Vibrational characteristics of brain magnetic resonance elastography

This thesis aims to investigate vibrational characteristics of magnetic resonance elastography (MRE) of the brain. MRE is a promising, non-invasive methodology for the mapping of shear stiffness of the brain. A mechanical actuator shakes the brain and generates shear waves, which are then imaged with a special MRI sequence sensitive to sub-millimeter displacements. This research focuses on exploring the profile of vibrations utilized in brain elastography from the standpoint of ultimately investigating nonlinear behavior of the tissue. The first objective seeks to demonstrate the effects of encoding off-frequency vibrations using standard MRE methodologies. Vibrations of this nature can arise from nonlinearities in the system and contaminate the results of the measurement. The second objective is to probe nonlinearity in the dynamic brain system using MRE. A non-parametric decomposition technique, novel to the MRE field, is introduced and investigated.

Suivi par élastographie ultrasonore après réparation endovasculaire d’anévrisme aorto-iliaque : étude de faisabilité in vivo

Les maladies cardiovasculaires sont la première cause de mortalité dans le monde et les anévrismes de l’aorte abdominale (AAAs) font partie de ce lot déplorable. Un anévrisme est la dilatation d’une artère pouvant conduire à la mort. Une rupture d’AAA s’avère fatale près de 80% du temps. Un moyen de traiter les AAAs est l’insertion d’une endoprothèse (SG) dans l’aorte, communément appelée la réparation endovasculaire (EVAR), afin de réduire la pression exercée par le flux sanguin sur la paroi. L’efficacité de ce traitement est compromise par la survenue d’endofuites (flux sanguins entre la prothèse et le sac anévrismal) pouvant conduire à la rupture de l’anévrisme. Ces flux sanguins peuvent survenir à n’importe quel moment après le traitement EVAR. Une surveillance par tomodensitométrie (CT-scan) annuelle est donc requise, augmentant ainsi le coût du suivi post-EVAR et exposant le patient à la radiation ionisante et aux complications des contrastes iodés. L’endotension est le concept de dilatation de l’anévrisme sans la présence d’une endofuite apparente au CT-scan. Après le traitement EVAR, le sang dans le sac anévrismal coagule pour former un thrombus frais, qui deviendra progressivement un thrombus plus fibreux et plus organisé, donnant lieu à un rétrécissement de l’anévrisme. Il y a très peu de données dans la littérature pour étudier ce processus temporel et la relation entre le thrombus frais et l’endotension. L’étalon d’or du suivi post-EVAR, le CT-scan, ne peut pas détecter la présence de thrombus frais. Il y a donc un besoin d’investir dans une technique sécuritaire et moins coûteuse pour le suivi d’AAAs après EVAR. Une méthode récente, l’élastographie dynamique, mesure l’élasticité des tissus en temps réel. Le principe de cette technique repose sur la génération d’ondes de cisaillement et l’étude de leur propagation afin de remonter aux propriétés mécaniques du milieu étudié. Cette thèse vise l’application de l’élastographie dynamique pour la détection des endofuites ainsi que de la caractérisation mécanique des tissus du sac anévrismal après le traitement EVAR. Ce projet dévoile le potentiel de l’élastographie afin de réduire les dangers de la radiation, de l’utilisation d’agent de contraste ainsi que des coûts du post-EVAR des AAAs. L’élastographie dynamique utilisant le « Shear Wave Imaging » (SWI) est prometteuse. Cette modalité pourrait complémenter l’échographie-Doppler (DUS) déjà utilisée pour le suivi d’examen post-EVAR. Le SWI a le potentiel de fournir des informations sur l’organisation fibreuse du thrombus ainsi que sur la détection d’endofuites. Tout d’abord, le premier objectif de cette thèse consistait à tester le SWI sur des AAAs dans des modèles canins pour la détection d’endofuites et la caractérisation du thrombus. Des SGs furent implantées dans un groupe de 18 chiens avec un anévrisme créé au moyen de la veine jugulaire. 