Decoding complex flow phenomena via Dynamic Mode Decomposition

In this thesis, the viability of the Dynamic Mode Decomposition (DMD) as a technique to analyze and model complex dynamic real-world systems is presented. This method derives, directly from data, computationally efficient reduced-order models (ROMs) which can replace too onerous or unavailable high-fidelity physics-based models. Optimizations and extensions to the standard implementation of the methodology are proposed, investigating diverse case studies related to the decoding of complex flow phenomena. The flexibility of this data-driven technique allows its application to high-fidelity fluid dynamics simulations, as well as time series of real systems observations. The resulting ROMs are tested against two tasks: (i) reduction of the storage requirements of high-fidelity simulations or observations; (ii) interpolation and extrapolation of missing data. The capabilities of DMD can also be exploited to alleviate the cost of onerous studies that require many simulations, such as uncertainty quantification analysis, especially when dealing with complex high-dimensional systems. In this context, a novel approach to address parameter variability issues when modeling systems with space and time-variant response is proposed. Specifically, DMD is merged with another model-reduction technique, namely the Polynomial Chaos Expansion, for uncertainty quantification purposes. Useful guidelines for DMD deployment result from the study, together with the demonstration of its potential to ease diagnosis and scenario analysis when complex flow processes are involved.

The benefits of one-dimensional detectors for high-pressure powder X-ray diffraction

High-pressure powder X-ray diffraction is a fundamental technique for investigating structural responses to externally applied force. Synchrotron sources and two-dimensional detectors are required. In contrast to this conventional setup, high-resolution beamlines equipped with one-dimensional detectors could offer much better resolved peaks but cannot deliver accurate structure factors because they only sample a small portion of the Debye rings, which are usually inhomogeneous and spotty because of the small amount of sample. In this study, a simple method to overcome this problem is presented and successfully applied to solving the structure of an L-serine polymorph from powder data. A comparison of the obtained high-resolution high-pressure data with conventional data shows that this technique, providing up to ten times better angular resolution, can be of advantage for indexing, for lattice parameter refinement, and even for structure refinement and solution in special cases.

Effects Of High Pressure Homogenization On The Activity, Stability, Kinetics And Three-dimensional Conformation Of A Glucose Oxidase Produced By Aspergillus Niger.

High pressure homogenization (HPH) is a non-thermal method, which has been employed to change the activity and stability of biotechnologically relevant enzymes. This work investigated how HPH affects the structural and functional characteristics of a glucose oxidase (GO) from Aspergillus niger. The enzyme was homogenized at 75 and 150 MPa and the effects were evaluated with respect to the enzyme activity, stability, kinetic parameters and molecular structure. The enzyme showed a pH-dependent response to the HPH treatment, with reduction or maintenance of activity at pH 4.5-6.0 and a remarkable activity increase (30-300%) at pH 6.5 in all tested temperatures (15, 50 and 75°C). The enzyme thermal tolerance was reduced due to HPH treatment and the storage for 24 h at high temperatures (50 and 75°C) also caused a reduction of activity. Interestingly, at lower temperatures (15°C) the activity levels were slightly higher than that observed for native enzyme or at least maintained. These effects of HPH treatment on function and stability of GO were further investigated by spectroscopic methods. Both fluorescence and circular dichroism revealed conformational changes in the molecular structure of the enzyme that might be associated with the distinct functional and stability behavior of GO.

High-order fractional microwave-induced resistance oscillations in two-dimensional systems

We report on the observation of microwave-induced resistance oscillations associated with the fractional ratio n/m of the microwave irradiation frequency to the cyclotron frequency for m up to 8 in a two-dimensional electron system with high electron density. The features are quenched at high microwave frequencies independent of the fractional order m. We analyze temperature, power, and frequency dependencies of the magnetoresistance oscillations and discuss them in connection with existing theories.

