A new discrete dipole kernel for quantitative susceptibility mapping

PURPOSE: Most approaches for quantitative susceptibility mapping (QSM) are based on a forward model approximation that employs a continuous Fourier transform operator to solve a differential equation system. Such formulation, however, is prone to high-frequency aliasing. The aim of this study was to reduce such errors using an alternative dipole kernel formulation based on the discrete Fourier transform and discrete operators. METHODS: The impact of such an approach on forward model calculation and susceptibility inversion was evaluated in contrast to the continuous formulation both with synthetic phantoms and in vivo MRI data. RESULTS: The discrete kernel demonstrated systematically better fits to analytic field solutions, and showed less over-oscillations and aliasing artifacts while preserving low- and medium-frequency responses relative to those obtained with the continuous kernel. In the context of QSM estimation, the use of the proposed discrete kernel resulted in error reduction and increased sharpness. CONCLUSION: This proof-of-concept study demonstrated that discretizing the dipole kernel is advantageous for QSM. The impact on small or narrow structures such as the venous vasculature might by particularly relevant to high-resolution QSM applications with ultra-high field MRI - a topic for future investigations. The proposed dipole kernel has a straightforward implementation to existing QSM routines

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, 2018. © 2018 International Society for Magnetic Resonance in Medicine

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

Quantitative susceptibility mapping: Report from the 2016 reconstruction challenge

PURPOSE: The aim of the 2016 quantitative susceptibility mapping (QSM) reconstruction challenge was to test the ability of various QSM algorithms to recover the underlying susceptibility from phase data faithfully. METHODS: Gradient-echo images of a healthy volunteer acquired at 3T in a single orientation with 1.06 mm isotropic resolution. A reference susceptibility map was provided, which was computed using the susceptibility tensor imaging algorithm on data acquired at 12 head orientations. Susceptibility maps calculated from the single orientation data were compared against the reference susceptibility map. Deviations were quantified using the following metrics: root mean squared error (RMSE), structure similarity index (SSIM), high-frequency error norm (HFEN), and the error in selected white and gray matter regions. RESULTS: Twenty-seven submissions were evaluated. Most of the best scoring approaches estimated the spatial frequency content in the ill-conditioned domain of the dipole kernel using compressed sensing strategies. The top 10 maps in each category had similar error metrics but substantially different visual appearance. CONCLUSION: Because QSM algorithms were optimized to minimize error metrics, the resulting susceptibility maps suffered from over-smoothing and conspicuity loss in fine features such as vessels. As such, the challenge highlighted the need for better numerical image quality criteria

Recommended Implementation of Quantitative Susceptibility Mapping for Clinical Research in The Brain: A Consensus of the ISMRM Electro-Magnetic Tissue Properties Study Group

This article provides recommendations for implementing quantitative susceptibility mapping (QSM) for clinical brain research. It is a consensus of the ISMRM Electro-Magnetic Tissue Properties Study Group. While QSM technical development continues to advance rapidly, the current QSM methods have been demonstrated to be repeatable and reproducible for generating quantitative tissue magnetic susceptibility maps in the brain. However, the many QSM approaches available give rise to the need in the neuroimaging community for guidelines on implementation. This article describes relevant considerations and provides specific implementation recommendations for all steps in QSM data acquisition, processing, analysis, and presentation in scientific publications. We recommend that data be acquired using a monopolar 3D multi-echo GRE sequence, that phase images be saved and exported in DICOM format and unwrapped using an exact unwrapping approach. Multi-echo images should be combined before background removal, and a brain mask created using a brain extraction tool with the incorporation of phase-quality-based masking. Background fields should be removed within the brain mask using a technique based on SHARP or PDF, and the optimization approach to dipole inversion should be employed with a sparsity-based regularization. Susceptibility values should be measured relative to a specified reference, including the common reference region of whole brain as a region of interest in the analysis, and QSM results should be reported with - as a minimum - the acquisition and processing specifications listed in the last section of the article. These recommendations should facilitate clinical QSM research and lead to increased harmonization in data acquisition, analysis, and reporting