4 anévrismes avaient une endofuite de type I, 13 avaient une endofuite de type II et un anévrisme n’avait pas d’endofuite. Des examens échographiques, DUS et SWI ont été réalisés à l’implantation, puis 1 semaine, 1 mois, 3 mois et 6 mois après le traitement EVAR. Une angiographie, un CT-scan et des coupes macroscopiques ont été produits au sacrifice. Les régions d’endofuites, de thrombus frais et de thrombus organisé furent identifiées et segmentées. Les valeurs de rigidité données par le SWI des différentes régions furent comparées. Celles-ci furent différentes de façon significative (P < 0.001). Également, le SWI a pu détecter la présence d’endofuites où le CT-scan (1) et le DUS (3) ont échoué. Dans la continuité de ces travaux, le deuxième objectif de ce projet fut de caractériser l’évolution du thrombus dans le temps, de même que l’évolution des endofuites après embolisation dans des modèles canins. Dix-huit anévrismes furent créés dans les artères iliaques de neuf modèles canins, suivis d’une endofuite de type I après EVAR. Deux gels embolisants (Chitosan (Chi) ou Chitosan-Sodium-Tetradecyl-Sulfate (Chi-STS)) furent injectés dans le sac anévrismal pour promouvoir la guérison. Des examens échographiques, DUS et SWI ont été effectués à l’implantation et après 1 semaine, 1 mois, 3 mois et 6 mois. Une angiographie, un CT-scan et un examen histologique ont été réalisés au sacrifice afin d’évaluer la présence, le type et la grosseur de l’endofuite. Les valeurs du module d’élasticité des régions d’intérêts ont été identifiées et segmentées sur les données pathologiques. Les régions d’endofuites et de thrombus frais furent différentes de façon significative comparativement aux autres régions (P < 0.001). Les valeurs d’élasticité du thrombus frais à 1 semaine et à 3 mois indiquent que le SWI peut évaluer la maturation du thrombus, de même que caractériser l’évolution et la dégradation des gels embolisants dans le temps. Le SWI a pu détecter des endofuites où le DUS a échoué (2) et, contrairement au CT-scan, détecter la présence de thrombus frais. Finalement, la dernière étape du projet doctoral consistait à appliquer le SWI dans une phase clinique, avec des patients humains ayant déjà un AAA, pour la détection d’endofuite et la caractérisation de l’élasticité des tissus. 25 patients furent sélectionnés pour participer à l’étude. Une comparaison d’imagerie a été produite entre le SWI, le CT-scan et le DUS. Les valeurs de rigidité données par le SWI des différentes régions (endofuite, thrombus) furent identifiées et segmentées. Celles-ci étaient distinctes de façon significative (P < 0.001). Le SWI a détecté 5 endofuites sur 6 (sensibilité de 83.3%) et a eu 6 faux positifs (spécificité de 76%). Le SWI a pu détecter la présence d’endofuites où le CT-scan (2) ainsi que le DUS (2) ont échoué. Il n’y avait pas de différence statistique notable entre la rigidité du thrombus pour un AAA avec endofuite et un AAA sans endofuite. Aucune corrélation n’a pu être établie de façon significative entre les diamètres des AAAs ainsi que leurs variations et l’élasticité du thrombus. Le SWI a le potentiel de détecter les endofuites et caractériser le thrombus selon leurs propriétés mécaniques. Cette technique pourrait être combinée au suivi des AAAs post-EVAR, complémentant ainsi l’imagerie DUS et réduisant le coût et l’exposition à la radiation ionisante et aux agents de contrastes néphrotoxiques.

