Noninvasive Measurement of Steady and Pulsating Velocity Profiles and Shear Rates in Arteries Using Echo PIV: In Vitro Validation Studies

Although accurate measurement of velocity profiles, multiple velocity vectors, and shear stress in arteries is important, there is still no easy method to obtain such information in vivo. We report on the utility of combining ultrasound contrast imaging with particle image velocimetry (PIV) for noninvasive measurement of velocity vectors. This method (echo PIV) takes advantage of the strong backscatter characteristics of small gas-filled microbubbles (contrast) seeded into the flow. The method was tested in vitro. The steady flow analytical solution and optical PIV measurements (for pulsatile flow) were used for comparison. When compared to the analytical solution, both echo PIV and optical PIV resolved the steady velocity profile well. Error in shear rate as measured by echo PIV (8%) was comparable to the error of optical PIV (6.5%). In pulsatile flow, echo PIV velocity profiles agreed well with optical PIV profiles. Echo PIV followed the general profile of pulsatile shear stress across the artery but underestimated wall shear at certain time points. However, error in shear from echo PIV was an order of magnitude less than error from current shear measurement methods. These studies indicate that echo PIV is a promising technique for noninvasive measurement of velocity profiles and shear stress.     

Comparative Study of Magnetic Resonance Imaging and Image-Based Computational Fluid Dynamics for Quantification of Pulsatile Flow in a Carotid Bifurcation Phantom

A combined magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modeling study was carried out for pulsatile flow in a carotid bifurcation phantom. The aim of the study was to quantify differences in flow patterns between MRI measurement and MRI-based CFD simulations and to further explore the potential for in vivo applications. The computational model was reconstructed from high resolution magnetic resonance (MR) scans. Velocities derived from phase-contrast MR measurements were used as boundary conditions for the CFD calculation. Detailed comparisons of velocity patterns were made between the CFD results and MRI measurements. Good agreement was achieved for the main velocity component in both well-behaved flow (in the common carotid) and disturbed region (in the carotid sinus). Comparison of in-plane velocity vectors showed less satisfactory consistency and revealed that the MR measurements obtained were inadequate to depict the secondary flow pattern as expected. It can be concluded that the combined MRI/CFD is expected to provide more reliable information about the full three-dimensional velocity field. © 2003 Biomedical Engineering Society. PAC2003: 8761Lh, 8719Uv, 8385Pt, 8710+e     

Development of a custom-designed echo particle image velocimetry system for multi-component hemodynamic measurements: system characterization and initial experimental results

We have recently developed an ultrasound-based velocimetry technique, termed echo particle image velocimetry (Echo PIV), to measure multi-component velocity vectors and local shear rates in arteries and opaque fluid flows by identifying and tracking flow tracers (ultrasound contrast microbubbles) within these flow fields. The original system was implemented on images obtained from a commercial echocardiography scanner. Although promising, this system was limited in spatial resolution and measurable velocity range. In this work, we propose standard rules for characterizing Echo PIV performance and report on a custom-designed Echo PIV system with increased spatial resolution and measurable velocity range. Then we employed this system for initial measurements on tube flows, rotating flows and in vitro carotid artery and abdominal aortic aneurysm (AAA) models to acquire the local velocity and shear rate distributions in these flow fields. The experimental results verified the accuracy of this technique and indicated the promise of the custom Echo PIV system in capturing complex flow fields non-invasively.     

Vortex Phenomena in Sidewall Aneurysm Hemodynamics: Experiment and Numerical Simulation

We carry out high-resolution laboratory experiments and numerical simulations to investigate the dynamics of unsteady vortex formation across the neck of an anatomic in vitro model of an intracranial aneurysm. A transparent acrylic replica of the aneurysm is manufactured and attached to a pulse duplicator system in the laboratory. Time-resolved three-dimensional three-component velocity measurements are obtained inside the aneurysm sac under physiologic pulsatile conditions. High-resolution numerical simulations are also carried out under conditions replicating as closely as possible those of the laboratory experiment. Comparison of the measured and computed flow fields shows very good agreement in terms of instantaneous velocity fields and three-dimensional coherent structures. Both experiments and numerical simulations show that a well-defined vortical structure is formed near the proximal neck at early systole. This vortical structure is advected by the flow across the aneurysm neck and impinges on the distal wall. The results underscore the complexity of aneurysm hemodynamics and point to the need for integrating high-resolution, time-resolved three-dimensional experimental and computational techniques. The current work emphasizes the importance of vortex formation phenomena at aneurysmal necks and reinforces the findings of previous computational work and recent clinical studies pointing to links between flow pulsatility and aneurysm growth and rupture.     

