Estimation of Fiber Orientations Using Neighborhood Information

Data from diffusion magnetic resonance imaging (dMRI) can be used to reconstruct fiber tracts, for example, in muscle and white matter. Estimation of fiber orientations (FOs) is a crucial step in the reconstruction process and these estimates can be corrupted by noise. In this paper, a new method called Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is described and shown to reduce the effects of noise and improve FO estimation performance by incorporating spatial consistency. FORNI uses a fixed tensor basis to model the diffusion weighted signals, which has the advantage of providing an explicit relationship between the basis vectors and the FOs. FO spatial coherence is encouraged using weighted l1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is encouraged using a squared error between the observed and reconstructed diffusion weighted signals. After appropriate weighting of these competing objectives, the resulting objective function is minimized using a block coordinate descent algorithm, and a straightforward parallelization strategy is used to speed up processing. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for both qualitative and quantitative evaluation. The results demonstrate that FORNI improves the quality of FO estimation over other state of the art algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16 figure

Spectral Clustering en IRM de diffusion pour Retrouver les Faisceaux de la Matière Blanche

White matter fiber clustering allows to get insight about anatomical structures in order to generate atlases, perform clear visualizations and compute statistics across subjects, all important and current neuroimaging problems. In this work, we present a Diffusion Maps clustering method applied to diffusion MRI in order to cluster and segment complex white matter fiber bundles. It is well-known that Diffusion Tensor Imaging (DTI) is restricted in complex fiber regions with crossings and this is why recent High Angular Resolution Diffusion Imaging (HARDI) such has Q-Ball Imaging (QBI) have been introduced to overcome these limitations. QBI reconstructs the diffusion orientation distribution function (ODF), a spherical function that has its maxima agreeing with the underlying fiber populations. In this paper, we introduce the usage of the Diffusion Maps technique and show how it can be used to directly cluster set of fiber tracts, that could be obtained through a streamline tractography for instance, and how it can also help in segmenting fields of ODF images, obtained through a linear and regularized ODF estimation algorithm based on a spherical harmonics representation of the Q-Ball data. We first show the advantage of using Diffusion Maps clustering over classical methods such as N-Cuts and Laplacian Eigenmaps in both cases. In particular, our Diffusion Maps requires a smaller number of hypothesis from the input data, reduces the number of artifacts in fiber tract clustering and ODF image segmentation and automatically exhibits the number of clusters in both cases by using an adaptive scale-space parameter. We also show that our ODF Diffusion Maps clustering can reproduce published results using the diffusion tensor (DT) clustering with N-Cuts on simple synthetic images without crossings. On more complex data with crossings, we show that our ODF-based method succeeds to separate fiber bundles and crossing regions whereas the DT-based methods generate artifacts and exhibit wrong number of clusters. Finally, we illustrate the potential of our approach on a real brain dataset where we successfully segment well-known fiber bundles

A Simplified Crossing Fiber Model in Diffusion Weighted Imaging

Diffusion MRI (dMRI) is a vital source of imaging data for identifying anatomical connections in the living human brain that form the substrate for information transfer between brain regions. dMRI can thus play a central role toward our understanding of brain function. The quantitative modeling and analysis of dMRI data deduces the features of neural fibers at the voxel level, such as direction and density. The modeling methods that have been developed range from deterministic to probabilistic approaches. Currently, the Ball-and-Stick model serves as a widely implemented probabilistic approach in the tractography toolbox of the popular FSL software package and FreeSurfer/TRACULA software package. However, estimation of the features of neural fibers is complex under the scenario of two crossing neural fibers, which occurs in a sizeable proportion of voxels within the brain. A Bayesian non-linear regression is adopted, comprised of a mixture of multiple non-linear components. Such models can pose a difficult statistical estimation problem computationally. To make the approach of Ball-and-Stick model more feasible and accurate, we propose a simplified version of Ball-and-Stick model that reduces parameter space dimensionality. This simplified model is vastly more efficient in the terms of computation time required in estimating parameters pertaining to two crossing neural fibers through Bayesian simulation approaches. Moreover, the performance of this new model is comparable or better in terms of bias and estimation variance as compared to existing models

Higher-Order Tensors and Differential Topology in Diffusion MRI Modeling and Visualization

