Steven Cao¹, Jingjia Chen¹, Hongjiang Wei², and Chunlei Liu^1
1UC Berkeley, Berkeley, CA, United States, ²Shanghai Jiao Tong University, Shanghai, China

Susceptibility Tensor Imaging (STI) is a recently developed technique that uses phase data to solve for the underlying susceptibility tensor of the tissue. While STI has the potential for early diagnosis of many diseases including Parkinson’s and Alzheimer’s, it suffers from low image quality. From physics, the susceptibility tensor can be shown to be symmetric, so current approaches impose a symmetry constraint during inversion. We propose an inversion algorithm without this constraint, and instead enforce symmetry post-inversion by decomposing the result into symmetric and antisymmetric parts. We justify this approach empirically by comparing reconstructions of mouse brain and kidney data.

Dimitrios G. Gkotsoulias¹, Riccardo Metere², Yanzhu Su¹, Cornelius Eichner¹, Torsten Schlumm¹, Roland Müller¹, Alfred Anwander¹, Toralf Mildner¹, Carsten Jäger¹, André Pampel¹, Catherine Crockford^3,4, Roman Wittig^3,4, Liran Samuni ^4,5, Kamilla Pleh ⁶, Chunlei Liu⁷, and Harald E. Möller^1
1Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany, ²Donders Institute for Brain, Cognition and Behaviour, Nijmegen, Netherlands, ³Max Planck Institute for Evolutionary Anthropology, Leipzig, Germany, ⁴Tai Chimpanzee Project, Centre Suisse de Recherches Scientifiques en Cote d'Ivoire, Abidjan, Cote D'ivoire, ⁵Department of Human Evolutionary Biology, Harvard University, Cambridge, MA, United States, ⁶Project Group Epidemiology of Highly Pathogenic Microorganisms, Robert Koch Institute, Berlin, Germany, ⁷EECS, UC Berkeley, Berkeley, CA, United States

We present a ‘high angular resolution’ approach to susceptibility tensor imaging (STI) consisting of susceptibility-weighted acquisitions at 60 independent orientations in post- mortem chimpanzee brain. The derived susceptibility tensor and metrics are compared with the corresponding diffusion tensor-derived metrics and single-orientation quantitative susceptibility mapping (QSM) results. A preliminary approach to assess the voxel-wise relationship of the two tensors in white matter is presented: using machine learning strategies, an effort to estimate the susceptibility tensor from the diffusion tensor and minimum single-orientation QSM data  in selected regions of interest was made.  

Anders Dyhr Sandgaard¹, Valerij G. Kiselev², Noam Shemesh³, and Sune Nørhøj Jespersen^1,4
1Department of Clinical Medicine, Center for Functionally Integrative Neuroscience, Aarhus University, Aarhus, Denmark, ²Medical Physics, Department of Radiology, Faculty of Medicine, University of Freiburg, Freiburg, Germany, ³Champalimaud Neuroscience Programme, Champalimaud Centre for the Unknown, Lisbon, Portugal, ⁴Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark

Mapping tissue magnetic properties may be a useful tool for understanding basic disease mechanism in neurodegenerative diseases. However, magnetic properties depend on the arrangement of magnetic susceptibility on all scales, including the microstructure, and typically require impractical sample rotations for robust estimation. By modeling white matter fibers as a system of cylinders, here we show that the first cumulant $$$\langle\Omega\rangle$$$ of the FID signal can be obtained without the need for sample rotation, by utilizing the fiber orientation distribution function estimated by diffusion imaging. 