Shear stress and sediment transport calculations for sheet flow under waves

A simple method is provided for calculating transport rates of not too fine (d(50) greater than or equal to 0.20 mm) sand under sheet flow conditions. The method consists of a Meyer-Peter-type transport formula operating on a time-varying Shields parameter, which accounts for both acceleration-asymmetry and boundary layer streaming. While velocity moment formulae, e.g.., = Constant x calibrated against U-tube measurements, fail spectacularly under some real waves (Ribberink, J.S., Dohmen-Janssen, C.M., Hanes, D.M., McLean, S.R., Vincent, C., 2000. Near-bed sand transport mechanisms under waves. Proc. 27th Int. Conf. Coastal Engineering, Sydney, ASCE, New York, pp. 3263-3276, Fig. 12), the new method predicts the real wave observations equally well. The reason that the velocity moment formulae fail under these waves is partly the presence of boundary layer streaming and partly the saw-tooth asymmetry, i.e., the front of the waves being steeper than the back. Waves with saw-tooth asymmetry may generate a net landward sediment transport even if = 0, because of the more abrupt acceleration under the steep front. More abrupt accelerations are associated with thinner boundary layers and greater pressure gradients for a given velocity magnitude. The two real wave effects are incorporated in a model of the form Q(s)(t) = Q(s)[theta(t)] rather than Q(S)(t) = Q(S)[u(infinity)(t)], i.e., by expressing the transport rate in terms of an instantaneous Shields parameter rather than in terms of the free stream velocity, and accounting for both streaming and accelerations in the 0(t) calculations. The instantaneous friction velocities u(*)(t) and subsequently theta(t) are calculated as follows. Firstly, a linear filter incorporating the grain roughness friction factor f(2.5) and a phase angle phi(tau) is applied to u(infinity)(t). This delivers u(*)(t) which is used to calculate an instantaneous grain roughness Shields parameter theta(2.5)(t). Secondly, a constant bed shear stress is added which corresponds to the streaming related bed shear stress -rho ($) over bar((u) over tilde(w) over tilde)(infinity) . The method can be applied to any u(infinity)(t) time series, but further experimental validation is recommended before application to conditions that differ strongly from the ones considered below. The method is not recommended for rippled beds or for sheet flow with typical prototype wave periods and d(50) < 0.20 turn. In such scenarios, time lags related to vertical sediment movement become important, and these are not considered by the present model. (C) 2002 Elsevier Science B.V. All rights reserved.

Spontaneous generation and impact of inertia-gravity waves in a stratified, two-layer shear flow

Inertia-gravity waves exist ubiquitously throughout the stratified parts of the atmosphere and ocean. They are generated by local velocity shears, interactions with topography, and as geostrophic (or spontaneous) adjustment radiation. Relatively little is known about the details of their interaction with the large-scale flow, however. We report on a joint model/laboratory study of a flow in which inertia-gravity waves are generated as spontaneous adjustment radiation by an evolving large-scale mode. We show that their subsequent impact upon the large-scale dynamics is generally small. However, near a potential transition from one large-scale mode to another, in a flow which is simultaneously baroclinically-unstable to more than one mode, the inertia-gravity waves may strongly influence the selection of the mode which actually occurs.

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air-water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417-445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate F, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as proportional to 1/Gamma), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Do magnetospheric shear Alfvén waves generate sufficient electron energy flux to power the aurora?

Using a self-consistent drift-kinetic simulation code, we investigate whether electron acceleration owing to shear Alfvén waves in the plasma sheet boundary layer is sufficient to cause auroral brightening in the ionosphere. The free parameters used in the simulation code are guided by in situ observations of wave and plasma parameters in the magnetosphere at distances >4 RE from the Earth. For the perpendicular wavelength used in the study, which maps to ∼4 km at 110 km altitude, there is a clear amplitude threshold which determines whether magnetospheric shear Alfvén waves above the classical auroral acceleration region can excite sufficient electrons to create the aurora. Previous studies reported wave amplitudes that easily exceed this threshold; hence, the results reported in this paper demonstrate that auroral acceleration owing to shear Alfvén waves can occur in the magnetosphere at distances >4 RE from the Earth.

Electron trapping in shear Alfvén waves that power the aurora

Results from 1D Vlasov drift-kinetic plasma simulations reveal how and where auroral electrons are accelerated along Earth’s geomagnetic field. In the warm plasma sheet, electrons become trapped in shear Alfven waves, preventing immediate wave damping. As waves move to regions with larger vTe=vA, their parallel electric field decreases, and the trapped electrons escape their influence. The resulting electron distribution functions compare favorably with in situ observations, demonstrating for the first time a self-consistent link between Alfven waves and electrons that form aurora.

