Analysis of regurgitant jets in natural and bio-prosthetic heart valves.

Artificial bio-prosthetic heart valves are prone to fatigue tearing, having a 50% failure rate in ten years. Tears in valves give rise to pulsing reverse flow back through the valve. This is termed regurgitant flow and the resultant jet of blood a regurgitant jet. The regurgitant volume of the jet during the pulsing cycle gives a measure of the severity of the valve defect and clinical significance. Hence, it is important for the cardiologists to be able to quantify this volume. Although the velocity of the regurgitant jet can be determined using Doppler ultrasound, the dimensions of the heart valve lesion cannot be measured directly; hence, the volumetric flow rate cannot be quantified accurately. At present the severity of the regurgitant jet is assessed qualitatively from the intrusion of the jet into the cardiac chamber. In the present study, classical mathematical theories of turbulent jets have been used to describe the velocity distributions for the types of jets expected in defective heart valves and these distributions have been verified experimentally. One of these models has been developed to enable the regurgitant volumetric flow through an axisymmetric orifice of unknown radius to be calculated from the velocity distribution of the jet. This relationship may be used in conjunction with ultrasound techniques to quantify the regurgitant volume within defective artificial heart valve implants. The present study shows that there is a significant difference in the velocity distributions in jets emanating from axisymmetric and high aspect ratio slots.(ABSTRACT TRUNCATED AT 250 WORDS)     

A three-dimensional insight into the complexity of flow convergence in mitral regurgitation: adjunctive benefit of anatomic regurgitant orifice area

Mitral effective regurgitant orifice area (EROA) using the flow convergence (FC) method is used to quantify the severity of mitral regurgitation (MR). However, it is challenging and prone to interobserver variability in complex valvular pathology. We hypothesized that real-time three-dimensional (3D) transesophageal echocardiography (RT3D TEE) derived anatomic regurgitant orifice area (AROA) can be a reasonable adjunct, irrespective of valvular geometry. Our goals were to 1) to determine the regurgitant orifice morphology and distance suitable for FC measurement using 3D computational flow dynamics and finite element analysis (FEA), and (2) to measure AROA from RT3D TEE and compare it with 2D FC derived EROA measurements. We studied 61 patients. EROA was calculated from 2D TEE images using the 2D-FC technique, and AROA was obtained from zoomed RT3DE TEE acquisitions using prototype software. 3D computational fluid dynamics by FEA were applied to 3D TEE images to determine the effects of mitral valve (MV) orifice geometry on FC pattern. 3D FEA analysis revealed that a central regurgitant orifice is suitable for FC measurements at an optimal distance from the orifice but complex MV orifice resulting in eccentric jets yielded nonaxisymmetric isovelocity contours close to the orifice where the assumptions underlying FC are problematic. EROA and AROA measurements correlated well (r = 0.81) with a nonsignificant bias. However, in patients with eccentric MR, the bias was larger than in central MR. Intermeasurement variability was higher for the 2D FC technique than for RT3DE-based measurements. With its superior reproducibility, 3D analysis of the AROA is a useful alternative to quantify MR when 2D FC measurements are challenging.     

A new theoretical model for noninvasive quantification of mitral regurgitation

The most common objective assessments of mitral regurgitation are limited by their invasive or semiquantitative nature. Recent attempts at correlation with jet size from Doppler flow maps have failed to produce a direct measure of regurgitant volume and are fundamentally limited by the dependence of jet dimensions on factors other than flow volume. The purpose of this paper was to develop an equation, based on the physics of turbulent regurgitant jets, for calculating regurgitant volume from quantities that can be measured by Doppler ultrasound. The result is an equation forw flow rate Q as a function of orifice velocity Uo, a downstream centerline velocity Um and the intervening distance chi: Q = pi U2m chi 2/160Uo. This equation can also be modified to obtain total regurgitant volume in clinical pulsatile flow. The assumptions made demand a free turbulent jet for which momentum is conserved, but should otherwise be physiologically applicable. The advantage of this technique compared to correlations with jet size are its theoretical justification and ability to quantify regurgitant volume directly.     