Hyeong-Geol Shin¹, Young Hyun Yun², Seong Ho Yoo², Sehoon Jung³, Sunhye Kim³, Hyung Jin Choi ², and Jongho Lee^1
1Seoul National University, Seoul, Korea, Republic of, ²Seoul National University College of Medicine, Seoul, Korea, Republic of, ³Research Institute of Industrial Science and Technology, Pohang, Korea, Republic of

We validate the magnetic susceptibility source separation method, which is recently proposed to separate paramagnetic (e.g., iron) and diamagnetic sources (e.g., myelin), by performing Monte-Carlo simulation. Then, the method is applied to ex-vivo and in-vivo human brains and compared to histology. In the simulation, we show the method successfully estimates the paramagnetic and diamagnetic susceptibility concentrations. When compared to histology, the ex-vivo and in-vivo results demonstrated that the positive and negative susceptibility maps from the method highly correspond to the iron and myelin distributions, respectively, proving its feasibility as a tool to map iron and myelin distributions in the brain. 

Jingjia Chen¹, Khallil Taverna Chaim², Maria Concepción García Otaduy², and Chunlei Liu^1,3
1Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, United States, ²LIM44, Instituto e Departamento de Radiologia, Faculdade de Medicina, Universidade de Sao Paulo, Sao Paulo, Brazil, ³Helen Wills Neuroscience Institute, University of California, Berkeley, Berkeley, CA, United States

A model and corresponding solver for estimating sub-voxel paramagnetic and diamagnetic susceptibility components are validated based on the temperature dependence of magnetic susceptibility. Two pieces of brainstem sample were scanned under various temperature conditions to test the properties of the separated paramagnetic and diamagnetic components.

Kwok-Shing Chan¹, Jeroen Mollink², Jenni Schulz¹, Anne-Marie van Cappellen van Walsum², and José P. Marques^1
1Donders Institute for Brain, Cognition and Behaviour, Radboud University, Nijmegen, Netherlands, ²Department of Medical Imaging, Anatomy, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, Netherlands

In this work, we study the feasibility of using formalin-fixed post-mortem specimen to investigate MRI phase contrast in brain tissue. Despite the magnetic susceptibility maps derived from in vivo and ex vivo imaging share similar contrasts, the non-susceptibility contributions on measured fields of ex vivo sample were clear affected by fixation process, and we found its microstructural compartmentalisation effect are also greatly reduced. Therefore, extra care has to be taken to directly translate ex vivo findings to in vivo applications.

Ashley Stewart^1,2, Simon Daniel Robinson^2,3, Kieran O'Brien^1,2,4, Jin Jin^1,2,4, Georg Widhalm⁵, Gilbert Hangel^3,5, Angela Walls⁶, Jonathan Goodwin^7,8, Korbinian Eckstein³, Markus Barth^1,2,9, and Steffen Bollmann^1,2,9
1Centre for Innovation in Biomedical Imaging Technology, University of Queensland, Brisbane, Australia, ²Centre for Advanced Imaging, University of Queensland, Brisbane, Australia, ³High Field MR Center, Department of Biomedical Imaging and Image-Guided Therapy, Medical University of Vienna, Vienna, Austria, ⁴Siemens Healthcare Pty Ltd, Brisbane, Australia, ⁵Department of Neurosurgery, Medical University of Vienna, Vienna, Austria, ⁶Clinical & Research Imaging Centre, South Australian Health and Medical Research Institute, Adelaide, Australia, ⁷Department of Radiation Oncology, Calvary Mater Hospital, Newcastle, Australia, ⁸School of Mathematical and Physical Science, University of Newcastle, Newcastle, Australia, ⁹School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, Australia

Quantitative Susceptibility Mapping (QSM) is a post-processing technique applied to gradient-echo phase data. QSM generally requires a signal mask to identify reliable phase values before reconstruction. Most QSM pipelines do not include masking procedures, and often suggest masking techniques that introduce artefacts, work only in the human brain, and lose critical information, especially near strong susceptibility sources. We propose two novel echo-dependent masking strategies and find that they significantly reduce streaking artefacts, particularly surrounding strong sources and tissue boundaries in multi-echo data. Our techniques are open-source and implemented in a new framework for automated, scalable, and robust QSM processing.

