An Optimal Dimensionality Multi-shell Sampling Scheme with Accurate and Efficient Transforms for Diffusion MRI

This paper proposes a multi-shell sampling scheme and corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The sampling scheme uses an optimal number of samples, equal to the degrees of freedom of the band-limited diffusion signal in the SPF domain, and allows for computationally efficient reconstruction. We use synthetic data sets to demonstrate that the proposed scheme allows for greater reconstruction accuracy of the diffusion signal than the multi-shell sampling schemes obtained using the generalised electrostatic energy minimisation (gEEM) method used in the Human Connectome Project. We also demonstrate that the proposed sampling scheme allows for increased angular discrimination and improved rotational invariance of reconstruction accuracy than the gEEM schemes.Comment: 4 pages, 4 figures presented at ISBI 201

(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior

Advanced diffusion magnetic resonance imaging (dMRI) techniques, like diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging (HARDI), remain underutilized compared to diffusion tensor imaging because the scan times needed to produce accurate estimations of fiber orientation are significantly longer. To accelerate DSI and HARDI, recent methods from compressed sensing (CS) exploit a sparse underlying representation of the data in the spatial and angular domains to undersample in the respective k- and q-spaces. State-of-the-art frameworks, however, impose sparsity in the spatial and angular domains separately and involve the sum of the corresponding sparse regularizers. In contrast, we propose a unified (k,q)-CS formulation which imposes sparsity jointly in the spatial-angular domain to further increase sparsity of dMRI signals and reduce the required subsampling rate. To efficiently solve this large-scale global reconstruction problem, we introduce a novel adaptation of the FISTA algorithm that exploits dictionary separability. We show on phantom and real HARDI data that our approach achieves significantly more accurate signal reconstructions than the state of the art while sampling only 2-4% of the (k,q)-space, allowing for the potential of new levels of dMRI acceleration.Comment: To be published in the 2017 Computational Diffusion MRI Workshop of MICCA

An Optimal Dimensionality Sampling Scheme on the Sphere for Antipodal Signals In Diffusion Magnetic Resonance Imaging

We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal symmetry, we design a sampling scheme that requires the optimal number of samples on the sphere, equal to the degrees of freedom required to represent the antipodally symmetric band-limited diffusion signal in the spectral (spherical harmonic) domain. Compared with existing sampling schemes on the sphere that allow for the accurate reconstruction of the diffusion signal, the proposed sampling scheme reduces the number of samples required by a factor of two or more. We analyse the numerical accuracy of the proposed SHT and show through experiments that the proposed sampling allows for the accurate and rotationally invariant computation of the SHT to near machine precision accuracy.Comment: Will be published in the proceedings of the International Conference Acoustics, Speech and Signal Processing 2015 (ICASSP'2015

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

HYDI-DSI revisited: Constrained non-parametric EAP imaging without q-space re-gridding

Producción CientíficaHybrid Diffusion Imaging (HYDI) was one of the first attempts to use multi-shell samplings of the q-space to infer diffusion properties beyond Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI). HYDI was intended as a flexible protocol embedding both DTI (for lower -values) and HARDI (for higher -values) processing, as well as Diffusion Spectrum Imaging (DSI) when the entire data set was exploited. In the latter case, the spherical sampling of the q-space is re-gridded by interpolation to a Cartesian lattice whose extent covers the range of acquired b-values, hence being acquisition-dependent. The Discrete Fourier Transform (DFT) is afterwards used to compute the corresponding Cartesian sampling of the Ensemble Average Propagator (EAP) in an entirely non-parametric way. From this lattice, diffusion markers such as the Return To Origin Probability (RTOP) or the Mean Squared Displacement (MSD) can be numerically estimated. We aim at re-formulating this scheme by means of a Fourier Transform encoding matrix that eliminates the need for q-space re-gridding at the same time it preserves the non-parametric nature of HYDI-DSI. The encoding matrix is adaptively designed at each voxel according to the underlying DTI approximation, so that an optimal sampling of the EAP can be pursued without being conditioned by the particular acquisition protocol. The estimation of the EAP is afterwards carried out as a regularized Quadratic Programming (QP) problem, which allows to impose positivity constraints that cannot be trivially embedded within the conventional HYDI-DSI. We demonstrate that the definition of the encoding matrix in the adaptive space allows to analytically (as opposed to numerically) compute several popular descriptors of diffusion with the unique source of error being the cropping of high frequency harmonics in the Fourier analysis of the attenuation signal. They include not only RTOP and MSD, but also Return to Axis/Plane Probabilities (RTAP/RTPP), which are defined in terms of specific spatial directions and are not available with the former HYDI-DSI. We report extensive experiments that suggest the benefits of our proposal in terms of accuracy, robustness and computational efficiency, especially when only standard, non-dedicated q-space samplings are available.Ministerio de Ciencia e Innovación (PID2021-124407NB-I00 and TED2021-130758B-I00)Ministry of Science and Higher Education (Poland) (PPN/BEK/ 2019/1/00421

