Evaluation of magnetic resonance velocimetry for steady flow

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.     

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.     

Multilaboratory particle image velocimetry analysis of the FDA benchmark nozzle model to support validation of computational fluid dynamics simulations

This study is part of a FDA-sponsored project to evaluate the use and limitations of computational fluid dynamics (CFD) in assessing blood flow parameters related to medical device safety. In an interlaboratory study, fluid velocities and pressures were measured in a nozzle model to provide experimental validation for a companion round-robin CFD study. The simple benchmark nozzle model, which mimicked the flow fields in several medical devices, consisted of a gradual flow constriction, a narrow throat region, and a sudden expansion region where a fluid jet exited the center of the nozzle with recirculation zones near the model walls. Measurements of mean velocity and turbulent flow quantities were made in the benchmark device at three independent laboratories using particle image velocimetry (PIV). Flow measurements were performed over a range of nozzle throat Reynolds numbers (Re(throat)) from 500 to 6500, covering the laminar, transitional, and turbulent flow regimes. A standard operating procedure was developed for performing experiments under controlled temperature and flow conditions and for minimizing systematic errors during PIV image acquisition and processing. For laminar (Re(throat)=500) and turbulent flow conditions (Re(throat)≥3500), the velocities measured by the three laboratories were similar with an interlaboratory uncertainty of ～10% at most of the locations. However, for the transitional flow case (Re(throat)=2000), the uncertainty in the size and the velocity of the jet at the nozzle exit increased to ～60% and was very sensitive to the flow conditions. An error analysis showed that by minimizing the variability in the experimental parameters such as flow rate and fluid viscosity to less than 5% and by matching the inlet turbulence level between the laboratories, the uncertainties in the velocities of the transitional flow case could be reduced to ～15%. The experimental procedure and flow results from this interlaboratory study (available at http://fdacfd.nci.nih.gov) will be useful in validating CFD simulations of the benchmark nozzle model and in performing PIV studies on other medical device models.     

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.     

Coronary artery flow measurement using navigator echo gated phase contrast magnetic resonance velocity mapping at 3.0 T

A validation study and early results for non-invasive, in vivo measurement of coronary artery blood flow using phase contrast magnetic resonance imaging (PC-MRI) at 3.0T is presented. Accuracy of coronary artery blood flow measurements by phase contrast MRI is limited by heart and respiratory motion as well as the small size of the coronary arteries. In this study, a navigator echo gated, cine phase velocity mapping technique is described to obtain time-resolved velocity and flow waveforms of small diameter vessels at 3.0T. Phantom experiments using steady, laminar flow are presented to validate the technique and show flow rates measured by 3.0T phase contrast MRI to be accurate within 15% of true flow rates. Subsequently, in vivo scans on healthy volunteers yield velocity measurements for blood flow in the right, left anterior descending, and left circumflex arteries. Measurements of average, cross-sectional velocity were obtainable in 224/243 (92%) of the cardiac phases. Time-averaged, cross-sectional velocity of the blood flow was 6.8+/-4.3cm/s in the LAD, 8.0+/-3.8cm/s in the LCX, and 6.0+/-1.6cm/s in the RCA.     

Biofilm deformation in response to fluid flow in capillaries

Biofilms are complex mixtures of microorganisms and extracellular matrix that exist on many wetted surfaces. Recently, magnetic resonance microscopy has been used to measure fluid velocities near biofilms that are attached to the walls of capillary channels. These velocity measurements showed unexpectedly high secondary velocities (i.e., high velocity magnitudes perpendicular to the direction of bulk flow and perpendicular to the surface that the biofilm is attached), and the presence of high secondary velocities near a biofilm could increase the delivery of substrates to the biofilm. A mathematical model, based on the immersed boundary method, is used here to examine the physical interaction between a biofilm and a moving fluid in a capillary and to analyze possible factors that may contribute to the elevated secondary velocities observed experimentally. The simulation predicts the formation of a recirculation downstream of a biofilm, and this recirculation deforms and lifts the biofilm upward from the surface to which the biofilm is attached. Changing the mechanical properties (i.e., stiffness) of the biofilm impacts both the lifting of the biofilm and the magnitude of the secondary velocities. The maximum lifting of the biofilm occurs when the biofilm properties are similar to previous experimental measurements, which indicates that the mechanical properties of the biofilm may be tuned for the generation of maximum secondary velocity magnitude and transport of substrates to the biofilm.     

In vivo micro particle image velocimetry measurements of blood-plasma in the embryonic avian heart

The measurement of blood-plasma velocity distributions with spatial and temporal resolution in vivo is inevitable for the determination of shear stress distributions in complex geometries at unsteady flow conditions like in the beating heart. A non-intrusive, whole-field velocity measurement technique is required that is capable of measuring instantaneous flow fields at sub-millimeter scales in highly unsteady flows. Micro particle image velocimetry (muPIV) meets these demands, but requires special consideration and methodologies in order to be utilized for in vivo studies in medical and biological research. We adapt muPIV to measure the blood-plasma velocity in the beating heart of a chicken embryo. In the current work, bio-inert, fluorescent liposomes with a nominal diameter of 400 nm are added to the flow as a tracer. Because of their small dimension and neutral buoyancy the liposomes closely follow the movement of the blood-plasma and allow the determination of the velocity gradient close to the wall. The measurements quantitatively resolve the velocity distribution in the developing ventricle and atrium of the embryo at nine different stages within the cardiac cycle. Up to 400 velocity vectors per measurement give detailed insight into the fluid dynamics of the primitive beating heart. A rapid peristaltic contraction accelerates the flow to peak velocities of 26 mm/s, with the velocity distribution showing a distinct asymmetrical profile in the highly curved section of the outflow tract. In relation to earlier published gene-expression experiments, the results underline the significance of fluid forces for embryonic cardiogenesis. In general, the measurements demonstrate that muPIV has the potential to develop into a general tool for instationary flow conditions in complex flow geometries encountered in cardiovascular research.     

Novel method to correct displacement profile images and calculate flow vector fields using saturation-tagging MR imaging.

Saturation-tagging Magnetic Resonance (MR) imaging provides a simple and robust means to directly visualize displacement profiles within fluid flow fields. Although useful for velocity quantitation as well as for qualitative depiction of flow patterns in certain well-defined flow fields, the technique is prone to distortions due to oblique flow (misregistration artifact) and ambiguity of fluid vector trajectories in complex flow situations. A novel method is proposed whereby two images are acquired, differing in the temporal position of the phase encoding gradient. Theoretical analysis shows that from the paired images, distortion of the two-dimensional displacement profile can be corrected and fluid velocity vectors extracted, even if the flow directions are unknown. In the simpler case of flow oblique to the gradient principal axes, but with a known trajectory, only one image is necessary to correct the displacement profile distortion and extract the velocity information. MRI experiments in a straight tube model have been carried out to evaluate the feasibility of this method. Good agreement is achieved between the results from MR imaging and those predicted via computer simulation.     

Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulations and in vitro MRI measurements

The presence of atherosclerotic plaques has been shown to be closely related to the vessel geometry. Studies on postmortem human arteries and on the experimental animal show positive correlation between the presence of plaque thickness and low shear stress, departure of unidirectional flow and regions of flow separation and recirculation. Numerical simulations of arterial blood flow and direct blood flow velocity measurements by magnetic resonance imaging (MRI) are two approaches for the assessment of arterial blood flow patterns. In order to verify that both approaches give equivalent results magnetic resonance velocity data measured in a compliant anatomical carotid bifurcation model were compared to the results of numerical simulations performed for a corresponding computational vessel model. Cross sectional axial velocity profiles were calculated and measured for the midsinus and endsinus internal carotid artery. At both locations a skewed velocity profile with slow velocities at the outer vessel wall, medium velocities at the side walls and high velocities at the flow divider (inner) wall were observed. Qualitative comparison of the axial velocity patterns revealed no significant differences between simulations and in vitro measurements. Even quantitative differences such as for axial peak flow velocities were less than 10%. Secondary flow patterns revealed some minor differences concerning the form of the vortices but maximum circumferential velocities were in the same range for both methods.     

Evaluation of the heat pulse velocity technique for measurement of sap flow in rainforest and eucalypt forest species of south-eastern Australia

Sap flow in the stems of two cut saplings each of Eucalyptus maculata (a canopy eucalypt forest tree), Doryphora sassafras and Ceratopetalum apetalum (both canopy rainforest trees of south-eastern coastal Australia) was measured by the heat pulse velocity technique and compared with water uptake from a potometer. Scanning electron micrographs of wounding caused by implantation of temperature sensor and heater probes into the sapwood showed that wounding was similar in rainforest and eucalypt species and was elliptical in shape. A circular wound has been implicitly assumed in previous studies. Accurate measurements of sapling water use were obtained using the smaller transverse wound dimension rather than the larger longitudinal dimension because maximum disruption of sap flow through the xylem vessels occurred in the transverse plane. Accurate measurements of sap flux were obtained above a minimum threshold sap velocity. These velocities were 15·7,10·9 and 9·4 cm h^?1 for E. maculata, C. apetalum and D. sassafras, respectively. Below the threshold sap velocity, however, sap flow could not be accurately calculated from measurements of heat pulse velocity. The minimum threshold sap velocity appeared to be determined by probe construction and xylem anatomy. Despite the elliptical wounding and inaccurate measurement of sap flow below the threshold sap velocity, total sap flow over the experimental period for two saplings of each species was within 7% of water use measured by the potometer.     

