Faculty Bibliography

OBJECTIVE:We extend the traditional framework for estimating subspace bases in quantitative MRI that maximize the preserved signal energy to additionally preserve the Cramér-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. METHODS:To this end, we introduce an approximate compressed CRB based on orthogonalized versions of the signal's derivatives with respect to the model parameters. This approximation permits singular value decomposition (SVD)-based minimization of both the CRB and signal losses during compression. RESULTS:Compared to the traditional SVD approach, the proposed method better preserves the CRB across all biophysical parameters with minimal cost to the preserved signal energy, leading to reduced bias and variance of the parameter estimates in simulation. In vivo, improved accuracy and precision are observed in two quantitative neuroimaging applications. CONCLUSION/CONCLUSIONS:The proposed method permits subspace reconstruction with a more compact basis, thereby offering significant computational savings. SIGNIFICANCE/CONCLUSIONS:Efficient subspace reconstruction facilitates the validation and translation of advanced quantitative MRI techniques, e.g., magnetization transfer and diffusion.

PURPOSE/OBJECTIVE:To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio-based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. METHODS:The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. RESULTS:RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. CONCLUSION/CONCLUSIONS:RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

PURPOSE/UNASSIGNED:The long scan times of quantitative MRI techniques make motion artifacts more likely. For MR-Fingerprinting-like approaches, this problem can be addressed with self-navigated retrospective motion correction based on reconstructions in a singular value decomposition (SVD) subspace. However, the SVD promotes high signal intensity in all tissues, which limits the contrast between tissue types and ultimately reduces the accuracy of registration. The purpose of this paper is to rotate the subspace for maximum contrast between two types of tissue and improve the accuracy of motion estimates. METHODS/UNASSIGNED:A subspace is derived that promotes contrasts between brain parenchyma and CSF, achieved through the generalized eigendecomposition of mean autocorrelation matrices, followed by a Gram-Schmidt process to maintain orthogonality.We tested our motion correction method on 85 scans with varying motion levels, acquired with a 3D hybrid-state sequence optimized for quantitative magnetization transfer imaging. RESULTS/UNASSIGNED:A comparative analysis shows that the contrast-optimized basis significantly improve the parenchyma-CSF contrast, leading to smoother motion estimates and reduced artifacts in the quantitative maps. CONCLUSION/UNASSIGNED:The proposed contrast-optimized subspace improves the accuracy of the motion estimation.

PURPOSE/OBJECTIVE:To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. THEORY AND METHODS/METHODS:We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. RESULTS:In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as nonlinear least-squares fitting, while state-of-the-art NNs show larger deviations. CONCLUSION/CONCLUSIONS:The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

PURPOSE/OBJECTIVE:To develop a generic radial sampling scheme that combines the advantages of golden ratio sampling with simplicity of equidistant angular patterns. The irrational angle between consecutive spokes in golden ratio based sampling schemes enables a flexible retrospective choice of temporal resolution, while preserving good coverage of k-space for each individual bin. Nevertheless, irrational increments prohibit precomputation of the point-spread function (PSF), can lead to numerical problems, and require more complex processing steps. To avoid these problems, a new sampling scheme based on a rational approximation of golden angles (RAGA) is developed. METHODS:The theoretical properties of RAGA sampling are mathematically derived. Sidelobe-to-peak ratios (SPR) are numerically computed and compared to the corresponding golden ratio sampling schemes. The sampling scheme is implemented in the BART toolbox and in a radial gradient-echo sequence. Feasibility is shown for quantitative imaging in a phantom and a cardiac scan of a healthy volunteer. RESULTS:RAGA sampling can accurately approximate golden ratio sampling and has almost identical PSF and SPR. In contrast to golden ratio sampling, each frame can be reconstructed with the same equidistant trajectory using different sampling masks, and the angle of each acquired spoke can be encoded as a small index, which simplifies processing of the acquired data. CONCLUSION/CONCLUSIONS:RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

