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OBJECTIVE: Intermittent pneumatic compression (IPC) systems are used for prophylaxis of venous thromboembolism. Both legs are wrapped with inflatable sleeves connected to a pneumatic controller to allow compression of the legs causing expulsion of venous blood. Venous refill between inflation periods causes leg expansion, which can be tracked by measuring pressure changes in the sleeve. The aim of our study, which utilized the SCD RESPONSE compression system in conjunction with an independent pressure transducer, was to investigate whether factors such as temperature changes within the sleeves during inflation and deflation affect the measured venous refill time (VRT). METHODS: Transducers were used to measure air pressure in the middle chamber of the sleeve. A thermocouple was also inserted into the bladder to measure temperature changes. Inflation, deflation and refill measurements were made with the sleeves around model systems (static, rigid plastic pipes or compliant paper rolls, and dynamic, latex tubes inserted between a rigid pipe and the sleeve to simulate veins) and on 10 subjects in semi-recumbent, supine and sitting positions. RESULTS: In all the experiments the maximum temperature change was 0.023 degrees C. With the static model systems, the pressure in the venous refill measuring bladder fell from the inflation pressure of 40 - 50 mmHg to 9 +/- 1 mmHg, but then rose by 2.1 +/- 0.2 mmHg (rigid pipes) and 1.4 +/- 0.2 mmHg (paper rolls). These pressure changes were associated with reported 'filling times' of 21 - 24 s (rigid pipes) and 22 - 29 s (paper rolls). In experiments on dynamic filling of the latex tube, there was a strong linear relationship between the filling time indicated by the SCD system and the time to empty the filling reservoir. In 170 measurements on human subjects, there were only three VRTs less than 30 s and 36 less than 35 s. VRT increased in all subjects when going from supine (34.6 +/- 1.8 s) to semi-recumbent (38.9 +/- 1.9 s) to sitting (42.6 +/- 0.9 s) positions. DISCUSSION: In all cases, temperature changes during the refill phase were too small to result in significant pressure changes that would affect VRT. The pressure increases observed with the static models after deflation appeared to be due to viscoelastic relaxation. Viscoelastic responses were present in human subjects, but the effect on VRT was negligible. This indicates that the increased VRT observed in humans is due to blood return. Body position affected VRTs, indicating the system's ability to detect changes in filling times and venous blood volume.
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Velocidad del Flujo Sanguíneo/fisiología , Determinación de la Presión Sanguínea/instrumentación , Volumen Sanguíneo/fisiología , Hemorreología/instrumentación , Aparatos de Compresión Neumática Intermitente , Pierna/fisiología , Venas/fisiología , Determinación de la Presión Sanguínea/métodos , Diseño de Equipo , Análisis de Falla de Equipo , Humanos , Pierna/irrigación sanguíneaRESUMEN
High-speed (video-rate) fluorescence lifetime imaging (FLIM) through a flexible endoscope is reported based on gated optical image intensifier technology. The optimization and potential application of FLIM to tissue autofluorescence for clinical applications are discussed.
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Endoscopios , Tecnología de Fibra Óptica/instrumentación , Aumento de la Imagen/instrumentación , Microscopía Fluorescente/instrumentación , Microscopía por Video/instrumentación , Animales , Sistemas de Computación , Diseño de Equipo , Análisis de Falla de Equipo , Aumento de la Imagen/métodos , Interpretación de Imagen Asistida por Computador/instrumentación , Interpretación de Imagen Asistida por Computador/métodos , Ratones , Microscopía Fluorescente/métodos , Microscopía por Video/métodos , Reproducibilidad de los Resultados , Sensibilidad y EspecificidadRESUMEN
We report the development of a high-speed wide-field fluorescence-lifetime imaging (FLIM) system that provides fluorescence-lifetime images at rates of as many as 29 frames/s. A FLIM multiwell plate reader and a potentially portable FLIM endoscopic system operating at 355-nm excitation have been demonstrated.
