MoDL-QSM: Model-based deep learning for quantitative susceptibility mapping

Quantitative susceptibility mapping via deep neural networks with iterative reverse concatenations and recurrent modules

BACKGROUND

Quantitative susceptibility mapping (QSM) is a post-processing magnetic resonance imaging (MRI) technique that extracts the distribution of tissue susceptibilities and holds significant promise in the study of neurological diseases. However, the ill-conditioned nature of dipole inversion often results in noise and artifacts during QSM reconstruction from the tissue field. Deep learning methods have shown great potential in addressing these issues; however, most existing approaches rely on basic U-net structures, leading to limited performances and reconstruction artifacts sometimes.

PURPOSE

This study aims to develop a novel deep learning-based method, IR2QSM, for improving QSM reconstruction accuracy while mitigating noise and artifacts by leveraging a unique network architecture that enhances latent feature utilization.

METHODS

IR2QSM, an advanced U-net architecture featuring four iterations of reverse concatenations and middle recurrent modules, was proposed to optimize feature fusion and improve QSM accuracy, and comparative experiments based on both simulated and in vivo datasets were carried out to compare IR2QSM with two traditional iterative methods (iLSQR, MEDI) and four recently proposed deep learning methods (U-net, xQSM, LPCNN, and MoDL-QSM).

RESULTS

In this work, IR2QSM outperformed all other methods in reducing artifacts and noise in QSM images. It achieved on average the lowest XSIM (84.81%) in simulations, showing improvements of 12.80%, 12.68%, 18.66%, 10.49%, 25.57%, and 19.78% over iLSQR, MEDI, U-net, xQSM, LPCNN, and MoDL-QSM, respectively, and yielded results with the least artifacts on the in vivo data and present the most visually appealing results. In the meantime, it successfully alleviated the over-smoothing and susceptibility underestimation in LPCNN results.

CONCLUSION

Overall, the proposed IR2QSM showed superior QSM results compared to iterative and deep learning-based methods, offering a more accurate QSM solution for clinical applications.

HDNLS: Hybrid Deep-Learning and Non-Linear Least Squares-Based Method for Fast Multi-Component T1ρ Mapping in the Knee Joint

Non-linear least squares (NLS) methods are commonly used for quantitative magnetic resonance imaging (MRI), especially for multi-exponential T1ρ mapping, which provides precise parameter estimation for different relaxation models in tissues, such as mono-exponential (ME), bi-exponential (BE), and stretched-exponential (SE) models. However, NLS may suffer from problems like sensitivity to initial guesses, slow convergence speed, and high computational cost. While deep learning (DL)-based T1ρ fitting methods offer faster alternatives, they often face challenges such as noise sensitivity and reliance on NLS-generated reference data for training. To address these limitations of both approaches, we propose the HDNLS, a hybrid model for fast multi-component parameter mapping, particularly targeted for T1ρ mapping in the knee joint. HDNLS combines voxel-wise DL, trained with synthetic data, with a few iterations of NLS to accelerate the fitting process, thus eliminating the need for reference MRI data for training. Due to the inverse-problem nature of the parameter mapping, certain parameters in a specific model may be more sensitive to noise, such as the short component in the BE model. To address this, the number of NLS iterations in HDNLS can act as a regularization, stabilizing the estimation to obtain meaningful solutions. Thus, in this work, we conducted a comprehensive analysis of the impact of NLS iterations on HDNLS performance and proposed four variants that balance estimation accuracy and computational speed. These variants are Ultrafast-NLS, Superfast-HDNLS, HDNLS, and Relaxed-HDNLS. These methods allow users to select a suitable configuration based on their specific speed and performance requirements. Among these, HDNLS emerges as the optimal trade-off between performance and fitting time. Extensive experiments on synthetic data demonstrate that HDNLS achieves comparable performance to NLS and regularized-NLS (RNLS) with a minimum of a 13-fold improvement in speed. HDNLS is just a little slower than DL-based methods; however, it significantly improves estimation quality, offering a solution for T1ρ fitting that is fast and reliable.

Chronic active lesions in multiple sclerosis: classification, terminology, and clinical significance

In multiple sclerosis (MS), increasing disability is considered to occur due to persistent, chronic inflammation trapped within the central nervous system (CNS). This condition, known as smoldering neuroinflammation, is present across the clinical spectrum of MS and is currently understood to be relatively resistant to treatment with existing disease-modifying therapies. Chronic active white matter lesions represent a key component of smoldering neuroinflammation. Initially characterized in autopsy specimens, multiple approaches to visualize chronic active lesions (CALs) in vivo using advanced neuroimaging techniques and postprocessing methods are rapidly emerging. Among these in vivo imaging correlates of CALs, paramagnetic rim lesions (PRLs) are defined by the presence of a perilesional rim formed by iron-laden microglia and macrophages, whereas slowly expanding lesions are identified based on linear, concentric lesion expansion over time. In recent years, several longitudinal studies have linked the occurrence of in vivo detected CALs to a more aggressive disease course. PRLs are highly specific to MS and therefore have recently been incorporated into the MS diagnostic criteria. They also have prognostic potential as biomarkers to identify patients at risk of early and severe disease progression. These developments could significantly affect MS care and the evaluation of new treatments. This review describes the latest knowledge on CAL biology and imaging and the relevance of CALs to the natural history of MS. In addition, we outline considerations for current and future in vivo biomarkers of CALs, emphasizing the need for validation, standardization, and automation in their assessment.

