Measurement of wall motion and wall shear in a compliant arterial cast

Initial measurements of the time-varying wall shear rate at two sites in a compliant cast of a human aortic bifurcation are presented. The shear rates were derived from flow velocities measured by laser Doppler velocimetry (LDV) near the moving walls of the cast. To derive these shear rate values, the distance from the velocimeter sampling volume to the cast wall must be known. The time variation of this distance was obtained from LDV measurements of the velocity of the wall itself.     

Effects of arterial compliance and non-Newtonian rheology on correlations between intimal thickness and wall shear.

A minimally diseased (mean intimal thickness = 56 microns) human aortic bifurcation was replicated in rigid and compliant flow-through casts. Both casts were perfused with physiological flow waves having the same Reynolds and unsteadiness numbers; the pulse pressure in the compliant cast produced radial strains similar to those expected from post-mortem measurements of the compliance of the original tissue. The compliant cast was perfused with a Newtonian fluid and one whose rheology was closer to that of blood. Wall shear rate histories were estimated from near-wall velocities obtained by laser Doppler velocimetry at identical sites in both casts. Intimal thickness was measured at corresponding sites in the original vessel and linear regressions were performed between these thicknesses and several normalized shear rate measures obtained from the histories. The correlations showed a positive slope--that is, the intima was thicker at sites exposed to higher shear rates--consistent with earlier results for relatively healthy vessels, but their significance was often poor. There was no significant effect of either model compliance or fluid rheology on the slopes of the correlations of intimal thickness against any normalized shear rate measure.     

Blood flow and vessel mechanics in a physiologically realistic model of a human carotid arterial bifurcation

The pulsatile flow in an anatomically realistic compliant human carotid bifurcation was simulated numerically. Pressure and mass flow waveforms in the carotid arteries were obtained from an individual subject using non-invasive techniques. The geometry of the computational model was reconstructed from magnetic resonance angiograms. Maps of time-average wall shear stress, contours of velocity in the flow field as well as wall movement and tensile stress on the arterial wall are all presented. Inconsistent with previous findings from idealised geometry models, flow in the carotid sinus is dominated by a strong helical flow accompanied by a single secondary vortex motion. This type of flow is induced primarily by the asymmetry and curvature of the in vivo geometry. Flow simulations have been carried out under the rigid wall assumption and for the compliant wall, respectively. Comparison of the results demonstrates the quantitative influence of the vessel wall motion. Generally there is a reduction in the magnitude of wall shear stress, with its degree depending on location and phase of the cardiac cycle. The region of slow or reversed flow was greater, in both spatial and temporal terms in the compliant model, but the global characteristics of the flow and stress patterns remain unchanged. The analysis of mechanical stresses on the vessel surface shows a complicated stress field. Stress concentration occurs at both the anterior and posterior aspects of the proximal internal bulb. These are also regions of low wall shear stress. The comparison of computed and measured wall movement generally shows good agreement.     

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

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study 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.     

Dynamic curvature strongly affects wall shear rates in a coronary artery bifurcation model

This study was motivated by the need for a better understanding of coronary artery blood flow patterns and their possible role in atherosclerosis formation. Of particular interest in this study was the effects of the dynamic deformation due to myocardial contraction on wall shear rate patterns in the coronary arteries. A better understanding of these effects on wall shear rate in a bifurcation geometry and an evaluation of the importance of these effects was desired. A three-dimensional computer model of a bifurcation lying on the surface of a sphere with time-varying radius of curvature was employed to simulate the motion and deformation of the arteries. The results indicated low mean shear rates along the myocardial wall and very high shear rate variations (over 100% of the static mean shear rate) along the outer wall. The results obtained using a quasi-static analysis were found to underestimate the dynamic wall shear rate variation along the myocardial and outer walls. It was concluded that dynamic geometry effects are important in determining sites of low mean and oscillating wall shear that have been associated with atherogenesis in curved, bifurcating arteries.     

