Comparison of parameter optimization methods for quantitative susceptibility mapping

Learning-Assisted Fast Determination of Regularization Parameter in Constrained Image Reconstruction

OBJECTIVE

To leverage machine learning (ML) for fast selection of optimal regularization parameter in constrained image reconstruction.

METHODS

Constrained image reconstruction is often formulated as a regularization problem and selecting a good regularization parameter value is an essential step. We solved this problem using an ML-based approach by leveraging the finding that for a specific constrained reconstruction problem defined for a fixed class of image functions, the optimal regularization parameter value is weakly subject-dependent and the dependence can be captured using few experimental data. The proposed method has four key steps: a) solution of a given constrained reconstruction problem for a few (say, 3) pre-selected regularization parameter values, b) extraction of multiple approximated quality metrics from the initial reconstructions, c) predicting the true quality metrics values from the approximated values using pre-trained neural networks, and d) determination of the optimal regularization parameter by fusing the predicted quality metrics.

RESULTS

The effectiveness of the proposed method was demonstrated in two constrained reconstruction problems. Compared with L-curve-based method, the proposed method determined the regularization parameters much faster and produced substantially improved reconstructions. Our method also outperformed state-of-the-art learning-based methods when trained with limited experimental data.

CONCLUSION

This paper demonstrates the feasibility and improved reconstruction quality by using machine learning to determine the regularization parameter in constrained reconstruction.

SIGNIFICANCE

The proposed method substantially reduces the computational burden of the traditional methods (e.g., L-curve) or relaxes the requirement of large training data by modern learning-based methods, thus enhancing the practical utility of constrained reconstruction.

Recommended implementation of quantitative susceptibility mapping for clinical research in the brain: A consensus of the ISMRM electro-magnetic tissue properties study group

This article provides recommendations for implementing QSM for clinical brain research. It is a consensus of the International Society of Magnetic Resonance in Medicine, Electro-Magnetic Tissue Properties Study Group. While QSM technical development continues to advance rapidly, the current QSM methods have been demonstrated to be repeatable and reproducible for generating quantitative tissue magnetic susceptibility maps in the brain. However, the many QSM approaches available have generated a need in the neuroimaging community for guidelines on implementation. This article outlines considerations and implementation recommendations for QSM data acquisition, processing, analysis, and publication. We recommend that data be acquired using a monopolar 3D multi-echo gradient echo (GRE) sequence and that phase images be saved and exported in Digital Imaging and Communications in Medicine (DICOM) format and unwrapped using an exact unwrapping approach. Multi-echo images should be combined before background field removal, and a brain mask created using a brain extraction tool with the incorporation of phase-quality-based masking. Background fields within the brain mask should be removed using a technique based on SHARP or PDF, and the optimization approach to dipole inversion should be employed with a sparsity-based regularization. Susceptibility values should be measured relative to a specified reference, including the common reference region of the whole brain as a region of interest in the analysis. The minimum acquisition and processing details required when reporting QSM results are also provided. These recommendations should facilitate clinical QSM research and promote harmonized data acquisition, analysis, and reporting.

Characterization of quantitative susceptibility mapping in the left ventricular myocardium

BACKGROUND

Myocardial quantitative susceptibility mapping (QSM) may offer better specificity to iron than conventional T2* imaging in the assessment of cardiac diseases, including intra-myocardial hemorrhage. However, the precision and repeatability of cardiac QSM have not yet been characterized. The aim of this study is to characterize these key metrics in a healthy volunteer cohort and show the feasibility of the method in patients.

METHODS

Free breathing respiratory-navigated multi-echo 3D gradient echo images were acquired, from which QSM maps were reconstructed using the Morphology Enhanced Dipole Inversion toolbox. This technique was first evaluated in a susceptibility phantom containing tubes with known concentrations of gadolinium. In vivo characterization of myocardial QSM was then performed in a cohort of 10 healthy volunteers where each subject was scanned twice. Mean segment susceptibility, precision (standard deviation of voxel magnetic susceptibilities within one segment), and repeatability (absolute difference in segment mean susceptibility between repeats) of QSM were calculated for each American Heart Association (AHA) myocardial segment. Finally, the feasibility of the method was shown in 10 patients, including four with hemorrhagic infarcts.

RESULTS

The phantom experiment showed a strong linear relationship between measured and predicted susceptibility shifts (R2 > 0.99). For the healthy volunteer cohort, AHA segment analysis showed the mean segment susceptibility was 0.00 ± 0.02 ppm, the mean precision was 0.05 ± 0.04 ppm, and the mean repeatability was 0.02 ± 0.02 ppm. Cardiac QSM was successfully performed in all patients. Focal iron deposits were successfully visualized in the patients with hemorrhagic myocardial infarctions.

