a highly accurate and numerically stable calculation of the derivatives. The state-transition matrices efficiently exploit repeating patterns in pulse sequences, speeding up the calculation by a factor of 10 for the examples considered in this work, while preserving the accuracy of native ordinary differential equations solvers. The generic model-based method reproduces quantitative results of previous model-based reconstructions based on the known analytical solutions for radial IR FLASH. For IR bSFFP it produces accurate T 1 $$ {\mathrm{T}}_1 $$ and T 2 $$ {\mathrm{T}}_2 $$ maps for the National Insitute of Standards and Technology (NIST) phantom in numerical simulations and experiments. Feasibility is also shown for human brain, although results are affected by magnetization transfer effects. CONCLUSION: By developing efficient tools for numerical optimizations using the Bloch equations as forward model, this work enables generic model-based reconstruction for quantitative MRI.

Free-breathing myocardial T1 mapping using inversion-recovery radial FLASH and motion-resolved model-based reconstruction.

PURPOSE: To develop a free-breathing myocardial T 1 $$ {\mathrm{T}}_1 $$ mapping technique using inversion-recovery (IR) radial fast low-angle shot (FLASH) and calibrationless motion-resolved model-based reconstruction. METHODS: Free-running (free-breathing, retrospective cardiac gating) IR radial FLASH is used for data acquisition at 3T. First, to reduce the waiting time between inversions, an analytical formula is derived that takes the incomplete T 1 $$ {\mathrm{T}}_1 $$ recovery into account for an accurate T 1 $$ {\mathrm{T}}_1 $$ calculation. Second, the respiratory motion signal is estimated from the k-space center of the contrast varying acquisition using an adapted singular spectrum analysis (SSA-FARY) technique. Third, a motion-resolved model-based reconstruction is used to estimate both parameter and coil sensitivity maps directly from the sorted k-space data. Thus, spatiotemporal total variation, in addition to the spatial sparsity constraints, can be directly applied to the parameter maps. Validations are performed on an experimental phantom, 11 human subjects, and a young landrace pig with myocardial infarction. RESULTS: In comparison to an IR spin-echo reference, phantom results confirm good T 1 $$ {\mathrm{T}}_1 $$ accuracy, when reducing the waiting time from 5 s to 1 s using the new correction. The motion-resolved model-based reconstruction further improves T 1 $$ {\mathrm{T}}_1 $$ precision compared to the spatial regularization-only reconstruction. Aside from showing that a reliable respiratory motion signal can be estimated using modified SSA-FARY, in vivo studies demonstrate that dynamic myocardial T 1 $$ {\mathrm{T}}_1 $$ maps can be obtained within 2 min with good precision and repeatability. CONCLUSION: Motion-resolved myocardial T 1 $$ {\mathrm{T}}_1 $$ mapping during free-breathing with good accuracy, precision and repeatability can be achieved by combining inversion-recovery radial FLASH, self-gating and a calibrationless motion-resolved model-based reconstruction.

Physics-based reconstruction methods for magnetic resonance imaging.

Conventional magnetic resonance imaging (MRI) is hampered by long scan times and only qualitative image contrasts that prohibit a direct comparison between different systems. To address these limitations, model-based reconstructions explicitly model the physical laws that govern the MRI signal generation. By formulating image reconstruction as an inverse problem, quantitative maps of the underlying physical parameters can then be extracted directly from efficiently acquired k-space signals without intermediate image reconstruction-addressing both shortcomings of conventional MRI at the same time. This review will discuss basic concepts of model-based reconstructions and report on our experience in developing several model-based methods over the last decade using selected examples that are provided complete with data and code. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Joint T1 and T2 Mapping With Tiny Dictionaries and Subspace-Constrained Reconstruction.

