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[en] ULTRASONIC TECHNOLOGY IN FLOW MEASUREMENT OF INCOMPRESSIBLE FLOW / [pt] TECNOLOGIA ULTRASSÔNICA NA MEDIÇÃO DE VAZÃO EM ESCOAMENTOS INCOMPRESSÍVEISANA LUISA AULER DA SILVA FERREIRA 11 January 2011 (has links)
[pt] O presente trabalho avalia a influência da instalação em medidores de vazão
ultrassônicos, utilizando simulação numérica. Foram apresentadas características
dos medidores ultrassônicos e questões sobre a configuração da modelagem do
escoamento que podem influenciar nos resultados numéricos. Foram descritos os
procedimentos utilizados para traçar as linhas e para calcular a velocidade média
no medidor e o erro de medição. Foi mostrado o efeito de uma curva, duas curvas
no mesmo plano e duas curvas em planos perpendiculares, em medidores
ultrassônicos de 1, 2, 3, 4, 5 e 8 canais, com diferentes arranjos. Também foi
analisado o efeito de um degrau no resultado do medidor ultrassônico por meio de
simulação de medidores 1 a 5 canais e por calibração de medidores de 3 canais.
Foram utilizados fatores, calculados pela razão entre a velocidade indicada pelo
medidor em um dado local e a velocidade que seria indicada pelo mesmo medidor
em escoamento completamente desenvolvido. Logo após uma curva, os fatores
para medidores de 1 canal variaram de 0,40 a 1,28; para medidores de 3 canais, de
0,5 a 1,42; e para medidores de 4 e 5 canais, as diferenças chegaram a ultrapassar
10%. A 20D após uma curva, medidores de 2 e 3 canais indicaram fatores de 0,9 a
1,08 e medidores de 4 e 5 canais, fatores de 0,99 a 1,04. Os parâmetros de
diagnóstico analisados não se mostraram eficazes e sua utilização não é
recomendada. Pela simulação, um degrau convergente de -4% gera diferenças na
ordem de 0,3% para medidores de 3 canais e, para degrau divergente de 4%, as
diferenças ultrapassam 0,5%. A diferença entre os resultados das calibrações com
e sem degrau ficou entre 0,18% a 0,3%. A simulação numérica é uma ferramenta
útil na análise dos medidores ultrassônicos e mostrou a sensibilidade desses
medidores a variações no perfil de velocidades. / [en] The present work evaluates the influence of the installation in ultrasonic
flow meters, using numerical simulation. Ultrasonic meter characteristics and
issues about the flow modeling configuration that may influence the numerical
results were presented. Procedures used to draw the lines and to calculate the
meter mean velocity and the measurement error were described. The effect of one
curve, two curves at the same plane and two curves at perpendicular planes at 1, 2,
3, 4, 5 and 8-path meters with different arrangements were shown. Also, the effect
of one step at the results of ultrasonic meters was analyzed by the simulation of 1
to 5-paths meters and by the calibration of a 3 path meters. Factors calculated by
the ratio between the velocity indicated by the meter in a certain position and the
velocity that would be indicated by the meter in a fully developed flow. Just after one
curve, the factors for 1-path meters varied from 0.40 to 1.28; for 3-path meters,
from 0.5 to 1.42; and for 4 and 5-path meters, the differences were higher than
10%. At 20D downstream of one curve, 2 and 3-path meters indicated factors
equal to 0.9 and 1.08; and 4 and 5-path meters, factors equal to 0.99 to 1.04. The
diagnostic parameters analyzed were not efficient and their use is not
recommended. By the simulation, a convergent step of -4% generates differences
about 0.3% for 3-path meters and for a divergent step -f 4%, the differences are
higher than 0.5%. The differences between the calibration results with and
without steps were from 0.18% to 0.3%. The numerical simulation is a useful tool
in the ultrasonic meter analyses and showed the sensitivity of these meters to
velocity profile variations.
