Intraluminal recording of cross-sectional blood velocity distribution of human ascending aorta by ultrasound Doppler technique

A pulsed Doppler ultrasound technique was used for mapping two-dimensional blood velocity profiles in the human ascending aorta during open-heart surgery. An electronic position-sensitive device was constructed and linked to an intraluminal 10 MHz Doppler ultrasound probe. From a plane perpendicular to the central direction of blood flow, velocity mapping was performed covering the entire cross-section of the ascending aorta 6–7 cm above the valve. This method is based on a sequential sampling of velocity from continuously changing locations during a stable haemodynamic period; typically velocity points are recorded from 150–300 beats. Further processing transformed data to suit a previously developed velocity distribution model for normal blood flow in the human ascending aorta, based on multiregression analyses. In this model, the time series of data from consecutive beats were computed into an average two-dimensional profile described through one cardiac cycle. This method allows high spatial resolution (1.5 mm), in addition to the high-frequency response (200 Hz) of the modified ultrasound Doppler meter. Together with the advantage of velocity directionality and minimal time interventions, this makes the method well suited for studies on normal flow conditions as well as flow velocity distribution distal to different heart valve prostheses.     

Physical characteristics and mathematical modelling of the pulsed ultrasonic flowmeter

A pulsed ultrasonic Doppler flowmeter for detailed measurements of velocity profiles in man is described. The device projects a beam of ultrasound in bursts of 0·4 μs duration, at 5 MHz, into the flow; the back-scattered signals are processed to produce a signal corresponding to the mean velocity over a small region of the flowing stream. The size and shape of this ‘sample volume’ determines the flowmeter sensitivity and accuracy. The velocity profile obtained from this instrument can be shown to be a weighted average of the ultrasonic intensity and the flowfield velocity over the sample volume, and is mathematically described by a convolution integral. A method of probing the ultrasonic beam and describing its characteristics in mathematical terms was developed. Using this model with a system whose velocity profile is parabolic, the pulsed ultrasonic Doppler-flowmeter output could be predicted via the convolution integral. Theoretical flowmeter-output curves were generated from the mathematical model by a digital-computer simulation and verified through experimental profiles in steady laminar flow. The modelling technique is sufficiently general for flowmeter output to be predicted for any general flow-velocity profile in steady or pulsetile flow.     

Method for simultaneous determination of red cell and plasma flow velocityin vitro andin vivo

A method is described which can be used to simultaneously determine the flow velocity of plasma and of red blood cells in small glass tubesin vitro or in living microvessels of the microcirculation. The principle of dual slit photometry is applied to the measurement of plasma flow by determining the passage time of a dye bolus across two photodetectors separated by a variable distance. Measurements performed bothin vitro andin vivo indicate a significant difference (up to 85%) between cellular and plasmatic flow velocity.     

<Emphasis Type="Italic">In vitro</Emphasis> blood flow in a rectangular PDMS microchannel: experimental observations using a confocal micro-PIV system

Progress in microfabricated technologies has attracted the attention of researchers in several areas, including microcirculation. Microfluidic devices are expected to provide powerful tools not only to better understand the biophysical behavior of blood flow in microvessels, but also for disease diagnosis. Such microfluidic devices for biomedical applications must be compatible with state-of-the-art flow measuring techniques, such as confocal microparticle image velocimetry (PIV). This confocal system has the ability to not only quantify flow patterns inside microchannels with high spatial and temporal resolution, but can also be used to obtain velocity measurements for several optically sectioned images along the depth of the microchannel. In this study, we investigated the ability to obtain velocity measurements using physiological saline (PS) and in vitro blood in a rectangular polydimethysiloxane (PDMS) microchannel (300 μm wide, 45 μm deep) using a confocal micro-PIV system. Applying this combination, measurements of trace particles seeded in the flow were performed for both fluids at a constant flow rate (Re = 0.02). Velocity profiles were acquired by successive measurements at different depth positions to obtain three-dimensional (3-D) information on the behavior of both fluid flows. Generally, the velocity profiles were found to be markedly blunt in the central region, mainly due to the low aspect ratio (h/w = 0.15) of the rectangular microchannel. Predictions using a theoretical model for the rectangular microchannel corresponded quite well with the experimental micro-PIV results for the PS fluid. However, for the in vitro blood with 20% hematocrit, small fluctuations were found in the velocity profiles. The present study clearly shows that confocal micro-PIV can be effectively integrated with a PDMS microchannel and used to obtain blood velocity profiles along the full depth of the microchannel because of its unique 3-D optical sectioning ability. Advantages and disadvantages of PDMS microchannels over glass capillaries are also discussed.     