Tuning of pulmonary arterial circulation evidenced by MR phase mapping in healthy volunteers.

Magnetic resonance (MR) phase mapping was used to noninvasively assess both blood flow and cross-sectional area (CSA) in the main pulmonary artery (MPA) of 12 healthy volunteers. Flow and CSA patterns exhibited two positive peaks: high systolic and small diastolic. This finding can be explained using a simple "distributed" theoretical model that takes into account the role of a reflected pressure wave from pulmonary vascular impedance in generating a diastolic flow. The mean reflection coefficient of pressure wave, MPA input impedance, and pulmonary vascular impedance were assessed. We verified, in this series, that pressure wave velocity appears to be age-dependent. MR phase mapping has been used to observe the tuning (resonance) of the right cardiovascular system at rest under physiological conditions. MR phase mapping could be used to assess pathological modifications of the tuning that occurs in cases of pulmonary arterial hypertension.     

Phase velocity measurement of flexural waves in human tibia

A method is proposed to measure the phase velocities of the first mode of flexural waves in the human tibia. Keeping in mind the dispersive nature of flexural waves in beam-like bodies, a two point measurement method was developed which enables the calculation of the phase difference of the propagating wave between two observation points for a selected frequency range. The method for dispersion analysis was tested with synthetic and observed signals for a cylinder. This was done by comparison of observed radial acceleration on the surface of a PVC-cylinder with computed synthetic signals consisting only of first mode flexural waves. An in vivo study was performed with 43 subjects. The phase velocity measurements in human tibia show a good correlation with the bone mineral content estimated by means of the Cameron-Sorenson technique (Cameron and Sorenson, 1963). The bone mineral loss is reflected by decreasing phase velocities. This indicates that phase velocity measurements of flexural waves can be used for an estimation of bone mineral content in vivo.     

An experimental analysis of the flow field in a three-dimensional model of the human carotid artery bifurcation

Steady flow measurements were carried out in a rigid three-dimensional model of the human carotid artery bifurcation at a Reynolds number of 640 and a flow division ratio of 50/50. Both axial and secondary velocities were measured with a laser-Doppler anemometer. In the bulb opposite to the flow divider a zone with negative axial velocities was found with a maximal diameter of about 60% of the local diameter of the branch and a cross-sectional extent of about 25% of the local cross-sectional area. In the bulb the maximum axial velocity shifted towards the divider wall and at the end of the bulb an axial velocity plateau arose near the non-divider wall. Halfway through the bulb, secondary flow showed a vortex through which fluid flowed towards the divider wall near the bifurcation plane and back towards the non-divider wall near the upper walls.     

Dynamics of coronary circulation in rats]

The blood flow velocities in left anterior descending coronary artery and ascending aorta have been measured in anesthetized rats by high frequency Doppler technique. The measurement of coronary blood flow velocity by miniature ultrasonic probe (2.0 x 1.5 mm) was performed through myocardial surface. Two different forms of coronary blood flow curves were recorded. These forms of the curves depend on the value of the coronary blood flow velocity and are connected with the ascending aorta blood flow velocity. The dynamics of the coronary blood flow reactions under coronary artery occlusion and asphyxia in the rat is similar to the one in the cat and the dog, but less expressive. In experiments with vasodilators the direct dependence between linear and volume coronary artery velocities under the measurement through myocardial surface was found.     

Flow Measurements in a Blood-Perfused Collagen Vessel Using X-Ray Micro-Particle Image Velocimetry

Blood-perfused tissue models are joining the emerging field of tumor engineering because they provide new avenues for modulation of the tumor microenvironment and preclinical evaluation of the therapeutic potential of new treatments. The characterization of fluid flow parameters in such in-vitro perfused tissue models is a critical step towards better understanding and manipulating the tumor microenvironment. However, traditional optical flow measurement methods are inapplicable because of the opacity of blood and the thickness of the tissue sample. In order to overcome the limitations of optical method we demonstrate the feasibility of using phase-contrast x-ray imaging to perform microscale particle image velocimetry (PIV) measurements of flow in blood perfused hydrated tissue-representative microvessels. However, phase contrast x-ray images significantly depart from the traditional PIV image paradigm, as they have high intensity background, very low signal-to-noise ratio, and volume integration effects. Hence, in order to achieve accurate measurements special attention must be paid to the image processing and PIV cross-correlation methodologies. Therefore we develop and demonstrate a methodology that incorporates image preprocessing as well as advanced PIV cross-correlation methods to result in measured velocities within experimental uncertainty.     

