Sparse-Representation-Based Direct Minimum L

A sparse-representation-based direct minimum Lp-norm algorithm is proposed for a two-dimensional MRI phase unwrapping. First, the algorithm converts the weighted-Lp-norm-minimization-based phase unwrapping problem into a linear system problem whose system (coefficient) matrix is a large, symmetric one. Then, the coefficient-matrix is represented in the sparse structure. Finally, standard direct solvers are employed to solve this linear system. Several wrapped phase datasets, including simulated and MR data, were used to evaluate this algorithm’s performance. The results demonstrated that the proposed algorithm for unwrapping MRI phase data is reliable and robust

Magnetic Resonance Imaging of Susceptibility Effects in Carotid Atherosclerosis

This thesis explores the use of susceptibility-weighted imaging (SWI) and quantitative susceptibility mapping (QSM), to characterize carotid artery plaques with and without the use of ultrasmall superparamagnetic iron oxide (USPIO) nanoparticle contrast agents. The overall hypothesis is that QSM can serve to differentiate carotid artery plaque features of different susceptibility and provide a positive contrast mechanism for imaging the uptake of USPIOs. Chapter 1 describes the pathophysiology of carotid atherosclerosis. Vulnerable plaques, i.e. those at risk of rupture, can be characterized by the presence of a lipid rich necrotic core (LRNC), intraplaque haemorrhage (IPH), and inflammation. In addition, plaques may develop calcifications that may be protective of rupture. The chapter describes the established multi-contrast imaging protocols used for characterizing plaques. Furthermore, the use of USPIO-contrast agents to image inflammation is described. Chapter 2 describes the physical principles of MR image generation including the sensitivity to magnetic susceptibility. The principles of T2*w imaging, and susceptibility weighted imaging (SWI) are explained. Chapter 3 reviews the principles and post-processing steps involved in commonly used algorithms for QSM in terms of the underlying physical and mathematical principles which are then demonstrated in the form of numerical simulations. Chapter 4 presents the application of SWI to a group of patients who underwent USPIO enhanced MRI on a 1.5T MRI system. Images were acquired prior to infusion and 48 hours post infusion. SWI and gradient echo phase images were used to depict the field inhomogeneities generated by diamagnetic and paramagnetic materials within the plaques, calcification and USPIO-uptake. These results were then compared to a conventional carotid multi-contrast protocol, which includes R2*-mapping and T2*w imaging, and, where available, CT and histology. In chapter 5 QSM is performed in the carotid artery wall of a cohort of normal volunteers on a 1.5T MRI system. Unlike the brain, the neck contains fat which can cause severe errors in the field estimate, which propagate into the susceptibility map. Therefore, QSM was combined with water-fat separation for application in the neck to correct for these artifacts. This correctly estimated a high fat-fraction in fatty tissue in the neck and allowed for a detailed depiction of the anatomy of healthy volunteers. The susceptibility value measured in fatty tissue agreed with literature values. Chapter 6 applies QSM with water-fat separation to a subset of the patient group on a 1.5T MRI system. On pre-contrast scans QSM successfully identified calcification as diamagnetic tissue and the water-fat separation identified a lipid core. On the post-contrast susceptibility maps, USPIO-uptake was identified as hyperintense signal. This allows QSM to provide quantitative contrast in carotid imaging that can identify multiple features simultaneously and to simplify the imaging of USPIO-contrast. The results were confirmed using the multi-contrast carotid MRI protocol and, where available, histology and CT. Chapter 7 discusses the limitations of the current studies and the potential future improvements of the current methodology in terms of MR acquisition, post-processing algorithms and MR protocols. Future studies could serve to further evaluate the potential of QSM in carotid imaging and use it as a novel tool to quantify USPIO uptake in atherosclerotic carotid arteries

