Separation of the reservoir and wave pressure and velocity from measurements at an arbitrary location in arteries

Previous studies based on measurements made in the ascending aorta have demonstrated that it can be useful to separate the arterial pressure P into a reservoir pressure P* generated by the windkessel effect and a wave pressure p generated by the arterial waves: P = P*+p. The separation in these studies was relatively straightforward since the flow into the arterial system was measured. In this study the idea is extended to measurements of pressure and velocity at sites distal to the aortic root where flow into the arterial system is not known. P* is calculated from P at an arbitrary location in a large artery by fitting the pressure fall-off in diastole to an exponential function and assuming that p is proportional to the flow into the arterial system. A local reservoir velocity U* that is proportional to P* is also defined. The separation algorithm is applied to in vivo human and canine data and to numerical data generated using a one-dimensional model of pulse wave propagation in the larger conduit arteries. The results show that the proposed algorithm is reasonably robust, allowing for the separation of the measured pressure and velocity into reservoir and wave pressures and velocities. Application to data measured simultaneously in the aorta of the dog shows that the reservoir pressure is fairly uniform along the aorta, a test of self-consistency of the assumptions leading to the algorithm. Application to data generated with a validated numerical model indicates that the parameters derived by fitting the pressure data are close to the known values which were used to generate the numerical data. Finally, application to data measured in the human thoracic aorta indicates the potential usefulness of the separation.     

A fluid-structure interaction analysis on hemodynamics in carotid artery based on patient-specific clinical data

The hemodynamics of the carotid artery was numerically investigated with an approach of fluid-structure interaction (FSI). To predict the blood flow and arterial deformation of carotid artery, a framework for the FSI analysis was developed by coupling computational fluid dynamics and structural analysis. Using this framework, the hemodynamics of the carotid artery was simulated with the patientspecific clinical data of the arterial geometry, pulsatile blood flow, blood rheology and arterial deformation. It is found that the hemodynamic characteristics of the carotid artery are significantly affected by its geometric factors and flow conditions, and relatively low values of the wall shear stress were observed in the post-plaque dilated region of the carotid bifurcated area, which is known to be responsible for the growth of an atherosclerotic plaque. Since the characteristics of the blood flow in a carotid artery are also affected by the hemodynamic factors, the effects of the cardiac output, distal vascular resistance and blood viscosity on hemodynamics were also numerically analyzed.     

Numerical simulation of fully developed flow and heat transfer characteristics in a curved tube with pulsating pressure gradient

Characteristics of fluid flow and convective heat transfer of a pulsating flow in a curved tube have been investigated numerically. The tube wall is assumed to be maintained at a uniform temperature peripherally in a fully developed pulsating flow region. The temperature and flow distributions over a cross-section of a curved tube with the associated velocity field need to be studied in detail. This problem is of particular interest in the design of Stirling engine heat exchangers and in understanding the blood flow in the aorta. The time-dependent, elliptic governing equations are solved, employing finite volume technique. The periodic steady state results are obtained for various governing dimensionless parameters, such as Womersley number, pulsation amplitude ration, curvature ratio and Reynolds number. The numerical results indicate that the phase difference between the pressure gradient and averaged axial velocity increases gradually up to π/2 as Womersley number increases. However, this phase difference is almost independent of the amplitude ratio of pulsation. It is also found that the secondary flow patterns are strongly affected by the curvature ratio and Reynolds number. These, in turn, give a strong influence on the convective heat transfer from the pipe wall to the pulsating flow. The results obtained lead to a better understanding of the underlying physical process and also provide input that may be used to design the relevant system. The numerical approach is discussed in detail, and the aspects that must be included for an accurate simulation are discussed.     

Multibody dynamics in arterial system

There are many things in common between hemodynamics in arterial systems and multibody dynamics in mechanical systems Hemodynamics is concerned with the forces generated by the heart and the resulting motion of blood through the multi-branched vascular system The conventional hemodynamics model has been intended to show the general behavior of the body arterial system with the frequency domain based linear model The need for detailed models to analyze the local part like coronary arterial tree and cerebral arterial tree has been required recently Non-linear analysis techniques are well-developed in multibody dynamics In this paper, the studies of hemodynamics are summarized from the view of multibody dynamics Computational algorithms of arterial tree analysis is derived, and proved by experiments on animals The flow and pressure of each branch are calculated from the measured flow data at the ascending aorta The simulated results of the carotid artery and the ihac artery show in good accordance with the measured results     