On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model

Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure–volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.     

一种避免多道脉冲多普勒的血管中流速（横向）剖面的估计方法

血流速度剖面是研究血管特性的重要信息，它的得到通常用多道脉冲多普勒系统才能完成，由于脉冲多普勒系统存在着测速精度和测距精度的相互制约，且系统比较复杂，不太实用。文中提出一种新的估计方法，从超声多普勒血流音频信号出发，先得出其最大频率值和平均频率值，然后根据假设条件估计血流的速度剖面，从而使在一定精度上对血流速度剖面的估计成为可能。本文还给出了利用这种方法对血流速度剖面进行估计的一些结果。     

A new perivascular multi-element pulsed Doppler ultrasound system forin vivo studies of velocity fields and turbulent stresses in large vessels

A pulsed Doppler ultrasound (PDU) multi-element system was developed for perivascular registration of velocity fields and turbulence in large vessels. In vivo evaluation and comparison with hot-film anemometry (HFA) was performed. C-shaped shells were designed with holes to fit five small 10 MHz ultrasonic probes directed at five measuring points along a diameter perpendicular to the vessel axis. By rotating the shell in 45° steps, blood velocities were measured in 17 points covering the entire cross-sectional vessel area. Measurements were performed in the ascending aorta and at three axial locations in the descending thoracic aorta in pigs. Simultaneous PDU and HFA measurements were performed distal to induced vascular stenoses of different degrees. Three-dimensional visualisation of velocity profiles was made, and Reynolds normal stresses (RNS) were calculated for different levels of turbulence intensities based on the simultaneous PDU and HFA measurements. The velocity profiles in the ascending aorta were skewed at top systole with the highest velocities towards the posterior wall. In the descending thoracic aorta at the ligamentum of Botalli, the velocity profiles were skewed throughout the entire systole with the highest velocities at the right anterior vessel wall. Further downstream in the descending aorta the velocity profiles appeared blunter. The frequency response of the modified PDU system was determined by a ‘random noise test’ revealing an upper −3dB cut-off frequency of approximately 200 Hz. Regression analysis showed a linear relationship between RNS measured with PDU and RNS measured with HFA (r=0.93). Two vessel diameters distal to a 75% stenosis RNS up to 28 N m⁻² were measured. The present perivascular PDU system is able to register velocity profiles covering the entire vessel area in a plane perpendicular to the flow axis, as well as turbulent velocity fluctuations within the restrictions imposed by the Doppler ambiguity process. Compared with HFA, PDU is easier to calibrate, easier to handle, semi-invasive, direction-sensitive, but still suffers from range-velocity limitations and a limited frequency response.     

Noninvasive measurement of the intracardiac blood flow by means of ultrasound techniques.

A new noninvasive method of measurement of the intracardiac blood flow by means of ultrasound techniques is described. In this system the "M-sequence modulated Doppler method" and the method of ultrasonotomography are used in combination. An arbitrary space within the heart can be selected by ultrasonocardiotomography and the blood flow profiles can be observed by the "M-sequence modulated Doppler method." The new Doppler flow meter system described in this paper can be applied not only for the diagnosis of heart diseases, but also for the study of pathophysiology of the blood flow and of the factors responsible for the dilatation of the heart. Further studies are required from the viewpoints of medicine and engineering to accumulate sufficient data before routine application of the method described in this paper is fully warranted.     

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.     

