arXiv subjects

Sebastian Flassbeck

Publications and source records attributed to Sebastian Flassbeck.

8 recordsLinked to original sources

arXiv2024

Contrast-Optimized Basis Functions for Self-Navigated Motion Correction in Quantitative MRI

Purpose: 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: 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: 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: The proposed contrast-optimized subspace improves the accuracy of the motion estimation.

physics.med-ph↗

arXiv2023

Bias-Reduced Neural Networks for Parameter Estimation in Quantitative MRI

Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cram\'er-Rao bound. Theory and 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 Cram\'er-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: 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.

physics.med-ph↗

arXiv2023

Cram\'er-Rao Bound Optimized Subspace Reconstruction in Quantitative MRI

We extend the traditional framework for estimating subspace bases that maximize the preserved signal energy to additionally preserve the Cram\'er-Rao bound (CRB) of the biophysical parameters and, ultimately, improve accuracy and precision in the quantitative maps. To this end, we introduce an \textit{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. Compared to the traditional SVD approach, the proposed method better preserves the CRB across all biophysical parameters with negligible 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, permitting the use of smaller basis sizes in subspace reconstruction and offering significant computational savings.

physics.med-ph↗

arXiv2023

Unconstrained quantitative magnetization transfer imaging: disentangling T1 of the free and semi-solid spin pools

Since the inception of magnetization transfer (MT) imaging, it has been widely assumed that Henkelman's two spin pools have similar longitudinal relaxation times, which motivated many researchers to constrain them to each other. However, several recent publications reported a $T_1^s$ of the semi-solid spin pool that is much shorter than $T_1^f$ of the free pool. While these studies tailored experiments for robust proofs-of-concept, we here aim to quantify the disentangled relaxation processes on a voxel-by-voxel basis in a clinical imaging setting, i.e., with an effective resolution of 1.24mm 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 four people with relapsing-remitting multiple sclerosis (MS) and four healthy controls with this pulse sequence and estimated $T_1^f \approx 1.84$s and $T_1^s \approx 0.34$s in healthy white matter. Our results confirm the reports that $T_1^s \ll T_1^f$ and we argue that this finding identifies MT as an inherent driver of longitudinal relaxation in brain tissue. Moreover, we estimated a fractional size of the semi-solid spin pool of $m_0^s \approx 0.212$, 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.

physics.med-ph↗

arXiv2022

Rapid quantitative magnetization transfer imaging: utilizing the hybrid state and the generalized Bloch model

Purpose: To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model Theory and 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 8 parameters of the 2-pool model. We sparsely sample each time frame along this spin dynamics with a 3D 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 1.24mm from a 12.6-minute 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 Conclusion: 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.

physics.med-ph↗

arXiv2022

Minimization of Eddy Current Artifacts in Sequences with Periodic Dynamics

Purpose: To minimize eddy current artifacts in periodic pulse sequences with balanced gradient moments as, e.g., used for quantitative MRI. Theory and 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: 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.

physics.med-ph↗

arXiv2021

Generalized Bloch model: a theory for pulsed magnetization transfer

Purpose: The paper introduces a classical model to describe the dynamics of large spin-1/2 ensembles associated with nuclei bound in large molecule structures, commonly referred to as the semi-solid spin pool, and their magnetization transfer (MT) to spins of nuclei in Theory and Methods: Like quantum-mechanical descriptions of spin dynamics and like the original Bloch equations, but unlike existing MT models, the proposed model is based on the algebra of angular momentum in the sense that it explicitly models the rotations induced by radio-frequency (RF) pulses. It generalizes the original Bloch model to non-exponential decays, which are, e.g., observed for semi-solid spin pools. The combination of rotations with non-exponential decays is facilitated by describing the latter as Green's functions, comprised in an integro-differential equation. Results: Our model describes the data of an inversion-recovery magnetization-transfer experiment with varying durations of the inversion pulse substantially better than established models. We made this observation for all measured data, but in particular for pulse durations small than 300$μ$s. Furthermore, we provide a linear approximation of the generalized Bloch model that reduces the simulation time by approximately a factor 15,000, enabling simulation of the spin dynamics caused by a rectangular RF-pulse in roughly 2$μ$s. Conclusion: The proposed theory unifies the original Bloch model, Henkelman's steady-state theory for magnetization transfer, and the commonly assumed rotation induced by hard pulses (i.e., strong and infinitesimally short applications of RF fields) and describes experimental data better than previous models.

physics.med-ph↗

arXiv2021

Cramér-Rao bound-informed training of neural networks for quantitative MRI

Neural networks are increasingly used to estimate parameters in quantitative MRI, in particular in magnetic resonance fingerprinting. Their advantages over the gold standard non-linear least square fitting are their superior speed and their immunity to the non-convexity of many fitting problems. We find, however, that in heterogeneous parameter spaces, i.e. in spaces in which the variance of the estimated parameters varies considerably, good performance is hard to achieve and requires arduous tweaking of the loss function, hyper parameters, and the distribution of the training data in parameter space. Here, we address these issues with a theoretically well-founded loss function: the Cramér-Rao bound (CRB) provides a theoretical lower bound for the variance of an unbiased estimator and we propose to normalize the squared error with respective CRB. With this normalization, we balance the contributions of hard-to-estimate and not-so-hard-to-estimate parameters and areas in parameter space, and avoid a dominance of the former in the overall training loss. Further, the CRB-based loss function equals one for a maximally-efficient unbiased estimator, which we consider the ideal estimator. Hence, the proposed CRB-based loss function provides an absolute evaluation metric. We compare a network trained with the CRB-based loss with a network trained with the commonly used means squared error loss and demonstrate the advantages of the former in numerical, phantom, and in vivo experiments.

cs.LG↗