A novel method is developed that adaptively generates tiny dictionaries for joint T1-T2 mapping in magnetic resonance imaging. This work breaks the bond between dictionary size and representation accuracy (i) by approximating the Bloch-response manifold by piece-wise linear functions and (ii) by adaptively refining the sampling grid depending on the locally-linear approximation error. Data acquisition is accomplished with use of an 2D radially sampled Inversion-Recovery Hybrid-State Free Precession sequence. Adaptive dictionaries are generated with different error tolerances and compared to a heuristically designed dictionary. Based on simulation results, tiny dictionaries were used for T1-T2 mapping in phantom and in vivo studies. Reconstruction and parameter mapping were performed entirely in subspace. All experiments demonstrated excellent agreement between the proposed mapping technique and template matching using heuristic dictionaries. Adaptive dictionaries in combination with manifold projection allow to reduce the necessary dictionary sizes by one to two orders of magnitude.

Frequency-modulated SSFP with radial sampling and subspace reconstruction: A time-efficient alternative to phase-cycled bSSFP.

PURPOSE: A novel subspace-based reconstruction method for frequency-modulated balanced steady-state free precession (fmSSFP) MRI is presented. In this work, suitable data acquisition schemes, subspace sizes, and efficiencies for banding removal are investigated. THEORY AND METHODS: By combining a fmSSFP MRI sequence with a 3D stack-of-stars trajectory, scan efficiency is maximized as spectral information is obtained without intermediate preparation phases. A memory-efficient reconstruction routine is implemented by introducing the low-frequency Fourier transform as a subspace which allows for the formulation of a convex reconstruction problem. The removal of banding artifacts is investigated by comparing the proposed acquisition and reconstruction technique to phase-cycled bSSFP MRI. Aliasing properties of different undersampling schemes are analyzed and water/fat separation is demonstrated by reweighting the reconstructed subspace coefficients to generate virtual spectral responses in a post-processing step. RESULTS: A simple root-of-sum-of-squares combination of the reconstructed subspace coefficients yields high-SNR images with the characteristic bSSFP contrast but without banding artifacts. Compared to Golden-Angle trajectories, turn-based sampling schemes were superior in minimizing aliasing across reconstructed subspace coefficients. Water/fat separated images of the human knee were obtained by reweighting subspace coefficients. CONCLUSIONS: The novel subspace-based fmSSFP MRI technique emerges as a time-efficient alternative to phase-cycled bSFFP. The method does not need intermediate preparation phases, offers high SNR and avoids banding artifacts. Reweighting of the reconstructed subspace coefficients allows for generating virtual spectral responses with applications to water/fat separation.

Fast Interleaved Multislice T1 Mapping: Model-Based Reconstruction of Single-Shot Inversion-Recovery Radial FLASH.

PURPOSE: To develop a high-speed multislice T1 mapping method based on a single-shot inversion-recovery (IR) radial FLASH acquisition and a regularized model-based reconstruction. METHODS: Multislice radial k-space data are continuously acquired after a single nonselective inversion pulse using a golden-angle sampling scheme in a spoke-interleaved manner with optimized flip angles. Parameter maps and coil sensitivities of each slice are estimated directly from highly undersampled radial k-space data using a model-based nonlinear inverse reconstruction in conjunction with joint sparsity constraints. The performance of the method has been validated using a numerical and experimental T1 phantom as well as demonstrated for studies of the human brain and liver at 3T. RESULTS: The proposed method allows for 7 simultaneous T1 maps of the brain at 0.5 × 0.5 × 4 mm3 resolution within a single IR experiment of 4 s duration. Phantom studies confirm similar accuracy and precision as obtained for a single-slice acquisition. For abdominal applications, the proposed method yields three simultaneous T1 maps at 1.25 × 1.25 × 6 mm3 resolution within a 4 s breath hold. CONCLUSION: Rapid, robust, accurate, and precise multislice T1 mapping may be achieved by combining the advantages of a model-based nonlinear inverse reconstruction, radial sampling, parallel imaging, and compressed sensing.

Model-based T1 mapping with sparsity constraints using single-shot inversion-recovery radial FLASH.