Continuous-wave Doppler for the noninvasive evaluation of aortic blood velocity and rate of change of velocity: evaluation in dogs

A new continuous-wave Doppler device is described, which has the capability of measuring peak aortic blood velocity and acceleration noninvasively in the ascending aorta of patients. To test the accuracy of the device, blood velocity and acceleration in the ascending aorta were compared with measurements obtained using an electromagnetic flowmeter in 16 open-chest anesthetized dogs. The Doppler probe was hand held directly on the aorta. Aortic flow was measured with a cuff electromagnetic flow transducer placed at the root of the aorta. Isoproterenol and propranolol, sometimes in combination with lidocaine, were administered intravenously to augment or reduce left ventricular contractile performance. Values of peak velocity, measured with the Doppler, corresponded closely to values measured with the electromagnetic flowmeter (r = 0.95). Values of peak acceleration also corresponded closely with the electromagnetic flow measurements (r = 0.96). The results indicate that valid measurements of blood acceleration in the ascending aorta, as well as blood velocity, can be obtained with continuous-wave Doppler.     

Two-phase non-linear model for the flow through stenosed blood vessels

Pulsatile flow of a two-phase model for blood flow through arterial stenosis is analyzed through a mathematical analysis. The effects of pulsatility, stenosis, peripheral layer and non-Newtonian behavior of blood, assuming the blood in the core region as a Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid, are discussed. A perturbation method is used to solve the resulting system of non-linear quasi-steady differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. It is noticed that the plug core radius and resistance to flow increase as the stenosis size increases while all other parameters held constant The wall shear stress increases with the increase of yield stress while keeping other parameters as invariables. It is observed that the velocity increases with the axial distance in the stenosed region of the tube upto the maximum projection of the stenosis. Currently on leave from Department of Mathematics, Crescent Engineering College Vandalur, Chennai-600 048, Tamil Nadu, India.     

Reconstruction of blood flow patterns in human arteries

Local haemodynamic factors in large arteries are associated with the pathophysiology of cardiovascular diseases such as atherosclerosis and strokes. In search of these factors and their correlation with atheroma formation, quantitative haemodynamic data in realistic arterial geometry become crucial. At present no in vivo non-invasive technique is available that can provide accurate measurement of three-dimensional blood velocities and shear stresses in curved and branching sites of vessels where atherosclerotic plaques are found frequently. This paper presents a computer modelling technique which combines state-of-the-art computational fluid dynamics (CFD) with new noninvasive magnetic resonance imaging techniques to provide the complete haemodynamic data in 'real' arterial geometries. Using magnetic resonance angiographic and velocity images acquired from the aortic bifurcation of a healthy human subject, CFD simulations have been carried out and the predicted flow patterns demonstrate the non-planar-type flow characteristics found in experimental studies.     

A venous pulse Doppler catheter-tip flowmeter for measuring arterial blood velocity, flow, and diameter in deep arteries.

Numerous schemes have been used for measuring hemodynamic properties of deeply lying arteries; however, all have their limitations. This paper describes a new relatively nontraumatic intravenous approach that uses a catheter in connection with a pulsed ultrasonic Doppler velocity meter (PUDVM) and an echo track. The catheter was initially tested in a hydraulic model system for calibration of velocity and flow parameters. Lately, the catheter has permittted measurements of local instantaneous blood velocity, flow, and wall motion characteristics in adult Beagle dogs in the abdominal aorta and iliac artery. Evaluation studies have been conducted to compare the catheter-tip recordings with an independent method for measuring blood flow and wall motion. Coupling of this catheter-tip device with the PUDVM and echo track provides chronic measurements of hemodynamic parameters in these deep vessels which were virtually impossible to obtain previously. This technique may prove useful in monitoring vessel pathology longitudinally as well as in basic experimental situations requiring flow and arterial wall mechanical properties.     

