Vorticity and vortical structures play a fundamental role affecting the evaluation of energetic aspects (mainly left ventricle work) of cardiovascular function. Vorticity can be derived from cardiovascular magnetic resonance (CMR) imaging velocity measurements. However, several numerical schemes can be used to evaluate the vorticity field. The main objective of this work is to assess different numerical schemes used to evaluate the vorticity field derived from CMR velocity measurements. We compared the vorticity field obtained using direct differentiation schemes (eight-point circulation and Chapra) and derivate differentiation schemes (Richardson 4* and compact Richardson 4*) from a theoretical velocity field and in vivo CMR velocity measurements. In all cases, the effect of artificial spatial resolution up-sampling and signal-to-noise ratio (SNR) on vorticity computation was evaluated. Theoretical and in vivo results showed that the eight-point circulation method underestimated vorticity. Up-sampling evaluation showed that the artificial improvement of spatial resolution had no effect on mean absolute vorticity estimation but it affected SNR for all methods. The Richardson 4* method and its compact version were the most accurate and stable methods for vorticity magnitude evaluation. Vorticity field determination using the eight-point circulation method, the most common method used in CMR, has reduced accuracy compared to other vorticity schemes. Richardson 4* and its compact version showed stable SNR using both theoretical and in vivo data.

Sperm velocity is long known to be an important indicator of sperm quality but without much biophysical theory explaining it. Contact mechanics based modeling was developed here to determine the effects that sperm velocity ( v s ) and sperm head density ( ρ s ) —which is an indicator of the stiffness of the head, have on the peak sperm-zona pellucida contact pressure ( p m ) during the early phase of sperm penetration. The modeling identified v s as being more influential on p m compared with the influence that ρ s has, which means that for spermatozoa competing on the same oocyte, greater v s is a more important advantage than higher ρ s . Specifically, p m was more sensitive by a power of 2 to changes in v s than to changes in ρ s . It was further demonstrated that each 0.1 g/cc increase in ρ s (within the physiologically relevant range of 1.3–1.7 g/cc) would be equivalent to just ∼ 3 % rise in v s , indicating again that faster swimming is a better strategy for spermatozoa compared with head stiffening. The modeling hence provided some useful insights regarding sperm biomechanics, which theoretically elucidate the well-recognized importance of sperm velocity measurements as being indicative of sperm quality.

This work introduces a method for the in vivo measurement and analysis of turbulence within the leakage of a mechanical heart valve. Several analysis techniques were applied to ultrasound measurements acquired within the atrium of a pig, and error associated with these techniques was analyzed. The technique chosen applies cyclic averaging to mean and maximum velocity measurements within small, normalized phase windows to calculate Reynolds normal stresses in the direction of the ultrasound beam. Maximum shear stresses are estimated from these normal stresses using an analytical technique. The stresses observed were smaller than those reported from previous in vitro simulations.

Wall shear has been widely implicated as a contributing factor in the development of intimal hyperplasia in the anastomoses of chronic arterial bypass grafts. Earlier studies have been restricted to either: (1) in vitro or computer simulation models detailing the complex hemodynamics within an anastomosis without corresponding biological responses, or (2) in vivo models that document biological effects with only approximate wall shear information. Recently, a specially designed pulse ultrasonic Doppler wall shear rate (PUDWSR) measuring device has made it possible to obtain three near-wall velocity measurements nonintrusively within 1.05 mm of the vessel luminal surface from which wall shear rates (WSRs) were derived. It was the purpose of this study to evaluate the effect of graft caliber, a surgically controllable variable, upon local hemodynamics, which, in turn, play an important role in the eventual development of anastomotic hyperplasia. Tapered (4–7 mm I.D.) 6-cm-long grafts were implanted bilaterally in an end-to-side fashion with 30 deg proximal and distal anastomoses to bypass occluded common carotid arteries of 16 canines. The bypass grafts were randomly paired in contralateral vessels and placed such that the graft-to-artery diameter ratio, DR, at the distal anastomosis was either 1.0 or 1.5. For all grafts, the average Re was 432 ± 112 and the average Womersley parameter,α, was 3.59 ± 0.39 based on artery diameter. There was a sharp skewing of flow toward the artery floor with the development of a stagnation point whose position varied with time (up to two artery diameters) and DR (generally more downstream for DR = 1.0). Mean WSRs along the artery floor for DR = 1.0 and 1.5 were found to range sharply from moderate to high retrograde values (589 s −1 and 1558 s −1 , respectively) upstream to high antegrade values (2704 s −1 and 2302 s −1 , respectively) immediately downstream of the stagnation point. Although there were no overall differences in mean and peak WSRs between groups, there were significant differences (p < 0.05) in oscillatory WSRs as well as in the absolute normalized mean and peak WSRs between groups. There were also significant differences (p < 0.05) in mean and peak WSRs with respect to axial position along the artery floor for both DR cases. In conclusion, WSR varies widely (1558 s −1 retrograde to 2704 s −1 antegrade) within end-to-side distal graft anastomoses, particularly along the artery floor, and may play a role in the development of intimal hyperplasia through local alteration of mass transport and mechano-signal transduction within the endothelium.