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Algoritmos , Endoscopios , Interpretación de Imagen Asistida por Computador/métodos , Microscopía Fluorescente/métodos , Sistemas en Línea/instrumentación , Espectrometría de Fluorescencia/métodos , Grabación en Video/instrumentación , Endoscopía/métodos , Diseño de Equipo , Análisis de Falla de Equipo , Estudios de Factibilidad , Grabación en Video/métodosRESUMEN
Fourier transform infrared (FTIR) spectroscopic imaging using a focal plane array detector has been used to study atherosclerotic arteries with a spatial resolution of 3-4 microm, i.e., at a level that is comparable with cellular dimensions. Such high spatial resolution is made possible using a micro-attenuated total reflection (ATR) germanium objective with a high refractive index and therefore high numerical aperture. This micro-ATR approach has enabled small structures within the vessel wall to be imaged for the first time by FTIR. Structures observed include the elastic lamellae of the tunica media and a heterogeneous distribution of small clusters of cholesterol esters within an atherosclerotic lesion, which may correspond to foam cells. A macro-ATR imaging method was also applied, which involves the use of a diamond macro-ATR accessory. This study of atherosclerosis is presented as an illustrative example of the wider potential of these ATR imaging approaches for cardiovascular medicine and biomedical applications.
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Aorta/patología , Arteriosclerosis/patología , Animales , Arteriopatías Oclusivas/patología , Colesterol/análisis , Modelos Animales de Enfermedad , Masculino , Conejos , Espectroscopía Infrarroja por Transformada de Fourier , Túnica Media/patologíaRESUMEN
We report a wide-field fluorescence lifetime imaging (FLIM) system that uses a blue picosecond pulsed diode laser as the excitation source. This represents a significant miniaturization and simplification compared with other time-domain FLIM instruments that should accelerate the development of clinical and real-world applications of FLIM. We have demonstrated this instrument in two configurations: a macroimaging setup applied to multiwell plate assays of chemically and biologically interesting fluorophores and a microscope system that has been applied to imaging of tissue sections. The importance of the adjustable repetition rate of this laser source is discussed with respect to noise reduction and precision in the lifetime determination, illustrating a further significant advantage over conventional mode-locked solid-state lasers.
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A whole-field time-domain fluorescence lifetime imaging (FLIM) microscope with the capability to perform optical sectioning is described. The excitation source is a mode-locked Ti:Sapphire laser that is regeneratively amplified and frequency doubled to 415 nm. Time-gated fluorescence intensity images at increasing delays after excitation are acquired using a gated microchannel plate image intensifier combined with an intensified CCD camera. By fitting a single or multiple exponential decay to each pixel in the field of view of the time-gated images, 2-D FLIM maps are obtained for each component of the fluorescence lifetime. This FLIM instrument was demonstrated to exhibit a temporal discrimination of better than 10 ps. It has been applied to chemically specific imaging, quantitative imaging of concentration ratios of mixed fluorophores and quantitative imaging of perturbations to fluorophore environment. Initially, standard fluorescent dyes were studied and then this FLIM microscope was applied to the imaging of biological tissue, successfully contrasting different tissues and different states of tissue using autofluorescence. To demonstrate the potential for real-world applications, the FLIM microscope has been configured using potentially compact, portable and low cost all-solid-state diode-pumped laser technology. Whole-field FLIM with optical sectioning (3D FLIM) has been realized using a structured illumination technique.
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Técnicas de Preparación Histocitológica/métodos , Microscopía Fluorescente/métodos , Animales , Oído , Transferencia de Energía , Fluorescencia , Colorantes Fluorescentes , Rayos Láser , Microscopía Fluorescente/instrumentación , RatasRESUMEN
Conventional analyses of fluorescence lifetime measurements resolve the fluorescence decay profile in terms of discrete exponential components with distinct lifetimes. In complex, heterogeneous biological samples such as tissue, multi-exponential decay functions can appear to provide a better fit to fluorescence decay data than the assumption of a mono-exponential decay, but the assumption of multiple discrete components is essentially arbitrary and is often erroneous. Moreover, interactions, both between fluorophores and with their environment, can result in complex fluorescence decay profiles that represent a continuous distribution of lifetimes. Such continuous distributions have been reported for tryptophan, which is one of the main fluorophores in tissue. This situation is better represented by the stretched-exponential function (StrEF). In this work, we have applied, for the first time to our knowledge, the StrEF to time-domain whole-field fluorescence lifetime imaging (FLIM), yielding both excellent tissue contrast and goodness of fit using data from rat tissue. We note that for many biological samples for which there is no a priori knowledge of multiple discrete exponential fluorescence decay profiles, the StrEF is likely to provide a truer representation of the underlying fluorescence dynamics. Furthermore, fitting to a StrEF significantly decreases the required processing time, compared with a multi-exponential component fit and typically provides improved contrast and signal/noise in the resulting FLIM images. In addition, the stretched-exponential decay model can provide a direct measure of the heterogeneity of the sample, and the resulting heterogeneity map can reveal subtle tissue differences that other models fail to show.