A new automated method for the quantification of mitral regurgitant volume and dynamic regurgitant orifice area based on a normalized centerline velocity distribution using color M-mode and continuous wave Doppler imaging

Previous echocardiographic techniques for quantifying valvular regurgitation (PISA) are limited by factors including uncertainties in orifice location and hemispheric convergence assumption. Using computational fluid dynamics simulations, we developed a new model for the estimation of orifice diameter and regurgitant volume without the aforementioned assumptions of the PISA technique. Using experimental data obtained from the in vitro flow model we successfully validated our new model. The model output (y) and reference (x) values were in close agreement (y = 0.95x + 0.38, r = 0.96, error = 1.68 +/- 7.54% for the orifice diameter and y = 1.18x - 4.72, r = 0.93, error = 6.48 +/- 16.81% for the regurgitant volume).     

Influence of pulsatility on the development of intracardiac jets: an in vitro laser Doppler study.

So far, it has been hypothesized that numerical data obtained in steady flow conditions apply to pulsatile flows. In order to study the modifications of the velocity fields due to pulsatility, jets were produced by 8 orifices (with a diameter "D" of 4.4 to 11.3 mm) included in a chamber of 50 mm. The velocity was measured using laser Doppler anemometry with a pulsatile flow ("pf") and compared to the values obtained in steady ("sf"): at maximum velocity, the longitudinal velocity profile is qualitatively similar to this observed in steady flow: it is made of a plateau followed by an hyperbolic velocity decay in the turbulent area. The length of the core ("Lpf") is strongly related to "D" (Lpf = 3.72 D + 5.49, r = .99) and the velocity decay depends on the ratio between the distance "x" from the orifice and "D" (V/Vo = 2.83D/x + 3.46, r = .85, where V is the velocity at "x" and Vo the initial velocity). During the acceleration and the deceleration, the laminar core is disturbed by turbulences. The comparison of "pf" data with "sf" data demonstrated similar diameters at the origin of the jets (Dpf = 0.96 Dsf + .12, r = .99), but significant (p less than .0001) differences both for "L" and "V/Vo": Lpf = .91Lsf + 6.58, r = .97, V/Vopf = .63 V/Vosf + .34, r = .76. Thus, pulsatility modifies velocity fields and the results obtained in steady flow conditions do not apply to pulsatile jets.     

Kinetics of chaperoning of dithiothreitol-denatured alpha-lactalbumin by alpha-crystallin

Molecular chaperones prevent the aggregation of partially folded or misfolded forms of protein. alpha-Crystallin performs such a function in the ocular lens. Dynamic light scattering (DLS) measurements were performed to gain insight into the kinetics and mechanism of alpha-crystallin chaperoning. Experiments were conducted as a function of alpha-lactalbumin concentration as well as the alpha-crystallin/alpha-lactalbumin ratio over a 24 h period. In the particle distribution patterns the lactalbumin concentration was partitioned into three compartments: (a) monomeric free lactalbumin; (b) lactalbumin in the chaperoning complex; and (c) lactalbumin aggregates. DLS intensities were converted to molar concentrations by assuming a model of a spherical chaperoning complex. In the model, alpha-crystallin is the central core and alpha-lactalbumin molecules occupy a ring surrounding the core. The kinetics of chaperoning was studied by proposing a simple scheme with four rate constants. The reversible reaction of the formation of the chaperoning complex is characterized by rate constants k(1) and k(2). The rate constants k(3) and k(4) govern the irreversible aggregation of lactalbumin: the former from the free monomeric lactalbumin pool and the latter describing the aggregation of the denatured lactalbumin released from the chaperoning complex. The rate constants, k(3) and k(4) are four magnitudes larger than k(1) and k(2). The equilibrium constant of chaperoning complex formation lies in favor of the reactants. k(4) is somewhat faster than k(3) and it is three times faster than k(s) governing the self-aggregation of lactalbumin in the absence of alpha-crystallin.     