To provide a quantitative description of the convection field of gas transport through the lung under both low and high-frequency ventilation conditions, volume-cycled, purely oscillatory flow has been investigated in a symmetrically bifurcating model bronchial bifurcation. Significant differences in the flow properties that developed as the Reynolds number varied from 750 to 950 and the dimensionless frequency varied from 3 to 12 are described. At low frequency, the axial velocity field was found to approximate closely that of a steady flow through a bifurcation. However, even at α = 3, secondary velocity fields were confined to within a few diameters of the bifurcation, with less than 10 percent of the magnitude of the axial velocity. At high frequency they were still slower and more limited. These secondary velocity observations are discussed in terms of a physical mechanism balancing inviscid centripetal acceleration with viscous retardation. As the dimensionless frequency increased but the flow amplitude decreased, the magnitude of the axial drift velocity field was found to decrease. In addition, a burst of high-frequency velocity fluctuations was detected in both the axial and secondary velocity measurements in the parent tube, in low-frequency flow, during the deceleration phase of expiration. The position and timing of this burst suggest that it derives from the free shear layer in the parent tube. Stability criteria for the flow were therefore evaluated.

Turbulence inducement from the glottis was scrutinized by employing an idealized model of the larynx and trachea for oscillatory flow conditions. The characterization of turbulence was achieved with the two-component velocity measurements of split-film probe anemometry and with the flow visualization of a smoke-wire technique. The apertures of two different (triangular and circular) shapes were utilized in the airway model to address the distinct effects of the triangular-shaped glottal aperture on the generation, development, and decay of turbulence. One of the salient turbulence characteristics for the triangular aperture case was found to be the relatively high turbulence levels around the center region (2r/D ~ 0) in conjunction with the asymmetric mean axial velocity across the frontal-rear (A-O-P) plane of the trachea at one tracheal diameter (x/D = 1) downstream from the glottis. The detailed turbulence properties such as the Reynolds shear stresses and turbulence intensities for the triangular aperture case differed significantly from those for the circular aperture case within a few tracheal diameters (x/D < 7) downstream from the apertures. The glottis-induced turbulence was incipient during the acceleration phase of inspiration and convected downstream with the traits of decaying turbulence.

A system was refined for the determination of the bulk ultrasonic wave propagation velocity in small cortical bone specimens. Longitudinal and shear wave propagations were measured using ceramic, piezoelectric 20 and 5 MHz transducers, respectively. Results of the pulse transmission technique were refined via the measurement of the system delay time. The precision and accuracy of the system were quantified using small specimens of polyoxymethylene, polystyrene-butadiene, and high-density polyethylene. These polymeric materials had known acoustic properties, similarity of propagation velocities to cortical bone, and minimal sample inhomogeneity. Dependence of longitudinal and transverse specimen dimensions upon propagation times was quantified. To confirm the consistency of longitudinal wave propagation in small cortical bone specimens (<1.0 mm), cut-down specimens were prepared from a normal rat femur. Finally, cortical samples were prepared from each of ten normal rat femora, and Young’s moduli (E ii ), shear moduli (G ij ), and Poisson ratios (v ij ) were measured. For all specimens (bone, polyoxymethylene, polystyrene-butadiene, and high-density polyethylene), strong linear correlations (R 2 > 0.997) were maintained between propagation time and distance throughout the size ranges down to less than 0.4 mm. Results for polyoxymethylene, polystyrene-butadiene, and high-density polyethylene were accurate to within 5 percent of reported literature values. Measurement repeatability (precision) improved with an increase in the wave transmission distance (propagating dimension). No statistically significant effect due to the transverse dimension was detected.