Christof Boehm¹, Maximilian N. Diefenbach^1,2, Sophia Kronthaler¹, Jakob Meineke³, Kilian Weiss⁴, Marcus R. Makowski¹, and Dimitrios C. Karampinos^1
1Department of Diagnostic and Interventional Radiology, School of Medicine, Klinikum rechts der Isar, Technical University of Munich, Munich, Germany, ²Division of Infectious Diseases and Tropical Medicine, University Hospital, LMU Munich, Munich, Germany, ³Philips Research Lab, Hamburg, Germany, ⁴Philips Healthcare, Hamburg, Germany

Gradient echo imaging using in-phase echoes has been proposed to reduce the field-map estimation in water–fat regions to a convex nonlinear least squares problem. However, it is known that the fat spectrum is complex and the definition of in-phase echo times remains problematic. In this work, the in-phase assumption is compared to standard water–fat imaging with respect to field- and quantitative susceptibility-mapping. The in-phase assumption is shown to be associated with quantification bias when subsequently estimating the field map and magnetic susceptibility in the spine, the liver and the breast.

Ronja C. Berg¹, Christine Preibisch¹, Claus Zimmer¹, David L. Thomas^2,3, Karin Shmueli⁴, and Emma Biondetti^5
1School of Medicine, Department of Neuroradiology, Technical University of Munich, Munich, Germany, ²Dementia Research Centre, UCL Queen Square Institute of Neurology, University College London, London, United Kingdom, ³Wellcome Centre for Human Neuroimaging, UCL Queen Square Institute of Neurology, University College London, London, United Kingdom, ⁴Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom, ⁵Institut du Cerveau – ICM, INSERM U 1127, CNRS UMR 7225, Sorbonne Université, Paris, France

Venous quantitative susceptibility mapping (QSM) enables quantification of venous oxygenation. Flow-compensated acquisition is generally recommended for venous QSM, although its effect on the accuracy of venous susceptibility values has not been systematically evaluated. Moreover, QSM processing methods tend to be optimized for brain parenchyma tissues rather than veins. Here, we compared five different acquisition protocols (incorporating distinct flow compensation schemes) and six QSM processing methods in ten healthy volunteers. We found that venous susceptibility values depend strongly on the QSM pipeline (effect size η_p²=0.861) and much less on acquisition parameters including flow compensation (effect size η_p²=0.016).

Nashwan Naji¹, M. Louis Lauzon^2,3, Peter Seres¹, Emily Stolz¹, Richard Frayne^2,3, Catherine Lebel⁴, Christian Beaulieu¹, and Alan H. Wilman^1
1Department of Biomedical Engineering, University of Alberta, Edmonton, AB, Canada, ²Departments of Radiology and Clinical Neurosciences, Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada, ³Seaman Family MR Research Centre, Foothills Medical Centre, Calgary, AB, Canada, ⁴Department of Radiology, Alberta Children’s Hospital Research Institute and Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada

R2* and QSM provide noninvasive ways to measure iron concentration in human brain. Performing multi-center studies help exploring wider demographical and pathological conditions. However, data pooled from multiple sites typically contain local acquisition sequence variations. In this study, the reproducibility of R2* and QSM at 3T are evaluated in 21 healthy adults (“traveling phantoms”) scanned 2x per site using  independently site-optimized sequences from three sites and two scanner vendors. Mean R2* and susceptibility measurements in four deep grey matter structures were found to be highly correlated (r² ≥ 0.98) and reproducible with SD of 1.2 s^-1 and 4.1 ppb, respectively.

Jannis Hanspach¹, Aurel Jolla¹, Michael Uder¹, Bernhard Hensel², Steffen Bollmann³, and Frederik Bernd Laun^1
1Institute of Radiology, University Hospital Erlangen, Friedrich‐Alexander‐Universität Erlangen‐Nürnberg (FAU), Erlangen, Germany, ²Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen, Center for Medical Physics and Engineering, Erlangen, Germany, ³University of Queensland, Brisbane, Australia, School of Information Technology and Electrical Engineering, Brisbane, Australia

Deep Learning reconstruction methods are increasingly investigated in Quantitative Susceptibility Mapping (QSM). In this work, we applied a UNET to reconstruct susceptibility maps in the presence of fat from unwrapped phase maps. The network was trained using synthetically generated multi-echo phase data and does not require explicit masking for the background field correction. Our results show that the proposed approach is well-suited to rapidly reconstruct high quality susceptibility maps in the presence of fat (e.g., outside the central nervous system) in in vivo data.