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Fluorescencia , Microscopía Fluorescente/instrumentación , Microscopía Fluorescente/métodos , Animales , Aorta/química , Aorta/metabolismo , Colágeno/química , Colágeno/metabolismo , Elastina/química , Elastina/metabolismo , Semivida , Ratas , Factores de TiempoRESUMEN
Uptake of circulating macromolecules by the aortic wall is greater downstream than upstream of branch sites in immature rabbits, but the opposite pattern is seen at later ages. The mature pattern is nitric oxide dependent; we tested whether it is also flow dependent. Intercostal arteries of anesthetized rabbits were occluded, sham operated, or left alone. Uptake of rhodamine-labeled albumin was assessed by quantitative fluorescence microscopy of the sections through the aorta. In mature animals, uptake was higher upstream than downstream of the control and sham-operated branches, but the pattern was reversed at occluded branches. In young animals, uptake was not significantly different between regions upstream and downstream of control, sham-operated, or occluded branches. The absence of the normal immature pattern may reflect an influence of anesthesia and will assist in the elucidation of mechanisms underlying this pattern. The data for mature animals provide the first direct evidence that flow determines permeability near arterial branches and may account for the inverse spatial correlation between shear stress and disease prevalence at branches of adult human arteries.
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Aorta/fisiología , Permeabilidad Capilar/fisiología , Costillas/inervación , Envejecimiento/fisiología , Animales , Arterias/fisiología , Colorantes Fluorescentes , Masculino , Microscopía Fluorescente , Conejos , Flujo Sanguíneo Regional/fisiología , Rodaminas , Albúmina Sérica/metabolismoRESUMEN
We report a novel whole-field three-dimensional fluorescence lifetime imaging microscope that incoporates multispectral imaging to provide five-dimensional (5-D) fluorescence microscopy. This instrument, which can acquire a 5-D data set in less than a minute, is based on potentially compact and inexpensive diode-pumped solid-state laser technology. We demonstrate that spectral discrimination as well as optical sectioning minimize artifacts in lifetime determination and illustrate how spectral discrimination improves the lifetime contrast of biological tissue.
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We describe a novel three-dimensional fluorescence lifetime imaging microscope that exploits structured illumination to achieve whole-field sectioned fluorescence lifetime images with a spatial resolution of a few micrometers.
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We describe a novel whole-field fluorescence lifetime imaging system, based on a time-gated image intensifier and a solid-state laser oscillator-amplifier, that images lifetime differences of less than 10 ps. This system was successfully applied to discrimination between biological tissue constituents.
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Abdominal aortic aneurysms are characterized by intimal atherosclerosis, disruption and attenuation of the elastic media, and a variable adventitial inflammatory infiltrate. We have developed an animal model of this disorder to evaluate the contribution of hypercholesterolemia, medial injury, and adventitial inflammation to aneurysmal dilatation. To accomplish this, we used periaortic application of calcium chloride, which induced both medial injury with calcification and endothelial injury. Ultrasonography was used to demonstrate the dilatation and thickening of the aortic wall. Over the first 3 weeks after periaortic application of 0.25 mol/L CaCl2, the external aortic diameter increased from 3.5 +/- 0.5 to 4.2 +/- 0.8 mm, but the ID remained unchanged. This apparent wall thickening was accompanied by vascular remodeling, and biochemical changes included approximately 50% reduction in tissue hydroxyproline concentration and increased activity of gelatinases (matrix metalloproteinase [MMP]-2 and MMP-9). Independently, cholesterol feeding to induce hypercholesterolemia or the concomitant periaortic application of thioglycollate had little effect on the histological, biochemical, or diameter changes. Together, hypercholesterolemia and thioglycollate were associated with rapid aortic dilatation in CaCl2, treated animals but not controls: after 3 weeks, the ID and OD had doubled, the OD increasing from 3.5 +/- 0.4 to 7.1 +/- 0.4 mm, P = .005. The remarkable feature that accompanied this dilatation was the infiltration of cells, mostly foamy macrophages, into the adventitia, with a further reduction in hydroxyproline concentration. Adventitial inflammation may provide the critical stimulus to dilatation of an aorta with preexisting intimal and medial injury.