Enhanced Reader Confidence and Differentiation of Calcification from Cerebral Microbleed Diagnosis Using QSM Relative to SWI

PURPOSE

Accurate detection of cerebral microbleeds (CMBs) is important for detection of multiple conditions. However, CMBs can be challenging to identify on MR images, especially for distinguishing CMBs from the mimic of calcification. We performed a comparative reader study to assess the diagnostic performance of two primary MR sequences for differentiating CMBs from calcification.

METHODS

Under IRB approved exempt retrospective protocol, 49 adult patients with identifiable intracranial hemorrhage who underwent multi-echo 3D Gradient Recall Echo (GRE) using 3T MRI were non-sequentially recruited under a retrospective IRB approved protocol. Multi-echo complex total field inversion quantitative susceptibility mapping (QSM) and susceptibility weighted imaging/phase (SWI/P) images were generated for all patients. 53 lesion ROIs were identified and classified on provided images by an expert panel of three neuroradiologists as either: CMB, Blood, Calcification, or Other. Three additional neuroradiologists subsequently reviewed the same SWI/P and QSM images in independent sessions and designated lesions as either blood and/or calcification using a 5-point Likert scale. Statistical analyses, on lesion classification and reader diagnostic accuracy, reader confidence-level, reader agreement-level, and the predictability of mean susceptibility values between SWI/P and QSM were conducted with logistic regression and calculation of Fleiss' κ, Kendall's w, Krippendorff's α.

RESULTS

Across all qualitative assessment and quantitative metrics measured (simple accuracy, confidence as degree of ground truth alignment, and inter-rater agreement) QSM outperformed SWI/P. Additionally, logistic regression of average QSM voxel susceptibility achieved near-perfect separation in differentiating between CMB and calcification in the limited number of CMB/Calcification ROIs, indicating a high predictability.

CONCLUSION

Our study demonstrates that QSM offers improved detectability and classification of CMBs compared to the conventionally utilized SWI/P sequence. In addition, QSM simplifies the interpretation workflow by reducing the number of requisite images compared with the conventional counterpart, with improved diagnostic confidence.

ProxiMO: Proximal Multi-operator Networks for Quantitative Susceptibility Mapping

Quantitative Susceptibility Mapping (QSM) is a technique that derives tissue magnetic susceptibility distributions from phase measurements obtained through Magnetic Resonance (MR) imaging. This involves solving an ill-posed dipole inversion problem, however, and thus time-consuming and cumbersome data acquisition from several distinct head orientations becomes necessary to obtain an accurate solution. Most recent (supervised) deep learning methods for single-phase QSM require training data obtained via multiple orientations. In this work, we present an alternative unsupervised learning approach that can efficiently train on single-orientation measurement data alone, named ProxiMO (Proximal Multi-Operator), combining Learned Proximal Convolutional Neural Networks (LP-CNN) with multi-operator imaging (MOI). This integration enables LP-CNN training for QSM on single-phase data without ground truth reconstructions. We further introduce a semi-supervised variant, which further boosts the reconstruction performance, compared to the traditional supervised fashions. Extensive experiments on multicenter datasets illustrate the advantage of unsupervised training and the superiority of the proposed approach for QSM reconstruction. Code is available at https://github.com/shmuelor/ProxiMO.

DF-QSM: Data Fidelity based Hybrid Approach for Improved Quantitative Susceptibility Mapping of the Brain

Quantitative Susceptibility Mapping (QSM) is an advanced magnetic resonance imaging (MRI) technique to quantify the magnetic susceptibility of the tissue under investigation. Deep learning methods have shown promising results in deconvolving the susceptibility distribution from the measured local field obtained from the MR phase. Although existing deep learning based QSM methods can produce high-quality reconstruction, they are highly biased toward training data distribution with less scope for generalizability. This work proposes a hybrid two-step reconstruction approach to improve deep learning based QSM reconstruction. The susceptibility map prediction obtained from the deep learning methods has been refined in the framework developed in this work to ensure consistency with the measured local field. The developed method was validated on existing deep learning and model-based deep learning methods for susceptibility mapping of the brain. The developed method resulted in improved reconstruction for MRI volumes obtained with different acquisition settings, including deep learning models trained on constrained (limited) data settings.