Magnetization transfer MRI is sensitive to semi-solid macromolecules, including amyloid beta, and has previously been used to discriminate Alzheimer's disease (AD) patients from controls. Here, we fit an unconstrained 2-pool quantitative MT (qMT) model, i.e., without constraints on the longitudinal relaxation rate

PURPOSE/UNASSIGNED:To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cramér-Rao bound. THEORY AND METHODS/UNASSIGNED:We generalize the mean squared error loss to control the bias and variance of the NN's estimates, which involves averaging over multiple noise realizations of the same measurements during training. Bias and variance properties of the resulting NNs are studied for two neuroimaging applications. RESULTS/UNASSIGNED:In simulations, the proposed strategy reduces the estimates' bias throughout parameter space and achieves a variance close to the Cramér-Rao bound. In vivo, we observe good concordance between parameter maps estimated with the proposed NNs and traditional estimators, such as non-linear least-squares fitting, while state-of-the-art NNs show larger deviations. CONCLUSION/UNASSIGNED:The proposed NNs have greatly reduced bias compared to those trained using the mean squared error and offer significantly improved computational efficiency over traditional estimators with comparable or better accuracy.

The purpose of this paper is to confirm previous reports that identified magnetization transfer (MT) as an inherent driver of longitudinal relaxation in brain tissue by asserting a substantial difference between the $T_1$ relaxation times of the free and the semi-solid spin pools. Further, we aim to identify an avenue towards the quantification of these relaxation processes on a voxel-by-voxel basis in a clinical imaging setting, i.e. with a nominal resolution of 1mm isotropic and full brain coverage in 12min. To this end, we optimized a hybrid-state pulse sequence for mapping the parameters of an unconstrained MT model. We scanned 4 people with relapsing-remitting multiple sclerosis (MS) and 4 healthy controls with this pulse sequence and estimated $T_1^f \approx 1.90$s and $T_1^s \approx 0.327$s for the free and semi-solid spin pool of healthy WM, respectively, confirming previous reports and questioning the commonly used assumptions $T_1^s = T_1^f$ or $T_1^s = 1$s. Further, we estimated a fractional size of the semi-solid spin pool of $m_0^s \approx 0.202$, which is larger than previously assumed. An analysis of $T_1^f$ in normal appearing white matter revealed statistically significant differences between individuals with MS and controls. In conclusion, we confirm that longitudinal spin relaxation in brain tissue is dominated by MT and that the hybrid state facilitates a voxel-wise fit of the unconstrained MT model, which enables the analysis of subtle neurodegeneration.

PURPOSE/OBJECTIVE:To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters. THEORY AND METHODS/METHODS:We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency. RESULTS:We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, consistent with previous reports. CONCLUSION/CONCLUSIONS:The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters.

PURPOSE/OBJECTIVE:To minimize eddy current artifacts in periodic pulse sequences with balanced gradient moments as, for example, used for quantitative MRI. THEORY AND METHODS/METHODS:Eddy current artifacts in balanced sequences result from large jumps in k-space. In quantitative MRI, one often samples some spin dynamics repeatedly while acquiring different parts of k-space. We swap individual k-space lines between different repetitions in order to minimize jumps in temporal succession without changing the overall trajectory. This reordering can be formulated as a traveling salesman problem and we tackle the discrete optimization with a simulated annealing algorithm. RESULTS:Compared to the default ordering, we observe a substantial reduction of artifacts in the reconstructed images and the derived quantitative parameter maps. Comparing two variants of our algorithm, one that resembles the pairing approach originally proposed by Bieri et al., and one that minimizes all k-space jumps equally, we observe slightly lower artifact levels in the latter. CONCLUSION/CONCLUSIONS:The proposed reordering scheme effectively reduces eddy current artifacts in sequences with balanced gradient moments. In contrast to previous approaches, we capitalize on the periodicity of the sampled signal dynamics, enabling both efficient k-space sampling and minimizing artifacts caused by eddy currents.