The flow field inside a model of a polytetrafluoroethylene (PTFE) canine artery end-to-side bypass graft was studied under steady flow conditions using laser-Doppler anemometry. The anatomically realistic in vitro model was constructed to incorporate the major geometric features of the in vivo canine anastomosis geometry, most notably a larger graft than host artery diameter. The velocity measurements at Reynolds number 208, based on the host artery diameter, show the flow field to be three dimensional in nature. The wall shear stress distribution, computed from the near-wall velocity gradients, reveals a relatively low wall shear stress region on the wall opposite to the graft near the stagnation point approximately one artery diameter in axial length at the midplane. This low wall shear stress region extends to the sidewalls, suture lines, and along the PTFE graft where its axial length at the midplane is more than two artery diameters. The velocity distribution inside the graft model presented here provides a data set well suited for validation of numerical solutions on a model of this type.

In the present study, finite element calculations are performed of blood flow in the carotid artery bifurcation under physiological flow conditions. The numerical results are compared in detail with laser-Doppler velocity measurements carried out in a perspex model. It may be concluded that the numerical model as presented here is well capable in predicting axial and secondary flow of incompressible Newtonian fluids in rigid-walled three-dimensional geometries. With regard to the flow phenomena occurring, a large region with reversed axial flow is found in the carotid sinus opposite to the flow divider. This region starts to grow at peak systole, has its maximal shape at minimal flow rate and totally disappears at the start of the acceleration phase. C-shaped axial velocity contours are formed in the deceleration phase, which are highly influenced by secondary flows. These latter flows are mainly induced by centrifugal forces, flow branching, and tapering of the carotid sinus. Lowering the sinus angle, the angle between the main branch and the carotid sinus, results in a smaller region with reversed axial flow.

Oscillations in near-wall velocity direction have been found to correlate with atherosclerotic plaque localization in the carotid sinus bifurcation. However, it remains unproven whether these conditions could account for the localization of the disease at other sites where atherosclerosis forms. The abdominal aorta is an important site of clinical disease in a relatively straight segment of artery. This study was initiated to quantify the velocity field in the abdominal aorta in order to determine if local differences in hemodynamic velocity directions could account for the localization of disease in this segment. Magnetic Resonance Imaging velocimetry was used to measure the pulsatile velocity profiles in an anatomically accurate in vitro model of the abdominal aorta. Velocities measured in the suprarenal aorta were laminar and reversed minimally, comparing well with theoretical solutions of Womersley flow (r = 0.96). The time-averaged velocity was +3.0 cm/s near-wall at a distance of 1 mm away from the wall. In the infrarenal aorta, the maximal velocities were skewed toward the anterior wall. At the posterior wall, velocity oscillated in direction and was retrograde for 82 percent of the cardiac cycle. The time-averaged velocity near the posterior wall was −12.5 cm/s as compared to +3.00 cm/s near the anterior wall. At the aortic bifurcation, the locations of maximal and minimal velocities in this slice were concentrated near the lateral posterior walls. This study quantifies the magnitude of low and oscillatory velocity that may exist in the abdominal aorta and suggests that there is a strong relationship between the velocities in the retrograde direction under resting conditions and the distribution of atherosclerotic plaque.

This study examines the hemodynamics of the abdominal aorta during physiological changes in flow rates and pulse rate that occur under exercise and postprandial conditions. Hemodynamic measurements were performed using an in vitro model which took into account seven major branches, the curvature, and the pulsatile nature of blood flow of the abdominal aorta. Magnetic Resonance Imaging velocimetry employing phase-velocity encoding was used to measure the pulsatile axial velocity profiles for the entire cross-section at three axial locations. Under simulated exercise conditions, the forward velocities were approximately double those seen during rest, and the flow reversal seen for resting conditions was greatly reduced. Near the posterior wall of the infrarenal aorta, the velocities were negative for only 21 percent of the cardiac cycle as compared with 82 percent for resting conditions. Postprandial conditions produced a 25 percent reduction in peak velocity and a 33 percent reduction in mean velocity near the left anterior wall of the aorta just distal to the superior mesenteric artery (in comparison with resting conditions). The changes that can occur in abdominal aorta hemodynamics under different physiologic conditions may affect the rate of progression of atherosclerosis at this site.