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Aneurisma de la Aorta Abdominal , Modelos Animales de Enfermedad , Hipercolesterolemia , Animales , Aorta/patología , Inflamación , ConejosRESUMEN
Various experiments are described that relate to measuring the uptake of plasma proteins by the walls of various large blood vessels of the rabbit. The rate of uptake across the intimal surface is not uniform, there being punctate regions of elevated transport. In addition, the rate of transport appears to be considerably higher across veins, pulmonary vessels, and the ascending aorta than across more peripheral arteries. Although larger proteins such as fibrinogen and low-density lipoprotein are transported more slowly than smaller ones, they appear to be retained to a greater extent in the inner layers of arteries than in pulmonary vessels and veins. Retention is greatly enhanced when collars are placed around the arteries and may be involved in the intimal hyperplasia that is seen in such vessels. Thus it appears that it may be the relative extent of entrapment of large atherogenic proteins that determines the appearance of lesions at different sites in the cardiovascular system, in addition to the rates at which they exchange across the blood-wall interface.
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Arterias/metabolismo , Arteriosclerosis/metabolismo , Fibrinógeno/metabolismo , Lipoproteínas/metabolismo , Albúmina Sérica/metabolismo , Animales , Aorta/metabolismo , Azul de Evans , Masculino , Arteria Pulmonar/metabolismo , Conejos , Vena Cava Inferior/metabolismoRESUMEN
Blood velocity profiles were measured in the renal branch (diameter 5.9 +/- 1.3 mm) of the aortorenal bifurcation using a 20-MHz 80-channel pulsed Doppler velocimeter during retroperitoneal surgery in 10 patients. The peak Reynolds number was 1145 +/- 140 and the frequency parameter (Wormersley parameter) was 3.0 +/- 0.8. Immediately distal to the ostium of the renal artery, reverse flow, indicating flow separation, was observed near the cranial wall mainly during the first part of the cardiac cycle. There were flows from the cranial to the caudal side of the artery at this location, indicating the presence of strong secondary flows. Two diameters downstream of the ostium, the velocity profiles were skewed to the caudal side in all patients. Four diameters downstream, the flow profile was symmetrical (3 patients) or only slightly skewed (7 patients) and virtually parabolic throughout the cardiac cycle. These observations mean that the flow on the cranial side of the renal branch of the human aortorenal bifurcation is characterized by (1) a bidirectional oscillation of the flow, (2) separation of the flow during systole, and (3) low time-averaged shear rate. These blood velocity patterns may be related to the localization and development of atheromatous plaque that occurs preferentially in this region of the renal artery. Conversely, the unidirectional, axisymmetrical flow found in more distal parts of the renal artery are associated with a very low incidence of lesions.
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Arteriosclerosis/fisiopatología , Flujometría por Láser-Doppler , Arteria Renal/fisiopatología , Adulto , Anciano , Aorta Abdominal/patología , Arteriosclerosis/patología , Velocidad del Flujo Sanguíneo , Presión Sanguínea , Femenino , Humanos , Masculino , Persona de Mediana Edad , Arteria Renal/patologíaRESUMEN
OBJECTIVE: The aim was to study the effects of altered heart rate and vasoactive drugs on the blood velocity patterns in the region of an arterial bifurcation. METHODS: Blood velocity profiles were measured in an exposed iliofemoral bifurcation of paced dogs using a pulsed Doppler ultrasound velocimeter with high temporal and spatial resolution. RESULTS: Decrease of the heart rate from 120 beats.min-1 (2 Hz) to 60 beats.min-1 (1 Hz) increased the peak forward velocity (30%), the peak reverse velocity (20%), and the duration of reverse flow (25%). Each drug caused qualitatively similar changes in velocity patterns at both heart rates. The systemic administration of angiotensin II reduced peak forward velocity (-26% at 2 Hz and -33% at 1 Hz) and forward flow duration (-15% at 1 Hz), the peak reverse velocity (-30% at 1 Hz), and reverse flow duration (-20% at 2 Hz and -28% at 1 Hz). Glyceryl trinitrate also reduced the peak forward velocity (-19% at both 2 and 1 Hz) but prolonged forward flow duration (28% at 2 Hz and 17% at 1 Hz) and that of reverse flow (45% at 2 Hz and 24% at 1 Hz), and also decreased the degree of oscillation (-16% at 2 Hz). Barnidipine hydrochloride (a calcium channel antagonist) also increased the duration of forward flow (48% at 1 Hz) and of reverse flow (31% at 2 Hz) but reduced the peak reverse velocity (-29% at 1 Hz) and flow oscillation (-22% at 2 Hz and 20% at 1 Hz). CONCLUSIONS: These dramatic changes in the pattern of blood flow, including alterations in the amplitudes and durations of the different phases of the flow cycle, are expected to have important consequences on the shear dependent responses of endothelial cells in the region of the bifurcation.