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Optical feedback interferometry sensing technique for flow measurements in microchannels / Conception de vélocimètres par amplification de la tension d'une diode laser soumise à une réinjection optique pour les applications microfluidiquesCampagnolo, Lucie 26 April 2013 (has links)
Le phénomène d’interférométrie par réinjection optique, ou effet self-mixing dans un laser permet de concevoir des capteurs non-invasifs, auto-alignés, ne nécessitant que peu d’éléments optiques et simples à implémenter. Ce type de capteur permet de mesurer avec la précision propre à l’interférométrie laser le déplacement, la vitesse ou la position de cibles dite coopératives (cibles réfléchissantes ou fortement diffusantes). Dans cette étude, ce type de capteurs est appliqué à la mesure de profil d’écoulement des fluides dans des microcanaux. Le faible coût et la polyvalence des capteurs à réinjection optique sont d’un grand intérêt dans l’industrie biomédicale et chimique, ainsi que pour la recherche en mécanique des fluides. Dans un premier temps, et en se basant sur les études réalisées dans des macro-canaux, nous avons proposé un modèle d’interferométrie par réinjection optique dans une diode laser lorsque la cible est constitué de particules en mouvement, en suspension dans un liquide. A partir de ce modèle, nous avons étudié expérimentalement l’impact du volume de mesure ainsi que du type de particules (taille et concentration) sur le signal mesuré. Nous avons ensuite proposé des méthodes de traitement du signal permettant de calculer le calcul du débit du fluide, ainsi que sous certaines conditions identifiées, la vitesse locale en tout point d’un microcanal. Ces études préliminaires nous ont permis de reconstruire le profil d’écoulement de différents liquides dans des canaux de 320µm de diamètre. Enfin, nous avons comparé les performances du capteur développé dans cette thèse avec un capteur basé sur la technique du Dual-Slit, technique déjà validée pour la microfluidique, en mesurant le profil d’écoulement dans un canal à section rectangulaire de 100x20µm. / The phenomenon of optical feedback interferometry (OFI) or self-mixing effect in a laser is used to design non-invasive and self-aligned sensors, requiring only few optical elements and simple to implement. This type of sensor is used to measure the displacement, velocity or position of cooperative targets (reflective or strongly scattering targets). In this study, this phenomenom is applied to the measurement of fluid flow profile in microchannels. The low cost and versatility of optical feedback sensors are of great interest in biomedical and chemical industry as well as research in fluid mechanics. Based on studies in macro-channels, we proposed first a theoretical model of OFI in a laser diode when the target consists of moving particles suspended in a liquid. Based on this model, we then studied experimentally the impact of the sensor’s sensing volume and the type of particles (size and concentration) on the OFI signal. We then proposed signal processing methods for calculating the fluid flow rate, as well as the local velocity at any point in a microchannel. These preliminary studies allowed us to reconstruct the flow profile of different liquids flowing in a circular channel of 320μm diameter. Finally, we compared the performance of the sensor developed in this thesis with a sensor based on the Dual-Slit technique, which has been already validated for microchannels, by measuring the flow profile in a rectangular shaped channel (100x20µm).
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Développements méthodologiques en imagerie cardiovasculaire par résonance magnétique chez le petit animal / Methodological developments in cardiovascular imaging in small animal using magnetic resonanceLefrançois, William 26 October 2011 (has links)
L’imagerie cardiovasculaire du rongeur par RMN est un véritable défi en ce qui concerne la résolution spatiale et temporelle, le contraste et le temps d’expérience. S’il est aujourd’hui admis que l’acquisition 3D doit être privilégiée chez le petit animal, les temps d’acquisition en 3D sont parfois très longs. Ils doivent pourtant rester compatibles avec les temps d’expérience in vivo. L’objectif de cette thèse était donc de développer de nouvelles méthodes d’imagerie cardiovasculaire 3D rapides pour le petit animal à 4.7 et 9.4 T. Tout d’abord, nous avons développé deux méthodes d’IRM cardiaque 4D (3D résolue dans le temps) à contraste «sang noir». La première méthode est basée sur une séquence TrueFISP (Fast Imaging with Steady-state Precession). Elle a permis d’obtenir le contraste sang noir en une heure d’acquisition. La deuxième méthode est basée sur une séquence FLASH (Fast Low Angle Shot). Elle utilise un gradient bipolaire pour supprimer le signal sanguin et le contraste a été rehaussé en Manganèse. Trente minutes d’acquisition ont alors été suffisantes. Ensuite, une méthode d’angiographie