CONCLUSION

The precision and repeatability of cardiac QSM were successfully characterized in phantom and in vivo experiments. The feasibility of the technique was also successfully demonstrated in patients. While challenges still remain, further clinical evaluation of the technique is now warranted.

TRIAL REGISTRATION

This work does not report on a health care intervention.

Quantitative susceptibility mapping identifies hippocampal and other subcortical grey matter tissue composition changes in temporal lobe epilepsy

Temporal lobe epilepsy (TLE) is associated with widespread brain alterations. Using quantitative susceptibility mapping (QSM) alongside transverse relaxation rate (R 2 * ), we investigated regional brain susceptibility changes in 36 patients with left-sided (LTLE) or right-sided TLE (RTLE) secondary to hippocampal sclerosis, and 27 healthy controls (HC). We compared three susceptibility calculation methods to ensure image quality. Correlations of susceptibility andR 2 * with age of epilepsy onset, frequency of focal-to-bilateral tonic-clonic seizures (FBTCS), and neuropsychological test scores were examined. Weak-harmonic QSM (WH-QSM) successfully reduced noise and removed residual background field artefacts. Significant susceptibility increases were identified in the left putamen in the RTLE group compared to the LTLE group, the right putamen and right thalamus in the RTLE group compared to HC, and a significant susceptibility decrease in the left hippocampus in LTLE versus HC. LTLE patients who underwent epilepsy surgery showed significantly lower left-versus-right hippocampal susceptibility. SignificantR 2 * changes were found between TLE and HC groups in the amygdala, putamen, thalamus, and in the hippocampus. Specifically, decreased R2 * was found in the left and right hippocampus in LTLE and RTLE, respectively, compared to HC. Susceptibility andR 2 * were significantly correlated with cognitive test scores in the hippocampus, globus pallidus, and thalamus. FBTCS frequency correlated positively with ipsilateral thalamic and contralateral putamen susceptibility and withR 2 * in bilateral globi pallidi. Age of onset was correlated with susceptibility in the hippocampus and putamen, and withR 2 * in the caudate. Susceptibility andR 2 * changes observed in TLE groups suggest selective loss of low-myelinated neurons alongside iron redistribution in the hippocampi, predominantly ipsilaterally, indicating QSM's sensitivity to local pathology. Increased susceptibility andR 2 * in the thalamus and putamen suggest increased iron content and reflect disease severity.

Robust quantitative susceptibility mapping via approximate message passing with parameter estimation

PURPOSE

For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with built-in parameter estimation, and incorporate the nonlinear formulation of the dipole inversion to achieve a robust recovery of the susceptibility maps.

THEORY

From a Bayesian perspective, the image wavelet coefficients are approximately sparse and modeled by the Laplace distribution. The measurement noise is modeled by a Gaussian-mixture distribution with two components, where the second component is used to model the noise outliers. Through probabilistic inference, the susceptibility map and distribution parameters can be jointly recovered using approximate message passing (AMP).

METHODS

We compare our proposed AMP with built-in parameter estimation (AMP-PE) to the state-of-the-art L1-QSM, FANSI, and MEDI approaches on the simulated and in vivo datasets, and perform experiments to explore the optimal settings of AMP-PE. Reproducible code is available at: https://github.com/EmoryCN2L/QSM_AMP_PE.

RESULTS

On the simulated Sim2Snr1 dataset, AMP-PE achieved the lowest NRMSE, deviation from calcification moment and the highest SSIM, while MEDI achieved the lowest high-frequency error norm. On the in vivo datasets, AMP-PE is robust and successfully recovers the susceptibility maps using the estimated parameters, whereas L1-QSM, FANSI and MEDI typically require additional visual fine-tuning to select or double-check working parameters.

CONCLUSION

AMP-PE provides automatic and adaptive parameter estimation for QSM and avoids the subjectivity from the visual fine-tuning step, making it an excellent choice for the clinical setting.

Quantitative Susceptibility Mapping MRI in Deep-Brain Nuclei in First-Episode Psychosis

BACKGROUND

Psychosis is related to neurochemical changes in deep-brain nuclei, particularly suggesting dopamine dysfunctions. We used an magnetic resonance imaging-based technique called quantitative susceptibility mapping (QSM) to study these regions in psychosis. QSM quantifies magnetic susceptibility in the brain, which is associated with iron concentrations. Since iron is a cofactor in dopamine pathways and co-localizes with inhibitory neurons, differences in QSM could reflect changes in these processes.

METHODS

We scanned 83 patients with first-episode psychosis and 64 healthy subjects. We reassessed 22 patients and 21 control subjects after 3 months. Mean susceptibility was measured in 6 deep-brain nuclei. Using linear mixed models, we analyzed the effect of case-control differences, region, age, gender, volume, framewise displacement (FD), treatment duration, dose, laterality, session, and psychotic symptoms on QSM.