The purpose of this study was to develop a method to accurately determine mean velocities and Reynolds stresses in pulsatile flows. The pulsatile flow used to develop this method was produced within a transparent model of a left ventricular assist device (LVAD). Velocity measurements were taken at locations within the LVAD using a two-component laser Doppler anemometry (LDA) system. At each measurement location, as many as 4096 realizations of two coincident orthogonal velocity components were collected during preselected time windows over the pump cycle. The number of realizations was varied to determine how the number of data points collected affects the accuracy of the results. The duration of the time windows was varied to determine the maximum window size consistent with an assumption of pseudostationary flow. Erroneous velocity realizations were discarded from individual data sets by implementing successive elliptical filters on the velocity components. The mean velocities and principal Reynolds stresses were determined for each of the filtered data sets. The filtering technique, while eliminating less than 5 percent of the original data points, significantly reduced the computed Reynolds stresses. The results indicate that, with proper filtering, reasonable accuracy can be achieved using a velocity data set of 250 points, provided the time window is small enough to ensure pseudostationary flow (typically 20 to 40 ms). The results also reveal that the time window which is required to assume pseudostationary flow varies with location and cycle time and can range from 100 ms to less than 20 ms. Rotation of the coordinate system to the principal stress axes can lead to large variations in the computed Reynolds stresses, up to 2440 dynes/cm 2 for the normal stress and 7620 dynes/cm 2 for the shear stress.

In vitro pulsatile flow visualization studies were conducted to assess the effects of varying radii of curvature of the right ventricular outflow tract (RVOT) and main pulmonary artery (MPA) on the flow fields in the main, right, and left pulmonary arteries of a one month lamb pulmonary artery model. Three glass flow-through models were studied; one with no curvature, one with the correct anatomic curvature, and one with an overaccentuated curvature on the RVOT and MPA. All other geometric parameters were held constant. Pulsatile flow visualization studies were conducted at nine flow conditions; heart rates of 70, 100, and 140 bpm, and cardiac outputs of 1.5, 2.5 and 3.5 l/min with corresponding mean pulmonary pressures of 10, 20, and 30 mmHg. Changes were observed in the pulmonary flow fields as the curvature of the outflow tract, heart rate and mean pulmonary pressure were varied. An increase in vessel curvature led to an increase in the overall radial nature of the flow field as well as flow separation regions which formed faster, originated further downstream, and occupied more of the vessel area. At higher heart rates, the maximum size of the separation regions decreased, while flow separation regions appeared earlier in the cardiac cycle and grew more quickly. Heart rate also affected the initiation of flow reversal; flow reversal occurred later in the cardiac cycle at lower heart rates. Both heart rate and mean pulmonary pressure influenced the stability of the pulmonary flow field and the appearance of coherent structures. In addition, an increase in mean pulmonary pressure increased the magnitude of reverse flow. These flow visualization observations have directed more quantitative studies such as pulsed Doppler ultrasound and laser Doppler anemometry velocity measurements.

Whole body magnetic resonance (MR) imaging has recently become an important diagnostic tool for cardiovascular diseases. The technique of magnetic resonance phase velocity encoding allows the quantitative measurement of velocity for an arbitrary component direction. A study was initiated to determine the ability and accuracy of MR velocimetry to measure a wide range of flow conditions including flow separation, three-dimensional secondary flow, high velocity gradients, and turbulence. A steady flow system pumped water doped with manganese chloride through a variety of test sections. Images were produced using gradient echo sequences on test sections including a straight tube, a curved tube, a smoothly converging-diverging nozzle, and an orifice. Magnetic resonance measurements of laminar and turbulent flows were depicted as cross-sectional velocity profiles. MR velocity measurements revealed such flow behavior as spatially varying velocity, recirculation and secondary flows over a wide range of conditions. Comparisons made with published experimental laser Doppler anemometry measurements and theoretical calculations for similar flow conditions revealed excellent accuracy and precision levels. The successful measurement of velocity profiles for a variety of flow conditions and geometries indicate that magnetic resonance imaging is an accurate, non-contacting velocimeter.

