XSIM: A structural similarity index measure optimized for MRI QSM.

PURPOSE: The structural similarity index measure (SSIM) has become a popular quality metric to evaluate QSM in a way that is closer to human perception than RMS error (RMSE). However, SSIM may overpenalize errors in diamagnetic tissues and underpenalize them in paramagnetic tissues, resulting in biasing. In addition, extreme artifacts may compress the dynamic range, resulting in unrealistically high SSIM scores (hacking). To overcome biasing and hacking, we propose XSIM: SSIM implemented in the native QSM range, and with internal parameters optimized for QSM. METHODS: We used forward simulations from a COSMOS ground-truth brain susceptibility map included in the 2016 QSM Reconstruction Challenge to investigate the effect of QSM reconstruction errors on the SSIM, XSIM, and RMSE metrics. We also used these metrics to optimize QSM reconstructions of the in vivo challenge data set. We repeated this experiment with the QSM abdominal phantom. To validate the use of XSIM instead of SSIM for QSM quality assessment across a range of different reconstruction techniques/algorithms, we analyzed the reconstructions submitted to the 2019 QSM Reconstruction Challenge 2.0. RESULTS: Our experiments confirmed the biasing and hacking effects on the SSIM metric applied to QSM. The XSIM metric was robust to those effects, penalizing the presence of streaking artifacts and reconstruction errors. Using XSIM to optimize QSM reconstruction regularization weights returned less overregularization than SSIM and RMSE. CONCLUSION: XSIM is recommended over traditional SSIM to evaluate QSM reconstructions against a known ground truth, as it avoids biasing and hacking effects and provides a larger dynamic range of scores.

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.

Toward a realistic in silico abdominal phantom for QSM.

PURPOSE: QSM outside the brain has recently gained interest, particularly in the abdominal region. However, the absence of reliable ground truths makes difficult to assess reconstruction algorithms, whose quality is already compromised by additional signal contributions from fat, gases, and different kinds of motion. This work presents a realistic in silico phantom for the development, evaluation and comparison of abdominal QSM reconstruction algorithms. METHODS: Synthetic susceptibility and R 2 * $$ {R}_2^{\ast } $$ maps were generated by segmenting and postprocessing the abdominal 3T MRI data from a healthy volunteer. Susceptibility and R 2 * $$ {R}_2^{\ast } $$ values in different tissues/organs were assigned according to literature and experimental values and were also provided with realistic textures. The signal was simulated using as input the synthetic QSM and R 2 * $$ {R}_2^{\ast } $$ maps and fat contributions. Three susceptibility scenarios and two acquisition protocols were simulated to compare different reconstruction algorithms. RESULTS: QSM reconstructions show that the phantom allows to identify the main strengths and limitations of the acquisition approaches and reconstruction algorithms, such as in-phase acquisitions, water-fat separation methods, and QSM dipole inversion algorithms. CONCLUSION: The phantom showed its potential as a ground truth to evaluate and compare reconstruction pipelines and algorithms. The publicly available source code, designed in a modular framework, allows users to easily modify the susceptibility, R 2 * $$ {R}_2^{\ast } $$ and TEs, and thus creates different abdominal scenarios.

Hybrid data fidelity term approach for quantitative susceptibility mapping.

PURPOSE: Susceptibility maps are usually derived from local magnetic field estimations by minimizing a functional composed of a data consistency term and a regularization term. The data-consistency term measures the difference between the desired solution and the measured data using typically the L2-norm. It has been proposed to replace this L2-norm with the L1-norm, due to its robustness to outliers and reduction of streaking artifacts arising from highly noisy or strongly perturbed regions. However, in regions with high SNR, the L1-norm yields a suboptimal denoising performance. In this work, we present a hybrid data fidelity approach that uses the L1-norm and subsequently the L2-norm to exploit the strengths of both norms. METHODS: We developed a hybrid data fidelity term approach for QSM (HD-QSM) based on linear susceptibility inversion methods, with total variation regularization. Each functional is solved with ADMM. The HD-QSM approach is a two-stage method that first finds a fast solution of the L1-norm functional and then uses this solution to initialize the L2-norm functional. In both norms we included spatially variable weights that improve the quality of the reconstructions. RESULTS: The HD-QSM approach produced good quantitative reconstructions in terms of structural definition, noise reduction, and avoiding streaking artifacts comparable with nonlinear methods, but with higher computational efficiency. Reconstructions performed with this method achieved first place at the lowest RMS error category in stage 1 of the 2019 QSM Reconstruction Challenge. CONCLUSIONS: The proposed method allows robust and accurate QSM reconstructions, obtaining superior performance to state-of-the-art methods.

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.

Comparison of parameter optimization methods for quantitative susceptibility mapping.

PURPOSE: Quantitative Susceptibility Mapping (QSM) is usually performed by minimizing a functional with data fidelity and regularization terms. A weighting parameter controls the balance between these terms. There is a need for techniques to find the proper balance that avoids artifact propagation and loss of details. Finding the point of maximum curvature in the L-curve is a popular choice, although it is slow, often unreliable when using variational penalties, and has a tendency to yield overregularized results. METHODS: We propose 2 alternative approaches to control the balance between the data fidelity and regularization terms: 1) searching for an inflection point in the log-log domain of the L-curve, and 2) comparing frequency components of QSM reconstructions. We compare these methods against the conventional L-curve and U-curve approaches. RESULTS: Our methods achieve predicted parameters that are better correlated with RMS error, high-frequency error norm, and structural similarity metric-based parameter optimizations than those obtained with traditional methods. The inflection point yields less overregularization and lower errors than traditional alternatives. The frequency analysis yields more visually appealing results, although with larger RMS error. CONCLUSION: Our methods provide a robust parameter optimization framework for variational penalties in QSM reconstruction. The L-curve-based zero-curvature search produced almost optimal results for typical QSM acquisition settings. The frequency analysis method may use a 1.5 to 2.0 correction factor to apply it as a stand-alone method for a wider range of signal-to-noise-ratio settings. This approach may also benefit from fast search algorithms such as the binary search to speed up the process.