Contributions of Continuous Max-Flow Theory to Medical Image Processing

Discrete graph cuts and continuous max-flow theory have created a paradigm shift in many areas of medical image processing. As previous methods limited themselves to analytically solvable optimization problems or guaranteed only local optimizability to increasingly complex and non-convex functionals, current methods based now rely on describing an optimization problem in a series of general yet simple functionals with a global, but non-analytic, solution algorithms. This has been increasingly spurred on by the availability of these general-purpose algorithms in an open-source context. Thus, graph-cuts and max-flow have changed every aspect of medical image processing from reconstruction to enhancement to segmentation and registration. To wax philosophical, continuous max-flow theory in particular has the potential to bring a high degree of mathematical elegance to the field, bridging the conceptual gap between the discrete and continuous domains in which we describe different imaging problems, properties and processes. In Chapter 1, we use the notion of infinitely dense and infinitely densely connected graphs to transfer between the discrete and continuous domains, which has a certain sense of mathematical pedantry to it, but the resulting variational energy equations have a sense of elegance and charm. As any application of the principle of duality, the variational equations have an enigmatic side that can only be decoded with time and patience. The goal of this thesis is to show the contributions of max-flow theory through image enhancement and segmentation, increasing incorporation of topological considerations and increasing the role played by user knowledge and interactivity. These methods will be rigorously grounded in calculus of variations, guaranteeing fuzzy optimality and providing multiple solution approaches to addressing each individual problem

New Advances in Susceptibility Weighted MRI to Determine Physiological Parameters

Die Magnetresonanztomographie bietet die Möglichkeit der Bestimmung des Blutoxygenierungsgrades kleiner venöser Gefäße und damit lokaler Hirnareale mit Hilfe einer Multiecho-Gradientenecho-Sequenz. Mit dieser Sequenz kann der Signalzerfall in einem Voxel, welches von einer einzelnen Vene bzw. von Blutkapillaren durchzogen ist, bestimmt werden. Der Signalzerfall ist charakteristisch für die von der Vene oder den Kapillaren erzeugten Feldinhomogenitäten, so dass sich Aussagen über den Blutoxygenierungsgrad und Blutvolumenanteil treffen lassen. Durch Fitten simulierter Signalverläufe an gemessene Phantom- und Probandendaten konnte gezeigt werden, dass es mit der hier vorgestellten Methode möglich ist, den venösen Blutoxygenierungsgrad zu quantifizieren. Weiterhin konnte eine durch gezielte Modulation des zerebralen Blutflusses hervorgerufene Änderung der Blutoxygenierung in vivo nachgewiesen werden. Die Erweiterung des Modells eines einzelnen Gefäßes auf ein Gefäßnetzwerk diente als Grundlage zur theoretischen Beschreibung der Blutkapillaren, die das Hirngewebe durchziehen und mit Sauerstoff versorgen. Dieses Netzwerkmodel konnte in Phantomexperimenten verifiziert werden. Dagegen zeigte sich bei einer Probandenmessung, dass es nicht möglich ist einzig anhand des gemessenen Signalverlaufs valide Werte für die Blutoxygenierung und den Blutvolumenanteil eindeutig zu bestimmen. Die hohe Korrelation zwischen beiden Parametern bewirkt, dass mehrere Paare von Oxygenierungs- und Volumenwerten passende Signalkurven liefern. Eine unabhängige Quantifizierung oder Abschätzung des venösen Blutvolumens kann hier helfen eindeutige Oxygenierungswerte zu erhalten. Im Rahmen der vorliegenden Dissertation konnte das Signalverhalten von suszeptibilitätssensitiven Messungen in der Magnetresonanztomographie genauer untersucht und eine Methode zur nicht-invasiven Bestimmung der venösen Blutoxygenierung an einzelnen Gefäßen entwickelt werden. Erste in vivo Ergebnisse des Gefäßnetzwerkes verdeutlichen, dass für eine genaue Quantifizierung der Blutoxygenierung weitere Parameter, wie das Blutvolumen, unabhängig bestimmt werden müssen. Dennoch ist es möglich, die Methode am einzelnen Blutgefäß zur besseren Charakterisierung von Pathologien sowie physiologischen Änderungen, z.B. bei der funktionellen Magnetresonanztomographie, einzusetzen.Magnetic resonance imaging allows to determine the blood oxygenation level of small venous vessels or the blood capillary network by evaluating the magnetic resonance signal acquired with multi-echo gradient-echo sequences. The signal formation of a voxel traversed by a vein or interspersed with capillaries shows a characteristic decay or modulation as a function of time from which the blood oxygenation and blood volume fraction can be derived. It could be demonstrated in phantom measurements that the signal of a single vessel traversed voxel correctly matched the calculations of numerical signal simulation. By fitting the signal simulation to in vivo measurements of cerebral venous vessels, vessel size and venous blood oxygenation was determined quantitatively. Furthermore, it was possible to detect and to quantify a physiologically induced change in cerebral venous blood oxygenation. To describe the signal of the blood capillary network in normal brain matter, an extension of the single vessel model to a vessel network was applied. This network model was also validated in phantom experiments. As a result of these investigations it was found that the two parameters describing the network, the blood volume fraction and blood oxygenation level, are correlated to each other and can not be separated without additional information by simply fitting the signal simulation to the measurement. This finding was of special importance in the initial in vivo measurements conducted in the present work. Where, independent blood volume determination may help to further validate the quantified blood oxygenation level. In the present work a non-invasive method was developed to quantify cerebral blood oxygenation levels in single veins. This was possible by investigating the signal evolution of susceptibility sensitive magnetic resonance imaging. The initial result of the vessel network signal reveals, that for obtaining a valid blood oxygenation level, the volume fraction has to be further determined by an independent measurement. Nevertheless, is has been demonstrated that the quantification of the blood oxygenation level in single venous vessels is possible and can be applied in clinical diagnosis for better characterization of cerebral pathologies or in physiological investigations, like in functional magnetic resonance imaging