Computational study of the effect of geometric and flow parameters on the steady flow field at the rabbit aorto-celiac bifurcation

Arterial hemodynamic forces may play a role in the localization of early atherosclerotic lesions. We have been developing numerical techniques based on overset or "Chimera" type formulations to solve the Navier-Stokes equations in complex geometries simulating arterial bifurcations. This paper presents three-dimensional steady flow computations in a model of the rabbit aorto-celiac bifurcation. The computational methods were validated by comparing the numerical results to previously-obtained flow visualization data. Once validated, the numerical algorithms were used to investigate the sensitivity of the computed flow field and resulting wall shear stress distribution to various geometric and hemodynamic parameters. The results demonstrated that a decrease in the extent of aortic taper downstream of the celiac artery induced looping fluid motion along the lateral walls of the aorta and shifted the peak wall shear stress from downstream of the celiac artery to upstream. Increasing the flow Reynolds number led to a sharp increase in spatial gradients of wall shear stress. The flow field was highly sensitive to the flow division ratio, i.e., the fraction of total flow rate that enters the celiac artery, with larger values of this ratio leading to the occurrence of flow separation along the dorsal wall of the aorta. Finally, skewness of the inlet velocity profile had a profound impact on the wall shear stress distribution near the celiac artery. While not physiological due to the assumption of steady flow, these results provide valuable insight into the fluid physics at geometries simulating arterial bifurcations.     

A numerical study on hemodynamics in the left coronary bifurcation with normal and hypertension conditions

In this study, a three-dimensional analysis of the non-Newtonian blood flow was carried out in the left coronary bifurcation. The Casson model and hyperelastic and rigid models were used as the constitutive equation for blood flow and vessel wall model, respectively. Physiological conditions were considered first normal and then compliant with hypertension disease with the aim of evaluating hemodynamic parameters and a better understanding of the onset and progression of atherosclerosis plaques in the coronary artery bifurcation. Two-way fluid–structure interaction method applying a fully implicit second-order backward Euler differencing scheme has been used which is performed in the commercial code ANSYS and ANSYS CFX (version 15.0). When artery deformations and blood pressure are associated, arbitrary Lagrangian–Eulerian formulation is employed to calculate the artery domain response using the temporal blood response. As a result of bifurcation, noticeable velocity reduction and backflow formation decrease shear stress and made it oscillatory at the starting point of the LCx branch which caused the shear stress to be less than 1 and 2 Pa in the LCx and the LAD branches, respectively. Oscillatory shear index (OSI) as a hemodynamic parameter represents the increase in residence time and oscillatory wall shear stress. Because of using the ideal 3D geometry and realistic physiological conditions, the values obtained for shear stress are more accurate than the previous studies. Comparing the results of this study with previous clinical investigations shows that the regions with low wall shear stress less than 1.20 Pa and with high OSI value more than 0.3 are in more potential risk to the atherosclerosis plaque development, especially in the posterior after the bifurcation.     

Experimental determination of velocity profiles and wall shear rate along the rabbit aortoiliac bifurcation: relationship to vessel wall low-density lipoprotein (LDL) metabolism.

We have determined the velocity profiles and wall shear rates along the New Zealand White (NZW) rabbit aortoiliac bifurcation. A pulsatile perfusion apparatus was used to impose physiologic pressure and flow waveforms on nine freshly excised NZW bifurcation segments. Pulsed Doppler velocimetry (PDV) was utilized to construct velocity profiles at five measurement sites: within the infrarenal aorta; immediately distal to the apex of the bifurcation; and, more distally along the iliac arteries. Wall shear rate was derived from a numerical differentiation of the experimental velocity profiles. The results of this study indicate that the average shear rate was lower along the lateral (approximately 40 s-1) vs medial (approximately 240 s-1) wall of the proximal iliac branch. The degree of flow reversal along the proximal lateral walls (20 +/- 2%) exceeded that along the proximal flow divider wall (1 +/- 1%). Flow at the distal iliac measurement sites and within the infrarenal aorta was approximately symmetric. These findings complement our companion in vivo study [Berceli et al., Arteriosclerosis 10, 688-694 (1990)] wherein we determined the rates of low-density lipoprotein (LDL) incorporation and catabolism along this symmetrically bifurcating conduit. Taken together, these studies provide original information regarding the effects of hemodynamics on one presumed atherogenic risk factor, namely, LDL metabolism.     