Knowledge-driven deep learning for fast MR imaging: Undersampled MR image reconstruction from supervised to un-supervised learning

Deep learning (DL) has emerged as a leading approach in accelerating MRI. It employs deep neural networks to extract knowledge from available datasets and then applies the trained networks to reconstruct accurate images from limited measurements. Unlike natural image restoration problems, MRI involves physics-based imaging processes, unique data properties, and diverse imaging tasks. This domain knowledge needs to be integrated with data-driven approaches. Our review will introduce the significant challenges faced by such knowledge-driven DL approaches in the context of fast MRI along with several notable solutions, which include learning neural networks and addressing different imaging application scenarios. The traits and trends of these techniques have also been given which have shifted from supervised learning to semi-supervised learning, and finally, to unsupervised learning methods. In addition, MR vendors' choices of DL reconstruction have been provided along with some discussions on open questions and future directions, which are critical for the reliable imaging systems.

Spinet-QSM: model-based deep learning with schatten p-norm regularization for improved quantitative susceptibility mapping

OBJECTIVE

Quantitative susceptibility mapping (QSM) provides an estimate of the magnetic susceptibility of tissue using magnetic resonance (MR) phase measurements. The tissue magnetic susceptibility (source) from the measured magnetic field distribution/local tissue field (effect) inherent in the MR phase images is estimated by numerically solving the inverse source-effect problem. This study aims to develop an effective model-based deep-learning framework to solve the inverse problem of QSM.

MATERIALS AND METHODS

This work proposes a Schatten p -norm-driven model-based deep learning framework for QSM with a learnable norm parameter p to adapt to the data. In contrast to other model-based architectures that enforce the l2 -norm or l1 -norm for the denoiser, the proposed approach can enforce any p -norm ( 0 < p ≤ 2 ) on a trainable regulariser.

RESULTS

The proposed method was compared with deep learning-based approaches, such as QSMnet, and model-based deep learning approaches, such as learned proximal convolutional neural network (LPCNN). Reconstructions performed using 77 imaging volumes with different acquisition protocols and clinical conditions, such as hemorrhage and multiple sclerosis, showed that the proposed approach outperformed existing state-of-the-art methods by a significant margin in terms of quantitative merits.

CONCLUSION

The proposed SpiNet-QSM showed a consistent improvement of at least 5% in terms of the high-frequency error norm (HFEN) and normalized root mean squared error (NRMSE) over other QSM reconstruction methods with limited training data.

A subject-specific unsupervised deep learning method for quantitative susceptibility mapping using implicit neural representation

Quantitative susceptibility mapping (QSM) is an MRI-based technique that estimates the underlying tissue magnetic susceptibility based on phase signal. Deep learning (DL)-based methods have shown promise in handling the challenging ill-posed inverse problem for QSM reconstruction. However, they require extensive paired training data that are typically unavailable and suffer from generalization problems. Recent model-incorporated DL approaches also overlook the non-local effect of the tissue phase in applying the source-to-field forward model due to patch-based training constraint, resulting in a discrepancy between the prediction and measurement and subsequently suboptimal QSM reconstruction. This study proposes an unsupervised and subject-specific DL method for QSM reconstruction based on implicit neural representation (INR), referred to as INR-QSM. INR has emerged as a powerful framework for learning a high-quality continuous representation of the signal (image) by exploiting its internal information without training labels. In INR-QSM, the desired susceptibility map is represented as a continuous function of the spatial coordinates, parameterized by a fully-connected neural network. The weights are learned by minimizing a loss function that includes a data fidelity term incorporated by the physical model and regularization terms. Additionally, a novel phase compensation strategy is proposed for the first time to account for the non-local effect of tissue phase in data consistency calculation to make the physical model more accurate. Our experiments show that INR-QSM outperforms traditional established QSM reconstruction methods and the compared unsupervised DL method both qualitatively and quantitatively, and is competitive against supervised DL methods under data perturbations.

Improving quantitative MRI using self-supervised deep learning with model reinforcement: Demonstration for rapid T1 mapping

PURPOSE

This paper proposes a novel self-supervised learning framework that uses model reinforcement, REference-free LAtent map eXtraction with MOdel REinforcement (RELAX-MORE), for accelerated quantitative MRI (qMRI) reconstruction. The proposed method uses an optimization algorithm to unroll an iterative model-based qMRI reconstruction into a deep learning framework, enabling accelerated MR parameter maps that are highly accurate and robust.

METHODS

Unlike conventional deep learning methods which require large amounts of training data, RELAX-MORE is a subject-specific method that can be trained on single-subject data through self-supervised learning, making it accessible and practically applicable to many qMRI studies. Using quantitativeT 1 $$ {\mathrm{T}}_1 $$ mapping as an example, the proposed method was applied to the brain, knee and phantom data.