Contribution of the second Landau level to the exchange energy of the three-dimensional electron gas in a high magnetic field

We derive a closed analytical expression for the exchange energy of the three-dimensional interacting electron gas in strong magnetic fields, which goes beyond the quantum limit (L=0) by explicitly including the effect of the second, L=1, Landau level and arbitrary spin polarization. The inclusion of the L=1 level brings the fields to which the formula applies closer to the laboratory range, as compared to previous expressions, valid only for L=0 and complete spin polarization. We identify and explain two distinct regimes separated by a critical density n(c). Below n(c), the per particle exchange energy is lowered by the contribution of L=1, whereas above n(c) it is increased. As special cases of our general equation we recover various known more limited results for higher fields, and we identify and correct a few inconsistencies in some of these earlier expressions.

Double-oblique free-breathing high resolution three-dimensional coronary magnetic resonance angiography.

OBJECTIVES: The goal of the present study was to develop a strategy for three-dimensional (3D) volume acquisition along the major axes of the coronary arteries. BACKGROUND: For high-resolution 3D free-breathing coronary magnetic resonance angiography (MRA), coverage of the coronary artery tree may be limited due to excessive measurement times associated with large volume acquisitions. Planning the 3D volume along the major axis of the coronary vessels may help to overcome such limitations. METHODS: Fifteen healthy adult volunteers and seven patients with X-ray angiographically confirmed coronary artery disease underwent free-breathing navigator-gated and corrected 3D coronary MRA. For an accurate volume targeting of the high resolution scans, a three-point planscan software tool was applied. RESULTS: The average length of contiguously visualized left main and left anterior descending coronary artery was 81.8 +/- 13.9 mm in the healthy volunteers and 76.2 +/- 16.5 mm in the patients (p = NS). For the right coronary artery, a total length of 111.7 +/- 27.7 mm was found in the healthy volunteers and 79.3 +/- 4.6 mm in the patients (p = NS). Comparing coronary MRA and X-ray angiography, a good agreement of anatomy and pathology was found in the patients. CONCLUSIONS: Double-oblique submillimeter free-breathing coronary MRA allows depiction of extensive parts of the native coronary arteries. The results obtained in patients suggest that the method has the potential to be applied in broader prospective multicenter studies where coronary MRA is compared with X-ray angiography.

High-resolution selective three-dimensional magnetic resonance coronary angiography with navigator-echo technique: segment-by-segment evaluation of coronary artery stenosis.

PURPOSE: To investigate the feasibility of high-resolution selective three-dimensional (3D) magnetic resonance coronary angiography (MRCA) in the evaluation of coronary artery stenoses. MATERIALS AND METHODS: In 12 patients with coronary artery stenoses, MRCA of the coronary artery groups, including the coronary segments with stenoses of 50% or greater based on conventional x-ray coronary angiography (CAG), was performed with double-oblique imaging planes by orienting the 3D slab along the major axis of each right coronary artery-left circumflex artery (RCA-LCX) group and each left main trunk-left anterior descending artery (LMT-LAD) group. Ten RCA-LCX and five LMT-LAD MR angiograms were obtained, and the results were compared with those of conventional x-ray angiography. RESULTS: Among 70 coronary artery segments expected to be covered, a total of 49 (70%) segments were fully demonstrated in diagnostic quality. The identification of segmental location of stenoses showed as high an accuracy as 96%. The retrospective analysis for stenosis of 50% or greater yielded the sensitivity, specificity, and accuracy of 80%, 85%, and 84%, respectively. CONCLUSION: Selective 3D MRCA has the potential for segment-by-segment evaluation of major portions of the right and left coronary arteries with high accuracy.

Three-dimensional high-resolution fast spin-echo coronary magnetic resonance angiography.