Reproduction of air velocity in the entrance region of the test pipe in a wind tunnel

The airflow development in the pipe, in the entrance region of the wind tunnel located in the Lithuanian Energy Institute, the laboratory of Heat Equipment Research and Testing is investigated to analyze the conditions for the reproduction of air velocity values. The analysis is performed to reveal undeveloped flow conditions where the calibration of the devices is usually made, the entrance region of the pipes, or free stream from the nozzles. In this study, different flow regimes have been investigated using different air velocity measurement methods. Experimental and numerical results clearly show the features of the developing flow. They both demonstrate the stable core of the velocity profile up to 5 D in the pipe and ≤1 D from the entrance into the free stream in the testing chamber. Ultrasonic anemometer (UA) installed in the aerodynamic test facility shows reliable and highly comparable results with another non-intrusive device – laser Doppler velocimeter (LDA) in a range of velocities from 0.05 m/s up to 30 m/s. UA integrated into the wind tunnel is not found to be used for metrological issues for air velocity. Due to the fast response, they both enabled to analyze fluctuations in the flow. Local vortices identified in the flow have influenced the low-frequency fluctuations and the scatter of measurement results. Moreover, high-frequency fluctuations found in the flow originated from the flow turbulence and might be due to the electronic or acoustic noise. The stabilization of the entrance region in the pipe influences the mean value of air velocity, the transversal distribution of velocity and the development of axial velocity in different test sections of the pipe in a wind tunnel. Along with the recirculation zones in cavities of ultrasonic transducers, these factors are essential that make an impact on the reproduction of air velocity value.     

Two-fluid Herschel-Bulkley model for blood flow in catheterized arteries

The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model. Presently on leave from Department of Mathematics, B. S. A. Crescent Engineering College, Vandalur, Chennai-48, India)     

Pulsatile flow of viscous and viscoelastic fluids in constricted tubes

The unsteady flow of blood through stenosed artery, driven by an oscillatory pressure gradient, is studied. An appropriate shape of the time-dependent stenoses which are overlapped in the realm of the formation of arterial narrowing is constructed mathematically. A msathematical model is developed by treating blood as a non-Newtonian fluid characterized by the Oldroyd-B and Cross models. A numerical scheme has been used to solve the unsteady nonlinear Navier-stokes equations in cylindrical coordinate system governing flow, assuming axial symmetry under laminar flow condition so that the problem effectively becomes two-dimensional. Finite difference technique was used to investigate the effects of parameters such as pulsatility, non-Newtonian properties and the flow time on the velocity components, the rate of flow, and the wall shear stress through their graphical representations quantitatively at the end of the paper in order to validate the applicability of the present improved mathematical model under consideration.     

Novel mass air flow meter for automobile industry based on thermal flow microsensor. I. Analytical model and microsensor

An analytical model of the thermal flow sensor has been developed. The results of analytical model application are utilized to develop a thermal flow microsensor with optimal functional characteristics. The technology to manufacture the microsensor is described. A prototype of the microsensor suitable to be used in the mass air flow meter has been designed. The basic characteristics of the microsensor are presented.     

Determination of the arterial flow fraction in normal and diseased livers using constrained deconvolution.

There is some evidence that the ratio of the blood flow to the liver through the hepatic artery to the total flow to the liver through the hepatic artery and portal vein (the hepatic arterial flow fraction, AFF) is altered in the presence of cirrhosis. Several methods have been published that seek to provide an index of this ratio. These indices are dependent on factors other than the AFF and cannot provide a true measure of it. The impulse retention function of the liver has two components and these may be derived using a model-driven deconvolution of the arterial tracer concentration curve and the curve of tracer concentration in the liver. The AFF may then be obtained from the relative heights of these two components. Simulation studies show that the AFF calculated using this method is reasonably accurate and a small clinical series shows that it is capable of appropriate clinical classification of patients into cirrhotic and non-cirrhotic groups.     

Flow instabilities in a graft anastomosis: a study of the instantaneous velocity fields

The major cause of arterial bypass graft failure is intimal hyperplasia. Fluctuating wall shear stresses in the graft, which are associated with disturbed flow, are believed to be important factors in the development and localization of intimal hyperplasia. This study, based upon water as the working fluid, has investigated the flow structure inside a 30 degree Y-junction with different fillet radii at the intersection between the graft and the host artery at various Reynolds numbers and distal outlet segment (DOS) to proximal outlet segment (POS) flow ratios. The structure of the flow has been investigated experimentally using particle image velocimetry (PIV). The two-dimensional instantaneous velocity fields confirm the existence of a very complex flow, especially in the toe and heel regions for the different fillet radii and clearly identify features such as sinks, sources, vortices and strong time dependency.     

FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries

A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.     