Analysis of Flow Phenomena in Gastric Contents Induced by Human Gastric Peristalsis Using CFD

This paper uses computational fluid dynamics to simulate and analyze intragastric fluid motions induced by human peristalsis. We created a two-dimensional computational domain of the distal stomach where peristalsis occurs. The motion of the gastric walls induced by an antral contraction wave (ACW) on the wall of the computational domain was well simulated using a function defined in this study. Retropulsive flow caused by ACW was observed near the occluded region, reaching its highest velocity of approximately 12 mm/s in the narrowest region. The viscosity of the model gastric contents applied in this study hardly affected the highest velocity, but greatly affected the velocity profile in the computational domain. The shear rate due to gastric fluid motion was calculated using the numerical output data. The shear rate reached relatively high values of approximately 20 s⁻¹ in the most occluded region. The shear rate profile was almost independent of the fluid viscosity. We also simulated mass transfer of a gastric digestive enzyme (pepsin) in model gastric content when peristalsis occurs on the gastric walls. The visualized simulation results suggest that gastric peristalsis is capable of efficiently mixing pepsin secreted from the gastric walls with an intragastric fluid.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.     

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.     

Effects of wall shear stress and fluid recirculation on the localization of circulating monocytes in a three-dimensional flow model

There is a correlation between the location of early atherosclerotic lesions and the hemodynamic characteristics at those sites. Circulating monocytes are key cells in the pathogenesis of atherosclerotic plaques and localize at sites of atherogenesis. The hypothesis that the distribution of monocyte adhesion to the vascular wall is determined in part by hemodynamic factors was addressed by studying monocyte adhesion in an in vitro flow model in the absence of any biological activity in the model wall.

Suspensions of U937 cells were perfused (Re = 200) through an axisymmetric silicone flow model with a stenosis followed by a reverse step. The model provided spatially varying wall shear stress, flow separation and reattachment, and a three-dimensional flow pattern. The cell rolling velocity and adhesion rates were determined by analysis of videomicrographs. Wall shear stress was obtained by numerical solution of the equations of fluid motion. Cell adhesion patterns were also studied in the presence of chemotactic peptide gradients.

The cell rolling velocity varied linearly with wall shear stress. The adhesion rate tended to decrease with increasing local wall shear stress, but was also affected by the radial component of velocity and the dynamics of the recirculation region and flow reattachment. Adhesion was increased in the vicinity of chemotactic peptide sources downstream of the expansion site. Results with human monocytes were qualitatively similar to the U937 experiments.

Differences in the adhesion rates of U937 cells occurring solely as a function of the fluid dynamic properties of the flow field were clearly demonstrated in the absence of any biological activity in the model wall.     

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.     

Coupled fluid–structure interaction hemodynamics in a zero-pressure state corrected arterial geometry

Hemodynamic conditions in large arteries are significantly affected by the interaction of the pulsatile blood flow with the distensible arterial wall. A numerical procedure for solving the fluid–structure interaction problem encountered in cardiovascular flows is presented. We consider a patient-specific carotid bifurcation geometry, obtained from 3D reconstruction of in vivo acquired tomography images, which yields a geometrical representation of the artery corresponding to its pressurized state. To recover the geometry of the artery in its zero-pressure state which is required for a fluid–structure interaction simulation we utilize inverse finite elastostatics. Time-dependent flow simulations with in vivo measured inflow volume flow rate in the 3D undeformed artery are performed through the finite element method. The coupled-momentum method for fluid–structure interaction is adopted to incorporate the influence of wall compliance in the numerical computation of the time varying flow domain. To demonstrate the importance in recovering the zero-pressure state of the artery in hemodynamic simulations we compute the time varying flow field with compliant walls for the original and the zero-pressure state corrected geometric configurations of the carotid bifurcation. The most important resulting effects in the hemodynamic environment are evaluated. Our results show a significant change in the wall shear stress distribution and the spatiotemporal extent of the recirculation regions.     