Due to SNR constraints, current "bright-blood" 3D coronary MRA approaches still suffer from limited spatial resolution when compared to conventional x-ray coronary angiography. Recent 2D fast spin-echo black-blood techniques maximize signal for coronary MRA at no loss in image spatial resolution. This suggests that the extension of black-blood coronary MRA with a 3D imaging technique would allow for a further signal increase, which may be traded for an improved spatial resolution. Therefore, a dual-inversion 3D fast spin-echo imaging sequence and real-time navigator technology were combined for high-resolution free-breathing black-blood coronary MRA. In-plane image resolution below 400 microm was obtained. Magn Reson Med 45:206-211, 2001.

Fast low-specific absorption rate B0 -mapping along projections at high field using two-dimensional radiofrequency pulses.

PURPOSE: At 7 Tesla (T), conventional static field (B0 ) projection mapping techniques, e.g., FASTMAP, FASTESTMAP, lead to elevated specific absorption rates (SAR), requiring longer total acquisition times (TA). In this work, the series of adiabatic pulses needed for slab selection in FASTMAP is replaced by a single two-dimensional radiofrequency (2D-RF) pulse to minimize TA while ensuring equal shimming performance. METHODS: Spiral gradients and 2D-RF pulses were designed to excite thin slabs in the small tip angle regime. The corresponding selection profile was characterized in phantoms and in vivo. After optimization of the shimming protocol, the spectral linewidths obtained after 2D localized shimming were compared with conventional techniques and published values from (Emir et al NMR Biomed 2012;25:152-160) in six different brain regions. RESULTS: Results on healthy volunteers show no significant difference (P > 0.5) between the spectroscopic linewidths obtained with the adiabatic (TA = 4 min) and the new low-SAR and time-efficient FASTMAP sequence (TA = 42 s). The SAR can be reduced by three orders of magnitude and TA accelerated six times without impact on the shimming performances or quality of the resulting spectra. CONCLUSION: Multidimensional pulses can be used to minimize the RF energy and time spent for automated shimming using projection mapping at high field. Magn Reson Med, 2014. © 2014 Wiley Periodicals, Inc.

High-resolution three-dimensional aortic magnetic resonance angiography and quantitative vessel wall characterization of different atherosclerotic stages in a rabbit model

PURPOSE: Atherosclerosis results in a considerable medical and socioeconomic impact on society. We sought to evaluate novel magnetic resonance imaging (MRI) angiography and vessel wall sequences to visualize and quantify different morphologic stages of atherosclerosis in a Watanabe hereditary hyperlipidemic (WHHL) rabbit model. MATERIAL AND METHODS: Aortic 3D steady-state free precession angiography and subrenal aortic 3D black-blood fast spin-echo vessel wall imaging pre- and post-Gadolinium (Gd) was performed in 14 WHHL rabbits (3 normal, 6 high-cholesterol diet, and 5 high-cholesterol diet plus endothelial denudation) on a commercial 1.5 T MR system. Angiographic lumen diameter, vessel wall thickness, signal-/contrast-to-noise analysis, total vessel area, lumen area, and vessel wall area were analyzed semiautomatically. RESULTS: Pre-Gd, both lumen and wall dimensions (total vessel area, lumen area, vessel wall area) of group 2 + 3 were significantly increased when compared with those of group 1 (all P < 0.01). Group 3 animals had significantly thicker vessel walls than groups 1 and 2 (P < 0.01), whereas angiographic lumen diameter was comparable among all groups. Post-Gd, only diseased animals of groups 2 + 3 showed a significant (>100%) signal-to-noise ratio and contrast-to-noise increase. CONCLUSIONS: A combination of novel 3D magnetic resonance angiography and high-resolution 3D vessel wall MRI enabled quantitative characterization of various atherosclerotic stages including positive arterial remodeling and Gd uptake in a WHHL rabbit model using a commercially available 1.5 T MRI system.

Three-Dimensional (3D) Microarchitecture Correlations with 2D Projection Image Gray-Level Variations Assessed by Trabecular Bone Score Using High-Resolution Computed Tomographic Acquisitions: Effects of Resolution and Noise.

