Learning-based Single-step Quantitative Susceptibility Mapping Reconstruction Without Brain Extraction

Quantitative susceptibility mapping (QSM) estimates the underlying tissue magnetic susceptibility from MRI gradient-echo phase signal and typically requires several processing steps. These steps involve phase unwrapping, brain volume extraction, background phase removal and solving an ill-posed inverse problem. The resulting susceptibility map is known to suffer from inaccuracy near the edges of the brain tissues, in part due to imperfect brain extraction, edge erosion of the brain tissue and the lack of phase measurement outside the brain. This inaccuracy has thus hindered the application of QSM for measuring the susceptibility of tissues near the brain edges, e.g., quantifying cortical layers and generating superficial venography. To address these challenges, we propose a learning-based QSM reconstruction method that directly estimates the magnetic susceptibility from total phase images without the need for brain extraction and background phase removal, referred to as autoQSM. The neural network has a modified U-net structure and is trained using QSM maps computed by a two-step QSM method. 209 healthy subjects with ages ranging from 11 to 82 years were employed for patch-wise network training. The network was validated on data dissimilar to the training data, e.g. in vivo mouse brain data and brains with lesions, which suggests that the network has generalized and learned the underlying mathematical relationship between magnetic field perturbation and magnetic susceptibility. AutoQSM was able to recover magnetic susceptibility of anatomical structures near the edges of the brain including the veins covering the cortical surface, spinal cord and nerve tracts near the mouse brain boundaries. The advantages of high-quality maps, no need for brain volume extraction and high reconstruction speed demonstrate its potential for future applications.Comment: 26 page

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

Robust Quantitative Susceptibility Mapping via Approximate Message Passing

Purpose: It is challenging to recover magnetic susceptibility in the presence of phase errors, which may be caused by noise or strong local-susceptibility shifts in cases of brain hemorrhage and calcification. We propose a Bayesian formulation for quantitative susceptibility mapping (QSM) where a customized Gaussian-mixture distribution is used to model the long-tailed noise distribution. Theory: Complex exponential functions of the phase are used as nonlinear measurements. Wavelet coefficients of the susceptibility map are modeled by the Laplace distribution. Measurement noise is modeled by a two-component Gaussian-mixture distribution, where the second component is reserved to model the noise outliers. The susceptibility map and distribution parameters are jointly recovered using approximate message passing (AMP). Methods: The proposed AMP with built-in parameter estimation (AMP-PE) is compared with the state-of-the-art nonlinear L1-QSM and MEDI approaches that adopt the L1-norm and L2-norm data-fidelity terms respectively. They are tested on the simulated and in vivo datasets. Results: On the simulated Sim2Snr1 dataset, AMP-PE achieved the lowest NRMSE and SSIM, MEDI achieved the lowest HFEN. On the in vivo datasets, AMP-PE is more robust and better at preserving structural details and removing streaking artifacts in the hemorrhage cases than L1-QSM and MEDI. Conclusion: By leveraging a customized Gaussian-mixture noise prior, AMP-PE achieves better performance in challenging cases of brain hemorrhage and calcification. It is equipped with built-in parameter estimation, which avoids subjective bias from the usual visual-tuning step of in vivo reconstruction.Comment: Keywords: Approximate message passing, Compressive sensing, Parameter estimation, QS

Investigating the effect of flow compensation and quantitative susceptibility mapping method on the accuracy of venous susceptibility measurement

Quantitative susceptibility mapping (QSM) is a promising non-invasive method for obtaining information relating to oxygen metabolism. However, the optimal acquisition sequence and QSM reconstruction method for reliable venous susceptibility measurements are unknown. Full flow compensation is generally recommended to correct for the influence of venous blood flow, although the effect of flow compensation on the accuracy of venous susceptibility values has not been systematically evaluated. In this study, we investigated the effect of different acquisition sequences, including different flow compensation schemes, and different QSM reconstruction methods on venous susceptibilities. Ten healthy subjects were scanned with five or six distinct QSM sequence designs using monopolar readout gradients and different flow compensation schemes. All data sets were processed using six different QSM pipelines and venous blood susceptibility was evaluated in whole-brain segmentations of the venous vasculature and single veins. The quality of vein segmentations and the accuracy of venous susceptibility values were analyzed and compared between all combinations of sequences and reconstruction methods. The influence of the QSM reconstruction method on average venous susceptibility values was found to be 2.7–11.6 times greater than the influence of the acquisition sequence, including flow compensation. The majority of the investigated QSM reconstruction methods tended to underestimate venous susceptibility values in the vein segmentations that were obtained. In summary, we found that multi-echo gradient-echo acquisition sequences without full flow compensation yielded venous susceptibility values comparable to sequences with full flow compensation. However, the QSM reconstruction method had a great influence on susceptibility values and thus needs to be selected carefully for accurate venous QSM

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI.

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains