Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

Wall shear stress distribution along the cusp of a tri-leaflet prosthetic valve

High levels of wall shear stress on the surface of valvular cusps can cause mechanical damage to the blood cells and the cusp surfaces. The shear stresses are also responsible for mechanical failure of prosthetic heart valves. Quatitative measurements of wall shear stress in the vicinity of the leaflets are thus essential for diagnosis of suspected complications and provide important information for the design and fabrication of bioprosthetic heart valves. For this purpose we measured the velocity distribution along the inside wall of the cusps of a tri-leaflet heart valve with a two colour laser Doppler anemometer system. The wall shear stresses on the cusp surface were computed and found to range from 80 to 120 N/m² during the ejection phase. Wall shear stresses of up to 180 N/m² were measured in loci of cusp flexure and the accelerated boundary layer. The results of this study show a correlation between the high shear stress loci and the clinically (animal) observed regions of cusp calcification.     

Wall shear stress during pulsatile flow distal to a normal porcine aortic valve

The shear stress at the wall has been of interest as one of the possible fluid dynamic factors that may be damaging in the region of prosthetic valves. The purpose of this study was to measure the axial wall shear stresses in the region of a 29 mm tissue annulus diameter porcine stent mounted prosthetic aortic valve (Hancock, Model 242). Studies were performed in an in vitro pulse duplicating system. The axial wall shear stress was calculated from velocities obtained near the wall with a laser Doppler anemometer. The largest axial wall shear stress was 29 dyn cm-2 and it occurred at the highest stroke volume used (80 ml). At a stroke volume of 50 ml, the largest axial wall shear stress was 17 dyn cm-2 and at a stroke volume of 35 ml, it was 15 dyn cm-2. Stresses of these magnitudes are far below those reported to be damaging to the endothelial surface. These stresses may be high enough, however, to affect platelet function.     

The influence of aortic dimensions on calculated wall shear stress in the mouse aortic arch

In this paper, the influence of the aortic dimensions of an investigated mouse on its resulting wall shear stress (WSS) was studied. A numerical model of a mouse aortic arch was created based on a micro-CT scan of a vascular corrosion cast of an 8-week-old wild type mouse. This model was then rescaled to obtain five models with aortic root diameters corresponding to five different stages in the mouse life cycle varying from late fetal (0.7 mm) to old adult (1.5 mm). Consistent with literature, WSS values much higher than those normally encountered in humans were found. WSS was found to decrease rapidly in early life stages and to reach a plateau in adulthood, thus supporting a mediating role for WSS in arterial growth. Our results show that WSS values for mice should be interpreted very cautiously, and if possible an animal-specific geometry with animal-specific boundary conditions should be used.     

Wall shear stress distribution in a model human aortic arch: assessment by an electrochemical technique

Wall shear stress (WSS) distribution in a human aortic arch model is studied using 130 cathode electrodes flush-mounted on the model walls. Flow visualizations are made in a transparent geometry model to identify the regions of fluid mechanical interests, e.g. regions of flow separation, eddy formation and flow stagnancy. The 130 electrodes are strategically positioned in the arch based on information obtained from the flow visualizations. The measured data indicate that the aortic arch may be categorized into eight regions: three along the inner wall of the arch (A,B,C); and five near the outer wall (D,E,F,G,H). (1) The regions of low WSS are distributed along the inner wall of the ascending aorta A; the inner wall of the descending aorta C; and the upstream inner wall of the innominate and the common carotid branchings F. (2) The high WSS regions are distributed along the outer wall of the arch E; and the inner wall in the arch opposite to the left subclavian branching B. (3) In certain regions, high and low WSS may be found next to each other (e.g. G and H) without a definable boundary in between; and (4) as the Reynolds number increases, the areas of low WSS decrease, while the high WSS areas increase with no obvious change in magnitude of the stress along the inner wall of the arch. At the branchings, the WSS distribution is not affected by the Reynolds number within the range of observations. The measured WSS distribution is compared with Rodkiewicz's map of early atherosclerotic lesions in the aortic arch of cholesterol fed rabbits.     