An analysis of turbulent shear stresses in leakage flow through a bileaflet mechanical prostheses

In this work, estimates of turbulence were made from pulsatile flow laser Doppler velocimetry measurements using traditional phase averaging and averaging after the removal of cyclic variation. These estimates were compared with estimates obtained from steady leakage flow LDV measurements and an analytical method. The results of these studies indicate that leakage jets which are free and planar in shape may be more unstable than other leakage jets, and that cyclic variation does not cause a gross overestimation of the Reynolds stresses at large distances from the leakage jet orifice.     

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

3D-PTV is a quantitative flow measurement technique that aims to track the Lagrangian paths of a set of particles in three dimensions using stereoscopic recording of image sequences. The basic components, features, constraints and optimization tips of a 3D-PTV topology consisting of a high-speed camera with a four-view splitter are described and discussed in this article. The technique is applied to the intermediate flow field (5 <x/d <25) of a circular jet at Re ≈ 7,000. Lagrangian flow features and turbulence quantities in an Eulerian frame are estimated around ten diameters downstream of the jet origin and at various radial distances from the jet core. Lagrangian properties include trajectory, velocity and acceleration of selected particles as well as curvature of the flow path, which are obtained from the Frenet-Serret equation. Estimation of the 3D velocity and turbulence fields around the jet core axis at a cross-plane located at ten diameters downstream of the jet is compared with literature, and the power spectrum of the large-scale streamwise velocity motions is obtained at various radial distances from the jet core.     

Velocity profiles in stenosed tube models using magnetic resonance imaging

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 approximately equal to 4,200), 2) measure mean jet velocities up to 172 cm/s, and, 3) detect low forward and reverse stenosis (0 less than or equal to L/D less than or equal to 2). Regions between the jet termination point and re-establishment of laminar flow (Re greater than or equal to 1500, greater than or equal to 1000, and greater than or equal to 110 downstream of 40, 60, and 80 percent stenosis, respectively) cannot presently be detected by this technique.     

Flow visualisation and high speed video analysis of water jets in the snapping shrimp (Alpheus heterochaelis)

Snapping shrimp (Alpheus heterochaelis) produce a fast, well-focused water jet by rapid closure of their specialised snapper claw. As shown previously, water jets may injure the opponent in interspecific encounters (e.g. with small crabs) although no damage was observed in intraspecific encounters. For conspecific receivers the jet represents a potential hydrodynamic signal and can be analysed with the help of mechanosensory hairs. To gain more insight in the biophysical characteristics of the water jet we visualised and analysed jets of tethered snapping shrimp using standard and high speed video recordings. Water jet width increases with increasing distance from the snapper claw tip, and both width and distance increase with increasing snapper claw size. Water jet distances do not increase with increasing claw cocking duration (building up muscle tension) but medium cocking durations of about 550 ms result in longest distances. Mean water jet velocity is 6.5 m s⁻¹ shortly after claw closure but rapidly decreases subsequently. At the mean distance between snapping conspecifics (9 mm) water jet velocities produced by snapping shrimp with larger snapper claws are significantly higher than those of animals with smaller claws. Interestingly, males with equal snapper claw size as females produce significantly faster water jets. Accepted: 31 March 1999     

The 12 cc Penn State pulsatile pediatric ventricular assist device: fluid dynamics associated with valve selection

The mortality rate for infants awaiting a heart transplant is 40% because of the extremely limited number of donor organs. Ventricular assist devices (VADs), a common bridge-to-transplant solution in adults, are becoming a viable option for pediatric patients. A major obstacle faced by VAD designers is thromboembolism. Previous studies have shown that the interrelated flow characteristics necessary for the prevention of thrombosis in a pulsatile VAD are a strong inlet jet, a late diastolic recirculating flow, and a wall shear rate greater than 500 s(-1). Particle image velocimetry was used to compare the flow fields in the chamber of the 12 cc Penn State pediatric pulsatile VAD using two mechanical heart valves: Bjork-Shiley monostrut (BSM) tilting disk valves and CarboMedics (CM) bileaflet valves. In conjunction with the flow evaluation, wall shear data were calculated and analyzed to help quantify wall washing. The major orifice inlet jet of the device containing BSM valves was more intense, which led to better recirculation and wall washing than the three jets produced by the CM valves. Regurgitation through the CM valve served as a significant hindrance to the development of the rotational flow.     