The aim of the present study is to determine the level of correlation between the 3-dimensional (3D) characteristics of trabecular bone microarchitecture, as evaluated using microcomputed tomography (μCT) reconstruction, and trabecular bone score (TBS), as evaluated using 2D projection images directly derived from 3D μCT reconstruction (TBSμCT). Moreover, we have evaluated the effects of image degradation (resolution and noise) and X-ray energy of projection on these correlations. Thirty human cadaveric vertebrae were acquired on a microscanner at an isotropic resolution of 93μm. The 3D microarchitecture parameters were obtained using MicroView (GE Healthcare, Wauwatosa, MI). The 2D projections of these 3D models were generated using the Beer-Lambert law at different X-ray energies. Degradation of image resolution was simulated (from 93 to 1488μm). Relationships between 3D microarchitecture parameters and TBSμCT at different resolutions were evaluated using linear regression analysis. Significant correlations were observed between TBSμCT and 3D microarchitecture parameters, regardless of the resolution. Correlations were detected that were strongly to intermediately positive for connectivity density (0.711≤r(2)≤0.752) and trabecular number (0.584≤r(2)≤0.648) and negative for trabecular space (-0.407 ≤r(2)≤-0.491), up to a pixel size of 1023μm. In addition, TBSμCT values were strongly correlated between each other (0.77≤r(2)≤0.96). Study results show that the correlations between TBSμCT at 93μm and 3D microarchitecture parameters are weakly impacted by the degradation of image resolution and the presence of noise.

Cardiovascular magnetic resonance imaging techniques for motion-suppressed multi-dimensional coronary artery imaging with high spatial and temporal resolution