temps-de-vol 3D du corps entier de la souris a été développée. Le contraste vasculaire a été amélioré grâce à l’adjonction de motifs de suppression du signal tissulaire. L’imagerie de l’arbre vasculaire entier a pu être réalisé en moins de 10 minutes. Enfin, une nouvelle méthode d’angiographie fonctionnelle ciné temps-de-vol 4D utilisant une acquisition écho-planar a été développée. Les résultats préliminaires montrent qu’il est possible de diviser par quatre les temps d’acquisition de l’angiographie fonctionnelle classique. Tous ces résultats montrent que l’imagerie cardiovasculaire 3D haute résolution est possible dans des temps d’acquisition raisonnables voire rapides / Cardiovascular MRI in rodents is a real challenge in terms of spatial and temporal resolution, contrast and experiment times. Though it is accepted that 3D acquisition should be preferred in small animals, 3D acquisition times can be very long. However, they must remain compatible with in vivo experiment times. The aim of this thesis was therefore to develop new fast 3D methods of cardiovascular imaging in small animals at 4.7 and 9.4 T. First, two 4D cardiac MRI methods (3D time resolved) were developed in «black-blood» contrast. The first method is based on a TrueFISP sequence (Fast Imaging with Steady-state Precession). It allowed to make black blood contrast in one hour acquisition time. The second method is based on a FLASH sequence (Fast Low Angle Shot). It uses a bipolar gradient to suppress the blood signal and the contrast was enhanced by using Manganese. Thirty minutes were then enough. Next, a time-of-flight angiography method for the whole body of mice was developed. The vascular contrast was improved by adding preparation modules to suppress the signal from tissues. The imaging of the whole arterial tree was realized within less than ten minutes. Finally, a new 4D time-of-flight method of functional cine angiography with echo-planar acquisition was developed. Preliminary results showed that acquisition times could be divided by four compared with those in classical functional angiography. All these results show that high resolution 3D cardiovascular imaging is possible in reasonable or even fast acquisition times.
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[pt] ANÁLISE METROLÓGICA DA APLICAÇÃO DE ACELERÔMETROS PIEZOELÉTRICOS À MEDIÇÃO DE VAZÃO NA INDÚSTRIA PETROLÍFERA / [en] METROLOGICAL ANALYSIS OF THE APPLICATION OF PIEZOELECTRIC ACCELEROMETERS TO FLOW RATE MEASUREMENT IN THE OIL INDUSTRY04 November 2021 (has links)
[pt] O objetivo desta dissertação é analisar metrologicamente a aplicação de acelerômetros piezoelétricos à medição de vazão na indústria petrolífera. A motivação deste trabalho é analisar uma técnica de medição de vazão, recentemente desenvolvida, baseada na vibração captada por um acelerômetro ligado à superfície do duto. A metodologia do presente trabalho consistiu em realizar um estudo experimental para obtenção de dados em um laboratório acreditado de calibração de medidores de vazão, estimando-se uma vazão para cada vibração medida, acompanhada por uma análise de incertezas. Os resultados obtidos não estão conformes aos limites aceitáveis do ponto de vista da regulamentação para aplicação em medição de vazão na indústria petrolífera, no que se refere à medição fiscal e à medição para apropriação, segundo o Regulamento Técnico de Medição de Petróleo e Gás Natural (RTM). Contudo, a aplicação de acelerômetros ainda mostra-se oportuna à medição de vazão na indústria petrolífera, apesar da incerteza encontrada não adequar-se à regulamentação vigente para o setor, pois pode ser adotada para fins de medição operacional, na medição de água, sem interferir na instalação, de modo não invasivo e não intrusivo. / [en] The objective of this dissertation is to analyze metrologically the application of piezoelectric accelerometers in the measurement of flow rate in the oil industry. The motivation of this work is to analyze a technique of flow measurement, recently developed, based on the vibration captured by an accelerometer attached to the pipe surface. The methodology of this study consists of performing an experimental study to obtain data in an accredited laboratory for calibration of flowmeters, estimating a flow rate for each vibration measured accompanied by an uncertainty analysis. The results do not conform to acceptable limits from the viewpoint of the regulation for application in flow measurement in the oil industry, in that refers to the fiscal metering and to the measurement for appropriation, in accordance with the Technical Rules of Measurement of Petroleum and Natural Gas (RTM). However, the use of accelerometers still can be useful to measure flow rates in the oil industry, despite the uncertainty being not suitable for the current regulation of the sector, because it can be adopted in the operational measurement of water flow, without interfering in the installation, so being non-invasive and non-intrusive.
