Fluid particle motion and Lagrangian velocities for pulsatile flow through a femoral artery branch model

A flow visualization study using selective dye injection and frame by frame analysis of a movie provided qualitative and quantitative data on the motion of marked fluid particles in a 60 degree artery branch model for simulation of physiological femoral artery flow. Physical flow features observed included jetting of the branch flow into the main lumen during the brief reverse flow period, flow separation along the main lumen wall during the near zero flow phase of diastole when the core flow was in the downstream direction, and inference of flow separation conditions along the wall opposite the branch later in systole at higher branch flow ratios. There were many similarities between dye particle motions in pulsatile flow and the comparative steady flow observations.     

In-vitro pulsatile flow visualization studies in a pulmonary artery model

In-vitro pulsatile flow visualization studies were conducted in an adult-sized pulmonary artery model to observe the effects of valvular pulmonic stenosis on the flow fields of the main, left and right pulmonary arteries. The flow patterns revealed that as the degree of stenosis increased, the jet-type flow created by the valve became narrower, and it impinged on the far (distal) wall of the left pulmonary artery further downstream from the junction of the bifurcation. This in turn led to larger regions of disturbed turbulent flow, as well as helical-type secondary flow motions in the left pulmonary artery, compared to the right pulmonary artery. The flow field in the main pulmonary artery also became more disturbed and turbulent, especially during peak systole and the deceleration phase. The flow visualization observations have been valuable in helping to conduct further quantitative studies such as pressure and velocity field mapping. Such studies are important to understanding the fluid mechanics characteristics of the main pulmonary artery and its two major branches.     

Laser Doppler anemometer measurements of pulsatile flow in a model carotid bifurcation

Hemodynamics at the human carotid bifurcation is important to the understanding of atherosclerotic plaque initiation and progression as well as to the diagnosis of clinically important disease. Laser Doppler anemometry was performed in a large scale model of an average human carotid. Pulsatile waveforms and physiologic flow divisions were incorporated. Disturbance levels and shear stresses were computed from ensemble averages of the velocity waveform measurements. Flow in the common carotid was laminar and symmetric. Flow patterns in the sinus, however, were complex and varied considerably during the cycle. Strong helical patterns and outer wall flow separation waxed and waned during each systole. The changing flow patterns resulted in an oscillatory shear stress at the outer wall ranging from -13 to 9 dyn cm-2 during systole with a time-averaged mean of only -0.5 dyn cm-2. This contrasts markedly with an inner wall shear stress range of 17-50, (mean 26) dyn cm-2. The region of transient separation was confined to the carotid sinus outer wall with no reverse velocities detected in the distal internal carotid. Notable disturbance velocities were also time-dependent, occurring only during the deceleration phase of systole and the beginning of diastole. The present pulsatile flow studies have aided in identifying hemodynamic conditions which correlate with early intimal thickening and predict the physiologic level of flow disturbances in the bulb of undiseased internal carotid arteries.     

Numerical investigation of the non-Newtonian pulsatile blood flow in a bifurcation model with a non-planar branch

The pulsatile flow of non-Newtonian fluid in a bifurcation model with a non-planar daughter branch is investigated numerically by using the Carreau-Yasuda model to take into account the shear thinning behavior of the analog blood fluid. The objective of this study is to deal with the influence of the non-Newtonian property of fluid and of out-of-plane curvature in the non-planar daughter vessel on wall shear stress (WSS), oscillatory shear index (OSI), and flow phenomena during the pulse cycle. The non-Newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior. The non-planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of WSS along the vessel, in particular in systole phase. Downstream of the bifurcation, the velocity profiles are shifted toward the flow divider, and low WSS and high shear stress temporal oscillations characterized by OSI occur on the outer wall region of the daughter vessels close to the bifurcation. Secondary motions become stronger with the addition of the out-of-plane curvature induced by the bending of the vessel, and the secondary flow patterns swirl along the non-planar daughter vessel. A significant difference between the non-Newtonian and the Newtonian pulsatile flow is revealed during the pulse cycle; however, reasonable agreement between the non-Newtonian and the rescaled Newtonian flow is found. Calculated results for the pulsatile flow support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