The 2016 QSM Challenge: Lessons learned and considerations for a future challenge design.

PURPOSE: The 4th International Workshop on MRI Phase Contrast and QSM (2016, Graz, Austria) hosted the first QSM Challenge. A single-orientation gradient recalled echo acquisition was provided, along with COSMOS and the χ33 STI component as ground truths. The submitted solutions differed more than expected depending on the error metric used for optimization and were generally over-regularized. This raised (unanswered) questions about the ground truths and the metrics utilized. METHODS: We investigated the influence of background field remnants by applying additional filters. We also estimated the anisotropic contributions from the STI tensor to the apparent susceptibility to amend the χ33 ground truth and to investigate the impact on the reconstructions. Lastly, we used forward simulations from the COSMOS reconstruction to investigate the impact noise had on the metric scores. RESULTS: Reconstructions compared against the amended STI ground truth returned lower errors. We show that the background field remnants had a minor impact in the errors. In the absence of inconsistencies, all metrics converged to the same regularization weights, whereas structural similarity index metric was more insensitive to such inconsistencies. CONCLUSION: There was a mismatch between the provided data and the ground truths due to the presence of unaccounted anisotropic susceptibility contributions and noise. Given the lack of reliable ground truths when using in vivo acquisitions, simulations are suggested for future QSM Challenges.

Weak-harmonic regularization for quantitative susceptibility mapping.

PURPOSE: Background-field removal is a crucial preprocessing step for quantitative susceptibility mapping (QSM). Remnants from this step often contaminate the estimated local field, which in turn leads to erroneous tissue-susceptibility reconstructions. The present work aimed to mitigate this undesirable behavior with the development of a new approach that simultaneously decouples background contributions and local susceptibility sources on QSM inversion. METHODS: Input phase data for QSM can be seen as a composite scalar field of local effects and residual background components. We developed a new weak-harmonic regularizer to constrain the latter and to separate the 2 components. The resulting optimization problem was solved with the alternating directions of multipliers method framework to achieve fast convergence. In addition, for convenience, a new alternating directions of multipliers method-based preconditioned nonlinear projection onto dipole fields solver was developed to enable initializations with wrapped-phase distributions. Weak-harmonic QSM, with and without nonlinear projection onto dipole fields preconditioning, was compared with the original (alternating directions of multipliers method-based) total variation QSM algorithm in phantom and in vivo experiments. RESULTS: Weak-harmonic QSM returned improved reconstructions regardless of the method used for background-field removal, although the proposed nonlinear projection onto dipole fields method often obtained better results. Streaking and shadowing artifacts were substantially suppressed, and residual background components were effectively removed. CONCLUSION: Weak-harmonic QSM with field preconditioning is a robust dipole inversion technique and has the potential to be extended as a single-step formulation for initialization with uncombined multi-echo data.

Fast nonlinear susceptibility inversion with variational regularization.

PURPOSE: Quantitative susceptibility mapping can be performed through the minimization of a function consisting of data fidelity and regularization terms. For data consistency, a Gaussian-phase noise distribution is often assumed, which breaks down when the signal-to-noise ratio is low. A previously proposed alternative is to use a nonlinear data fidelity term, which reduces streaking artifacts, mitigates noise amplification, and results in more accurate susceptibility estimates. We hereby present a novel algorithm that solves the nonlinear functional while achieving computation speeds comparable to those for a linear formulation. METHODS: We developed a nonlinear quantitative susceptibility mapping algorithm (fast nonlinear susceptibility inversion) based on the variable splitting and alternating direction method of multipliers, in which the problem is split into simpler subproblems with closed-form solutions and a decoupled nonlinear inversion hereby solved with a Newton-Raphson iterative procedure. Fast nonlinear susceptibility inversion performance was assessed using numerical phantom and in vivo experiments, and was compared against the nonlinear morphology-enabled dipole inversion method. RESULTS: Fast nonlinear susceptibility inversion achieves similar accuracy to nonlinear morphology-enabled dipole inversion but with significantly improved computational efficiency. CONCLUSION: The proposed method enables accurate reconstructions in a fraction of the time required by state-of-the-art quantitative susceptibility mapping methods. Magn Reson Med 80:814-821, 2018. © 2018 International Society for Magnetic Resonance in Medicine.

Calcium (Ca2+) waves data calibration and analysis using image processing techniques.

BACKGROUND: Calcium (Ca2+) propagates within tissues serving as an important information carrier. In particular, cilia beat frequency in oviduct cells is partially regulated by Ca2+ changes. Thus, measuring the calcium density and characterizing the traveling wave plays a key role in understanding biological phenomena. However, current methods to measure propagation velocities and other wave characteristics involve several manual or time-consuming procedures. This limits the amount of information that can be extracted, and the statistical quality of the analysis. RESULTS: Our work provides a framework based on image processing procedures that enables a fast, automatic and robust characterization of data from two-filter fluorescence Ca2+ experiments. We calculate the mean velocity of the wave-front, and use theoretical models to extract meaningful parameters like wave amplitude, decay rate and time of excitation. CONCLUSIONS: Measurements done by different operators showed a high degree of reproducibility. This framework is also extended to a single filter fluorescence experiments, allowing higher sampling rates, and thus an increased accuracy in velocity measurements.