Diffusion Weighted Magnetic Resonance Imaging (DW-MRI) is a noninvasive method for creating three-dimensional scans of the human brain. It originated mostly in the 1970s and started its use in clinical applications in the 1980s. Due to its low risk and relatively high image quality it proved to be an indispensable tool for studying medical conditions as well as for general scientific research. For example, it allows to map fiber bundles, the major neuronal pathways through the brain. But all evaluation of scanned data depends on mathematical signal models that describe the raw signal output and map it to biologically more meaningful values. And here we find the most potential for improvement. In this thesis we first present a new multi-tensor kurtosis signal model for DW-MRI. That means it can detect multiple overlapping fiber bundles and map them to a set of tensors. Compared to other already widely used multi-tensor models, we also add higher order kurtosis terms to each fiber. This gives a more detailed quantification of fibers. These additional values can also be estimated by the Diffusion Kurtosis Imaging (DKI) method, but we show that these values are drastically affected by fiber crossings in DKI, whereas our model handles them as intrinsic properties of fiber bundles. This reduces the effects of fiber crossings and allows a more direct examination of fibers. Next, we take a closer look at spherical deconvolution. It can be seen as a generalization of multi-fiber signal models to a continuous distribution of fiber directions. To this approach we introduce a novel mathematical constraint. We show, that state-of-the-art methods for estimating the fiber distribution become more robust and gain accuracy when enforcing our constraint. Additionally, in the context of our own deconvolution scheme, it is algebraically equivalent to enforcing that the signal can be decomposed into fibers. This means, tractography and other methods that depend on identifying a discrete set of fiber directions greatly benefit from our constraint. Our third major contribution to DW-MRI deals with macroscopic structures of fiber bundle geometry. In recent years the question emerged, whether or not, crossing bundles form two-dimensional surfaces inside the brain. Although not completely obvious, there is a mathematical obstacle coming from differential topology, that prevents general tangential planes spanned by fiber directions at each point to be connected into consistent surfaces. Research into how well this constraint is fulfilled in our brain is hindered by the high precision and complexity needed by previous evaluation methods. This is why we present a drastically simpler method that negates the need for precisely finding fiber directions and instead only depends on the simple diffusion tensor method (DTI). We then use our new method to explore and improve streamsurface visualization.<br /

Fast diffusion MRI based on sparse acquisition and reconstruction for long-term population imaging