A model of a radially expanding and contracting lymphangion

The lymphatic system is an extensive vascular network featuring valves and contractile walls that pump interstitial fluid and plasma proteins back to the main circulation. Immune function also relies on the lymphatic system's ability to transport white blood cells. Failure to drain and pump this excess fluid results in edema characterized by fluid retention and swelling of limbs. It is, therefore, important to understand the mechanisms of fluid transport and pumping of lymphatic vessels. Unfortunately, there are very few studies in this area, most of which assume Poiseuille flow conditions. In vivo observations reveal that these vessels contract strongly, with diameter changes of the order of magnitude of the diameter itself over a cycle that lasts typically 2-3s. The radial velocity of the contracting vessel is on the order of the axial fluid velocity, suggesting that modeling flow in these vessels with a Poiseuille model is inappropriate. In this paper, we describe a model of a radially expanding and contracting lymphatic vessel and investigate the validity of assuming Poiseuille flow to estimate wall shear stress, which is presumably important for lymphatic endothelial cell mechanotransduction. Three different wall motions, periodic sinusoidal, skewed sinusoidal and physiologic wall motions, were investigated with steady and unsteady parabolic inlet velocities. Despite high radial velocities resulting from the wall motion, wall shear stress values were within 4% of quasi-static Poiseuille values. Therefore, Poiseuille flow is valid for the estimation of wall shear stress for the majority of the lymphangion contractile cycle.     

Numerical modeling of simulated blood flow in idealized composite arterial coronary grafts: steady state simulations

This paper presents a comparative study of simulated blood flow in different configurations of simplified composite arterial coronary grafts (CACGs). Even though the composite arterial grafting is increasingly used in cardiac surgery, it is still questionable whether or not the blood flow in such grafts can adequately meet the demands of the native myocardial circulation. A computational fluid dynamics (CFD) model was developed to conduct computer-based studies of simulated blood flow in four different geometric configurations of CACGs, corresponding to routinely used networks in cardiac surgery coronary grafts (T, Y, Pi and sequential). The flow was assumed three-dimensional, laminar and steady and the fluid as Newtonian, while the vessel walls were considered as inelastic and impermeable. It was concluded that local haemodynamics, practically described by velocity, pressure drop, wall shear stress (WSS) and flow rates, may be strongly influenced by the local geometry, especially at the anastomotic sites. The computations were made at mean flow rates of 37.5, 75 and 150ml/min. The side-branch outflow rates, computed for each bypass graft, showed noticeable differences. The results, which were found both qualitatively and quantitatively consistent with other studies, indicate that the Pi-graft exhibits significantly less uniform distribution of outflow rates than the other geometric configurations. Moreover, prominent variations in WSS and velocity distribution among the assessed CACGs were predicted, showing remarkable flow interactions among the arterial branches. The lowest shear stress regions were found on the lateral walls of bifurcations, which are predominantly susceptible to the occurrence of coronary artery disease (CAD). In contrast, the highest WSS were observed at the turn of the arterial branches.     

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.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.     

The effect of blood viscoelasticity on pulsatile flow in stationary and axially moving tubes

An analytical solution for pulsatile flow of a generalized Maxwell fluid in straight rigid tubes, with and without axial vessel motion, has been used to calculate the effect of blood viscoelasticity on velocity profiles and shear stress in flows representative of those in the large arteries. Measured bulk flow rate Q waveforms were used as starting points in the calculations for the aorta and femoral arteries, from which axial pressure gradient ▿P waves were derived that would reproduce the starting Q waves for viscoelastic flow. The ▿P waves were then used to calculate velocity profiles for both viscoelastic and purely viscous flow. For the coronary artery, published ▿P and axial vessel acceleration waveforms were used in a similar procedure to determine the separate and combined influences of viscoelasticity and vessel motion.Differences in local velocities, comparing viscous flow to viscoelastic flow, were in all cases less than about 2% of the peak local velocity. Differences in peak wall shear stress were less than about 3%.In the coronary artery, wall shear stress differences between viscous and viscoelastic flow were small, regardless of whether axial vessel motion was included. The shape of the wall shear stress waveform and its difference, however, changed dramatically between the stationary and moving vessel cases. The peaks in wall shear stress difference corresponded with large temporal gradients in the combined driving force for the flow.