Electric properties of flowing blood and impedance cardiography

An effective resistivity is defined for axisymmetric flow through a circular tube with a uniform electric field in the longitudinal direction. The resistivity of flowing blood is found to be a function of the shear rate profile. Under axisymmetric conditions shear rate profiles are a function of a single parameter: the reduced average velocity, which is the average velocity divided by the radius of the tube. The resistivity of human blood was investigated while the blood was in laminar flow in a circular tube with different constant flow rates. The relative change in resistivity in % is given by: −0.45·H·{1-exp[−0.26·(〈v〉/R)^0.39]}; where H is the packed cell volume in % and 〈v〉/R is the reduced average velocity in s⁻¹. In accelerating flow the resistivity change is synchronous with the change in flow rate, but in decelerating flow there is an exponential decay characterized by a relaxation time τ. For packed cell volumes of 36.4% and 47.5% τ was estimated to be 0.21 s, for a packed cell volume of 53.7% τ was estimated to be 0.29 s. The resistivity changes in elastic tubes are influenced by both velocity changes and changes in diameter, but in opposite directions.     

Nearly automated analysis of coronary Doppler flow velocity from transthoracic ultrasound images: validation with manual tracings

Coronary flow velocity reserve is obtained by manual tracings of transthoracic coronary Doppler flow velocity profiles as the ratio of stress versus baseline diastolic peak velocities. This approach introduces subjectivity in the measurements and limits the information which could be exploited from the Doppler velocity profile. Accordingly, our goals were to develop a technique for nearly automated detection of Doppler coronary flow velocity profile, and automatically compute both conventional and additional amplitude, derivative and temporal parameters, and validate it with manual tracings. A total of 100 patients (17 normals, 15 patients with severe coronary stenosis, 41 with connective tissue disease and 27 with diabetes mellitus) were studied. Linear correlation and Bland–Altman analyses showed that the proposed method was highly accurate and repeatable compared to the manual measurements. Comparison between groups evidenced significant differences in some of the automated parameters, thus representing potentially additional indices useful for the noninvasive diagnosis of microcirculatory or coronary artery disease.     

Airway Wall Stiffening Increases Peak Wall Shear Stress: A Fluid–Structure Interaction Study in Rigid and Compliant Airways

The airflow characteristics in a computed tomography (CT) based human airway bifurcation model with rigid and compliant walls are investigated numerically. An in-house three-dimensional (3D) fluid–structure interaction (FSI) method is applied to simulate the flow at different Reynolds numbers and airway wall stiffness. As the Reynolds number increases, the airway wall deformation increases and the secondary flow becomes more prominent. It is found that the peak wall shear stress on the rigid airway wall can be five times stronger than that on the compliant airway wall. When adding tethering forces to the model, we find that these forces, which produce larger airway deformation than without tethering, lead to more skewed velocity profiles in the lower branches and further reduced wall shear stresses via a larger airway lumen. This implies that pathologic changes in the lung such as fibrosis or remodeling of the airway wall—both of which can serve to restrain airway wall motion—have the potential to increase wall shear stress and thus can form a positive feed-back loop for the development of altered flow profiles and airway remodeling. These observations are particularly interesting as we try to understand flow and structural changes seen in, for instance, asthma, emphysema, cystic fibrosis, and interstitial lung disease.     

Laser-doppler anemometer to study velocity fields in the vicinity of prosthetic heart valves

Laser-Doppler anemometry is relatively new technique which is used for measuring velocity fields. It has major applications in the field ofin vitro biofluid mechanics. The laser-Doppler anemometers have many advantages compared with the traditional hot-wire or hot-film anemometers which are still mainly used in studies of biofluid mechanics. A laser-Doppler anemometer (I.d.a) system which can be used to measurein vitro velocity and shear-stress profiles in the vicinity of prosthetic heart valves is described. Accurate velocity measurements in the vicinity of prosthetic heart valves are very scarce, and the use of I.d.a systems will facilitate acquisition of these data.     