Spherical deconvolution of multichannel diffusion MRI data with non-Gaussian noise models and spatial regularization

Spherical deconvolution (SD) methods are widely used to estimate the intra-voxel white-matter fiber orientations from diffusion MRI data. However, while some of these methods assume a zero-mean Gaussian distribution for the underlying noise, its real distribution is known to be non-Gaussian and to depend on the methodology used to combine multichannel signals. Indeed, the two prevailing methods for multichannel signal combination lead to Rician and noncentral Chi noise distributions. Here we develop a Robust and Unbiased Model-BAsed Spherical Deconvolution (RUMBA-SD) technique, intended to deal with realistic MRI noise, based on a Richardson-Lucy (RL) algorithm adapted to Rician and noncentral Chi likelihood models. To quantify the benefits of using proper noise models, RUMBA-SD was compared with dRL-SD, a well-established method based on the RL algorithm for Gaussian noise. Another aim of the study was to quantify the impact of including a total variation (TV) spatial regularization term in the estimation framework. To do this, we developed TV spatially-regularized versions of both RUMBA-SD and dRL-SD algorithms. The evaluation was performed by comparing various quality metrics on 132 three-dimensional synthetic phantoms involving different inter-fiber angles and volume fractions, which were contaminated with noise mimicking patterns generated by data processing in multichannel scanners. The results demonstrate that the inclusion of proper likelihood models leads to an increased ability to resolve fiber crossings with smaller inter-fiber angles and to better detect non-dominant fibers. The inclusion of TV regularization dramatically improved the resolution power of both techniques. The above findings were also verified in brain data

A Unified Single-stage Learning Model for Estimating Fiber Orientation Distribution Functions on Heterogeneous Multi-shell Diffusion-weighted MRI

Diffusion-weighted (DW) MRI measures the direction and scale of the local diffusion process in every voxel through its spectrum in q-space, typically acquired in one or more shells. Recent developments in micro-structure imaging and multi-tissue decomposition have sparked renewed attention to the radial b-value dependence of the signal. Applications in tissue classification and micro-architecture estimation, therefore, require a signal representation that extends over the radial as well as angular domain. Multiple approaches have been proposed that can model the non-linear relationship between the DW-MRI signal and biological microstructure. In the past few years, many deep learning-based methods have been developed towards faster inference speed and higher inter-scan consistency compared with traditional model-based methods (e.g., multi-shell multi-tissue constrained spherical deconvolution). However, a multi-stage learning strategy is typically required since the learning process relied on various middle representations, such as simple harmonic oscillator reconstruction (SHORE) representation. In this work, we present a unified dynamic network with a single-stage spherical convolutional neural network, which allows efficient fiber orientation distribution function (fODF) estimation through heterogeneous multi-shell diffusion MRI sequences. We study the Human Connectome Project (HCP) young adults with test-retest scans. From the experimental results, the proposed single-stage method outperforms prior multi-stage approaches in repeated fODF estimation with shell dropoff and single-shell DW-MRI sequences