Peak velocity determination using fast Fourier velocity encoding with minimal spatial encoding

For quantitative peak velocity determination, a technique was developed that uses Fourier velocity encoding (FVE) for the fast acquisition of images of velocity with no spatial encoding other than slice selection. The technique produces images of velocity versus temporal frequency. In applications where the quantity of interest is the peak velocity and in-plane spatial localization is not required, high SNR images are produced with reduced sensitivity to errors due to slice thickness and motion. The technique was validated using steady and pulsatile flow in a straight tube, and compared to both phase contrast measurements and numerical models using steady flow in a 50% and a 75% cosinusoidal stenosis phantom. Results show that for slices as large as 2 cm and/or undergoing periodic motion, FVE can accurately measure the peak velocity in cases where a distribution of velocities exist.     

On the Use of Optical Flow Methods with Spin-Tagging Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) is a versatile noninvasive tool for achieving full-field quantitative visualization of biomedical fluid flows. In this study, two MRI velocimetry techniques (spin tagging and phase contrast) are used to obtain velocity measurements in a Poiseuille flow for Reynolds numbers below 1000. Spin-tagging MRI velocimetry supplies the displacement of tagged grids of nuclear spins from which the velocity field can be inferred, while phase contrast MRI velocimetry directly provides velocity data for every pixel in the field of view. Although the phase contrast method is more accurate for this flow, this technique is more sensitive to errors from magnetic susceptibility gradients, higher order motions, and has limited dynamic range. Spin-tagging MRI velocimetry is a viable alternative if automatic methods for extracting velocity fields from the tags can be found. Optical flow, a technique originally developed for machine vision applications, is proposed here as a postprocessing step to obtain two-dimensional velocity fields from spin-tagging MRI images. Results with artificially generated grids demonstrate the robustness of the optical flow algorithm to noise and indicate that a 7%–10% average error can be expected from the optical flow calculations alone, independent of MRI image artifacts. Experiments on spin-tagging MRI images for a Re=230 Poiseuille flow gave an average error of 6.41%, which was consistent with the measurement error of the generated (synthetic) images with the same level of random noise superimposed. © 2001 Biomedical Engineering Society. PAC01: 8761-c, 8719Uv, 8757Ce     

Comparison of 4D Flow MRI and Particle Image Velocimetry Using an <Emphasis Type="Italic">In Vitro</Emphasis> Carotid Bifurcation Model

Four-dimensional (4D) Flow magnetic resonance imaging (MRI) enables the acquisition and assessment of complex hemodynamics in vivo from different vascular territories. This study investigated the viability of stereoscopic and tomographic particle image velocimetry (stereo- and tomo-PIV, respectively) as experimental validation techniques for 4D Flow MRI. The experiments were performed using continuous and pulsatile flows through an idealized carotid artery bifurcation model. Transverse and longitudinal planes were extracted from the acquired velocity data sets at different regions of interest and were analyzed with a point-by-point comparison. An overall root-mean-square error (RMSE) was calculated resulting in errors as low as 0.06 and 0.03 m/s when comparing 4D Flow MRI with stereo- and tomo-PIV, respectively. Quantitative agreement between techniques was determined by evaluating the relationship for individual velocity components and their magnitudes. These resulted in correlation coefficients (R²) of 4D Flow MRI with stereo- and tomo-PIV, as low as 0.76 and 0.73, respectively. The 3D velocity measurements from PIV showed qualitative agreement when compared to 4D Flow MRI, especially with tomo-PIV due to the addition of volumetric velocity measurements. These results suggest that tomo-PIV can be used as a validation technique for 4D Flow MRI, serving as the basis for future validation protocols.     