Bone remodeling simulations: challenges, problems and applications

La remodelación ósea es el mecanismo que regula la relación entre la morfología del hueso y sus cargas mecánicas externas. Se basa en el hecho de que el hueso se adapta a las condiciones mecánicas a las que está expuesto. Varios factores mecánicos y bioquímicos pueden regular la respuesta final de la remodelación ósea. De hecho, se considera que la remodelación ósea pretende alcanzar varios objetivos mecánicos: reparar el daño para reducir el riesgo de fractura y optimizar la rigidez y resistencia con el mínimo peso. Durante las últimas décadas, se han propuesto un gran número de leyes matemáticas implementadas numéricamente, pero la mayoría de ellas presentan diferentes problemas como la estabilidad, la convergencia o la dependencia de las condiciones iniciales. Por tanto, el objetivo principal de esta tesis es estudiar los modelos de remodelación ósea, mostrando sus retos, su problemática y su aplicación en el ámbito clínico. En primer lugar, se han revisado dos teorías clásicas de la remodelación ósea (conocidas como modelo de Stanford y modelo de Doblaré y García). En ambos casos, se propone un aspecto novedoso planteando que el estímulo homeostático de referencia no es constante, sino que depende localmente de la historia de carga que cada punto local está soportando. Como consecuencia directa de esta hipótesis, se demuestra que las inestabilidades numéricas que normalmente presentan estos algoritmos, pueden quedar resueltas, mejorando claramente los resultados finales. Esta metodología se aplicó a un modelo de elementos finitos 2D/3D mejorando la convergencia de la solución y asegurando su estabilidad numérica a largo plazo. Por otra parte, en un intento de dilucidar las características de adaptación mecánica del hueso en diferentes escalas, se plantea una relación a nivel órgano y a nivel de tejido que depende de un cambio en el estímulo homeostático de referencia acorde con la densidad aparente, mientras que se considera que la densidad de energía de deformación a nivel de tejido permanece invariante. Esta hipótesis mejora la unicidad de la solución y la hace independiente de las condiciones iniciales, ayudando también a su estabilidad numérica. Además, en esta tesis se aborda el modelado de paciente específico que es un tema que está adquiriendo cada vez más importancia. Una de las principales dificultades en la creación de modelos de paciente específico, es la determinación de las cargas que el hueso está realmente soportando. Los datos relativos a pacientes específicos, como la geometría ósea y la distribución de la densidad ósea, puede ser utilizados para determinar estas cargas. Por lo tanto, se ha estudiado la estimación de la cargas con tres diferentes técnicas matemáticas: regresión lineal, redes neuronales artificiales y máquinas de soporte vector. Estas técnicas se han aplicado a un ejemplo teórico para obtener las cargas a través de la densidad aparente que se predice con los modelos de remodelación ósea. Para concluir, la metodología desarrollada que combina modelos de remodelación ósea con redes neuronales se ha aplicado a la predicción de las cargas de cinco tibias de pacientes. Para ello, se han determinado la geometría y la distribución de la densidad a partir de un TAC y se han introducido los valores de densidad en el modelo previamente desarrollado, obteniendo así, las cargas específicas de las tibias de los pacientes. Con el fin de validar la capacidad de esta novedosa técnica, se han comparado las cargas obtenidas de la técnica propuesta con las cargas obtenidas en un análisis de marcha de dichos pacientes. Los errores obtenidos en las predicciones han sido menores de un 6 %. Por lo tanto, se puede concluir que la metodología aquí propuesta, permite determinar de forma aproximada las cargas que un hueso específico soporta.Bone remodeling is the mechanism that regulates the relationship between bone morphology and its external mechanical loads. It is based on the fact that bone adapts itself to the mechanical conditions to which it is exposed. Several mechanical and biochemical factors may regulate the final bone remodeling response. In fact, bone remodeling is hypothesized to achieve several mechanical objectives: repair damage to reduce the risk of fracture and optimize stiffness and strength with minimum weight. During recent decades, a great number of numerically implemented mathematical laws have been proposed, but most of them present different problems as stability, convergence or dependence of the initial conditions. Thus, the main scope of this Thesis is to study bone remodeling models, showing their challenges, their problematic and their applicability in the clinical setting. Firstly, we revisit two classical bone remodeling theories (Stanford model and Doblaré and García model). In both of them, the reference homeostatic stimulus is hypothesized that is not constant, but it is locally dependent on the loading history that each local point is effectively supporting. As a direct consequence of this assumption, we demonstrate that the numerical instabilities that all these algorithms normally present can be solved, clearly improving the final results. For this reason, we applied this methodology to 2D/3D finite element models. This contribution improves the convergence of the solution, leading to its numerical stability in the long-term. In an attempt to elucidate the features of bone adaptation at the di erent scales, we hypothesize that the relationship between the organ level and tissue level depends on the reference homeostatic stimulus changes according to the density and the tissue effective energy remains unchanged. This assumption improves the uniqueness of the solution, independently of the initial conditions selected and clearly helps in its numerical stability. In addition, patient-specific modeling is becoming increasingly important. One of the most challenging diffculties in creating patient-specific models is the determination of the specific load that the bone is really supporting. Real information related to specific patients, such as bone geometry and bone density distribution, can be used to determine patient loads. Therefore, we studied three different mathematical techniques: linear regression, artificial neural networks (ANN) and support vector machines (SVM). These techniques have been applied to a theoretical femur to obtain the load through the density that came from many bone remodeling simulations. Finally, the application of this novel methodology has been applied for the loading prediction of five real tibias. We are able to determine the subject-specific forces from CT data, from which we obtain bone geometry and density distribuviition of the five tibias. Then, the density values at certain bone regions have been introduced in the methodology developed that combines bone remodeling models and artificial neuronal networks (ANN) for obtaining the predicted subject-specific loads. Finally, in order to validate this novel technique for tibia loading predictions, we compare predicted loads with the loads obtained from the patientspecific musculoskeletal model. The errors between both loads were lower tan 6%. Therefore, the methodology proposed has been validate