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Angiotensina II/farmacología , Bloqueadores de los Canales de Calcio/farmacología , Arteria Femoral/fisiología , Frecuencia Cardíaca/fisiología , Arteria Ilíaca/fisiología , Nifedipino/análogos & derivados , Nitroglicerina/farmacología , Animales , Velocidad del Flujo Sanguíneo , Perros , Femenino , Arteria Femoral/diagnóstico por imagen , Arteria Ilíaca/diagnóstico por imagen , Masculino , Nifedipino/farmacología , Flujo Sanguíneo Regional/efectos de los fármacos , Ultrasonografía Doppler de PulsoRESUMEN
To investigate the mechanisms controlling the flux of plasma proteins into and through the walls of blood vessels, we have studied the effects of two inert protein analogues, Dextran 500 and Poly(ethylene)oxide (PEO) on fluid transport across the walls of intact rabbit common carotid arteries. Transmural fluxes were first measured in vessels pressurized to 150 cmH2O with a solution containing 10 mg/ml albumin alone (control solution) and then with one containing 10 mg/ml albumin plus 10 or 50 mg/ml dextran, or 10 or 30 mg/ml PEO (test solutions). The macromolecule solutions caused a decrease in transmural filtration; the ratios of fluxes with the test solutions to those with the control solutions were 0.89 +/- 0.11 (7), 0.63 +/- 0.08 (8), 0.69 +/- 0.24 (9) and 0.41 +/- 0.09 (4), respectively (Mean +/- SD (n)). These reductions in fluid movement through the vessel wall may be explained quantitatively in terms of the formation of concentration-polarized layers of the macromolecules at the luminal surface or interactions of the macromolecules with the endothelial glycocalyx, causing a decrease in its permeability.
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Albúminas/farmacocinética , Arteria Carótida Común/metabolismo , Permeabilidad de la Membrana Celular , Dextranos/farmacocinética , Polietilenglicoles/farmacocinética , Animales , Transporte Biológico/efectos de los fármacos , Arteria Carótida Común/fisiología , Permeabilidad de la Membrana Celular/efectos de los fármacos , Técnicas In Vitro , Modelos Teóricos , Peso Molecular , Presión Osmótica , ConejosRESUMEN
The early stages of atherosclerosis involve the accumulation of plasma constituents, including fibrinogen, lipoproteins and lipids and their modified forms. To assess the role of haemodynamics in these processes, we have measured the pressure dependence of the fluxes of albumin, fibrinogen and fluid through the whole thickness of the walls of the carotid artery and the inferior vena cava. Fluxes were much higher across the vein, the vessel which is less susceptible to atherosclerosis. Protein fluxes showed a marked non-linear dependence on transmural pressure which was greater than the pressure dependence of the fluid fluxes. Protein movement across the artery wall could be modelled assuming a significant convective component with the protein reflection coefficient decreasing as the wall tissue was stretched by the increasing pressure. Protein movement across the vein wall appeared to be dependent on ultrafiltration with the formation of a concentration polarization layer at the luminal interface; such a layer would be extremely sensitive to flow within the vessel lumen.