RESULTS

The proposed method generates high-quality MR parameter maps that correct for image artifacts, removes noise, and recovers image features in regions of imperfect image conditions. Compared with other state-of-the-art conventional and deep learning methods, RELAX-MORE significantly improves efficiency, accuracy, robustness, and generalizability for rapid MR parameter mapping.

CONCLUSION

This work demonstrates the feasibility of a new self-supervised learning method for rapid MR parameter mapping, that is readily adaptable to the clinical translation of qMRI.

Plug-and-Play latent feature editing for orientation-adaptive quantitative susceptibility mapping neural networks

Quantitative susceptibility mapping (QSM) is a post-processing technique for deriving tissue magnetic susceptibility distribution from MRI phase measurements. Deep learning (DL) algorithms hold great potential for solving the ill-posed QSM reconstruction problem. However, a significant challenge facing current DL-QSM approaches is their limited adaptability to magnetic dipole field orientation variations during training and testing. In this work, we propose a novel Orientation-Adaptive Latent Feature Editing (OA-LFE) module to learn the encoding of acquisition orientation vectors and seamlessly integrate them into the latent features of deep networks. Importantly, it can be directly Plug-and-Play (PnP) into various existing DL-QSM architectures, enabling reconstructions of QSM from arbitrary magnetic dipole orientations. Its effectiveness is demonstrated by combining the OA-LFE module into our previously proposed phase-to-susceptibility single-step instant QSM (iQSM) network, which was initially tailored for pure-axial acquisitions. The proposed OA-LFE-empowered iQSM, which we refer to as iQSM+, is trained in a simulated-supervised manner on a specially-designed simulation brain dataset. Comprehensive experiments are conducted on simulated and in vivo human brain datasets, encompassing subjects ranging from healthy individuals to those with pathological conditions. These experiments involve various MRI platforms (3T and 7T) and aim to compare our proposed iQSM+ against several established QSM reconstruction frameworks, including the original iQSM. The iQSM+ yields QSM images with significantly improved accuracies and mitigates artifacts, surpassing other state-of-the-art DL-QSM algorithms. The PnP OA-LFE module's versatility was further demonstrated by its successful application to xQSM, a distinct DL-QSM network for dipole inversion. In conclusion, this work introduces a new DL paradigm, allowing researchers to develop innovative QSM methods without requiring a complete overhaul of their existing architectures.

Quantitative susceptibility mapping through model-based deep image prior (MoDIP)

The data-driven approach of supervised learning methods has limited applicability in solving dipole inversion in Quantitative Susceptibility Mapping (QSM) with varying scan parameters across different objects. To address this generalization issue in supervised QSM methods, we propose a novel training-free model-based unsupervised method called MoDIP (Model-based Deep Image Prior). MoDIP comprises a small, untrained network and a Data Fidelity Optimization (DFO) module. The network converges to an interim state, acting as an implicit prior for image regularization, while the optimization process enforces the physical model of QSM dipole inversion. Experimental results demonstrate MoDIP's excellent generalizability in solving QSM dipole inversion across different scan parameters. It exhibits robustness against pathological brain QSM, achieving over 32 % accuracy improvement than supervised deep learning methods. It is also 33 % more computationally efficient and runs 4 times faster than conventional DIP-based approaches, enabling 3D high-resolution image reconstruction in under 4.5 min.

Incorporating a-priori information in deep learning models for quantitative susceptibility mapping via adaptive convolution

Quantitative susceptibility mapping (QSM) has attracted considerable interest for tissue characterization (e.g., iron and calcium accumulation, myelination, venous vasculature) in the human brain and relies on extensive data processing of gradient-echo MRI phase images. While deep learning-based field-to-susceptibility inversion has shown great potential, the acquisition parameters applied in clinical settings such as image resolution or image orientation with respect to the magnetic field have not been fully accounted for. Furthermore, the lack of comprehensive training data covering a wide range of acquisition parameters further limits the current QSM deep learning approaches. Here, we propose the integration of a priori information of imaging parameters into convolutional neural networks with our approach, adaptive convolution, that learns the mapping between the additional presented information (acquisition parameters) and the changes in the phase images associated with these varying acquisition parameters. By associating a-priori information with the network parameters itself, the optimal set of convolution weights is selected based on data-specific attributes, leading to generalizability towards changes in acquisition parameters. Moreover, we demonstrate the feasibility of pre-training on synthetic data and transfer learning to clinical brain data to achieve substantial improvements in the computation of susceptibility maps. The adaptive convolution 3D U-Net demonstrated generalizability in acquisition parameters on synthetic and in-vivo data and outperformed models lacking adaptive convolution or transfer learning. Further experiments demonstrate the impact of the side information on the adaptive model and assessed susceptibility map computation on simulated pathologic data sets and measured phase data.