RESULTS

Patients showed a significant susceptibility reduction in the putamen and globus pallidus externa (GPe). Patients also showed a significant R2* reduction in GPe. Age, gender, FD, session, group, and region are significant predictor variables for QSM. Dose, treatment duration, and volume were not predictor variables of QSM.

CONCLUSIONS

Reduction in QSM and R2* suggests a decreased iron concentration in the GPe of patients. Susceptibility reduction in putamen cannot be associated with iron changes. Since changes observed in putamen and GPe were not associated with symptoms, dose, and treatment duration, we hypothesize that susceptibility may be a trait marker rather than a state marker, but this must be verified with long-term studies.

Comparison of quantitative susceptibility mapping methods for iron-sensitive susceptibility imaging at 7T: An evaluation in healthy subjects and patients with Huntington's disease

Quantitative susceptibility mapping (QSM) is a promising tool for investigating iron dysregulation in neurodegenerative diseases, including Huntington's disease (HD). Many diverse methods have been proposed to generate accurate and robust QSM images. In this study, we evaluated the performance of different dipole inversion algorithms for iron-sensitive susceptibility imaging at 7T on healthy subjects of a large age range and patients with HD. We compared an iterative least-squares-based method (iLSQR), iterative methods that use regularization, single-step approaches, and deep learning-based techniques. Their performance was evaluated by comparing: (1) deviations from a multiple-orientation QSM reference; (2) visual appearance of QSM maps and the presence of artifacts; (3) susceptibility in subcortical brain regions with age; (4) regional brain susceptibility with published postmortem brain iron quantification; and (5) susceptibility in HD-affected basal ganglia regions between HD subjects and healthy controls. We found that single-step QSM methods with either total variation or total generalized variation constraints (SSTV/SSTGV) and the single-step deep learning method iQSM generally provided the best performance in terms of correlation with iron deposition and were better at differentiating between healthy controls and premanifest HD individuals, while deep learning QSM methods trained with multiple-orientation susceptibility data created QSM maps that were most similar to the multiple orientation reference and with the best visual scores.

Hybrid data fidelity term approach for quantitative susceptibility mapping

Purpose

Methods

Results

Conclusions

Streaking artifact suppression of quantitative susceptibility mapping reconstructions via L1-norm data fidelity optimization (L1-QSM)

PURPOSE

The presence of dipole-inconsistent data due to substantial noise or artifacts causes streaking artifacts in quantitative susceptibility mapping (QSM) reconstructions. Often used Bayesian approaches rely on regularizers, which in turn yield reduced sharpness. To overcome this problem, we present a novel L1-norm data fidelity approach that is robust with respect to outliers, and therefore prevents streaking artifacts.

METHODS

QSM functionals are solved with linear and nonlinear L1-norm data fidelity terms using functional augmentation, and are compared with equivalent L2-norm methods. Algorithms were tested on synthetic data, with phase inconsistencies added to mimic lesions, QSM Challenge 2.0 data, and in vivo brain images with hemorrhages.

RESULTS

The nonlinear L1-norm-based approach achieved the best overall error metric scores and better streaking artifact suppression. Notably, L1-norm methods could reconstruct QSM images without using a brain mask, with similar regularization weights for different data fidelity weighting or masking setups.

CONCLUSION

The proposed L1-approach provides a robust method to prevent streaking artifacts generated by dipole-inconsistent data, renders brain mask calculation unessential, and opens novel challenging clinical applications such asassessing brain hemorrhages and cortical layers.

Physics-constrained intraventricular vector flow mapping by color Doppler

Color Doppler by transthoracic echocardiography creates two-dimensional fan-shaped maps of blood velocities in the cardiac cavities. It is a one-component velocimetric technique since it only returns the velocity components parallel to the ultrasound beams. Intraventricular vector flow mapping (iVFM) is a method to recover the blood velocity vectors from the Doppler scalar fields in an echocardiographic three-chamber view. We improved ouriVFM numerical scheme by imposing physical constraints. TheiVFM consisted in minimizing regularized Doppler residuals subject to the condition that two fluid-dynamics constraints were satisfied, namely planar mass conservation, and free-slip boundary conditions. The optimization problem was solved by using the Lagrange multiplier method. A finite-difference discretization of the optimization problem, written in the polar coordinate system centered on the cardiac ultrasound probe, led to a sparse linear system. The single regularization parameter was determined automatically for non-supervision considerations. The physics-constrained method was validated using realistic intracardiac flow data from a patient-specific computational fluid dynamics (CFD) model. The numerical evaluations showed that theiVFM-derived velocity vectors were in very good agreement with the CFD-based original velocities, with relative errors ranged between 0.3% and 12%. We calculated two macroscopic measures of flow in the cardiac region of interest, the mean vorticity and mean stream function, and observed an excellent concordance between physics-constrainediVFM and CFD. The capability of physics-constrainediVFM was finally tested within vivocolor Doppler data acquired in patients routinely examined in the echocardiographic laboratory. The vortex that forms during the rapid filling was deciphered. The physics-constrainediVFM algorithm is ready for pilot clinical studies and is expected to have a significant clinical impact on the assessment of diastolic function.

