Pavlos P. Vlachos

Digital particle image velocimetry (DPIV) robust phase correlation

A novel correlation technique, the robust phase correlation (RPC), is introduced which amplifies the signal-to-noise ratio of the DPIV cross-correlation to produce velocity estimations that are accurate and robust to a variety of image conditions. Specifically, this estimator shows substantial resilience against additive background noise non-uniform illumination and thermal noise effects. In addition, the RPC is able to substantially reduce bias errors and peak locking in the presence of high shear and rotational motion in comparison with standard cross-correlation algorithms. The success of this technique relies upon an analytical decomposition of the DPIV signal-to-noise ratio, which is then applied as a spectral filter in a novel implementation of the generalized cross-correlation (GCC). The RPC also utilizes advanced windowing techniques to attenuate Fourier-based errors. Because of the GCC filtering, the application of windowing in the RPC is not susceptible to the effects of additive background noise that commonly causes errors for windowed cross-correlation estimation. The RPC estimator is validated using both artificial images and experimental data to demonstrate its enhanced measurement capabilities.

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.

Assessment of advanced windowing techniques for digital particle image velocimetry (DPIV)

The Fourier-based cross-correlation is the most common evaluation technique for DPIV estimation, due to its computational simplicity. However, because Fourier transforms are taken over discrete finite size regions, systematic errors are introduced due to the improper filtering of the input signals. This study explores the potential of advanced windowing techniques to attenuate these Fourier-based errors. The choice of window is shown to impact the spatial resolution, the measurement accuracy and the peak detection process. Error analysis using artificial image simulations is able to characterize a set of optimal windows onto a single performance characteristic. Using this analysis, a set of criteria is defined for an optimal windowing from which the analysis focused on the use of the 50% Gaussian window. The Gaussian window is further compared against standard evaluation techniques in both shear and vortex simulations, which indicate substantial performance benefits with this advanced technique. Further simulations reveal that background noise greatly amplifies the loss of correlation errors, which affect the peak detection process. However, these effects are easily overcome through the use of image preprocessing or the robust phase correlation. Images from the 2003 PIV challenge are used to validate the Gaussian window technique, which is able to remove nearly all of the erroneous vectors in comparison to standard windows.

Collaborative framework for PIV uncertainty quantification: comparative assessment of methods

A posteriori uncertainty quantification of particle image velocimetry (PIV) data is essential to obtain accurate estimates of the uncertainty associated with a given experiment. This is particularly relevant when measurements are used to validate computational models or in design and decision processes. In spite of the importance of the subject, the first PIV uncertainty quantification (PIV-UQ) methods have been developed only in the last three years. The present work is a comparative assessment of four approaches recently proposed in the literature: the uncertainty surface method (Timmins et al 2012), the particle disparity approach (Sciacchitano et al 2013), the peak ratio criterion (Charonko and Vlachos 2013) and the correlation statistics method (Wieneke 2015). The analysis is based upon experiments conducted for this specific purpose, where several measurement techniques are employed simultaneously. The performances of the above approaches are surveyed across different measurement conditions and flow regimes.

The Effect of Vortex Formation on Left Ventricular Filling and Mitral Valve Efficiency

A new mechanism for quantifying the filling energetics in the left ventricle (LV) and past mechanical heart valves (MHV) is identified and presented. This mechanism is attributed to vortex formation dynamics past MHV leaflets. Recent studies support the conjecture that the natural healthy left ventricle (LV) performs in an optimum, energy-preserving manner by redirecting the flow with high efficiency. Yet to date, no quantitative proof has been presented. The present work provides quantitative results and validation of a theory based on the dynamics of vortex ring formation, which is governed by a critical formation number (FN) that corresponds to the dimensionless time at which the vortex ring has reached its maximum circulation content, in support of this hypothesis. Herein, several parameters (vortex ring circulation, vortex ring energy, critical FN, hydrodynamic efficiencies, vortex ring propagation speed) have been quantified and presented as a means of bridging the physics of vortex formation in the LV. In fact, the diastolic hydrodynamic efficiencies were found to be 60, 41, and 29%, respectively, for the porcine, anti-anatomical, and anatomical valve configurations. This assessment provides quantitative proof of vortex formation, which is dependent of valve design and orientation, being an important flow characteristic and associated to LV energetics. Time resolved digital particle image velocimetry with kilohertz sampling rate was used to study the ejection of fluid into the LV and resolve the spatiotemporal evolution of the flow. The clinical significance of this study is quantifying vortex formation and the critical FN that can potentially serve as a parameter to quantify the LV filling process and the performance of heart valves.