PURPOSE: To develop a model-based reconstruction technique for single-shot T1 mapping with high spatial resolution, accuracy, and precision using an inversion-recovery (IR) fast low-angle shot (FLASH) acquisition with radial encoding. METHODS: The proposed model-based reconstruction jointly estimates all model parameters, that is, the equilibrium magnetization, steady-state magnetization, 1/ T1*, and all coil sensitivities from the data of a single-shot IR FLASH acquisition with a small golden-angle radial trajectory. Joint sparsity constraints on the parameter maps are exploited to improve the performance of the iteratively regularized Gauss-Newton method chosen for solving the nonlinear inverse problem. Validations include both a numerical and experimental T1 phantom, as well as in vivo studies of the human brain and liver at 3 T. RESULTS: In comparison to previous reconstruction methods for single-shot T1 mapping, which are based on real-time MRI with pixel-wise fitting and a model-based approach with a predetermination of coil sensitivities, the proposed method presents with improved robustness against phase errors and numerical precision in both phantom and in vivo studies. CONCLUSION: The comprehensive model-based reconstruction with L1 regularization offers rapid and robust T1 mapping with high accuracy and precision. The method warrants accelerated computing and online implementation for extended clinical trials. Magn Reson Med 79:730-740, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Simultaneous mapping of water shift and B1 (WASABI)-Application to field-Inhomogeneity correction of CEST MRI data.

PURPOSE: Together with the development of MRI contrasts that are inherently small in their magnitude, increased magnetic field accuracy is also required. Hence, mapping of the static magnetic field (B0 ) and the excitation field (B1 ) is not only important to feedback shim algorithms, but also for postprocess contrast-correction procedures. METHODS: A novel field-inhomogeneity mapping method is presented that allows simultaneous mapping of the water shift and B1 (WASABI) using an off-resonant rectangular preparation pulse. The induced Rabi oscillations lead to a sinc-like spectrum in the frequency-offset dimension and allow for determination of B0 by its symmetry axis and of B1 by its oscillation frequency. RESULTS: Stability of the WASABI method with regard to the influences of T1 , T2 , magnetization transfer, and repetition time was investigated and its convergence interval was verified. B0 and B1 maps obtained simultaneously by means of WASABI in the human brain at 3 T and 7 T can compete well with maps obtained by standard methods. Finally, the method was applied successfully for B0 and B1 correction of chemical exchange saturation transfer MRI (CEST-MRI) data of the human brain. CONCLUSION: The proposed WASABI method yields a novel simultaneous B0 and B1 mapping within 1 min that is robust and easy to implement. Magn Reson Med 77:571-580, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Model-based reconstruction for real-time phase-contrast flow MRI: Improved spatiotemporal accuracy.

PURPOSE: To develop a model-based reconstruction technique for real-time phase-contrast flow MRI with improved spatiotemporal accuracy in comparison to methods using phase differences of two separately reconstructed images with differential flow encodings. METHODS: The proposed method jointly computes a common image, a phase-contrast map, and a set of coil sensitivities from every pair of flow-compensated and flow-encoded datasets obtained by highly undersampled radial FLASH. Real-time acquisitions with five and seven radial spokes per image resulted in 25.6 and 35.7 ms measuring time per phase-contrast map, respectively. The signal model for phase-contrast flow MRI requires the solution of a nonlinear inverse problem, which is accomplished by an iteratively regularized Gauss-Newton method. Aspects of regularization and scaling are discussed. The model-based reconstruction was validated for a numerical and experimental flow phantom and applied to real-time phase-contrast MRI of the human aorta for 10 healthy subjects and 2 patients. RESULTS: Under all conditions, and compared with a previously developed real-time flow MRI method, the proposed method yields quantitatively accurate phase-contrast maps (i.e., flow velocities) with improved spatial acuity, reduced phase noise and reduced streaking artifacts. CONCLUSION: This novel model-based reconstruction technique may become a new tool for clinical flow MRI in real time. Magn Reson Med 77:1082-1093, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

High-resolution myocardial T1 mapping using single-shot inversion recovery fast low-angle shot MRI with radial undersampling and iterative reconstruction.