Effects of the velocity waveform of the physiological flow on the hemodynamics in the bifurcated tube

The periodicity of the physiological flow has been the major interest of analytic research in this field up to now. Among the mechanical forces stimulating the biochemical reaction of endothelial cells on the wall, the wall shear stresses show the strongest effect to the biochemical product. The objective of present study is to find the effects of velocity waveform on the wall shear stresses and pressure distribution along the artery and to present some correlation of the velocity waveform with the clinical observations. In order to investigate the complex flow phenomena in the bifurcated tube, constitutive equations, which are suitable to describe the rheological properties of the non-Newtonian fluids, are determined, and pulsatile momemtum equations are solved by the finite volume prediction. The results show that pressure and wall shear stresses are related to the velocity waveform of the physiological flow and the blood viscosity. And the variational tendency of the wall shear stresses along the flow direction is very similar to the applied sinusoidal and physiological velocity waveforms, but the stress values are quite different depending on the local region. Under the sinusoidal velocity waveform, a Newtonian fluid and blood show big differences in velocity, pressure, and wall shear stress as a function of time, but the differences under the physiological velocity waveform are negligibly small.     

Non-invasive measurement of mechanical properties of arteries in health and disease.

Major conduit arteries should, by their elastic nature, be able to store blood volume temporarily during systole and release it during diastole. This reduces the systolic blood pressure required for the flow of a given volume quantity and gradually suppresses the pulsatile flow pattern. The haemodynamic characteristics of arteries have consequences for the load of the heart but also for the mechanical load of the arterial wall. The repetitive stretching of the wall (strains of up to 10 per cent) may cause fragmentation of the elastic fibres in the wall, modifying wall elasticity. To maintain wall stress the elastic arteries respond with a diameter increase in combination with an increase of arterial wall thickness. A larger diameter for a smaller distension (change in artery diameter from diastole to systole) will restrict the reduction in storage capacity. Alternatively, pulse pressure may go up increasing the mechanical load on the wall. In recent years various methods have been developed to assess and monitor the above interaction. Most of these methods are based on ultrasound techniques because of its wide availability and its non-invasive and non-traumatic nature. Presently these techniques enable the assessment of wall thickness, diastolic diameter, distension waveform, i.e., the tie-dependent change in diameter, the relative pulsatile increase in diameter, and pulse wave velocity, for elastic and muscular arteries in humans but also in small animals such as rats and mice. The present paper discusses the techniques in more detail.     

Particle image velocimetry of a flow at a vaulted wall

The assessment of flow along a vaulted wall (with two main finite radii of curvature) is of general interest; in biofluid mechanics, it is of special interest. Unlike the geometry of flows in engineering, flow geometry in nature is often determined by vaulted walls. Specifically the flow adjacent to the wall of blood vessels is particularly interesting since this is where either thrombi are formed or atherosclerosis develops. Current measurement methods have problems assessing the flow along vaulted walls. In contrast with conventional particle image velocimetry (PIV), this new method, called wall PIV, allows the investigation of a flow adjacent to transparent flexible surfaces with two finite radii of curvature. Using an optical method which allows the observation of particles up to a predefined depth enables the visualization solely of the boundary layer flow. This is accomplished by adding a specific dye to the fluid which absorbs the monochromatic light used to illuminate the region of observation. The obtained images can be analysed with the methods of conventional PIV and result in a vector field of the velocities along the wall. With wall PIV, the steady flow adjacent to the vaulted wall of a blood pump was investigated and the resulting velocity field as well as the velocity fluctuations were assessed.     

Direct Numerical simulation of 3-Dimensional axial turbulent boundary layers with spanwise curvature

Direct numerical simulation has been used to study turbulent boundary layers with convex curvature. A direct numerical simulation program has been developed to solve incompressible Navier-Stokes equations in generalized coordinates with the finite volume method. We considered two boundary layer thicknesses. When the curvature effect is small, mean velocity statistics show little difference with those of a plane channel flow. Turbulent intensity decreases as curvature increases. Contours suggest that streamwise vorticities are strong where large pressure fluctuations exist.     

Ultrasonic transesophageal measurement of hemodynamic parameters in humans.

A noninvasive method has been developed to monitor centerline blood velocity waveforms and vessel diameter in the descending aorta and pulmonary artery of conscious humans. An esophageal endoscope fitted with miniature ultrasound transducers is swallowed and positioned in the esophagus near vessels of interest. The transducers are connected to ultrasound Doppler velocimeters and echotrack instrumentation to obtain the pertinent hemodynamic parameters. This paper describes the design and fabrication of the esophageal ultrasound transducers and the techniques involved in human applications. In addition, blood velocity and wall motion measurements obtained in conscious men at rest and during exercise are described.