Application of Phase Imaging at High Field - MR Thermometry at 7 Tesla

The main purpose of this research was to develop improved methods for RF coil characterisation, and for non-invasive spatio-temporal mapping of temperature in the living body, in order to utilise the full potential of magnetic resonance imaging (MRI) at high magnetic fields by ensuring radiofrequency (RF) safety. Current RF power limits are often overly conservative, unnecessarily limiting the full potential of MRI, especially at high field. Thus it is useful to monitor tissue temperature while running MR imaging sequences which may deposit high RF power. Proton resonance frequency (PRF) MR thermometry can employ the phase of the complex MR signal to estimate temperature change over time. However, the shift of the water PRF with temperature is relatively small, making phase-based MR thermometry inherently sensitive to any extraneously caused changes of local frequency or MR phase. A potential source of error to PRF MR thermometry is a change in surround air susceptibility. The considerable impact of air susceptibility changes on PRF MR thermometry was demonstrated and quantified in experiments and magnetic field simulations. One way of correcting MR thermometry is to use a chemically shifted reference substance, in combination with a phase-sensitive chemical shift-selective MR thermometry sequence. The requirement of having a reliable separation of substances based on their resonance frequency was met by a novel frequency-selective phase-sensitive spin-echo (SE) MR thermometry sequence. This sequence was thoroughly tested in phantom and in-vivo experiments as well as in extensive Bloch simulations. The sequence limitations and advantages are discussed in detail. This technique acquires unsaturated water and fat images in rapid succession at the same position in space. The acquisition of a water and fat slice in less than 100 ms allows the correction of rapid field fluctuations in the brain caused by breathing and heartbeat, while still ensuring the correction of long term drift. With no assumptions required regarding temperature distribution in the tissue, this novel MR thermometry technique can measure brain temperature within a single (1.5 mm)3 voxel with a very low standard deviation (SD) of 0.3 K. Using an MRI phantom with a dimethyl sulfoxide reference, heating experiments achieved a MR temperature measurement with an SD of approximately 0.1 K in a single (1.5 mm)3 voxel. In conclusion, the work presented in this thesis assists the development of a real-time in-vivo temperature monitoring system that guarantees patient RF safety at high field

Phase unwrapping of MR images using ΦUN - A fast and robust region growing algorithm

We present a fully automated phase unwrapping algorithm (ΦUN) which is optimized for high-resolution magnetic resonance imaging data. The algorithm is a region growing method and uses separate quality maps for seed finding and unwrapping which are retrieved from the full complex information of the data. We compared our algorithm with an established method in various phantom and in vivo data and found a very good agreement between the results of both techniques. ΦUN, however, was significantly faster at low signal to noise ratio (SNR) and data with a more complex phase topography, making it particularly suitable for applications with low SNR and high spatial resolution. ΦUN is freely available to the scientific community