OBJECTIVE: To develop a novel method for rapid myocardial T1 mapping at high spatial resolution. METHODS: The proposed strategy represents a single-shot inversion recovery experiment triggered to early diastole during a brief breath-hold. The measurement combines an adiabatic inversion pulse with a real-time readout by highly undersampled radial FLASH, iterative image reconstruction and T1 fitting with automatic deletion of systolic frames. The method was implemented on a 3-T MRI system using a graphics processing unit-equipped bypass computer for online application. Validations employed a T1 reference phantom including analyses at simulated heart rates from 40 to 100 beats per minute. In vivo applications involved myocardial T1 mapping in short-axis views of healthy young volunteers. RESULTS: At 1-mm in-plane resolution and 6-mm section thickness, the inversion recovery measurement could be shortened to 3 s without compromising T1 quantitation. Phantom studies demonstrated T1 accuracy and high precision for values ranging from 300 to 1500 ms and up to a heart rate of 100 beats per minute. Similar results were obtained in vivo yielding septal T1 values of 1246 ± 24 ms (base), 1256 ± 33 ms (mid-ventricular) and 1288 ± 30 ms (apex), respectively (mean ± standard deviation, n = 6). CONCLUSION: Diastolic myocardial T1 mapping with use of single-shot inversion recovery FLASH offers high spatial resolution, T1 accuracy and precision, and practical robustness and speed. Advances in knowledge: The proposed method will be beneficial for clinical applications relying on native and post-contrast T1 quantitation.

Spoiling without additional gradients: Radial FLASH MRI with randomized radiofrequency phases.

PURPOSE: To develop a method for spoiling transverse magnetizations without additional gradients to minimize repetition times for radial fast low angle shot (FLASH) MRI. METHODS: Residual steady state transverse magnetizations and corresponding image artifacts were analyzed for radial gradient echo sequences with constant and randomized RF phases in comparison with a sequence with refocused frequency-encoding gradients, constant spoiler gradient, and conventional RF spoiling (gold standard). The spoiling performance was assessed for different radial trajectories using numerical simulations, phantom experiments, and in vivo MRI studies of the human brain. RESULTS: Simulations as well as phantom and in vivo measurements reveal a highly efficient spoiling capacity for randomized RF phases and radial FLASH sequences without the need for gradient rewinding and spoiler gradients. The data also demonstrate a strong dependence of the spoiling performance on the chosen radial trajectory (ie, the azimuthal angular increment between successive projections) with excellent results for an interleaved multiturn scheme. CONCLUSION: Effective spoiling of transverse magnetizations in radial FLASH MRI may be achieved by randomized RF phases without additional spoiler gradients. The technique allows for short repetition times as required for high-speed real-time MRI.

Advances in real-time phase-contrast flow MRI using asymmetric radial gradient echoes.

PURPOSE: To provide multidimensional velocity compensation for real-time phase-contrast flow MRI. METHODS: The proposed method introduces asymmetric gradient echoes for highly undersampled radial FLASH MRI with phase-sensitive image reconstruction by regularized nonlinear inversion (NLINV). Using an adapted gradient delay correction the resulting image quality was analyzed by simulations and experimentally validated at 3 Tesla. For real-time flow MRI the reduced gradient-echo timing allowed for the incorporation of velocity-compensating waveforms for all imaging gradients at even shorter repetition times. RESULTS: The results reveal a usable degree of 20% asymmetry. Real-time flow MRI with full velocity compensation eliminated signal void in a flow phantom, confirmed flow parameters in healthy subjects and demonstrated signal recovery and phase conservation in a patient with aortic valve insufficiency and stenosis. Exemplary protocols at 1.4-1.5 mm resolution and 6 mm slice thickness achieved total acquisition times of 33.3-35.7 ms for two images (7 spokes each) with and without flow-encoding gradient. CONCLUSION: Asymmetric gradient echoes were successfully implemented for highly undersampled radial trajectories. The resulting temporal gain offers full velocity compensation for real-time phase-contrast flow MRI which minimizes false-positive contributions from complex flow and further enhances the temporal resolution compared with acquisitions with symmetric echoes.

