arXiv subjects

Jakob Assländer

Publications and source records attributed to Jakob Assländer.

15 recordsLinked to original sources

arXiv2025

Sensitivity of literature T1 mapping methods to the underlying magnetization transfer parameters

Purpose: Magnetization transfer (MT) has been identified as the principal source of $T_1$ variability in the MRI literature. This study assesses the sensitivity of established $T_1$ mapping techniques to variations in the underlying MT parameters. Methods: For each $T_1$-mapping method, the observed $T_1$ was simulated as a function of the underlying MT parameters $p_i^\text{MT}$, corresponding to different brain regions of interest (ROIs) at 3T. As measures of sensitivity, the derivatives $\partial T_1^\text{observed} / \partial p_i^\text{MT}$ were computed and analyzed with a linear mixed-effects model as a function of $p_i^\text{MT}$, ROI, pulse sequence type (e.g., inversion recovery, variable flip angle), and the individual sequences. Results: The analyzed $T_1$-mapping sequences have a considerable sensitivity to changes in the semi-solid spin pool size $m_0^\text{s}$, $T_1^\text{f}$ of the free, $T_1^\text{s}$ of the semi-solid spin pool, and the (inverse) exchange rate $T_\text{x}$. All derivatives vary considerably with the underlying MT parameters and between pulse sequences. In general, the derivatives cannot be determined by the sequence type, but rather depend on the implementation details of the sequence. One notable exception is that variable-flip-angle methods are, in general, more sensitive to the exchange rate than inversion-recovery methods. Conclusion: Variations in the observed $T_1$ can be caused by several underlying MT parameters, and the sensitivity to each parameter depends on both the underlying MT parameters and the sequence.

physics.med-ph↗

arXiv2025

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↗

arXiv2025

Magnetization transfer explains most of the $T_1$ variability in the MRI literature

Purpose: To identify the predominant source of the $T_1$ variability described in the literature, which ranges from 0.6-1.1 s for brain white matter at 3 T. Methods: 25 $T_1$-mapping methods from the literature were simulated with a mono-exponential and various magnetization-transfer (MT) models, each followed by mono-exponential fitting. A single set of model parameters was assumed for the simulation of all methods, and these parameters were estimated by fitting the simulation-based to the corresponding literature $T_1$ values of white matter at 3 T. We acquired in vivo data with a quantitative magnetization transfer and three $T_1$-mapping techniques. The former was used to synthesize MR images that correspond to the three $T_1$-mapping methods. A mono-exponential model was fitted to the experimental and corresponding synthesized MR images. Results: Mono-exponential simulations suggest good inter-method reproducibility and fail to explain the highly variable $T_1$ estimates in the literature. In contrast, MT simulations suggest that a mono-exponential fit results in a variable $T_1$ and explain up to 62% of the literature's variability. In our own in vivo experiments, MT explains 70% of the observed variability. Conclusion: The results suggest that a mono-exponential model does not adequately describe longitudinal relaxation in biological tissue. Therefore, $T_1$ in biological tissue should be considered only a semi-quantitative metric that is inherently contingent upon the imaging methodology; and comparisons between different $T_1$-mapping methods and the use of simplistic spin systems - such as doped-water phantoms - for validation should be viewed with caution.

physics.med-ph↗

arXiv2024

Rational Approximation of Golden Angles: Accelerated Reconstructions for Radial MRI

Purpose: 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: RAGA sampling provides the advantages of golden ratio sampling while simplifying data processing, rendering it a valuable tool for dynamic and quantitative MRI.

physics.med-ph↗

arXiv2024

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 Cramér-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 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: 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↗

arXiv2024

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↗

arXiv2023

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↗

arXiv2023

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↗

arXiv2023

Cramér-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 Cramér-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↗

