John J. Charonko

Estimation of uncertainty bounds for individual particle image velocimetry measurements from cross-correlation peak ratio

Numerous studies have established firmly that particle image velocimetry (PIV) is a robust method for non-invasive, quantitative measurements of fluid velocity, and that when carefully conducted, typical measurements can accurately detect displacements in digital images with a resolution well below a single pixel (in some cases well below a hundredth of a pixel). However, to date, these estimates have only been able to provide guidance on the expected error for an average measurement under specific image quality and flow conditions. This paper demonstrates a new method for estimating the uncertainty bounds to within a given confidence interval for a specific, individual measurement. Here, cross-correlation peak ratio, the ratio of primary to secondary peak height, is shown to correlate strongly with the range of observed error values for a given measurement, regardless of flow condition or image quality. This relationship is significantly stronger for phase-only generalized cross-correlation PIV processing, while the standard correlation approach showed weaker performance. Using an analytical model of the relationship derived from synthetic data sets, the uncertainty bounds at a 95% confidence interval are then computed for several artificial and experimental flow fields, and the resulting errors are shown to match closely to the predicted uncertainties. While this method stops short of being able to predict the true error for a given measurement, knowledge of the uncertainty level for a PIV experiment should provide great benefits when applying the results of PIV analysis to engineering design studies and computational fluid dynamics validation efforts. Moreover, this approach is exceptionally simple to implement and requires negligible additional computational cost.

Assessment of pressure field calculations from particle image velocimetry measurements

This paper explores the challenges associated with the determination of in-field pressure from DPIV (digital particle image velocimetry)-measured planar velocity fields for time-dependent incompressible flows. Several methods that have been previously explored in the literature are compared, including direct integration of the pressure gradients and solution of different forms of the pressure Poisson equations. Their dependence on grid resolution, sampling rate, velocity measurement error levels and off-axis recording was quantified using artificial data of two ideal sample flow fields—a decaying vortex flow and pulsatile flow between two parallel plates, and real DPIV and pressure data from oscillating flow through a diffuser. The need for special attention to mitigate the velocity error propagation in the pressure estimation is also addressed using a physics-preserving approach based on proper orthogonal decomposition (POD). The results demonstrate that there is no unique or optimum method for estimating the pressure field and the resulting error will depend highly on the type of the flow. However, the virtual boundary, omni-directional pressure integration scheme first proposed by Liu and Katz (2006 Exp. Fluids 41 227–40) performed consistently well in both synthetic and experimental flows. Estimated errors can vary from less than 1% to over 100% with respect to the expected value, though in contrast to more traditional smoothing algorithms, the newly proposed POD-based filtering approach can reduce errors for a given set of conditions by an order of magnitude or more. This analysis offers valuable insight that allows optimizing the choice of methods and parameters based on the flow under consideration.

Vortices Formed on the Mitral Valve Tips Aid Normal Left Ventricular Filling

For the left ventricle (LV) to function as an effective pump it must be able to fill from a low left atrial pressure. However, this ability is lost in patients with heart failure. We investigated LV filling by measuring the cardiac blood flow using 2D phase contrast magnetic resonance imaging and quantified the intraventricular pressure gradients and the strength and location of vortices. In normal subjects, blood flows towards the apex prior to the mitral valve opening, and the mitral annulus moves rapidly away after the valve opens, with both effects enhancing the vortex ring at the mitral valve tips. Instead of being a passive by-product of the process as was previously believed, this ring facilitates filling by reducing convective losses and enhancing the function of the LV as a suction pump. The virtual channel thus created by the vortices may help insure efficient mass transfer for the left atrium to the LV apex. Impairment of this mechanism contributes to diastolic dysfunction, with LV filling becoming dependent on left atrial pressure, which can lead to eventual heart failure. Better understanding of the mechanics of this progression may lead to more accurate diagnosis and treatment of this disease.

Robust wall gradient estimation using radial basis functions and proper orthogonal decomposition (POD) for particle image velocimetry (PIV) measured fields

A robust method for improving the estimation of near-wall velocity gradients from noisy flow data using Gaussian (GA) and generalized multiquadratic (GMQ) radial basis functions (RBFs) that optimizes fitting parameters to minimize the biharmonic equation is introduced. Error analysis of the wall gradient estimation was performed for RBFs, standard finite difference schemes, and polynomial and spline interpolations at various spatial resolutions, interpolation grid sizes and noise levels in synthetically generated Poiseuille and Womersley flow fields. Also, the effectiveness of the methods on digital particle image velocimetry (DPIV) data is tested by processing images generated using velocity fields obtained from direct numerical simulation (DNS) of an open turbulent channel, and the estimated gradients were compared against gradients obtained from DNS data. In the absence of noise, all methods perform well for Poiseuille and Womersley flows yielding a total error under 10% at all resolutions. In the presence of noise, the GMQ performed robustly with a total error under 10–20% even with 10% noise. With DPIV processed data for the turbulent channel flow, the error is on the order of 25–40% using thin plate spline and GMQ interpolations. Optimization of the RBF fitting parameters that minimize the energy functional associated with the analytical surface results in robust velocity gradient estimators but is computationally expensive. This computational expense is reduced and the accuracy of the proposed techniques is further improved by introducing a novel approach that combines the gradient estimators with proper orthogonal decomposition (POD). The implementation of the interpolation schemes on the POD modes results in improving accuracy by 10–15% and reducing the computational cost by approximately 75%.