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Proteínas Sanguíneas/farmacocinética , Arterias Carótidas/metabolismo , Vena Cava Inferior/metabolismo , Albúminas/metabolismo , Animales , Arteriosclerosis/fisiopatología , Transporte Biológico , Permeabilidad Capilar , Difusión , Fibrinógeno/metabolismo , Hemodinámica/fisiología , Técnicas In Vitro , Modelos Cardiovasculares , ConejosRESUMEN
The steady-state flow of fluid across the wall of the isolated rabbit common carotid artery has been measured in the presence and absence of flow within the lumen of the vessel. The perfusate solution contained either 10 or 40 mg ml-1 albumin and transmural flux was measured by monitoring the rate of movement of fluid into a chamber enclosing the artery. Vasomotion was minimized by the inclusion of the vasodilator sodium nitrite in both the perfusate and the outer bathing solution. A relatively slow luminal flow caused a reversible increase in the transmural flux by 20-30% relative to the value in the absence of flow. The mechanism responsible for the increase is not clear, but since it was not affected by the H1 antagonist, mepyramine, it would not appear to have been mediated by histamine release.
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Líquidos Corporales/metabolismo , Arterias Carótidas/fisiología , Animales , Transporte Biológico , Arterias Carótidas/metabolismo , Antagonistas de los Receptores Histamínicos H1/farmacología , Técnicas In Vitro , Pirilamina/farmacología , Conejos , Flujo Sanguíneo Regional , Estrés MecánicoRESUMEN
As local variations in blood flow are implicated in atherogenesis at bifurcations, we measured in vivo blood velocities in different planes within exposed iliofemoral arterial bifurcations in 8 dogs using 20-MHz, 80-channel Doppler ultrasound velocimetry. Cardiac frequency was fixed at 2 Hz by pacing. Local geometry was characterized using 25-MHz, B-mode ultrasound images, photographs, and methacrylate casts. The bifurcations were asymmetrical and planar to within 5 degrees, the diameter ratios of the daughter vessels ranged from 1.47 to 2.00, and the angles between them ranged from 40 to 76 degrees. Measured velocities indicated that just upstream of the bifurcation mean peak Reynolds numbers ranged from 196 to 564 and Womersley (frequency) parameters ranged from 2.00 to 4.1. At the level of the bifurcation, secondary flows were insignificant in the normal plane but strong in the plane of the bifurcation. As a result, two-dimensional velocity fields, reconstructed by vector addition of velocities measured in the plane of the bifurcation, differed markedly from the one-dimensional profiles calculated assuming flow parallel to the vessel axis. In the two-dimensional velocity fields, forward flow was directed toward the flow divider and reversal occurred earliest near the outer wall. Wide spatial and temporal variations in the shear stress at the endothelium are implied by these detailed, in vivo measurements of the bifurcation velocity fields.
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Velocidad del Flujo Sanguíneo , Arteria Femoral/fisiología , Arteria Ilíaca/fisiología , Animales , Perros , Arteria Femoral/anatomía & histología , Arteria Femoral/diagnóstico por imagen , Arteria Ilíaca/anatomía & histología , Arteria Ilíaca/diagnóstico por imagen , Flujo Sanguíneo Regional , UltrasonografíaRESUMEN
Using a 20-MHz 80-channel pulsed Doppler velocimeter and 30-MHz high-resolution echo ultrasound, we investigated the in vivo hemodynamics at the origin of the renal artery by measuring the velocity profiles and bifurcation geometry of a surgically exposed left renal artery in 10 anesthetized dogs. The angle between the aorta and the renal artery ranged from 60 degrees to 90 degrees (mean, 84 degrees) although the bifurcation did not lie in a single anterodorsal plane and the diameter of the renal artery ranged from 1.5 to 3.5 mm (mean, 2.4 mm). Despite different geometries, the velocity profiles in the different aortorenal bifurcations were similar. Although regions of reverse velocity were observed, the net flow in the renal artery was in the forward direction throughout the cardiac cycle. The peak Reynolds' number was 486 +/- 63. The velocity profiles in the proximal renal artery in the plane parallel to the bifurcation showed velocity vectors directed toward the caudal wall throughout the cardiac cycle. Reverse flow, indicating flow separation, was observed near the cranial wall even during systole. When the probe was placed on the cranial wall perpendicular to the wall, a velocity component from the cranial side to the caudal side was observed. At a distance of four diameters from the renal ostia, velocity profiles were almost parabolic. These results indicate that the velocity pattern near the cranial wall at the renal ostia, at which atherosclerotic lesions are prone to develop, are characterized by 1) a low time-averaged shear rate, 2) separation of the flow, and 3) a time-varying oscillation of the flow.