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↗

arXiv2018

Optimized Quantification of Spin Relaxation Times in the Hybrid State

Purpose: The analysis of optimized spin ensemble trajectories for relaxometry in the hybrid state. Methods: First, we constructed visual representations to elucidate the differential equation that governs spin dynamics in hybrid state. Subsequently, numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramér-Rao bound for $T_1$-encoding, $T_2$-encoding, and their weighted sum, respectively, followed by a comparison of the Cramér-Rao bounds obtained with our optimized spin-trajectories, as well as Look-Locker and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. Results: After a nonrecurring inversion segment on the southern hemisphere of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern half of the sphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance $T_1$- and $T_2$-encoding still result in near optimal signal-to-noise efficiency. Thus, the second parameter can be encoded at virtually no extra cost. Conclusion: We provide insights regarding the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We find that joint acquisitions of $T_1$ and $T_2$ in the hybrid state are substantially more efficient than sequential encoding techniques.

physics.med-ph↗

arXiv2018

Hybrid-State Free Precession in Nuclear Magnetic Resonance

The dynamics of large spin-1/2 ensembles in the presence of a varying magnetic field are commonly described by the Bloch equation. Most magnetic field variations result in unintuitive spin dynamics, which are sensitive to small deviations in the driving field. Although simplistic field variations can produce robust dynamics, the captured information content is impoverished. Here, we identify adiabaticity conditions that span a rich experiment design space with tractable dynamics. These adiabaticity conditions trap the spin dynamics in a one-dimensional subspace. Namely, the dynamics is captured by the absolute value of the magnetization, which is in a transient state, while its direction adiabatically follows the steady state. We define the hybrid state as the co-existence of these two states and identify the polar angle as the effective driving force of the spin dynamics. As an example, we optimize this drive for robust and efficient quantification of spin relaxation times and utilize it for magnetic resonance imaging of the human brain.

physics.med-ph↗

arXiv2018

Multicompartment Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is a technique for quantitative estimation of spin-relaxation parameters from magnetic-resonance data. Most current MRF approaches assume that only one tissue is present in each voxel, which neglects the tissue's microstructure, and may lead to artifacts in the recovered parameter maps at boundaries between tissues. In this work, we propose a multicompartment MRF model that accounts for the presence of multiple tissues per voxel. The model is fit to the data by iteratively solving a sparse linear inverse problem at each voxel, in order to express the magnetization signal as a linear combination of a few fingerprints in the precomputed dictionary. Thresholding-based methods commonly used for sparse recovery and compressed sensing do not perform well in this setting due to the high local coherence of the dictionary. Instead, we solve this challenging sparse-recovery problem by applying reweighted-l1-norm regularization, implemented using an efficient interior-point method. The proposed approach is validated with simulated data at different noise levels and undersampling factors, as well as with a controlled phantom imaging experiment on a clinical magnetic-resonance system.

physics.med-ph↗

arXiv2016

Low Rank Alternating Direction Method of Multipliers Reconstruction for MR Fingerprinting

Purpose The proposed reconstruction framework addresses the reconstruction accuracy, noise propagation and computation time for Magnetic Resonance Fingerprinting (MRF). Methods Based on a singular value decomposition (SVD) of the signal evolution, MRF is formulated as a low rank inverse problem in which one image is reconstructed for each singular value under consideration. This low rank approximation of the signal evolution reduces the computational burden by reducing the number of Fourier transformations. Also, the low rank approximation improves the conditioning of the problem, which is further improved by extending the low rank inverse problem to an augmented Lagrangian that is solved by the alternating direction method of multipliers (ADMM). The root mean square error and the noise propagation are analyzed in simulations. For verification, in vivo examples are provided. Results The proposed low rank ADMM approach shows a reduced root mean square error compared to the original fingerprinting reconstruction, to a low rank approximation alone and to an ADMM approach without a low rank approximation. Incorporating sensitivity encoding allows for further artifact reduction. Conclusion The proposed reconstruction provides robust convergence, reduced computational burden and improved image quality compared to other MRF reconstruction approaches evaluated in this study.

physics.med-ph↗