The implementation and application of quantitative susceptibility mapping in the pre-clinical liver

Quantitative Susceptibility Mapping (QSM) is a relatively new Magnetic Resonance Imaging (MRI) technique that gives information about the relative quantities of magnetically active constituents of a biological system. Using phase data, not normally utilised in standard MRI, measurements are made of local variations in the main magnetic field, B0. This data is then processed to calculate a map of local magnetic susceptibility within an organ of interest. This map yields relatively quantitative information, and compositional inferences can be made regarding the organ. Thus far, the body of literature on QSM has focussed almost exclusively on the brain, and has been performed on clinical data. This will be a preclinical project, and will focus primarily on the liver. The first two chapters of this thesis will establish the context of the research, as well as the background theory of QSM, including a detailed discussion of the set of algorithms selected to calculate the susceptibility maps for this body of work. The implementation of QSM in the preclinical liver has not been performed previously, and the novelty of the technique and the experimental work performed necessitated optimising both data acquisition and processing protocols. This was done on an empirical basis, and comprises the experimental work detailed in chapter 3. Chapters 4 – 6 describe the application of QSM to a number of hepatic conditions. It was established in chapter 4 that QSM is sensitive to changes in the oxygen saturation of blood in large branches of the major hepatic blood vessels in healthy mice. Chapter 5 discusses the application of QSM to a preclinical model of colorectal liver metastases, and also examines the ability of QSM to assess the efficacy of a Vascular Disrupting Agent (VDA), a novel chemotherapeutic drug. Finally, chapter 6 details the application of QSM to a model of liver cirrhosis