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.

Flow shear stress regulates endothelial barrier function and expression of angiogenic factors in a 3D microfluidic tumor vascular model.

Endothelial cells lining blood vessels are exposed to various hemodynamic forces associated with blood flow. These include fluid shear, the tangential force derived from the friction of blood flowing across the luminal cell surface, tensile stress due to deformation of the vessel wall by transvascular flow, and normal stress caused by the hydrodynamic pressure differential across the vessel wall. While it is well known that these fluid forces induce changes in endothelial morphology, cytoskeletal remodeling, and altered gene expression, the effect of flow on endothelial organization within the context of the tumor microenvironment is largely unknown. Using a previously established microfluidic tumor vascular model, the objective of this study was to investigate the effect of normal (4 dyn/cm2), low (1 dyn/cm2), and high (10 dyn/cm2) microvascular wall shear stress (WSS) on tumor-endothelial paracrine signaling associated with angiogenesis. It is hypothesized that high WSS will alter the endothelial phenotype such that vascular permeability and tumor-expressed angiogenic factors are reduced. Results demonstrate that endothelial permeability decreases as a function of increasing WSS, while co-culture with tumor cells increases permeability relative to mono-cultures. This response is likely due to shear stress-mediated endothelial cell alignment and tumor-VEGF-induced permeability. In addition, gene expression analysis revealed that high WSS (10 dyn/cm2) significantly down-regulates tumor-expressed MMP9, HIF1, VEGFA, ANG1, and ANG2, all of which are important factors implicated in tumor angiogenesis. This result was not observed in tumor mono-cultures or static conditioned media experiments, suggesting a flow-mediated paracrine signaling mechanism exists with surrounding tumor cells that elicits a change in expression of angiogenic factors. Findings from this work have significant implications regarding low blood velocities commonly seen in the tumor vasculature, suggesting high shear stress-regulation of angiogenic activity is lacking in many vessels, thereby driving tumor angiogenesis.

Time-Resolved DPIV Analysis of Vortex Dynamics in a Left Ventricular Model Through Bileaflet Mechanical and Porcine Heart Valve Prostheses

The performance of the heart after a mitral valve replacement operation greatly depends on the flow character downstream of the valve. The design and implanting orientation of valves may considerably affect the flow development. A study of the hemodynamics of two orientations, anatomical and anti-anatomical, of the St. Jude Medical (SJM) bileaflet valve are presented and compared with those of the SJM Biocor porcine valve, which served also to represent the natural valve. We document the velocity field in a flexible, transparent (LV) using time-resolved digital particle image velocimetry (TRDPIV). Vortex formation and vortex interaction are two important physical phenomena that dominate the filling and emptying of the ventricle. For the three configurations, the following effects were examined: mitral valve inlet jet asymmetry, survival of vortical structures upstream of the aortic valve, vortex-induced velocities and redirection of theflow in abidance of the Biot-Savart law, domain segmentation, resonant times of vortical structures, and regions of stagnantflow. The presence of three distinct flow patterns, for the three configurations, was identified by the location of vortical structures and level of coherence corresponding to a significant variation in the turbulence level distribution inside the LV. The adverse effect of these observations could potentially compromise the efficiency of the LV and result in flow patterns that deviate from those in the natural heart.

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%.