Photophysics of the fluorescent Ca2+ indicator Fura-2.

The photophysics of the complex forming reaction of Ca2+ and Fura-2 are investigated using steady-state and time-resolved fluorescence measurements. The fluorescence decay traces were analyzed with global compartmental analysis yielding the following values for the rate constants at room temperature in aqueous solution with BAPTA as Ca2+ buffer: k01 = 1.2 x 10(9)s-1, k21 = 1.0 x 10(11) M-1 s-1, k02 = 5.5 x 10(8) s-1, k12 = 2.2 x 10(7) s-1, and with EGTA as Ca2+ buffer: k01 = 1.4 x 10(9) s-1, k21 = 5.0 x 10(10) M-1 s-1, k02 = 5.5 x 10(8) s-1, k12 = 3.2 x 10(7) s-1. k01 and k02 denote the respective deactivation rate constants of the Ca2+ free and bound forms of Fura-2 in the excited state. k21 represents the second-order rate constant of binding of Ca2+ and Fura-2 in the excited state, whereas k12 is the first-order rate constant of dissociation of the excited Ca2+:Fura-2 complex. The ionic strength of the solution was shown not to influence the recovered values of the rate constants. From the estimated values of k12 and k21, the dissociation constant K*d in the excited state was calculated. It was found that in EGTA Ca2+ buffer pK*d (3.2) is smaller than pKd (6.9) and that there is negligible interference of the excited-state reaction with the determination of Kd and [Ca2+] from fluorimetric titration curves. Hence, Fura-2 can be safely used as an Ca2+ indicator. From the obtained fluorescence decay parameters and the steady-state excitation spectra, the species-associated excitation spectra of the Ca2+ free and bound forms of Fura-2 were calculated at intermediate Ca2+ concentrations.     

Influence of structural geometry on the severity of bicuspid aortic stenosis

Doppler-derived gradients may overestimate total pressure loss in degenerative and prosthetic aortic valve stenosis (AS) due to unaccounted pressure recovery distal to the orifice. However, in congenitally bicuspid valves, jet eccentricity may result in a higher anatomic-to-effective orifice contraction ratio, resulting in an increased pressure loss at the valve and a reduced pressure recovery distal to the orifice leading to greater functional severity. The objective of our study was to determine the impact of local geometry on the total versus Doppler-derived pressure loss and therefore the assessed severity of the stenosis in bicuspid valves. On the basis of clinically obtained measurements, two- and three-dimensional computer simulations were created with various local geometries by altering the diameters of the left ventricular outflow tract (LVOT; 1.8-3.0 cm), orifice diameter (OD; 0.8-1.6 cm), and aortic root diameter (AR; 3.0-5.4 cm). Jet eccentricity was altered in the models from 0 to 25 degrees. Simulations were performed under steady-flow conditions. Axisymmetric simulations indicate that the overall differences in pressure recovery were minor for variations in LVOT diameter (<3%). However, both OD and AR had a significant impact on pressure recovery (6-20%), with greatest recovery being the larger OD and the smaller recovery being the AR. In addition, three-dimensional data illustrate a greater pressure loss for eccentric jets with the same orifice area, thus increasing functional severity. In conclusion, jet eccentricity results in greater pressure loss in bicuspid valve AS due to reduced effective orifice area. Functional severity may also be enhanced by larger aortic roots, commonly occurring in these patients, leading to reduced pressure recovery. Thus, for the same anatomic orifice area, functional severity is greater in bicuspid than in degenerative tricuspid AS.     

Kinetic mechanism of myofibril ATPase.