Diffusion weighted magnetic resonance imaging (dMRI) is a unique MRI modality to probe the diffusive molecular transport in biological tissue. Due to its noninvasiveness and its ability to investigate the living human brain at submillimeter scale, dMRI is frequently performed in clinical and biomedical research to study the brain’s complex microstructural architecture. Over the last decades large prospective cohort studies have been set up with the aim to gain new insights into the development and progression of brain diseases across the life span and to discover biomarkers for disease prediction and potentially prevention. To allow for diverse brain imaging using different MRI modalities, stringent scan time limits are typically imposed in population imaging. Nevertheless, population studies aim to apply advanced and thereby time consuming dMRI protocols that deliver high quality data with great potential for future analysis. To allow for time-efficient but also versatile diffusion imaging, this thesis contributes to the investigation of accelerating diffusion spectrum imaging (DSI), an advanced dMRI technique that acquires imaging data with high intra-voxel resolution of tissue microstructure. Combining state-of-the-art parallel imaging and the theory of compressed sensing (CS) enables the acceleration of spatial encoding and diffusion encoding in dMRI. In this way, the otherwise long acquisition times in DSI can be reduced significantly. In this thesis, first, suitable q-space sampling strategies and basis functions are explored that fulfill the requirements of CS theory for accurate sparse DSI reconstruction. Novel 3D q-space sample distributions are investigated for CS-DSI. Moreover, conventional CS-DSI based on the discrete Fourier transform is compared for the first time to CS-DSI based on the continuous SHORE (simple harmonic oscillator based reconstruction and estimation) basis functions. Based on these findings, a CS-DSI protocol is proposed for application in a prospective cohort study, the Rhineland Study. A pilot study was designed and conducted to evaluate the CS-DSI protocol in comparison with state-of-the-art 3-shell dMRI and dedicated protocols for diffusion tensor imaging (DTI) and for the combined hindered and restricted model of diffusion (CHARMED). Population imaging requires processing techniques preferably with low computational cost to process and analyze the acquired big data within a reasonable time frame. Therefore, a pipeline for automated processing of CS-DSI acquisitions was implemented including both in-house developed and existing state-of-the-art processing tools. The last contribution of this thesis is a novel method for automatic detection and imputation of signal dropout due to fast bulk motion during the diffusion encoding in dMRI. Subject motion is a common source of artifacts, especially when conducting clinical or population studies with children, the elderly or patients. Related artifacts degrade image quality and adversely affect data analysis. It is, thus, highly desired to detect and then exclude or potentially impute defective measurements prior to dMRI analysis. Our proposed method applies dMRI signal modeling in the SHORE basis and determines outliers based on the weighted model residuals. Signal imputation reconstructs corrupted and therefore discarded measurements from the sparse set of inliers. This approach allows for fast and robust correction of imaging artifacts in dMRI which is essential to estimate accurate and precise model parameters that reflect the diffusive transport of water molecules and the underlying microstructural environment in brain tissue.Die diffusionsgewichtete Magnetresonanztomographie (dMRT) ist ein einzigartiges MRTBildgebungsverfahren, um die Diffusionsbewegung von Wassermolekülen in biologischem Gewebe zu messen. Aufgrund der Möglichkeit Schichtbilder nicht invasiv aufzunehmen und das lebende menschliche Gehirn im Submillimeter-Bereich zu untersuchen, ist die dMRT ein häufig verwendetes Bildgebungsverfahren in klinischen und biomedizinischen Studien zur Erforschung der komplexen mikrostrukturellen Architektur des Gehirns. In den letzten Jahrzehnten wurden große prospektive Kohortenstudien angelegt, um neue Einblicke in die Entwicklung und den Verlauf von Gehirnkrankheiten über die Lebenspanne zu erhalten und um Biomarker zur Krankheitserkennung und -vorbeugung zu bestimmen. Um durch die Verwendung unterschiedlicher MRT-Verfahren verschiedenartige Schichtbildaufnahmen des Gehirns zu ermöglich, müssen Scanzeiten typischerweise stark begrenzt werden. Dennoch streben Populationsstudien die Anwendung von fortschrittlichen und daher zeitintensiven dMRT-Protokollen an, um Bilddaten in hoher Qualität und mit großem Potential für zukünftige Analysen zu akquirieren. Um eine zeiteffizente und gleichzeitig vielseitige Diffusionsbildgebung zu ermöglichen, leistet diese Dissertation Beiträge zur Untersuchung von Beschleunigungsverfahren für die Bildgebung mittels diffusion spectrum imaging (DSI). DSI ist ein fortschrittliches dMRT-Verfahren, das Bilddaten mit hoher intra-voxel Auflösung der Gewebestruktur erhebt. Werden modernste Verfahren zur parallelen MRT-Bildgebung mit der compressed sensing (CS) Theorie kombiniert, ermöglicht dies eine Beschleunigung der räumliche Kodierung und der Diffusionskodierung in der dMRT. Dadurch können die ansonsten langen Aufnahmezeiten für DSI erheblich reduziert werden. In dieser Arbeit werden zuerst geeigenete Strategien zur Abtastung des q-space sowie Basisfunktionen untersucht, welche die Anforderungen der CS-Theorie für eine korrekte Signalrekonstruktion der dünnbesetzten DSI-Daten erfüllen. Neue 3D-Verteilungen von Messpunkten im q-space werden für die Verwendung in CS-DSI untersucht. Außerdem wird konventionell auf der diskreten Fourier-Transformation basierendes CS-DSI zum ersten Mal mit einem CS-DSI Verfahren verglichen, welches kontinuierliche SHORE (simple harmonic oscillator based reconstruction and estimation) Basisfunktionen verwendet. Aufbauend auf diesen Ergebnissen wird ein CS-DSI-Protokoll zur Anwendung in einer prospektiven Kohortenstudie, der Rheinland Studie, vorgestellt. Eine Pilotstudie wurde entworfen und durchgeführt, um das CS-DSI-Protokoll im Vergleich mit modernster 3-shell-dMRT und mit dedizierten Protokollen für diffusion tensor imaging (DTI) und für das combined hindered and restricted model of diffusion (CHARMED) zu evaluieren. Populationsbildgebung erfordert Prozessierungsverfahren mit möglichst geringem Rechenaufwand, um große akquirierte Datenmengen in einem angemessenen Zeitrahmen zu verarbeiten und zu analysieren. Dafür wurde eine Pipeline zur automatisierten Verarbeitung von CS-DSI-Daten implementiert, welche sowohl eigenentwickelte als auch bereits existierende moderene Verarbeitungsprogramme enthält. Der letzte Beitrag dieser Arbeit ist eine neue Methode zur automatischen Detektion und Imputation von Signalabfall, welcher durch schnelle Bewegungen während der Diffusionskodierung in der dMRT entsteht. Bewegungen der Probanden während der dMRT-Aufnahme sind eine häufige Ursache für Bildfehler, vor allem in klinischen oder Populationsstudien mit Kindern, alten Menschen oder Patienten. Diese Artefakte vermindern die Datenqualität und haben einen negativen Einfluss auf die Datenanalyse. Daher ist es das Ziel, fehlerhafte Messungen vor der dMRI-Analyse zu erkennen und dann auszuschließen oder wenn möglich zu ersetzen. Die vorgestellte Methode verwendet die SHORE-Basis zur dMRT-Signalmodellierung und bestimmt Ausreißer mit Hilfe von gewichteten Modellresidualen. Die Datenimputation rekonstruiert die unbrauchbaren und daher verworfenen Messungen mit Hilfe der verbleibenden, dünnbesetzten Menge an Messungen. Dieser Ansatz ermöglicht eine schnelle und robuste Korrektur von Bildartefakten in der dMRT, welche erforderlich ist, um korrekte und präzise Modellparameter zu schätzen, die die Diffusionsbewegung von Wassermolekülen und die zugrundeliegende Mikrostruktur des Gehirngewebes reflektieren