Age-related magnetic susceptibility changes in deep grey matter and cerebral cortex of normal young and middle-aged adults depicted by whole brain analysis

Background

Iron accumulates in brain tissue in healthy subjects during aging. Our goal was to conduct a detailed analysis of iron deposition patterns in the cerebral deep grey matter and cortex using region-based and whole-brain analyses of brain magnetic susceptibility.

Methods

Brain MRI was performed in 95 healthy individuals aged between 21 and 58 years on a 3T scanner. MRI protocol included T1-weighted (T1W) magnetization-prepared rapid acquisition with gradient echo images and 3D flow-compensated multi-echo gradient-echo images for quantitative susceptibility mapping (QSM). In the region-based analysis, QSM and T1W images entered an automated multi-atlas segmentation pipeline and regional mean bulk susceptibility values were calculated. The whole-brain analysis included a non-linear transformation of QSM images to the standard MNI template. For the whole-brain analysis voxel-wise maps of linear regression slopes β and P values were calculated. Regional masks of cortical voxels with a significant association between susceptibility and age were created and further analyzed.

Results

In cortical regions, the highest increase of susceptibility values with age was found in areas involved in motor functions (precentral and postcentral areas, premotor cortex), in cognitive processing (prefrontal cortex, superior temporal gyrus, insula, precuneus), and visual processing (occipital gyri, cuneus, posterior cingulum, fusiform, calcarine and lingual gyrus). Thalamic susceptibility increased until the fourth decade and decreased thereafter with the exception of the pulvinar where susceptibility increase was observed throughout the adult lifespan. Deep grey matter structures with the highest increase of susceptibility values with age included the red nucleus, putamen, substantia nigra, dentate nucleus, external globus pallidus, caudate nucleus, and the subthalamic nucleus in decreasing order.

Conclusions

Accumulation of iron in basal ganglia follows a linear pattern whereas in the thalamus, pulvinar, precentral cortex, and precuneus, it follows a quadratic or exponential pattern. Age-related changes of iron content are different in the pulvinar and the rest of the thalamus as well as in internal and external globus pallidus. In the cortex, areas involved in motor and cognitive functions and visual processing show the highest iron increase with aging. We suggest that the departure from normal patterns of regional brain iron trajectories during aging may be helpful in the detection of subtle neurodegenerative and neuroinflammatory processes.

On the separation of susceptibility sources in quantitative susceptibility mapping: Theory and phantom validation with an in vivo application to multiple sclerosis lesions of different age

PURPOSE

In biological tissue, phase contrast is determined by multiple substances such as iron, myelin or calcifications. Often, these substances occur co-located within the same measurement volume. However, quantitative susceptibility mapping can solely measure the average susceptibility per voxel. To provide new insight in disease progression and mechanisms in neurological diseases, where multiple processes such as demyelination and iron accumulation occur simultaneously in the same location, a separation of susceptibility sources is desirable to disentangle the underlying susceptibility proportions.

METHODS

The basic concept of separating the susceptibility effects from sources with different sign within one voxel is to include information on relaxation rate ΔR₂^∗ in the quantitative susceptibility mapping reconstruction pipeline. The presented reconstruction algorithm is implemented as a constrained minimization problem and solved using conjugate gradients. The algorithm is evaluated using a software phantom and validated in MRI measurements with a phantom containing mixtures of microscopic positive and negative susceptibility sources. Data from three multiple sclerosis patients are used to show in vivo feasibility.

RESULTS

In numerical simulations, the feasibility of disentangling susceptibility sources within the same voxel was confirmed provided the critera of the static dephasing regime were fulfilled. In phantom experiments, the magnitude decay kernel, which is an essential reconstruction parameter of the algorithm, was determined to be D_m=194.5T^-1s^-1ppm^-1, and susceptibility sources could be separated in MRI measurement data.

CONCLUSIONS

In conclusion, in this study a detailed description of the implementation of an algorithm for the separation of positive and negative susceptibility sources within the same volume element as well as its limitations is presented and validated quantitatively in both simulation and phantom experiments for the first time. An application to multiple sclerosis lesions shows promising results for in vivo usability.