Experimental investigation and computational modeling of hydrodynamics in bifurcating microchannels

Methods involving microfluidics have been used in several chemical, biological and medical applications. In particular, a network of bifurcating microchannels can be used to distribute flow in a large space. In this work, we carried out experiments to determine hydrodynamic characteristics of bifurcating microfluidic networks. We measured pressure drop across bifurcating networks of various complexities for various flow rates. We also measured planar velocity fields in these networks by using particle image velocimetry. We further analyzed hydrodynamics in these networks using mathematical and computational modeling. Our results show that the experimental frictional resistances of complex bifurcating microchannels are 25–30% greater than that predicted by Navier–Stokes equations. Experimentally measured velocity profiles indicate that flow distributes equally at a bifurcation regardless of the complexity of the network. Flow division other than bifurcation such as trifurcation or quadruplication can lead to heterogeneities. These findings were verified by the results from the numerical simulations.     

Boundary Conditions by Schwarz-Christoffel Mapping in Anatomically Accurate Hemodynamics

Appropriate velocity boundary conditions are a prerequisite in computational hemodynamics. A method for mapping analytical or experimental velocity profiles on anatomically realistic boundary cross-sections is presented. Interpolation is required because the computational and experimental domains are seldom aligned. In the absence of velocity information one alternative is the adaptation of analytical profiles based on volumetric flux constraints. The presented algorithms are based on the Schwarz-Christoffel (S-C) mapping of singly or doubly connected polygons to the unit circle or an annulus with unary external radius. S-C transformations are combined to construct a one-to-one invertible map between the target surface and the measurement domain or the support of the source analytical profile. The proposed technique permits us to segment each space separately and map one onto the other in its entirety. Tests are performed with normal velocity boundary conditions for computational simulations of blood flow in the ascending aorta and cerebrospinal fluid flow in the spinal cavity. Mappings of axisymmetric velocity profiles of the Womersley type through a simply connected circular pipe as well as through a doubly connected circular annulus, and interpolations from in-vivo phase-contrast magnetic resonance imaging velocity measurements under instantaneous volumetric flux constraints are considered.     

Doppler optical coherence imaging of converging flow

The experimental methods of Doppler optical coherence tomography are applied for two-dimensional flow mapping of highly scattering fluid in flow with complex geometry. Converging flow (die entry) is used to demonstrate non-invasive methods to map varying velocity profiles before and after the entry. Complex geometry flow is scanned with approximately 10 x 10 x 10 microm3 spatial resolution. Structural images of the phantom and specific velocity images are demonstrated. A variety of velocity profiles have been obtained before and after the entry. Concave, blunted, parabolic and triangular profiles are obtained at different distances after the entry. Application of the technique to the study of blood circulation is discussed.     

Mathematical mdoel for turbulent blood flow through a disk-type prosthetic heart valve

Computational fluid dynamic techniques are used to construct a mathematical model for turbulent blood flow through a disk-type prosthetic heart valve in the aortic position. The TEACH computer code is used to solve the k-6 turbulence model numerically over the axisymmetric flow field of the valve during systole. Stream function, mean axial velocity profiles, turbulent shear stresses and wall shear stress distributions are computed for Reynolds numbers between Re_D=600 and 10 000 (corresponding to steady flow rates of 2·63 lmin⁻¹ and 43·89lmin⁻¹, respectively). The location, length and maximum reverse flow velocities of separated, flow regions are presented and compared with experimental observations. The largest computed mean axial velocities are 4·4 to 4·8 times the inflow velocity and occur near the downstream corner of the sewing ring. The maximum wall shear stress computed is 229·7 Nm⁻² at the upstream corner of the disk occluder for Re_D=10000. The location of maximum walls shear stress occurs at the downstream corner of the sewing ring for Re_D≤2000. Turbulent shear stresses of up to 380·7 Nm⁻² are computed in the region between the sewing ring and the disk occluder for the physiological Reynolds number Re_D=6054. The numerical solutions are shown to compare favourably with available experimental measurements.     