A spatially adaptive regularization based three-dimensional reconstruction network for quantitative susceptibility mapping

Objective.Quantitative susceptibility mapping (QSM) is a new imaging technique for non-invasive characterization of the composition and microstructure ofin vivotissues, and it can be reconstructed from local field measurements by solving an ill-posed inverse problem. Even for deep learning networks, it is not an easy task to establish an accurate quantitative mapping between two physical quantities of different units, i.e. field shift in Hz and susceptibility value in ppm for QSM.Approach. In this paper, we propose a spatially adaptive regularization based three-dimensional reconstruction network SAQSM. A spatially adaptive module is specially designed and a set of them at different resolutions are inserted into the network decoder, playing a role of cross-modality based regularization constraint. Therefore, the exact information of both field and magnitude data is exploited to adjust the scale and shift of feature maps, and thus any information loss or deviation occurred in previous layers could be effectively corrected. The network encoding has a dynamic perceptual initialization, which enables the network to overcome receptive field intervals and also strengthens its ability to detect features of various sizes.Main results. Experimental results on the brain data of healthy volunteers, clinical hemorrhage and simulated phantom with calcification demonstrate that SAQSM can achieve more accurate reconstruction with less susceptibility artifacts, while perform well on the stability and generalization even for severe lesion areas.Significance. This proposed framework may provide a valuable paradigm to quantitative mapping or multimodal reconstruction.

A latent code based multi-variable modulation network for susceptibility mapping

Quantitative susceptibility mapping (QSM) is a technique for obtaining quantitative information on tissue susceptibility and has shown promising potential for clinical applications, in which the magnetic susceptibility is calculated by solving an ill-posed inverse problem. Recently, deep learning-based methods are proposed to address this issue, but the diversity of data distribution was not well considered, and thus the model generalization is limited in clinical applications. In this paper, we propose a Latent Code based Multi-Variable modulation network for QSM reconstruction (LCMnet). Particularly, a specific modulation module is exploited to incorporate three variables, i.e., field map, magnitude image, and initial susceptibility. The latent code in the modulated convolution is learned from feature maps of the field data using the encoder-decoder framework. The susceptibility map pre-estimated from simple thresholding is the constant input of the module, thereby enhancing the network stability and accelerating training convergence. As another input, multi-level features generated by a cross-fusion block integrate the information of field and magnitude data effectively. Experimental results on in vivo human brain data, challenge data, clinical data and synthetic data demonstrate that the proposed method LCMnet can achieve outstanding performance on accurate susceptibility measurement and also excellent generalization.

Quantitative susceptibility mapping using multi-channel convolutional neural networks with dipole-adaptive multi-frequency inputs

Quantitative susceptibility mapping (QSM) quantifies the distribution of magnetic susceptibility and shows great potential in assessing tissue contents such as iron, myelin, and calcium in numerous brain diseases. The accuracy of QSM reconstruction was challenged by an ill-posed field-to-susceptibility inversion problem, which is related to the impaired information near the zero-frequency response of the dipole kernel. Recently, deep learning methods demonstrated great capability in improving the accuracy and efficiency of QSM reconstruction. However, the construction of neural networks in most deep learning-based QSM methods did not take the intrinsic nature of the dipole kernel into account. In this study, we propose a dipole kernel-adaptive multi-channel convolutional neural network (DIAM-CNN) method for the dipole inversion problem in QSM. DIAM-CNN first divided the original tissue field into high-fidelity and low-fidelity components by thresholding the dipole kernel in the frequency domain, and it then inputs the two components as additional channels into a multichannel 3D Unet. QSM maps from the calculation of susceptibility through multiple orientation sampling (COSMOS) were used as training labels and evaluation reference. DIAM-CNN was compared with two conventional model-based methods [morphology enabled dipole inversion (MEDI) and improved sparse linear equation and least squares (iLSQR) and one deep learning method (QSMnet)]. High-frequency error norm (HFEN), peak signal-to-noise-ratio (PSNR), normalized root mean squared error (NRMSE), and the structural similarity index (SSIM) were reported for quantitative comparisons. Experiments on healthy volunteers demonstrated that the DIAM-CNN results had superior image quality to those of the MEDI, iLSQR, or QSMnet results. Experiments on data with simulated hemorrhagic lesions demonstrated that DIAM-CNN produced fewer shadow artifacts around the bleeding lesion than the compared methods. This study demonstrates that the incorporation of dipole-related knowledge into the network construction has a potential to improve deep learning-based QSM reconstruction.

msQSM: Morphology-based Self-supervised Deep Learning for Quantitative Susceptibility Mapping