L'imagerie par résonance magnétique (IRM) peut fournir aux cardiologues des informations diagnostiques importantes sur l'état de la maladie de l'artère coronarienne dans les patients. Le défi majeur pour l'IRM cardiaque est de gérer toutes les sources de mouvement qui peuvent affecter la qualité des images en réduisant l'information diagnostique. Cette thèse a donc comme but de développer des nouvelles techniques d'acquisitions des images IRM, en changeant les techniques de compensation du mouvement, pour en augmenter l'efficacité, la flexibilité, la robustesse et pour obtenir plus d'information sur le tissu et plus d'information temporelle. Les techniques proposées favorisent donc l'avancement de l'imagerie des coronaires dans une direction plus maniable et multi-usage qui peut facilement être transférée dans l'environnement clinique. La première partie de la thèse s'est concentrée sur l'étude du mouvement des artères coronariennes sur des patients en utilisant la techniques d'imagerie standard (rayons x), pour mesurer la précision avec laquelle les artères coronariennes retournent dans la même position battement après battement (repositionnement des coronaires). Nous avons découvert qu'il y a des intervalles dans le cycle cardiaque, tôt dans la systole et à moitié de la diastole, où le repositionnement des coronaires est au minimum. En réponse nous avons développé une nouvelle séquence d'acquisition (T2-post) capable d'acquérir les données aussi tôt dans la systole. Cette séquence a été testée sur des volontaires sains et on a pu constater que la qualité de visualisation des artère coronariennes est égale à celle obtenue avec les techniques standard. De plus, le rapport signal sur bruit fourni par la séquence d'acquisition proposée est supérieur à celui obtenu avec les techniques d'imagerie standard. La deuxième partie de la thèse a exploré un paradigme d'acquisition des images cardiaques complètement nouveau pour l'imagerie du coeur entier. La technique proposée dans ce travail acquiert les données sans arrêt (free-running) au lieu d'être synchronisée avec le mouvement cardiaque. De cette façon, l'efficacité de la séquence d'acquisition est augmentée de manière significative et les images produites représentent le coeur entier dans toutes les phases cardiaques (quatre dimensions, 4D). Par ailleurs, l'auto-navigation de la respiration permet d'effectuer cette acquisition en respiration libre. Cette technologie rend possible de visualiser et évaluer l'anatomie du coeur et de ses vaisseaux ainsi que la fonction cardiaque en quatre dimensions et avec une très haute résolution spatiale et temporelle, sans la nécessité d'injecter un moyen de contraste. Le pas essentiel qui a permis le développement de cette technique est l'utilisation d'une trajectoire d'acquisition radiale 3D basée sur l'angle d'or. Avec cette trajectoire, il est possible d'acquérir continûment les données d'espace k, puis de réordonner les données et choisir les paramètres temporel des images 4D a posteriori. L'acquisition 4D a été aussi couplée avec un algorithme de reconstructions itératif (compressed sensing) qui permet d'augmenter la résolution temporelle tout en augmentant la qualité des images. Grâce aux images 4D, il est possible maintenant de visualiser les artères coronariennes entières dans chaque phase du cycle cardiaque et, avec les mêmes données, de visualiser et mesurer la fonction cardiaque. La qualité des artères coronariennes dans les images 4D est la même que dans les images obtenues avec une acquisition 3D standard, acquise en diastole Par ailleurs, les valeurs de fonction cardiaque mesurées au moyen des images 4D concorde avec les valeurs obtenues avec les images 2D standard. Finalement, dans la dernière partie de la thèse une technique d'acquisition a temps d'écho ultra-court (UTE) a été développée pour la visualisation in vivo des calcifications des artères coronariennes. Des études récentes ont démontré que les acquisitions UTE permettent de visualiser les calcifications dans des plaques athérosclérotiques ex vivo. Cepandent le mouvement du coeur a entravé jusqu'à maintenant l'utilisation des techniques UTE in vivo. Pour résoudre ce problème nous avons développé une séquence d'acquisition UTE avec trajectoire radiale 3D et l'avons testée sur des volontaires. La technique proposée utilise une auto-navigation 3D pour corriger le mouvement respiratoire et est synchronisée avec l'ECG. Trois échos sont acquis pour extraire le signal de la calcification avec des composants au T2 très court tout en permettant de séparer le signal de la graisse depuis le signal de l'eau. Les résultats sont encore préliminaires mais on peut affirmer que la technique développé peut potentiellement montrer les calcifications des artères coronariennes in vivo. En conclusion, ce travail de thèse présente trois nouvelles techniques pour l'IRM du coeur entier capables d'améliorer la visualisation et la caractérisation de la maladie athérosclérotique des coronaires. Ces techniques fournissent des informations anatomiques et fonctionnelles en quatre dimensions et des informations sur la composition du tissu auparavant indisponibles. CORONARY artery magnetic resonance imaging (MRI) has the potential to provide the cardiologist with relevant diagnostic information relative to coronary artery disease of patients. The major challenge of cardiac MRI, though, is dealing with all sources of motions that can corrupt the images affecting the diagnostic information provided. The current thesis, thus, focused on the development of new MRI techniques that change the standard approach to cardiac motion compensation in order to increase the efficiency of cardioavscular MRI, to provide more flexibility and robustness, new temporal information and new tissue information. The proposed approaches help in advancing coronary magnetic resonance angiography (MRA) in the direction of an easy-to-use and multipurpose tool that can be translated to the clinical environment. The first part of the thesis focused on the study of coronary artery motion through gold standard imaging techniques (x-ray angiography) in patients, in order to measure the precision with which the coronary arteries assume the same position beat after beat (coronary artery repositioning). We learned that intervals with minimal coronary artery repositioning occur in peak systole and in mid diastole and we responded with a new pulse sequence (T2~post) that is able to provide peak-systolic imaging. Such a sequence was tested in healthy volunteers and, from the image quality comparison, we learned that the proposed approach provides coronary artery visualization and contrast-to-noise ratio (CNR) comparable with the standard acquisition approach, but with increased signal-to-noise ratio (SNR). The second part of the thesis explored a completely new paradigm for whole- heart cardiovascular MRI. The proposed techniques acquires the data continuously (free-running), instead of being triggered, thus increasing the efficiency of the acquisition and providing four dimensional images of the whole heart, while respiratory self navigation allows for the scan to be performed in free breathing. This enabling technology allows for anatomical and functional evaluation in four dimensions, with high spatial and temporal resolution and without the need for contrast agent injection. The enabling step is the use of a golden-angle based 3D radial trajectory, which allows for a continuous sampling of the k-space and a retrospective selection of the timing parameters of the reconstructed dataset. The free-running 4D acquisition was then combined with a compressed sensing reconstruction algorithm that further increases the temporal resolution of the 4D dataset, while at the same time increasing the overall image quality by removing undersampling artifacts. The obtained 4D images provide visualization of the whole coronary artery tree in each phases of the cardiac cycle and, at the same time, allow for the assessment of the cardiac function with a single free- breathing scan. The quality of the coronary arteries provided by the frames of the free-running 4D acquisition is in line with the one obtained with the standard ECG-triggered one, and the cardiac function evaluation matched the one measured with gold-standard stack of 2D cine approaches. Finally, the last part of the thesis focused on the development of ultrashort echo time (UTE) acquisition scheme for in vivo detection of calcification in the coronary arteries. Recent studies showed that UTE imaging allows for the coronary artery plaque calcification ex vivo, since it is able to detect the short T2 components of the calcification. The heart motion, though, prevented this technique from being applied in vivo. An ECG-triggered self-navigated 3D radial triple- echo UTE acquisition has then been developed and tested in healthy volunteers. The proposed sequence combines a 3D self-navigation approach with a 3D radial UTE acquisition enabling data collection during free breathing. Three echoes are simultaneously acquired to extract the short T2 components of the calcification while a water and fat separation technique allows for proper visualization of the coronary arteries. Even though the results are still preliminary, the proposed sequence showed great potential for the in vivo visualization of coronary artery calcification. In conclusion, the thesis presents three novel MRI approaches aimed at improved characterization and assessment of atherosclerotic coronary artery disease. These approaches provide new anatomical and functional information in four dimensions, and support tissue characterization for coronary artery plaques.