Loss of Adrenergic Augmentation of Diastolic Intra-LV Pressure Difference in Patients With Diastolic Dysfunction : Evaluation by Color M-Mode Echocardiography

OBJECTIVES The aim of this study was to evaluate the hypothesis that the adrenergic response of the intraventricular pressure difference (IVPD) is reduced in patients with preserved ejection fraction (EF) and diastolic dysfunction (DD). BACKGROUND In early diastole, there is a progressive IVPD extending from the left atrium (LA) to the left ventricular (LV) apex. In response to adrenergic stimulation, as occurs during exercise, the IVPD increases allowing rapid filling without an abnormal increase in LA pressure. Patients with heart failure with a reduced EF have impaired adrenergic augmentation of the IVPD. METHODS We studied 166 consecutive patients undergoing dobutamine stress echocardiography who had no inducible ischemia and an EF ≥50%, of which 21 had normal diastolic function, 14 had impaired relaxation (grade 1), 80 had pseudonormal filling (grade 2), and 51 had restrictive filling (grade 3). Color M-mode Doppler (CMMD) images of mitral inflow were obtained at rest and during low (10 μg/kg/min) and peak (20 to 40 μg/kg/min) doses of dobutamine. The total IVPD from the LA to LV apex, LA to mid-LV, and mid-LV to the LV apex were calculated using the CMMD data to integrate the Euler equation. RESULTS Total IVPD was not different between groups at rest. With dobutamine, the total IVPD increased by 2.20 ± 1.95 mm Hg in normal subjects and by only 0.73 ± 1.33 mm Hg, 1.84 ± 1.63 mm Hg, and 1.08 ± 1.57 mm Hg in patients with grades 1, 2, and 3 DD, respectively. This difference was due to a failure in augmentation of IVPD from the mid-LV to the LV apex, indicating reduced apical ventricular suction with DD, whereas the IVPD from the LA to the mid-LV responded similarly to dobutamine in normal subjects and those with DD. CONCLUSIONS In patients with preserved EF, DD is associated with a reduced adrenergic augmentation of the IVPD from the mid-LV to the LV apex, reflecting less apical suction.

Evaluation of LV Diastolic Function From Color M-Mode Echocardiography

OBJECTIVES this study evaluated early diastolic filling dynamics using a semiautomated objective analysis of filling velocities obtained from color M-mode echocardiography. BACKGROUND diastolic function can be evaluated from color M-mode echocardiography by measuring the early diastolic flow propagation velocity (Vp) from the slope of a single linear approximation of an isovelocity contour. However, this method has limitations and may not accurately represent diastolic filling. METHODS we used a semiautomated objective analysis of color M-mode echocardiograms from a development cohort of 125 patients with varying diastolic function to quantify left ventricular filling velocities. Early diastolic filling was not accurately described with a single propagation velocity; instead, the rapid initial filling velocity abruptly decelerated to a slower terminal velocity. Then, we evaluated a new measure of diastolic function in a separate group of 160 patients. RESULTS compared with normal filling, diastolic dysfunction with restricted filling had a lower initial velocity (53 ± 21 cm/s vs. 87 ± 29 cm/s, p < 0.001), and the deceleration point occurred closer to the mitral annulus (2.4 ± 0.6 cm vs. 3.1 ± 0.7 cm, p < 0.05). The product of the initial velocity and the distance to the deceleration point from the mitral annulus, indicating the strength of the early filling (Vs), was progressively reduced with diastolic dysfunction. In a separate validation cohort of 160 patients, Vs better recognized diastolic dysfunction (classified by reduced diastolic intraventricular pressure gradient, elevated pulmonary capillary wedge pressure, or elevated B-type natriuretic peptide) than Vp did. CONCLUSIONS early diastolic flow propagation occurs with an initial rapid velocity that abruptly decelerates to a terminal velocity. With diastolic dysfunction, the initial velocity is slower and the deceleration point occurs closer to the mitral annulus than with normal filling. A new parameter that combines these 2 effects (Vs) provides a more accurate assessment of diastolic function than the conventional propagation velocity.