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Unified Equations for Cutthroat Flumes Derived from a Three-Dimensional Hydraulic ModelTemeepattanapongsa, Sathaporn 01 August 2012 (has links)
Computational fluid dynamics software was used to simulate the hydraulic behavior of 51 Cutthroat flume (CTF) sizes under various flow conditions, including 24 standard sizes with throat widths (W) from 0.051 to 1.219 m (2 inches to 4 ft), flume scale lengths (L) ranging from 0.457 to 2.743 m (1.5 - 9 ft), constriction ratios (W/L) of 1/9, 2/9, 3/9, and 4/9, and 27 non-standard flumes of intermediate sizes. The validity and accuracy of the simulation results were demonstrated using laboratory data from other studies for 16 of the standard flume sizes and three non-standard sizes. By using the depth-discharge data for 24 standard CTFs obtained from the modeling, a series of "best-fit" calibrations of existing separate free- and submerged-flow rating equations were performed for each of the 24 standard-sized CTFs. A new unified rating equation for free- and submerged-flow conditions for the standard CTF sizes was proposed by comparing a set of empirical equations. The performance of the unified rating equation was also analyzed in order to determine the technical desirability of the equations as substitutes for the existing separate free- and submerged-flow rating equations. For the free-flow rating, the discharge parameters in the traditional equation are generalized to be applicable to any of the CTF sizes with flume lengths ranging from 0.457 to 2.743 m (1.5 - 9 ft), and the constriction ratio ranging from 1/9 to 4/9. This allows the application of CTFs with greater accuracy than the previously available equation. With the new generic-fit equations for the free-flow rating parameters, the discharge error is 4% from the standard discharge, with an average error of 2.2% for full-scale discharge. The generic unified rating equations proposed herein are also applicable to any of the CTF sizes, varying among the 24 standard sizes with flume lengths ranging from 0.457 to 2.743 m (1.5 - 9 ft) and the constriction ratio ranging from 1/9 to 4/9. With the generic-fit equations for the calibration parameters as derived herein, the discharge error is 6 - 8% compared to the standard discharge, and 2 - 3% for full-scale discharge.
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High frame rate imaging of arterial wall mechanics and blood flow dynamics for atherosclerosis diagnosis and monitoringKarageorgos, Grigorios Marios January 2022 (has links)
Carotid artery wall stiffness has been widely considered as an index of vascular health, and has been associated with occurrence of cardiovascular events, such as stroke. In addition, the blood flow patterns in the carotid artery can yield crucial information on atherosclerosis progression and cerebrovascular impairment. Pulse wave imaging (PWI) is a non-invasive ultrasound imaging technique that tracks the propagation of the arterial pulse wave, providing thus regional arterial wall stiffness mapping. Moreover, towards enabling accurate visualization of blood flow patterns, ultrasound-based vector flow imaging (VFI) modalities have been developed.
Building upon PWI and VFI techniques, the overall goal of this dissertation is to develop ultrasound-based methodologies that can provide simultaneous imaging of the carotid artery wall mechanics and blood flow dynamics at high temporal and spatial resolutions. The developed techniques are validated through vessel phantom experiments and simulations. Furthermore, their potential to diagnose pre-clinical stages of carotid artery disease and provide additional insights in risk for stroke assessment, is demonstrated in an atherosclerotic swine study and human subjects in vivo. More specifically:
A method is presented that analyzes the pattern of arterial wall motion derived by PWI, in order to detect spatial mechanical inhomogeneity across an imaged artery, and provide piecewise arterial wall stiffness estimates. The proposed technique is validated in a phantom consisting of a soft and a stiff segment, while its feasibility is demonstrated to identify inhomogeneous wall properties in atherosclerotic human carotid arteries, as well as provide atherosclerotic plaque mechanical characterization in vivo.
Subsequently, PWI is integrated with VFI techniques in the same ultrasound acquisition sequence, in order to enable simultaneous and co-localized imaging of arterial wall stiffness and blood vector flow velocity. The performance of the technique is investigated through experiments and FSI simulations. Moreover, its feasibility was shown to investigate associations between carotid artery Pulse Wave Velocity and blood flow patterns, in vivo.