Chungseok Oh¹, Woojin Jung¹, Hwihun Jeong¹, and Jongho Lee^1
1Seoul National University, Seoul, Korea, Republic of

We demonstrated that at least two conditions are required for a fair comparison between deep neural networks for dipole inversion: First, test data need to have the same characteristics as training data. Second, hyperparameter tuning should be performed if training dataset is changed. Our study implies that a common dataset is necessary for a fair comparison of deep neural networks for QSM.

Woojin Jung¹, Steffen Bollmann², Se-Hong Oh³, Hyeong-geol Shin¹, Sooyeon Ji¹, and Jongho Lee^1
1Department of Electrical and Computer Engineering, Seoul National University, Seoul, Korea, Republic of, ²The University of Queensland, Brisbane, Australia, ³Biomedical Engineering, Hankuk University of Foreign Studies, Yongin, Korea, Republic of

In this work, the effect of spatial gradients in the training data on deep learning-based QSM is explored. We observe that deep learning-based QSM underestimates the susceptibility values when spatial gradients differ between training and test data. For demonstration, three types of networks were trained by using different spatial gradients of training images and evaluated on test data with varying spatial gradients. The results indicate that expanding the spatial gradient distribution of training data improves the performance of deep learning-based QSM. Furthermore, we demonstrate that augmenting spatial gradients may improve deep-learning based QSM to work for various image resolutions.

Francesco Cognolato^1,2, Kieran O’Brien^2,3, Jin Jin^2,3, Simon Robinson^4,5, Markus Barth^1,2,6, and Steffen Bollmann^1,2,6
1Centre for Advanced Imaging, The University of Queensland, Brisbane, Australia, ²ARC Training Centre for Innovation in Biomedical Imaging Technology, The University of Queensland, Brisbane, Australia, ³Siemens Healthcare Pty Ltd, Brisbane, Australia, ⁴High Field MR Center, Department of Biomedical Imaging and Image-Guided Therapy, Medical University of Vienna, Vienna, Austria, ⁵Department of Neurology, Medical University of Graz, Graz, Austria, ⁶School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, Australia

Deep learning based quantitative susceptibility mapping has shown great potential in recent years, outperforming traditional non-learning approaches in speed and accuracy in many applications. Here we aim to overcome the limitations of in vivo training data and model-agnostic deep learning approaches commonly used in the field. We developed a new synthetic training data generation method that enables the background field correction and a data-consistent solution of the dipole inversion to be learned using a variational network in one pipeline. NeXtQSM is a complete deep learning based pipeline for computing robust, fast and accurate quantitative susceptibility maps.

Carlos Milovic¹, Jose Manuel Larrain^2,3, and Karin Shmueli^1
1Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom, ²Department of Electrical Engineering, Pontificia Universidad Catolica de Chile, Santiago, Chile, ³Biomedical Imaging Center, Pontificia Universidad Catolica de Chile, Santiago, Chile

Quantitative Susceptibility Mapping (QSM) is an ill-posed inverse problem. Traditionally, it is solved by minimization of a functional. Regularization terms may be interpreted as a denoising process. Many state-of-the-art methods are based on Total Variation regularization terms, with great success. With the advent of Deep Learning, new regularization strategies have been derived from training datasets. Total Deep Variation (TDV) is a recently proposed technique, showing impressive results. We applied a pre-trained TDV network as a denoising step in an iterative QSM solver. Results show improved error metrics for synthetic brain phantoms and enhanced in-vivo reconstructions, compared to Total-Variation-based algorithms.