Optimal Sub-Pixel arrangements and coding for ultra-high resolution three-dimensional OLED displays

Information display technology is a rapidly growing research and development field. Using state-of-the-art technology, optical resolution can be increased dramatically by organic light-emitting diode - since the light emitting layer is very thin, under 100nm. The main question is what pixel size is achievable technologically? The next generation of display will considers three-dimensional image display. In 2D , one is considering vertical and horizontal resolutions. In 3D or holographic images, there is another dimension – depth. The major requirement is the high resolution horizontal dimension in order to sustain the third dimension using special lenticular glass or barrier masks, separate views for each eye. The high-resolution 3D display offers hundreds of more different views of objects or landscape. OLEDs have potential to be a key technology for information displays in the future. The display technology presented in this work promises to bring into use bright colour 3D flat panel displays in a unique way. Unlike the conventional TFT matrix, OLED displays have constant brightness and colour, independent from the viewing angle i.e. the observer's position in front of the screen. A sandwich (just 0.1 micron thick) of organic thin films between two conductors makes an OLE Display device. These special materials are named electroluminescent organic semi-conductors (or organic photoconductors (OPC )). When electrical current is applied, a bright light is emitted (electrophosphorescence) from the formed Organic Light-Emitting Diode. Usually for OLED an ITO layer is used as a transparent electrode. Such types of displays were the first for volume manufacture and only a few products are available in the market at present. The key challenges that OLED technology faces in the application areas are: producing high-quality white light achieving low manufacturing costs increasing efficiency and lifetime at high brightness. Looking towards the future, by combining OLED with specially constructed surface lenses and proper image management software it will be possible to achieve 3D images.