Quantitative susceptibility mapping (QSM) has been applied to the measurement of iron deposition and the auxiliary diagnosis of neurodegenerative disease. There still exists a dipole inversion problem in QSM reconstruction. Recently, deep learning approaches have been proposed to resolve this problem. However, most of these approaches are supervised methods that need pairs of the input phase and ground-truth. It remains a challenge to train a model for all resolutions without using the ground-truth and only using one resolution data. To address this, we proposed a self-supervised QSM deep learning method based on morphology. It consists of a morphological QSM builder to decouple the dependency of the QSM on acquisition resolution, and a morphological loss to reduce artifacts effectively and save training time efficiently. The proposed method can reconstruct arbitrary resolution QSM on both human data and animal data, regardless of whether the resolution is higher or lower than that of the training set. Our method outperforms the previous best unsupervised method with a 3.6% higher peak signal-to-noise ratio, 16.2% lower normalized root mean square error, and 22.1% lower high-frequency error norm. The morphological loss reduces training time by 22.1% with respect to the cycle gradient loss used in the previous unsupervised methods. Experimental results show that the proposed method accurately measures QSM with arbitrary resolutions, and achieves state-of-the-art results among unsupervised deep learning methods. Research on applications in neurodegenerative diseases found that our method is robust enough to measure significant increase in striatal magnetic susceptibility in patients during Alzheimer's disease progression, as well as significant increase in substantia nigra susceptibility in Parkinson's disease patients, and can be used as an auxiliary differential diagnosis tool for Alzheimer's disease and Parkinson's disease.

Reconstruction of Quantitative Susceptibility Mapping From Total Field Maps With Local Field Maps Guided UU-Net

Quantitative susceptibility mapping (QSM) is an emerging computational technique based on the magnetic resonance imaging (MRI) phase signal, which can provide magnetic susceptibility values of tissues. The existing deep learning-based models mainly reconstruct QSM from local field maps. However, the complicated inconsecutive reconstruction steps not only accumulate errors for inaccurate estimation, but also are inefficient in clinical practice. To this end, a novel local field maps guided UU-Net with Self- and Cross-Guided Transformer (LGUU-SCT-Net) is proposed to reconstruct QSM directly from the total field maps. Specifically, we propose to additionally generate the local field maps as the auxiliary supervision during the training stage. This strategy decomposes the more complicated mapping from total maps to QSM into two relatively easier ones, effectively alleviating the difficulty of direct mapping. Meanwhile, an improved U-Net model, named LGUU-SCT-Net, is further designed to promote the nonlinear mapping ability. The long-range connections are designed between two sequentially stacked U-Nets to bring more feature fusions and facilitate the information flow. The Self- and Cross-Guided Transformer integrated into these connections further captures multi-scale channel-wise correlations and guides the fusion of multi-scale transferred features, assisting in the more accurate reconstruction. The experimental results on an in-vivo dataset demonstrate the superior reconstruction results of our proposed algorithm.

Deep learning-regularized, single-step quantitative susceptibility mapping quantification

The purpose of the current study was to develop deep learning-regularized, single-step quantitative susceptibility mapping (QSM) quantification, directly generating QSM from the total phase map. A deep learning-regularized, single-step QSM quantification model, named SS-POCSnet, was trained with datasets created using the QSM synthesis approach in QSM reconstruction challenge 2.0. In SS-POCSnet, a data fidelity term based on a single-step model was iteratively applied that combined the spherical mean value kernel and dipole model. Meanwhile, SS-POCSnet regularized susceptibility maps, avoiding underestimating susceptibility values. We evaluated the SS-POCSnet on 10 synthetic datasets, 24 clinical datasets with lesions of cerebral microbleed (CMB) and calcification, and 10 datasets with multiple sclerosis (MS).On synthetic datasets, SS-POCSnet showed the best performance among the methods evaluated, with a normalized root mean squared error of 37.3% ± 4.2%, susceptibility-tuned structured similarity index measure of 0.823 ± 0.02, high-frequency error norm of 37.0 ± 5.7, and peak signal-to-noise ratio of 42.8 ± 1.1. SS-POCSnet also reduced the underestimations of susceptibility values in deep brain nuclei compared with those from the other models evaluated. Furthermore, SS-POCSnet was sensitive to CMB/calcification and MS lesions, demonstrating its clinical applicability. Our method also supported variable imaging parameters, including matrix size and resolution. It was concluded that deep learning-regularized, single-step QSM quantification can mitigate underestimating susceptibility values in deep brain nuclei.