JUAN LIU¹ and Kevin Koch^2
1Yale University, New Haven, CT, United States, ²Medical College of Wisconsin, Milwaukee, WI, United States

We aim to address the domain adaption problem of neural networks for QSM reconstruction which are learned from synthetic data while applied on real data. To address the unsupervised domain adaption, we apply domain-specific batch normalization layers in convolutional neural networks while allowing them to share all other model parameters. The proposed method is evaluated on multiple orientation datasets and single-orientation QSM datasets. Compared withTKD, MEDI, and DL-based method first training on synthetic datasets then model-based fine-tuning on real datasets, the proposed method achieved better performance.

Christian Kames^1,2, Jonathan Doucette^1,2, and Alexander Rauscher^1,2,3
1UBC MRI Research Centre, The University of British Columbia, Vancouver, BC, Canada, ²Department of Physics and Astronomy, The University of British Columbia, Vancouver, BC, Canada, ³Department of Pediatrics, The University of British Columbia, Vancouver, BC, Canada

We propose an extension of nonlinear dipole inversion (NDI), a first order method for solving the nonlinear formulation of the dipole inversion in quantitative susceptibility mapping (QSM), by using a second order method to increase the convergence rate of the minimization. The proposed method, Hessian Accelerated Nonlinear Dipole Inversion (HANDI), is shown to require fewer iterations than NDI, resulting in reconstruction times of a few seconds, more than 10x faster than NDI, without sacrificing accuracy. We further propose a learned proximal Newton method (HANDINet) and show that it outperforms learned variational networks based on NDI and standard dipole deconvolution minimizations.

Carlos Milovic¹ and Karin Shmueli^1
1Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom

Quantitative Susceptibility Mapping (QSM) is an ill-posed inverse problem often solved by regularization: minimizing a functional until it converges. This is usually time-consuming, requiring fine-tuning of several parameters by many repetitions of the whole optimization solver. Nonlinear Dipole Inversion is a QSM method that solves a nonlinear Tikhonov-regularized functional with a gradient descent solver. We show that stopping this method early provides optimal results, largely independent of the regularization weight. Here, we propose a non-regularized nonlinear conjugate gradient solver with a new stopping criterion based on analysing susceptibility map spatial frequency coefficients to achieve fast, parameter-free and automatic QSM.

Mathias Gabriel Lambert^1,2,3, Carlos Milovic⁴, and Cristian Tejos^1,2,3
1Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile, ²Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile, ³Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, Chile, ⁴Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom

Compared to L2-norm based QSM reconstructions, methods based on L1-norm data consistency are less prone to artifact generation caused by phase inconsistencies (e.g. unwrapping artifacts, intravoxel dephasing). However, L2-norm methods present better denoising performance in high SNR regions. Here, we present a QSM algorithm that combines the strengths of the L1 and L2 norms, using Huber's loss function as the data consistency term. Simulations and in vivo reconstructions showed enhanced performance, with superior artifact suppression capabilities of our proposed method.

Mathias Gabriel Lambert^1,2,3, Cristian Tejos^1,2,3, and Carlos Milovic^4
1Department of Electrical Engineering, Pontificia Universidad Católica de Chile, Santiago, Chile, ²Biomedical Imaging Center, Pontificia Universidad Católica de Chile, Santiago, Chile, ³Millennium Nucleus for Cardiovascular Magnetic Resonance, Santiago, Chile, ⁴Department of Medical Physics and Biomedical Engineering, University College London, London, United Kingdom

Non-regularized QSM reconstructions are feasible by stopping gradient descent methods before they diverge. These methods consume less computation time, while avoiding the time required for parameter selection. In this work we present a linear dipole inversion method without regularization that uses the L1-norm in a proximal step to prevent streaking propagation and present more robustness against phase outliers. Compared to the Nonlinear Dipole Inversion method, our implementation achieved lower RMSE scores in phantom experiments and in vivo reconstructions with fewer artifacts.