On Rossby waves modified by weak sinusoidal shear

The spatial structure of beta-plane Rossby waves in a sinusoidal basic zonal flow U 0cos(γ,y) is determined analytically in the (stable) asymptotic limit of weak shear, U 0γ2 0/β≈1. The propagating neutral normal modes are found to take their greatest amplitude in the region of maximum westerly flow, while their most rapid phase variation is achieved in the region of maximum easterly flow. These results are shown to be consistent with what is obtained by ray-tracing methods in the limit of small meridional disturbance wavelength.

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Infiltration effects on sediment mobility under waves

Sediment mobility measurements with a horizontal sand bed under non-breaking waves are reported. Conditions include no seepage and steady downward seepage corresponding to head gradients up to 2.5. The results indicate that infiltration tends to inhibit sediment mobility for a horizontal bcd of 0.2 mm quartz sand exposed to moderated wave induced bed shear stresses. The effect is weak for the parameter range of the present study. The two opposing effects of shear stress increase due to boundary layer thinning and the stabilizing downward drag are successfully accounted for through the modified Shields parameter of Nielsen [Nielsen, P., 1997. Coastal groundwater dynamics. Proc. Coastal Dynamics '97, Plymouth, ASCE, Dp, 546-555] using coefficients derived from independent studies. That is, from the shear stress experiments of Conley [Conley, D.C., 1993. Ventilated oscillatory boundary layers. PhD Thesis, University of California, San Diego, 74 pp.] and the slope stability experiments of Martin and Aral [Martin, C.S. and M.M. Aral, 1971. Seepage force on interfacial bed particles. J. Hydraulics Div., proc. ASCE, Vol. 97, No. Hy7, pp. 1081-1100]. (C) 2001 Elsevier Science B.V. All rights reserved.

Linear amplification of marginally neutral baroclinic waves

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear

We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. $F\,{>}\,F_\mathrm{critical}\,{\equiv}\, \upi^2/2$), and are therefore consistent with generation by a baroclinic instability. The unbalanced short-wavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia–gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baro-clinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin–Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. $\hbox{\it Ri}\,{<}\,\hbox{\it Ri}_\mathrm{critical}\,{\equiv}\, 1$), and are therefore consistent with generation by a Kelvin–Helmholtz instability. We calculate five indicators of short-wave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of short-wave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia–gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia–gravity waves generated by spontaneous adjustment of the large-scale flow.

Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization

We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.

Equatorial waves in the lower stratosphere. II: Annual and interannual variability

The annual and interannual variability of idealized, linear, equatorial waves in the lower stratosphere is investigated using the temperature and velocity fields from the ECMWF 15-year re-analysis dataset. Peak Kelvin wave activity occurs during solstice seasons at 100 hPa, during December-February at 70 hPa and in the easterly to westerly quasi-biennial oscillation (QBO) phase transition at 50 hPa. Peak Rossby-gravity wave activity occurs during equinox seasons at 100 hPa, during June-August/September-November at 70 hPa and in the westerly to easterly QBO phase transition at 50 hPa. Although neglect of wind shear means that the results for inertio-gravity waves are likely to be less accurate, they are still qualitatively reasonable and an annual cycle is observed in these waves at 100 hPa and 70 hPa. Inertio-gravity waves with n = 1 are correlated with the QBO at 50 hPa, but the eastward inertio-gravity n = 0 wave is not, due to its very fast vertical group velocity in all background winds. The relative importance of different wave types in driving the QBO at 50 hPa is also discussed. The strongest acceleration appears to be provided by the Kelvin wave while the acceleration provided by the Rossby-gravity wave is negligible. Of the higher-frequency waves, the westward inertio-gravity n = 1 wave appears able to contribute more to the acceleration of the 50 hPa mean zonal wind than the eastward inertio-gravity n = 1 wave.