Turbulent stress measurements downstream of six mechanical aortic valves in a pulsatile flow model

In a pulsatile flow model aortic Bj?rk-Shiley Standard, Convex-Concave and Monostrut valves were investigated together with the Hall-Kaster (Medtronic-Hall), St Jude Medical and Starr-Edwards Silastic Ball valve using hot-film anemometry. Three-dimensional visualization of average systolic Reynolds normal stresses (RNS) reflected the design of the valves. Mean average RNS were used for comparison of the fluid dynamic performance along with Velocity Energy Ratio (VER100) and Turbulence Energy Ratio (TER) as a relative turbulence intensity for pulsatile flow. Mean average RNS ranged from 13.2 to 37.6 Nm-2 for all the valves with the highest levels for the Bj?rk-Shiley Standard and Starr-Edwards Ball valve and lowest values for the St Jude Medical valve and with the Hall-Kaster (Medtronic-Hall), Bj?rk-Shiley Convex-Concave and Monostrut valves in between.     

Flow measurements in a human femoral artery model with reverse lumen curvature

Flow visualization and wall pressure measurements were made in a smooth reverse curvature model that conformed to the gentle "s" shape of a left femoral artery angiogram of a patient in a clinical trial. Observed lesion localization at the inner (lesser) curvatures appeared to be associated with secondary flows in the wall vicinity directed toward the inner curvatures that tended to reverse direction in the flow entering the reverse curvature region. Moderate flow resistance increases of about 20 percent above the Poiseuille flow relation were found at the higher physiological Reynolds numbers Re above about 600-700 and thus Dean numbers for steady flow. For pulsatile flow simulation, flow resistances did not increase up to the largest Re of 470 tested. Apparently, the large variations in velocity during the cardiac cycle disrupted the stronger secondary flow patterns observed at the higher Reynolds numbers for steady flow.     

Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.     

Simple pulsatile flow in an artery with a constriction

A smooth isolated, axisymmetric occlusion in a straight vascular tube is a tractable problem for pulsatile flow calculations via finite-difference approximations to the Navier-Stokes equation. Steady flow depends on the Reynolds number and two geometric parameters which describe the stenosis. The mere addition of a simple harmonic to the mean flow adds two more parameters. One is the reduced frequency, or Strokes number, and the other epsilon, the ratio of unsteady to steady flux. After describing steady stenosis flow examples, the dynamic patterns of pulsatile flow are illustrated indicating the inadequacy of basing hypotheses of atherosclerosis on mean (steady) flow.     

Pressure drop and flow rate measurements in a human aortic bifurcation cast for steady and pulsatile flow

Pressure drop and flow rate measurements in a rigid cast of a human aortic bifurcation under both steady and physiological pulsatile flow conditions are reported. Integral momentum and mechanical energy balances are used to calculate impedance, spatially averaged wall shear stress and viscous dissipation rate from the data. In the daughter branches, steady flow impedance is within 30% of the Poiseuille flow prediction, while pulsatile flow impedance is within a factor of 2 of fully developed, oscillatory, straight tube flow theory (Womersley theory). Estimates of wall shear stress are in accord with measurements obtained from velocity profiles. Mean pressure drop and viscous dissipation rate are elevated in pulsatile flow relative to steady flow at the mean flow rate, and the exponents of their Reynolds number dependence are in accord with available theory.     

Fluid dynamic study in a femoral artery branch casting of man with upstream main lumen curvature for steady flow

An in-vitro, steady flow investigation was conducted in a hollow, transparent vascular replica of the profunda femoris branch of man for a range of physiological flow conditions. The replica casting tested was obtained from a human cadaver and indicated some plaque formation along the main lumen and branch. The flow visualization observations and measured pressure distributions indicated the highly three-dimensional flow characteristics with arterial curvature and branching, and the important role of centrifugal effects in fluid transport mechanisms.     