Development and validation of a computational fluid dynamics methodology for simulation of pulsatile left ventricular assist devices

An unsteady computational fluid dynamic methodology was developed so that design analyses could be undertaken for devices such as the 50cc Penn State positive-displacement left ventricular assist device (LVAD). The piston motion observed in vitro was modeled, yielding the physiologic flow waveform observed during pulsatile experiments. Valve closure was modeled numerically by locally increasing fluid viscosity during the closed phase. Computational geometry contained Bjork-Shiley Monostrut mechanical heart valves in mitral and aortic positions. Cases for computational analysis included LVAD operation under steady-flow and pulsatile-flow conditions. Computations were validated by comparing simulation results with previously obtained in vitro particle image velocimetry (PIV) measurements. The steady portion of the analysis studied effects of mitral valve orientation, comparing the computational results with in vitro data obtained from mock circulatory loop experiments. The velocity field showed good qualitative agreement with the in vitro PIV data. The pulsatile flow simulations modeled the unsteady flow phenomena associated with a positive-displacement LVAD operating through several beat cycles. Flow velocity gradients allowed computation of the scalar wall strain rate, an important factor for determining hemodynamics of the device. Velocity magnitude contours compared well with PIV data throughout the cycle. Computational wall shear rates over the pulsatile cycle were found to be in the same range as wall shear rates observed in vitro.     

Quantification of wall shear stress in large blood vessels using Lagrangian interpolation functions with cine phase-contrast magnetic resonance imaging

Arterial wall shear stress is hypothesized to be an important factor in the localization of atherosclerosis. Current methods to compute wall shear stress from magnetic resonance imaging (MRI) data do not account for flow profiles characteristic of pulsatile flow in noncircular vessel lumens. We describe a method to quantify wall shear stress in large blood vessels by differentiating velocity interpolation functions defined using cine phase-contrast MRI data on a band of elements in the neighborhood of the vessel wall. Validation was performed with software phantoms and an in vitro flow phantom. At an image resolution corresponding to in vivo imaging data of the human abdominal aorta, time-averaged, spatially averaged wall shear stress for steady and pulsatile flow were determined to be within 16% and 23% of the analytic solution, respectively. These errors were reduced to 5% and 8% with doubling in image resolution. For the pulsatile software phantom, the oscillation in shear stress was predicted to within 5%. The mean absolute error of circumferentially resolved shear stress for the nonaxisymmetric phantom decreased from 28% to 15% with a doubling in image resolution. The irregularly shaped phantom and in vitro investigation demonstrated convergence of the calculated values with increased image resolution. We quantified the shear stress at the supraceliac and infrarenal regions of a human abdominal aorta to be 3.4 and 2.3 dyn/cm², respectively. © 2002 Biomedical Engineering Society. PAC2002: 8761-c, 8719Uv     

In vitro LDA and flow visualization analysis of the spiral vortex pump: effect of inlet valve orientation

The spiral vortex pump (SV), an innovative, penumatically driven ventricular assist device, was tested using the flow visualization technique and laser Doppler anemometry to study the effect of inlet valve orientation under steady and pulsatile flow conditions in a purposely constructed flow circuit aimed at obtaining flow field data. Qualitative information was obtained using the flow visualization technique. The slit-lighting technique and fluorescent bees provided a clear flow field view at the desired location, and a 200 frames/s high-speed video camera was used, capturing the vortex nature of the flow field. Mean velocity and fluctuating velocity profile were obtained using a Kanomax single-channel FLV system. Three diametrically transverse locations and three vertical locations were selected for measurements. The particle-tracking method was also incorporated to obtain velocity vectors. Based on the experimental data, the following general conclusions can be drawn: (1) The SV pump created a vortex flow field under steady and pulsatile flow conditions. (2) The inlet valve orientation sharply influenced the flow inside the SV pump. (3) A relatively strong circulatory flow field was observed when the major orifice was oriented toward the HD junction under steady flow. (4) A relatively weak circulatory flow field was observed when the major orifice was oriented toward the center under steady flow. (5) The directional flow field was more accentuated under pulsatile flow conditions. (6) A relatively stable flow field was observed when the major orifice was oriented upward (pump outlet direction). (7) Directional flow toward the diaphragm was observed when the major orifice was oriented downward. (8) A strong circulatory flow with possible colliding flow toward the peripheral area was observed when the major orifice was oriented outward. (9) A relatively weak circulatory flow was observed when the major orifice was oriented inward. (10) The strength of the circulatory flow during the peak flow phase under pulsatile conditions was not affected by the orientation of the inlet valve.