The kinetic mechanism of myofibril ATPase was investigated using psoas and mixed back muscle over a range of ionic strengths. Myofibrils were labeled with pyrene iodoacetamide to measure the rate constants for the binding of ATP and formation of the weakly attached state. The velocity of shortening was measured by stopping the contraction at various times by mixing with pH 4.5 buffer. The transient and steady-state rates of ATP hydrolysis were measured by the quench flow method. The results fitted the kinetic scheme [formula: see text] The rate constants (or equilibrium constants for steps 1 and 6) were obtained for the six steps. k5 was calculated from the KM for shortening velocity, K1, and k2. The rate constants were essentially equal for myofibrils and acto-S-1 at low ionic strength. Increasing the ionic strength up to 100 mM in NaCl increased the rate of the hydrolysis step and the size of the phosphate burst and the effective rate of product release became the rate-limiting step. The step calculated from the velocity of shortening, k5, and k2 is 15 nm, based on a model in which step 4 is the force-generating step.     

Kinetic study on the successive four-step reduction of Cyt c3

A detailed kinetic study on the successive four-step reduction of cyt c3, which has four heme units in a single protein, III4 leads to III3II leads to III2II2 leads to III II3 leads to II4, was carried out by stopped-flow electronic spectroscopy (SF-UV) and stopped-flow circular dichroism spectroscopy (SF-CD). Based on the absorbance change vs. time and the ellipticity change vs. time at the characteristic CD, together with the electronic absorption of the enzyme, rate constants for the successive four electron transfer steps, k1-k4, were successfully estimated by computer simulation. The rate constants of the four steps (k1 = 19.8 s-1, k2 = 11.9 s-1, k3 = 8.9 s-1, and k4 = 1.6 s-1; 8.0 10(-4) M Na2S2O4) are quite different from the statistical values (4: 3: 2: 1), thus excluding the possibility of random reduction of hemes of equal reactivities. Instead, each heme has its own reactivity, probably dependent on its local environment. The value of k3 is somewhat higher than the statistical value, indicating the existence of an autoacceleration effect, although small. This autoacceleration is most probably due to a unique heme-heme and/or heme-environment interaction since unusual CD and electronic absorptions were observed at 350-400 nm at about the time corresponding.     

Kinetics of glu- and lys-plasminogen activation by the tissue activator in a fibrin clot

Using a modified procedure for measuring the time of fibrin clot lysis, the kinetics of Glu- and Lys-plasminogen activation by the tissue activator was studied. Within the plasminogen concentration range of 0.4-100 nM the rate of activation of both protein forms obeys the Michaelis-Menten kinetics. At Lys-plasminogen concentration equimolar to that of fibrin, the rate of activation of the former decreases down to that of Glu-plasminogen activation. The kinetic constants for Glu- and Lys-plasminogen activation (Km) are equal to 0.055 and 0.013 microM; k = 0.19 and 0.21 s-1, respectively. The Km values for fibrin-bound Glu- and Lys-plasminogen are equal to 0.25 nM and 8 nM, respectively (k = 0.08 and 0.26 s-1, respectively). It is assumed that the tissue activator exhibits a higher affinity for the Glu-plasminogen--fibrin complex than for the Lys-plasminogen-fibrin complex.     

Jet injection into polyacrylamide gels: investigation of jet injection mechanics

Jet injectors employ high-velocity liquid jets that penetrate into human skin and deposit drugs in the dermal or subdermal region. Although jet injectors have been marketed for a number of years, relatively little is known about the interactions of high-speed jets with soft materials such as skin. Using polyacrylamide gels as a model system, the mechanics of jet penetration, including the dependence of jet penetration on mechanical properties, was studied. Jets employed in a typical commercial injector, (orifice diameter: 152 microm, velocity: 170-180 m/s) were used to inject fluid into polyacrylamide gels possessing Young's moduli in the range of 0.06-0.77 MPa and hardness values in the range of 4-70 H(OO). Motion analysis of jet entry into polyacrylamide gels revealed that jet penetration can be divided into three distinct events: erosion, stagnation, and dispersion. During the erosion phase, the jet removed the gel at the impact site and led to the formation of a distinct cylindrical hole. Cessation of erosion induced a period of jet stagnation ( approximately 600 micros) characterized by constant penetration depth. This stage was followed by dispersion of the liquid into the gel. The dispersion took place by crack propagation and was nearly symmetrical with the exception of injections into 10% acrylamide (Young's modulus of 0.06 MPa). The penetration depth of the jets as well as the rate of erosion decreased with increasing Young's modulus. The mechanics of jet penetration into polyacrylamide gels provides an important tool for understanding jet injection into skin.     