Affine transformation edited and refined deep neural network for quantitative susceptibility mapping

Deep neural networks have demonstrated great potential in solving dipole inversion for Quantitative Susceptibility Mapping (QSM). However, the performances of most existing deep learning methods drastically degrade with mismatched sequence parameters such as acquisition orientation and spatial resolution. We propose an end-to-end AFfine Transformation Edited and Refined (AFTER) deep neural network for QSM, which is robust against arbitrary acquisition orientation and spatial resolution up to 0.6 mm isotropic at the finest. The AFTER-QSM neural network starts with a forward affine transformation layer, followed by a Unet for dipole inversion, then an inverse affine transformation layer, followed by a Residual Dense Network (RDN) for QSM refinement. Simulation and in-vivo experiments demonstrated that the proposed AFTER-QSM network architecture had excellent generalizability. It can successfully reconstruct susceptibility maps from highly oblique and anisotropic scans, leading to the best image quality assessments in simulation tests and suppressed streaking artifacts and noise levels for in-vivo experiments compared with other methods. Furthermore, ablation studies showed that the RDN refinement network significantly reduced image blurring and susceptibility underestimation due to affine transformations. In addition, the AFTER-QSM network substantially shortened the reconstruction time from minutes using conventional methods to only a few seconds.

SwinGAN: A dual-domain Swin Transformer-based generative adversarial network for MRI reconstruction

Magnetic resonance imaging (MRI) is one of the most important modalities for clinical diagnosis. However, the main disadvantages of MRI are the long scanning time and the moving artifact caused by patient movement during prolonged imaging. It can also lead to patient anxiety and discomfort, so accelerated imaging is indispensable for MRI. Convolutional neural network (CNN) based methods have become the fact standard for medical image reconstruction, and generative adversarial network (GAN) have also been widely used. Nevertheless, due to the limited ability of CNN to capture long-distance information, it may lead to defects in the structure of the reconstructed images such as blurry contour. In this paper, we propose a novel Swin Transformer-based dual-domain generative adversarial network (SwinGAN) for accelerated MRI reconstruction. The SwinGAN consists of two generators: a frequency-domain generator and an image-domain generator. Both the generators utilize Swin Transformer as backbone for effectively capturing the long-distance dependencies. A contextual image relative position encoder (ciRPE) is designed to enhance the ability to capture local information. We extensively evaluate the method on the IXI brain dataset, MICCAI 2013 dataset and MRNet knee dataset. Compared with KIGAN, the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) are improved by 6.1% and 1.49% to 37.64 dB and 0.98 on IXI dataset respectively, which demonstrates that our model can sufficiently utilize the local and global information of image. The model shows promising performance and robustness under different undersampling masks, different acceleration rates and different datasets. But it needs high hardware requirements with the increasing of the network parameters. The code is available at: https://github.com/learnerzx/SwinGAN.

NeXtQSM-A complete deep learning pipeline for data-consistent Quantitative Susceptibility Mapping trained with hybrid data

Deep learning based Quantitative Susceptibility Mapping (QSM) has shown great potential in recent years, obtaining similar results to established non-learning approaches. Many current deep learning approaches are not data consistent, require in vivo training data or solve the QSM problem in consecutive steps resulting in the propagation of errors. Here we aim to overcome these limitations and developed a framework to solve the QSM processing steps jointly. We developed a new hybrid training data generation method that enables the end-to-end training for solving background field correction and dipole inversion in a data-consistent fashion using a variational network that combines the QSM model term and a learned regularizer. We demonstrate that NeXtQSM overcomes the limitations of previous deep learning methods. NeXtQSM offers a new deep learning based pipeline for computing quantitative susceptibility maps that integrates each processing step into the training and provides results that are robust and fast.

Towards in vivo ground truth susceptibility for single-orientation deep learning QSM: a multi-orientation gradient-echo MRI dataset

Recently, deep neural networks have shown great potential for solving dipole inversion of quantitative susceptibility mapping (QSM) with improved results. However, these studies utilized their limited dataset for network training and inference, which may lead to untrustworthy conclusions. Thus, a common dataset is needed for a fair comparison between different QSM reconstruction networks. Additionally, finding an in vivo reference susceptibility map that matches acquired single-orientation phase data remains an open problem. Susceptibility tensor imaging (STI) χ₃₃ and Calculation of Susceptibility through Multiple Orientation Sampling (COSMOS) are considered reference susceptibility candidates. However, a large number of multi-orientation GRE data for both STI and COSMOS reconstruction are now unavailable for training supervised neural networks for QSM. In this study, we reported the largest multi-orientation dataset, to the best of our knowledge in the QSM research field, with a total of 144 scans from 8 healthy subjects collected using a 3D GRE sequence from the same MR scanner. In addition, the parcellation of deep gray matter is also provided for automatically extracting susceptibility values. Five recently developed deep neural networks, i.e., xQSM, QSMnet, autoQSM, LPCNN, and MoDL-QSM were performed on this dataset. This potential data source could provide a common framework and labels to test the accuracy and robustness of deep neural networks for QSM reconstruction. This dataset has the potential to provide a benchmark of reference susceptibility for the deep learning-based QSM methods. Additionally, the trained COSMOS-labeled and χ₃₃-labeled networks were tested on the pathological data to explore their potential applications. The data together with deep gray matter parcellation maps are now publicly available via an open repository at https://osf.io/yfms7/, and the raw multi-orientation GRE data were also available at https://osf.io/y6rc3/.