Adaptive gappy proper orthogonal decomposition for particle image velocimetry data reconstruction

This work presents a novel method for replacing erroneous measurements in digital particle image velocimetry (DPIV) data using an adaptive reconstruction with gappy proper orthogonal decomposition (POD). Previous studies have shown that gappy POD can be used to replace erroneous data with high accuracy. Conventional gappy POD methods employ a spatially constant number of modes for reconstructing the missing information across the entire field. In contrast, the method presented herein proposes a locally adaptive criterion that allows for determination of the optimum number of POD modes required for the reconstruction of each replaced measurement. This reconstruction produces higher accuracy results using more POD modes than with previous POD methods. The new method was compared against commonly utilized techniques for DPIV vector replacement, namely Kriging, bootstrapping and basic interpolation, as well as previously presented POD reconstruction techniques. The results showed that the adaptive gappy POD reconstruction provides higher accuracy and robustness.

Structure, sulfatide binding properties, and inhibition of platelet aggregation by a disabled-2 protein-derived peptide.

Background: Binding of Dab2 to sulfatides results in platelet aggregation inhibition. Results: The structure of a Dab2-derived peptide (SBM) embedded in dodecylphosphocholine micelles, characterization of its minimal functional sulfatide-binding site, and its inhibitory platelet aggregation activity were determined. Conclusion: An amphipathic helical region of Dab2 SBM binds sulfatides, leading to platelet aggregation inhibition. Significance: Dab2 SBM may lead to the design of novel aggregatory inhibitors. Disabled-2 (Dab2) targets membranes and triggers a wide range of biological events, including endocytosis and platelet aggregation. Dab2, through its phosphotyrosine-binding (PTB) domain, inhibits platelet aggregation by competing with fibrinogen for αIIbβ3 integrin receptor binding. We have recently shown that the N-terminal region, including the PTB domain (N-PTB), drives Dab2 to the platelet membrane surface by binding to sulfatides through two sulfatide-binding motifs, modulating the extent of platelet aggregation. The three-dimensional structure of a Dab2-derived peptide encompassing the sulfatide-binding motifs has been determined in dodecylphosphocholine micelles using NMR spectroscopy. Dab2 sulfatide-binding motif contains two helices when embedded in micelles, reversibly binds to sulfatides with moderate affinity, lies parallel to the micelle surface, and when added to a platelet mixture, reduces the number and size of sulfatide-induced aggregates. Overall, our findings identify and structurally characterize a minimal region in Dab2 that modulates platelet homotypic interactions, all of which provide the foundation for rational design of a new generation of anti-aggregatory low-molecular mass molecules for therapeutic purposes.

Disabled-2 modulates homotypic and heterotypic platelet interactions by binding to sulfatides

Disabled‐2 (Dab2) inhibits platelet aggregation by competing with fibrinogen for binding to the αIIbβ3 integrin receptor, an interaction that is modulated by Dab2 binding to sulfatides at the outer leaflet of the platelet plasma membrane. The disaggregatory function of Dab2 has been mapped to its N‐terminus phosphotyrosine‐binding (N‐PTB) domain. Our data show that the surface levels of P‐selectin, a platelet transmembrane protein known to bind sulfatides and promote cell‐cell interactions, are reduced by Dab2 N‐PTB, an event that is reversed in the presence of a mutant form of the protein that is deficient in sulfatide but not in integrin binding. Importantly, Dab2 N‐PTB, but not its sulfatide binding‐deficient form, was able to prevent sulfatide‐induced platelet aggregation when tested under haemodynamic conditions in microfluidic devices at flow rates with shear stress levels corresponding to those found in vein microcirculation. Moreover, the regulatory role of Dab2 N‐PTB extends to platelet‐leucocyte adhesion and aggregation events, suggesting a multi‐target role for Dab2 in haemostasis.

Estimation of Uncertainty Bounds From Cross Correlation Peak Ratio for Individual PIV Measurements

Numerous studies have established firmly that particle image velocimetry (PIV) is a robust method for non-invasive, quantitative measurements of fluid velocity, and that when carefully conducted, typical measurements can accurately detect displacements in digital images with a resolution well below a single pixel (in some cases well below a hundredth of a pixel). However, previously these estimates have only been able to provide guidance on the expected error for an average measurement under specific image quality and flow conditions. This paper demonstrates a new method for estimating the uncertainty bounds to within a given confidence interval for a specific, individual measurement. Here, the ratio of primary to secondary peak heights in a phase-only generalized cross-correlation is shown to correlate strongly with the range of observed error values for a given measurement, regardless of flow condition or image quality. Using an analytical model of the relationship derived from synthetic data sets, the uncertainty bounds at a 95% confidence interval are then computed for several artificial and experimental flow fields, and the resulting errors are shown to match closely to the predicted uncertainties. While this method stops short of being able to predict the true error for a given measurement, knowledge of the uncertainty level for a PIV experiment should provide great benefits when applying the results of PIV analysis to engineering design studies and CFD (computational fluid dynamics) validation efforts.Copyright