Effects of wall motion and compliance on flow patterns in the ascending aorta

Helical flows have been observed in the ascending aorta in vivo, and geometric curvature has been suggested to be a major contributing factor. We employed magnetic resonance imaging (MRI) and velocity mapping to develop a computational model to examine the effects of curvature and also wall compliance and movement upon flow patterns. In the computational model, MRI-derived geometry and velocities were imposed as boundary conditions, which included both radial expansion-contraction and translational motion of the wall. The computed results were in agreement with the MR data only when full wall motion was included in the model, suggesting that the flow patterns observed in the ascending aorta arise not only from geometric curvature of the arch but also from the motion of the aorta resulting from its attachment to the beating heart.     

Near-bottom performance of the Acoustic Doppler Velocimeter (ADV) – a comparative study

In a laboratory flume, a comparative study on the near-bottom performance of the Acoustic Doppler Velocimeter (ADV) was conducted. Two different ADV systems were tested for different configurations and two flow velocities (9 cm s⁻¹, 18 cm s⁻¹). The results were compared with synchronous measurements with a Laser Doppler Anemometer (LDA). Near-bottom velocity measurements with the ADV have to be interpreted carefully as the ADV technique underestimates flow velocities in a zone close to the sediment. The height of this zone above the sediment varies with different ADV systems and configurations. The values for nominal sampling volume height (SVH) given by the software often underestimate the true, effective sampling volume heights. Smaller nominal SVH improve the ADV near-bottom performance, but the vertical extent of the zone in which the ADV underestimates flow by more than 20% may be larger than true SVH/2 by a factor of 2 (=true SVH). When the measurement volume approaches the bottom, ADV data quality parameters (signal-to-noise-ratio (SNR) and signal amplitude) exceeding the average ‘open water’ level, are clear indicators that the ADV has begun to underestimate the flow velocity. Unfortunately, this is not a safe indicator for the range of reliable measurements as the ADV may begin to underestimate velocities even with unchanged ‘open water’ data quality parameters. Thus, one can only recommend avoiding measurements below a distance from the bottom that was defined empirically comparing the ADV and the LDA velocity profiles. This distance is 2.5 times nominal sampling volume height for the tested ADV systems and experimental settings.     

Two-component laser velocimeter measurements downstream of heart valve prostheses in pulsatile flow

Elevated turbulent shear stresses resulting from disturbed blood flow through prosthetic heart valves can cause damage to red blood cells and platelets. The purpose of this study was to measure the turbulent shear stresses occurring downstream of aortic prosthetic valves during in-vitro pulsatile flow. By matching the indices of refraction of the blood analog fluid and model aorta, correlated, simultaneous two-component laser velocimeter measurements of the axial and radial velocity components were made immediately downstream of two aortic prosthetic valves. Velocity data were ensemble averaged over 200 or more cycles for a 15-ms window opened at peak systolic flow. The systolic duration for cardiac flows of 8.4 L/min was 200 ms. Ensemble-averaged total shear stress levels of 2820 dynes/cm2 and 2070 dynes/cm2 were found downstream of a trileaflet valve and a tilting disk valve, respectively. These shear stress levels decreased with axial distance downstream much faster for the tilting disk valve than for the trileaflet valve.     

Noninvasive assessment of pulmonary arterial hypertension by MR phase-mapping method.

We describe a magnetic resonance (MR) imaging method that emphasizes pressure wave velocity to noninvasively assess pulmonary arterial hypertension. Both the blood flow and the corresponding vessel cross-sectional area (CSA) were measured by MR phase mapping in the main pulmonary artery (MPA) in 15 patients. MPA pressures were also measured, in the same patients, by right-side heart catheterization. Two significant relationships were established: 1) between the pressure wave velocity in the MPA and the mean pressure in the MPA (Ppa) writing pressure wave velocity = 9.25 Ppa - 202.51 (r = 0.82) and 2) between the ratio of pressure wave velocity to the systolic blood velocity peak in the MPA (R) and the mean pressure in the MPA writing R = 0.68 Ppa - 4.33 (r = 0.89). Using these relationships, we estimated two pressure values to frame the actual Ppa value in each patient from the present series with a reasonable reliability percentage (87%).