Instant tissue field and magnetic susceptibility mapping from MRI raw phase using Laplacian enhanced deep neural networks

Quantitative susceptibility mapping (QSM) is an MRI post-processing technique that produces spatially resolved magnetic susceptibility maps from phase data. However, the traditional QSM reconstruction pipeline involves multiple non-trivial steps, including phase unwrapping, background field removal, and dipole inversion. These intermediate steps not only increase the reconstruction time but accumulates errors. This study aims to overcome existing limitations by developing a Laplacian-of-Trigonometric-functions (LoT) enhanced deep neural network for near-instant quantitative field and susceptibility mapping (i.e., iQFM and iQSM) from raw MRI phase data. The proposed iQFM and iQSM methods were compared with established reconstruction pipelines on simulated and in vivo datasets. In addition, experiments on patients with intracranial hemorrhage and multiple sclerosis were also performed to test the generalization of the proposed neural networks. The proposed iQFM and iQSM methods in healthy subjects yielded comparable results to those involving the intermediate steps while dramatically improving reconstruction accuracies on intracranial hemorrhages with large susceptibilities. High susceptibility contrast between multiple sclerosis lesions and healthy tissue was also achieved using the proposed methods. Comparative studies indicated that the most significant contributor to iQFM and iQSM over conventional multi-step methods was the elimination of traditional Laplacian unwrapping. The reconstruction time on the order of minutes for traditional approaches was shortened to around 0.1 seconds using the trained iQFM and iQSM neural networks.

Regularized Asymmetric Susceptibility Tensor Imaging in the Human Brain in vivo

Susceptibility tensor imaging (STI) is a promising tool for studying orientation-dependent tissue magnetic susceptibility and for mapping white matter fiber orientations complementary to diffusion tensor imaging (DTI). However, the limited head rotation range within modern head coils for data acquisition makes in vivo STI reconstruction ill-conditioned. Conventional STI reconstruction method is usually vulnerable to noise and requires sufficiently large head rotations to solve this ill-conditioned inverse problem. In this study, based on the recently proposed asymmetric STI (aSTI) model, a new method termed aSTI+ was proposed to improve in vivo STI reconstruction by enforcing isotropic susceptibility tensor inside cerebrospinal fluid (CSF) and applying morphology constraint in white matter. Experimental results showed superior performance of the proposed method with reduced noise, improved tissue contrast and better fiber orientation estimation over previous methods. Thus aSTI+ may promote in vivo human brain STI studies on white matter and myelin-related brain diseases.

Learn Less, Infer More: Learning in the Fourier Domain for Quantitative Susceptibility Mapping

Quantitative susceptibility mapping (QSM) aims to evaluate the distribution of magnetic susceptibility from magnetic resonance phase measurements by solving the ill-conditioned dipole inversion problem. Removing the artifacts and preserving the anisotropy of tissue susceptibility simultaneously is still a challenge in QSM. To deal with this issue, a novel k-QSM network is proposed to resolve dipole inversion issues in QSM reconstruction. The k-QSM network converts the results obtained by truncated k-space division (TKD) into the Fourier domain as inputs. After passing through several convolutional and residual blocks, the ill-posed signals of TKD are corrected by making the network output close to the calculation of susceptibility through multiple orientation sampling (COSMOS)-labeled QSM. To evaluate the superiority of k-QSM, comparisons with several state-of-the-art methods are performed in terms of QSM artifacts removing, anisotropy preserving, generalization ability, and clinical applications. Compared to existing methods, the k-QSM achieves a 22.31% lower normalized root mean square error, 10.30% higher peak signal-to-noise ratio (PSNR), 33.10% lower high-frequency error norm, and 1.06% higher structural similarity. In addition, the orientation-dependent susceptibility variation obtained by k-QSM is significant, verifying that k-QSM has the ability to preserve susceptibility anisotropy. When the trained models are tested on the dataset from different centers, our k-QSM shows a strong generalization ability with the highest PSNR. Moreover, by comparing the susceptibility maps between healthy controls and drug addicts with different methods, we found the proposed k-QSM is more sensitive to the susceptibility abnormality in the patients. The proposed k-QSM method learns less—only to fix the ill-posed signals of TKD, but infers more—both COSMOS-like and anisotropy-preserving QSM results. Its generalization ability and great sensitivity to susceptibility changes can make it a potential method for distinguishing some diseases.