Based on the previously developed PWI and VFI modalities, a novel ultrasound-based technique is developed that combines high frame rate vector flow imaging with a data clustering approach, in order to enable direct and robust wall shear stress measurements. The performance of the proposed method is evaluated through vessel phantom experiments and simulations, while its feasibility is shown to detect pre-clinical stages of carotid artery disease in a swine model in vivo. In addition, a pilot clinical study is presented involving application of the developed modality in normal and atherosclerotic human carotid arteries in-vivo.
Moving forward, the developed imaging modalities are used to implement novel clinical biomarkers based on carotid artery arterial wall mechanics and blood flow dynamics, that can potentially assist in risk for stroke assessment. The patterns of those biomarkers are investigated in the common carotid arteries of subjects with low degree of stenosis and medical history of stroke, against subjects without history of stroke. The same biomarkers are also analyzed with respect to stroke symptomatology in atherosclerotic patients with moderate to high degree of stenosis. Moreover, the developed techniques are used to identify vulnerable plaque components in subjects with fully developed plaques, as compared with CTA scans.
Finally, a deep learning-based approach for motion tracking of the arterial wall throughout the cardiac cycle is proposed. A neural network is trained to learn the motion patterns of the carotid artery and potentially improve the quality of PWI. The performance of the technique is assessed in vessel phantom experiments and its feasibility is demonstrated in healthy human carotid arteries in-vivo.
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Hydraulic Effects of Perpendicular Water Approach Velocity on Meter Gate Flow MeasurementThorburn, John M 01 August 2020 (has links) (PDF)
Accurate flow measurement is required to effectively manage water resources. California Senate Bill X7-7 (SB X7-7), legislates this need by requiring agricultural water providers serving areas greater than 25,000 acres to develop an Agricultural Water Management Plan (AWMP) and adopt pricing based at least partly on volumetric water deliveries (DWR, 2009). This study focused on two of the most common flow measurement/flow control devices used in California open channel water conveyance systems: the circular meter gate and the rectangular meter gate. Testing was conducted on three Armco-type (round gates over round discharge pipe) gates measuring 12”, 18”, and 24” and two rectangular gates (rectangular gates over round discharge pipe) measuring 18” and 24”. The three round gates used in the study were the Model 101C produced and provided by Fresno Valve and Castings Incorporated. The two rectangular meter gates were manufactured by Mechanical Associates located in Visalia, California and provided by the San Luis Canal Company located in Dos Palos, California. Testing was conducted in an outdoor laboratory setting at the Irrigation Training and Research Center’s (ITRC) Water Resources Facility at the California Polytechnic State University in San Luis Obispo, California under a variety of flow conditions as experienced in the field in order to: 1) evaluate the effectiveness of these gates as flow measurement devices and determine whether they meet the volumetric accuracy requirements outlined in SB X7-7, 2) develop standards for installation and use that improve flow measurement accuracy, 3) configure more accurate gate rating tables based on updated coefficient of discharge values, and 4) determine if additional gate rating tables are needed for “high” supply channel velocities. The meter gate was set perpendicular to the supply channel. Baseline data was first collected through testing with low supply channel water velocities. Additional testing was then conducted with high supply channel water velocities to analyze the effect on the coefficient of discharge. Based on previous studies it was hypothesized that as the Froude number (FR#) in the supply channel increased (water approach velocity increased), the coefficient of discharge would decrease as a result of an increase in energy needed for the perpendicular velocity transition. Data evaluation, however, indicated no statistically significant effect of water approach velocity on the coefficient of discharge for the 12”, 18” and 24” circular gates or the 18” and 24” rectangular gates at an α-level = 0.01. When operating the gates under recommended conditions relative flow uncertainty was within +/- 5%. This meets the accuracy requirements set by SB X7-7 for turnout flow measurement devices. Based on the results of this study, Cd values do not need to be adjusted for Froude numbers up to 0.35 for any of the studied gates. It should be noted, however, that while most meter gates used will be in conditions where supply channel Froude numbers do not exceed 0.35, further research is needed to study potential effects from Froude numbers exceeding the range found in this study.