Wall shear stress as measured in vivo: consequences for the design of the arterial system

Based upon theory, wall shear stress (WSS), an important determinant of endothelial function and gene expression, has been assumed to be constant along the arterial tree and the same in a particular artery across species. In vivo measurements of WSS, however, have shown that these assumptions are far from valid. In this survey we will discuss the assessment of WSS in the arterial system in vivo and present the results obtained in large arteries and arterioles. In vivo WSS can be estimated from wall shear rate, as derived from non-invasively recorded velocity profiles, and whole blood viscosity in large arteries and plasma viscosity in arterioles, avoiding theoretical assumptions. In large arteries velocity profiles can be recorded by means of a specially designed ultrasound system and in arterioles via optical techniques using fluorescent flow velocity tracers. It is shown that in humans mean WSS is substantially higher in the carotid artery (1.1–1.3 Pa) than in the brachial (0.4–0.5 Pa) and femoral (0.3–0.5 Pa) arteries. Also in animals mean WSS varies substantially along the arterial tree. Mean WSS in arterioles varies between about 1.0 and 5.0 Pa in the various studies and is dependent on the site of measurement in these vessels. Across species mean WSS in a particular artery decreases linearly with body mass, e.g., in the infra-renal aorta from 8.8 Pa in mice to 0.5 Pa in humans. The observation that mean WSS is far from constant along the arterial tree implies that Murray’s cube law on flow-diameter relations cannot be applied to the whole arterial system. Because blood flow velocity is not constant along the arterial tree either, a square law also does not hold. The exponent in the power law likely varies along the arterial system, probably from 2 in large arteries near the heart to 3 in arterioles. The in vivo findings also imply that in in vitro studies no average shear stress value can be taken to study effects on endothelial cells derived from different vascular areas or from the same artery in different species. The cells have to be studied under the shear stress conditions they are exposed to in real life.     

Analysis of the dynamic properties of a hot-film anemometer system for blood velocity measurements in humans

Increasing emphasis has been put on the occurrence of turbulent blood flow in the great arteries in humans and on the possible role of this phenomenon in various pathological vascular conditions. The hot-film anemometer has been widely used to register fluid velocity (and turbulence—if any). In the present paper the dynamic properties of a commercially available hot-film anemometer system are determined. Simulating a turbulent velocity component, a conical 1 mm needle probe was vibrated with a frequency from 10–2000 Hz in rotating steady state human heparinised whole blood, varying the laminar velocity from 5 to 150 cm s⁻¹. Both the sine sweep test and the random noise test were used for frequency response determinations. No significant difference was found between the results from the tests. The cut-off frequency (−3 dB) increased with increasing laminar velocity as a second order function (e.g. 200, 500 and 1500 Hz at laminar velocities of 25, 50 and 100 cm s⁻¹). The cut-off frequency decreased to a minor degree with increasing amplitude of the turbulent velocity component. It is concluded that the hot-film anemometer system with the used conical quartz coated blood velocity probe is well suited for in vivo turbulence analysis on the arterial side.     

Radiofrequency ablation with a vibrating catheter: A new method for electrode cooling

A new electrode cooling system using a vibrating catheter is described for conditions of low blood flow when saline irrigation cannot be used. Vibrations of the catheter are hypothesized to disturb blood flow around the electrode, leading to increased convective cooling of the electrode. The aim of this study is to confirm the cooling effect of vibration and investigate the associated mechanisms. As methods, an in vitro system with polyvinyl alcohol-hydrogel (PVA-H) as ablated tissue and saline flow in an open channel was used to measure changes in electrode and tissue temperatures under vibration of 0–63 Hz and flow velocity of 0–0.1 m/s. Flow around the catheter was observed using particle image velocimetry (PIV). Results show that under conditions of no flow, electrode temperatures decreased with increasing vibration frequency, and in the absence of vibrations, electrode temperatures decreased with increasing flow velocity. In the presence of vibrations, electrode temperatures decreased under conditions of low flow velocity, but not under those of high flow velocity. PIV analyses showed disturbed flow around the vibrating catheter, and flow velocity around the catheter increased with higher-frequency vibrations. In conclusion, catheter vibration facilitated electrode cooling by increasing flow around the catheter, and cooling was proportional to vibration frequency.