Amide proton transfer of carnosine in aqueous solution studied in vitro by WEX and CEST experiments.

Amide protons of peptide bonds induce an important chemical exchange saturation transfer (CEST) contrast in vivo. As a simple in vitro model for a peptide amide proton CEST effect, we suggest herein the dipeptide carnosine. We show that the metabolite carnosine creates a CEST effect and we study the properties of the exchange of the amide proton (-NH) of the carnosine peptide bond (NHCPB) in model solutions for a pH range from 6 to 8.3 and a temperature range from T = 5 °C to 43 °C by means of CEST and water exchange spectroscopy (WEX) experiments on a 3 T whole-body MR tomograph. The dependence of the NHCPB chemical exchange rate k(sw) on pH and temperature T was determined using WEX. For physiological conditions (T = 37 °C, pH = 7.10) we obtained k(sw) = (47.07 ± 7.90)/s. With similar chemical shift and exchange properties to amide protons in vivo, carnosine forms a simple model system for optimization of CEST pulse sequences in vitro. The potential for direct detection of the metabolite carnosine in vivo is discussed.

Single-shot T1 mapping of the corpus callosum: a rapid characterization of fiber bundle anatomy.

Using diffusion-tensor magnetic resonance imaging and fiber tractography the topographic organization of the human corpus callosum (CC) has been described to comprise five segments with fibers projecting into prefrontal (I), premotor and supplementary motor (II), primary motor (III), and primary sensory areas (IV), as well as into parietal, temporal, and occipital cortical areas (V). In order to more rapidly characterize the underlying anatomy of these segments, this study used a novel single-shot T1 mapping method to quantitatively determine T1 relaxation times in the human CC. A region-of-interest analysis revealed a tendency for the lowest T1 relaxation times in the genu and the highest T1 relaxation times in the somatomotor region of the CC. This observation separates regions dominated by myelinated fibers with large diameters (somatomotor area) from densely packed smaller axonal bundles (genu) with less myelin. The results indicate that characteristic T1 relaxation times in callosal profiles provide an additional means to monitor differences in fiber anatomy, fiber density, and gray matter in respective neocortical areas. In conclusion, rapid T1 mapping allows for a characterization of the axonal architecture in an individual CC in less than 10 s. The approach emerges as a valuable means for studying neocortical brain anatomy with possible implications for the diagnosis of neurodegenerative processes.

Towards quantification of pulsed spinlock and CEST at clinical MR scanners: an analytical interleaved saturation-relaxation (ISAR) approach.

Off-resonant spinlock (SL) enables an NMR imaging technique that can detect dilute metabolites similar to chemical exchange saturation transfer. However, in clinical MR scanners, RF pulse widths are restricted due to recommended specific absorption rate limits. Therefore, trains of short RF pulses that provide effective saturation during the required irradiation period are commonly employed. Quantitative evaluation of spectra obtained by pulsed saturation schemes is harder to achieve, since the theory of continuous wave saturation cannot be applied directly. In this paper we demonstrate the general feasibility of quantifying proton exchange rates from data obtained in pulsed SL experiments on a clinical 3 T MR scanner. We also propose a theoretical treatment of pulsed SL in the presence of chemical exchange using an interleaved saturation-relaxation approach. We show that modeling magnetization transfer during the pauses between the RF pulses is crucial, especially in the case of exchange rates that are small with respect to the delay times. The dynamics is still governed by a monoexponential decay towards steady state, for which we give the effective rate constant. The derived analytical model agrees well with the full numerical simulation of the Bloch-McConnell equations for a broad range of values of the system parameters.