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An Experimental Study of Longitudinally Embedded Vortices in a Turbulent Boundary Layer via the Non-Invasive Comprehensive LDV TechniqueDerlaga, Joseph Michael 05 June 2012 (has links)
This report documents the measurements of turbulence quantities resulting from vortices embedded in a zero pressure gradient turbulent boundary layer. Turbulent boundary layers are found in most flow regimes over large scale vehicles and have been studied for many years. Various systems to control separation of boundary layers have been proposed, but vortex generators have proven to be an economical choice as they are often used to fix deficiencies in a flow field after large scale production of a vehicle has commenced. In order to better understand the interaction between vortex generators and the boundary layer in which they are embedded, an experiment has been performed using through non-invasive Comprehensive Laser Doppler Velocimeter.
The results show that normalization on edge velocity is appropriate for comparison with previous work. The 1/S parameter and vq^2 parameter were found to be most appropriate to correlate the Reynolds stresses and triple products, respectively. The higher inflow edge velocity and greater momentum thickness, creating a lower vortex generator to boundary layer height ratio, result in a more diffuse vortex as compared to previous work conducted in the same wind tunnel, with the same geometry, but with different inflow conditions. / Master of Science
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Uncertainty quantification techniques with diverse applications to stochastic dynamics of structural and nanomechanical systems and to modeling of cerebral autoregulationKatsidoniotaki, Maria January 2022 (has links)
This dissertation develops uncertainty quantification methodologies for modeling, response analysis and optimization of diverse dynamical systems. Two distinct application platforms are considered pertaining to engineering dynamics and precision medicine.
First, the recently developed Wiener path integral (WPI) technique for determining, accurately and in a computationally efficient manner, the stochastic response of diverse dynamical systems is employed for solving a high-dimensional, nonlinear system of stochastic differential equations governing the dynamics of a representative model of electrostatically coupled micromechanical oscillators. Compared to alternative modeling and solution treatments in the literature, the current development exhibits the following novelties: a) typically adopted linear, or higher-order polynomial, approximations of the nonlinear electrostatic forces are circumvented; and b) stochastic modeling is employed, for the first time, by considering a random excitation component representing the effect of diverse noise sources on the system dynamics.
Further, the WPI technique is enhanced and extended based on a Bayesian compressive sampling (CS) treatment. Specifically, sparse expansions for the system response joint PDF are utilized. Next, exploiting the localization capabilities of the WPI technique for direct evaluation of specific PDF points leads to an underdetermined linear system of equations for the expansion coefficients. Furthermore, relying on a Bayesian CS solution formulation yields a posterior distribution for the expansion coefficient vector. In this regard, a significant advantage of the herein-developed methodology relates to the fact that the uncertainty of the response PDF estimates obtained by the WPI technique is quantified. Also, an adaptive scheme is proposed based on the quantified uncertainty of the estimates for the optimal selection of PDF sample points. This yields considerably fewer boundary value problems to be solved as part of the WPI technique, and thus, the associated computational cost is significantly reduced.
Second, modeling and analysis of the physiological mechanism of dynamic cerebral autoregulation (DCA) is pursued based on the concept of diffusion maps. Specifically, a state-space description of DCA dynamics is considered based on arterial blood pressure (ABP), cerebral blood flow velocity (CBFV), and their time derivatives. Next, an eigenvalue analysis of the Markov matrix of a random walk on a graph over the dataset domain yields a low-dimensional representation of the intrinsic dynamics. Further dimension reduction is made possible by accounting only for the two most significant eigenvalues. The value of their ratio indicates whether the underlying system is governed by active or hypoactive dynamics, indicating healthy or impaired DCA function, respectively. The reliability of the technique is assessed by considering healthy individuals and patients with unilateral carotid artery stenosis or occlusion.
It is shown that the proposed ratio of eigenvalues can be used as a reliable and robust biomarker for assessing how active the intrinsic dynamics of the autoregulation is and for indicating healthy versus impaired DCA function. Further, an alternative joint time-frequency analysis methodology based on generalized harmonic wavelets is utilized for assessing DCA performance in patients with preeclampsia within one week postpartum, which is associated with an increased risk for postpartum maternal cerebrovascular complications. The results are compared with normotensive postpartum individuals and healthy non-pregnant female volunteers and suggest a faster, but less effective response of the cerebral autoregulatory mechanism in the first week postpartum, regardless of preeclampsia diagnosis.
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The construction of a wind tunnel and the prosecution of certain problems of research connected with itLybrook, Robert Custis, Price, William David January 1931 (has links)
M.S.
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