A time-of-flight MRI velocity measurement technique is evaluated against corresponding LDV measurements in a constriction tube model over a range of physiologic flow conditions. Results from this study show that MR displacement images can: 1) be obtained within both laminar and turbulent jets (maximum stenotic Re≅4,200), 2) measure mean jet velocities up to 172 cm/s, and, 3) detect low forward and reverse stenosis (0≤L/D≤2). Regions between the jet termination point and re-establishment of laminar flow (Re≥1500, ≥1000, and ≥110 downstream of 40, 60, and 80 percent stenosis, respectively) cannot presently be detected by this technique.

An experimental and numerical study of pulsatile laminar flow in a plane 90-degree bifurcation is presented. Detailed LDA velocity measurements of the oscillatory flow field have been carried out. The numerical predictions, which are based on an iterative, finite-difference numerical procedure using primitive dependent variables, are in good agreement with the measurements. The results show that one separation zone is established near the bottom wall of the main duct and another near the upstream wall of the branch. The location and size of the separation zones vary within the cycle and are influenced by the Reynolds number, the flow rate ratio, and the Stokes number.

The fluid dynamic behavior of a Newtonian water/glycerol solution, a non-Newtonian polymer (separan) solution, and bovine blood were compared in the Penn State Electrical Ventricular Assist Device (EVAD). Pulsed doppler ultrasound velocimetry was used to measure velocities in the near wall region (0.95–2.7 mm) along the perimeter of the pump. Mean velocity, turbulence intensity, local and convective acceleration, and shear rate were calculated from the PDU velocity measurements. Flow visualization provided qualitative information about the general flow patterns in the EVAD. Results indicate that water/glycerol does not accurately model the flow characteristics of bovine blood in the EVAD. The non-Newtonian separan solution produced results closer to those of the bovine blood than did the water/glycerol solution. Near wall velocity magnitudes for the separan were similar to those of the bovine blood, but the profile shapes differed for portions of the pump cycle. All three fluids exhibited periods of stagnation. Bovine blood results indicated the presence of a desired rotational washout pattern at mid-systole, while results with the other fluids did not show this feature.

In this study we have employed a single channel, pulsed ultrasonic Doppler velocimeter to measure instantaneous velocity distributions within the pumping chamber of a ventricular assist device. Instantaneous velocities have been decomposed into periodic mean and turbulent fluctuating components from which estimates of Reynolds stresses within the chamber and mean shear stresses along the wall of the chamber have been obtained. A review of the complete data set indicates a maximum value of the mean wall shear stress of 25 dynes/cm 2 and a maximum Reynolds stress of 212 dynes/cm 2 . These values are lower than those measured distal to aortic valve prostheses in vitro and are well below levels known to damage blood components. Core flow patterns, wall washing patterns and flow stagnation points are also revealed.

The need for better and longer lasting trileaflet valves has led to the design and development of the Abiomed polymeric trileaflet valve prosthesis. In-vitro fluid dynamic studies on sizes 25 and 21 mm valves in the aortic position indicate an overall improvement in performance compared to the Carpentier-Edwards and Ionescu-Shiley tissue valves in current clinical use. The pressure drop studies yielded effective orifice areas of 1.99 and 1.54 cm 2 , and performance indices of 0.41 and 0.45 for the Nos. 25 and 21 valves, respectively. Leaflet photography studies indicated that the two valve sizes had maximum opening areas of 225 and 145 mm 2 , respectively, at a normal resting cardiac output. Steady and pulsatile flow velocity measurements with a laser-Doppler anemometer (LDA) system indicate that the flow field downstream of the Abiomed valve is jetlike and turbulent. Maximum mean square axial velocity fluctuations of 55 and 83 cm/s, and turbulent shear stresses of 220 and 450 N/m 2 were measured in the immediate vicinity of the nos. 25 and 21 valves, respectively. The Abiomed valves studied had been originally configured for use in valved conduits, and it is therefore our opinion that further improvements can be made to the valve and stent design, which would enhance its fluid dynamic performance.

A new approach is presented for studying the vascular response to hemodynamic stress. A laser doppler anemometer is used to make velocity measurements very near the walls of human arterial casts; these measurements are then correlated with the histology of the artery from which the cast was made. Several illustrative results are given which suggest that the velocity profiles along the outer walls of aortic bifurcations may be significantly determined by the longitudinal variation of cross-sectional area. The shapes of these profiles were qualitatively different for each cast studied. In one specimen, the location of initial lipid deposits appeared to correlate with flow acceleration.