Three-dimensional visualization of velocity fields downstream of six mechanical aortic valves in a pulsatile flow model

Velocity fields downstream of 27 mm Bj?rk-Shiley Standard, Bj?rk-Shiley Convex-Concave, Bj?rk-Shiley Monostrut, Hall-Kaster (Medtronic-Hall), St. Jude Medical and Starr-Edwards Silastic Ball aortic valves were studied in a pulsatile mock circulation. Stroke volume was 70 cm3 and frequency 71 min-1 and 88 min-1. Fluid velocity was measured by a catheter mounted hot-film anemometer probe in a glycerol water mixture one and two diameters downstream of the aortic valve. Velocity fields were dynamically visualized by a three-dimensional technique and revealed qualitative independence of frequency. All profiles were flat in the acceleration phase of systole. From peak systole and throughout the systolic deceleration phase profiles characteristic of the individual valves appeared. The pivoting and tilting disc valves caused a skewed velocity profile with highest velocities downstream of the major orifice and lowest velocities downstream of the minor orifice. The differences between the three investigated Bj?rk-Shiley valves were remarkable. The St. Jude Medical valve generated velocity peaks downstream of the two major orifices and the central slit, and lower velocities in the hinge areas. A rather flat profile with central hollowing was seen downstream of the Starr-Edwards Ball valve. All velocity profiles were more or less dampened two diameters downstream.     

Mixing time and oxygen transfer characteristics of double draft tube airlift fermentor

Despite the increasing importance of airlift fermentors, very little published information is available on how the geometric configurations of the draft tubes and the air-sparging system affect the mixing and oxygen transfer characteristics of the fermentor. A 14-L air-lift fermentor was designed and build with a fixed liquid height to diameter ratio of 1.5 utilizing four equally spaced air jets at the bottom. Two jet orifice sizes were used, 1.27 and 3.81 mm i.d., and for each jet size the following four geometric configurations were used: Single inner concentric draft tube, single outer concentric draft tube, two concentric draft tubes, and no draft tubes where the fermentor was operated as a shallow bubble column. It was found that the presence of draft tubes stabilized liquid circulation patterns and gave systemically higher mixing times than those obtained in the absence of draft tubes. In addition, the double draft tube geometry resulted in higher mixing times than the single draft tubes. For the power unit volume range 20 to about 250 W/m³ the larger 3.81-mm orifices gave systemically higher k_L a values than the smaller 1.27-mm i.d. orifices. At 200 W/m³ the use of a single outer draft tube with the 3.81-mm orifices resulted in 94% increase in k_L a values over that obtained with no draft tubes. However, the effect of draft tube geometry on k_L a values when the 1.27-mm orifices were used was not significant. The air bubble formation characteristics at the jet orifices were found to be different, which reflected the differences observed in mass transfer and mixing characteristics. The power economy for oxygen transfer was found to be depend strongly on the orifice size and less on the geometric configuration of draft tubes.     

A formulation for calculating the translational velocity of a vortex ring or pair

Cephalopods, among other marine animals, use jet propulsion for swimming. A simple actuator is designed to loosely mimic pulsatile jet formation in squid and jellyfish. The actuator is comprised of a cavity with an oscillating diaphragm and an exit orifice. Periodic oscillation of the diaphragm results in the formation of an array of vortex rings and eventually could generate a periodic pulsatile jet. A general formulation for calculating the velocity of a steadily translating vortical structure in two-dimensional and axi-symmetric shear flows is presented. This technique is based on taking the variational derivative of an energetic function at its critical point. This technique is general, applicable to vortices in liquid and gas media, with no limitation on the relative size of the vortex core. The technique is then implemented to estimate the translational velocity of a vortex ring in a Helmholtz vortex ring generator.