Multiphase hemodynamic simulation of pulsatile flow in a coronary artery

A multiphase transient non-Newtonian three-dimensional (3-D) computational fluid dynamics (CFD) simulation has been performed for pulsatile hemodynamics in an idealized curved section of a human coronary artery. We present the first prediction, to the authors' knowledge, of particulate buildup on the inside curvature using the multiphase theory of dense suspension hemodynamics. In this study, the particulates are red blood cells (RBCs). The location of RBC buildup on the inside curvature correlates with lower wall shear stress (WSS) relative to the outside curvature. These predictions provide insight into how blood-borne particulates interact with artery walls and hence, have relevance for understanding atherogenesis since clinical observations show that atherosclerotic plaques generally form on the inside curvatures of arteries. The buildup of RBCs on the inside curvature is driven by the secondary flow and higher residence times. The higher viscosity in the central portion of the curved vessel tends to block their flow, causing them to migrate preferentially through the boundary layer. The reason for this is the nearly neutrally buoyant nature of the dense two-phase hemodynamic flow. The two-phase non-Newtonian viscosity model predicts greater shear thinning than the single-phase non-Newtonian model. Consequently, the secondary flow induced in the curvature is weaker. The waveforms for computed hemodynamic parameters, such as hematocrit, WSS, and viscosity, follow the prescribed inlet velocity waveforms. The lower oscillatory WSS produced on the inside curvature has implications for understanding thickening of the intimal layer.     

Microcontinuum model for pulsatile blood flow through a stenosed tube

The effects of polar nature of blood and pulsatility on flow through a stenosed tube have been analysed by assuming blood as a micropolar fluid. Linearized solutions of basic equations are obtained through consecutive applications of finite Hankel and Laplace transforms. The analytical expressions for axial and particle angular velocities, wall shear stress, resistance to flow and apparent viscosity have been obtained. The axial velocity profiles for Newtonian and micropolar fluids have been compared. The interesting observation of this analysis is velocity, in certain parts of cycle, for micropolar fluid is higher than Newtonain fluid. Variation of apparent viscosity eta a with tube radius shows both inverse Fahraeus-Lindqvist and Fahraeus-Lindqvist effects. Finally, the resistance to flow and wall shear stress for normal and diseased blood have been computed and compared.     

Combined effects of pulsatile flow and dynamic curvature on wall shear stress in a coronary artery bifurcation model

A three-dimensional model with simplified geometry for the branched coronary artery is presented. The bifurcation is defined by an analytical intersection of two cylindrical tubes lying on a sphere that represents an idealized heart surface. The model takes into account the repetitive variation of curvature and motion to which the vessel is subject during each cardiac cycle, and also includes the phase difference between arterial motion and blood flowrate, which may be nonzero for patients with pathologies such as aortic regurgitation. An arbitrary Lagrangian Eulerian (ALE) formulation of the unsteady, incompressible, three-dimensional Navier-Stokes equations is employed to solve for the flow field, and numerical simulations are performed using the spectral/hp element method. The results indicate that the combined effect of pulsatile inflow and dynamic geometry depends strongly on the aforementioned phase difference. Specifically, the main findings of this work show that the time-variation of flowrate ratio between the two branches is minimal (less than 5%) for the simulation with phase difference angle equal to 90 degrees, and maximal (51%) for 270 degrees. In two flow pulsatile simulation cases for fixed geometry and dynamic geometry with phase angle 270 degrees, there is a local minimum of the normalized wall shear rate amplitude in the vicinity of the bifurcation, while in other simulations a local maximum is observed.     

Flow measurements in an atherosclerotic curved, tapered femoral artery model of man

Flow visualization and pressure measurements were made for physiological conditions in a model derived from a femoral angiogram of a patient with lesion localization on the inner curvature wall and with vessel taper. Effects of curvature and taper were evaluated separately in other curved, tapered, smooth and straight, tapered, smooth models. Double helical secondary flow patterns were modified by plaque on the inner wall, and flow separations were observed between plaques at higher flow rates and Reynolds numbers. Pressure drop data for the plaque simulation model were similar in trend with Reynolds number as for the smooth model, but flow resistances were 25 to 40 percent higher. Significant pressure drops were measured due to the mild taper which could be estimated from momentum considerations, and smaller increased pressure drops were found due to curvature effects at the higher Dean numbers. Flow resistances for in vivo pulsatile flow simulation were about 10 percent higher than for steady flow for the plaque model, whereas no differences were observed for the smooth model.     

Comparison of steady and pulsatile flow in a double branching arterial model

Data are presented to compare fluid flow parameters for steady flow with those for time-varying flow in a simplified two branch model which simulates the region of the abdominal aorta near the celiac and superior mesenteric branches of the dog. Measurements in the model included laser doppler anemometry velocity profiles during steady flow, sinusoidal flow with a superimposed mean flow (referred to as simple oscillatory flow) and arterial pulsatile flow. Shear rate measurements were made by an electrochemical technique during steady flow. Flow visualization studies were done during steady and pulsatile flow. Fluid flow effects in the simplified model during steady flow showed many similarities to the results from previous steady flow studies in a canine aortic cast. Shear rates in the region of the proximal (first, or celiac) branch were independent of flow rates in the distal (second, or mesenteric) branch, but the shear pattern within the proximal branch changed significantly as flow in the proximal branch increased. Shear rates on the proximal flow divider (leading edge into the distal branch) depended primarily on the flow rate to the proximal branch, but not on flow to the distal branch. At certain daughter branch flow ratios (approximately 2:1, proximal to distal), flow separation was promoted at the outer wall of the second branch, but flow separation did not occur in the first branch. In contrast to the canine aortic case results, flow separation was never detected on the distal (mesenteric) flow divider of the simplified model. This observation reflects the subtle effects of geometry on flow since the mesenteric flow divider in the canine cast protrudes into the main flow whereas the distal flow divider in the simplified model does not. There were distinct differences in the flow phenomena between steady, simple oscillatory and arterial pulsatile flow. Peak shear rates during pulsatile flow were as much as 10--100 times greater than steady flow shear rates at comparable mean flow rates. Particularly noteworthy for the pulsatile flow with a Womersley parameter of sixteen were very blunt velocity profiles throughout systole, and the absence of flow separation or reversal in those regions of the model that exhibited flow separation during steady flow. The shape of the waveform influences the nature of the flow during time-varying flows. Future studies of fluid dynamics in model systems must consider the pulsatile nature of the flow if a true interpretation of arterial flow phenomena is to be made.     

Structure of pulsatile flow in a model of elastic cerebral aneurysm

This study examines the effect of aneurysmal wall elasticity on the structure of flow within an elastic aneurysm during pulsatile flow. We visualized flow structure in a model of an elastic saccular aneurysm located at the bifurcation of the anterior cerebral artery and extending to the anterior communicating artery, and measured changes in the diameter of the aneurysm wall during pulsatile flow using particle imaging velocimetry (PIV). We similarly measured these features during steady flow by PIV and found that dilation of the aneurysmal wall absorbed the dynamic energy within the aneurysm. Accordingly, aneurysm wall elasticity functions as a biocompatible reaction that relieves wall shear stress acting on the vascular wall during pulsatile flow, and should thus inhibit the development and rupture of an aneurysm.     

Bio-medico-mechanical behavior of natural artery blood vessel under constant and variable internal pulsatile pressure flow test in vitro

Studies have been carried out on the bio-medico-mechanical behavior in vitro of natural blood vessel (dogs) under constant and variable internal pulsatile pressure flow. The apparatus designed by us well simulated the arterial system. The studies were made for the case of pressure amplitude kept as constant, of the two-step-multi-duplicated pulsatile pressure and of the fluctuating pressure. For the case of the fluctuating pressure, the strength of the artery becomes considerably lower than those under constant amplitude and two-step-multi-duplicated pulsatile pressure. SEM observations of the inner walls of the artery shows that collagen fibers are more elongated under fluctuating pulsatile pressure flow. In conclusion, in order to avoid the mechanical deterioration of the artery strength, it is useful to keep the pulsatile blood pressure at constant amplitude. Even for the case of the blood pressure fluctuation, it is necessary to manage to keep the blood pressure as near a regular wave as possible, the total number of repeated pulse being equal.