Three-dimensional macro-scale assessment of regional and temporal wall shear stress characteristics on aortic valve leaflets

The aortic valve (AV) achieves unidirectional blood flow between the left ventricle and the aorta. Although hemodynamic stresses have been shown to regulate valvular biology, the native wall shear stress (WSS) experienced by AV leaflets remains largely unknown. The objective of this study was to quantify computationally the macro-scale leaflet WSS environment using fluid–structure interaction modeling. An arbitrary Lagrangian–Eulerian approach was implemented to predict valvular flow and leaflet dynamics in a three-dimensional AV geometry subjected to physiologic transvalvular pressure. Local WSS characteristics were quantified in terms of temporal shear magnitude (TSM), oscillatory shear index (OSI) and temporal shear gradient (TSG). The dominant radial WSS predicted on the leaflets exhibited high amplitude and unidirectionality on the ventricularis (TSM>7.50 dyn/cm², OSI < 0.17, TSG>325.54 dyn/cm² s) but low amplitude and bidirectionality on the fibrosa (TSM < 2.73 dyn/cm², OSI>0.38, TSG < 191.17 dyn/cm² s). The radial WSS component computed in the leaflet base, belly and tip demonstrated strong regional variability (ventricularis TSM: 7.50–22.32 dyn/cm², fibrosa TSM: 1.26–2.73 dyn/cm²). While the circumferential WSS exhibited similar spatially dependent magnitude (ventricularis TSM: 1.41–3.40 dyn/cm², fibrosa TSM: 0.42–0.76 dyn/cm²) and side-specific amplitude (ventricularis TSG: 101.73–184.43 dyn/cm² s, fibrosa TSG: 41.92–54.10 dyn/cm² s), its temporal variations were consistently bidirectional (OSI>0.25). This study provides new insights into the role played by leaflet–blood flow interactions in valvular function and critical hemodynamic stress data for the assessment of the hemodynamic theory of AV disease.     

Turbulent shear stress measurements in the vicinity of aortic heart valve prostheses

A two dimensional laser Doppler anemometer system has been used to measure the turbulent shear fields in the immediate downstream vicinity of a variety of mechanical and bioprosthetic aortic heart valves. The measurements revealed that all the mechanical valves studied, created regions of elevated levels of turbulent shear stress during the major portion of systole. The tissue bioprostheses also created elevated levels of turbulence, but they were confined to narrow regions in the bulk of the flow field. The newer generation of bioprostheses create turbulent shear stresses which are considerably lower than those created by the older generation tissue valve designs. All the aortic valves studied (mechanical and tissue) create turbulent shear stress levels which are capable of causing sub-lethal and/or lethal damage to blood elements.     

A reduced-order model for wall shear stress in abdominal aortic aneurysms by proper orthogonal decomposition

In this paper, we introduce a method to construct a Reduced-Order Model (ROM) to study the physiological flow and the Wall Shear Stress (WSS) conditions in Abdominal Aortic Aneurysms (AAA). We start the process by running a training case using Computational Fluid Dynamics (CFD) simulations with time-varying flow parameters, such that these parameters cover the range of parameters that we would like to consider in our ROM. We use the inflow angle as the variable parameter in the current study. Then we use the snapshot Proper Orthogonal Decomposition (POD) to construct the reduced-order bases, which are subsequently enhanced using a QR-factorization technique to satisfy the relevant fluid boundary conditions. The resulting ROM enables us to study the flow pattern and the WSS distribution over a range of system parameters computationally very efficiently. We have used this method to show how the WSS varies significantly for an AAA with a simplified geometry, over a range of inflow angles usually considered mild in clinical terms. We have validated the ROM results with CFD results. This approach enables comprehensive analysis of the model system across a range of inflow angles and frequencies without the need to re-compute the simulation for small changes.     

Experimental measurement of dynamic fluid shear stress on the aortic surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. Although exact causes and mechanisms of AV calcification are unclear, previous studies suggest that mechanical forces play a role. Since calcium deposits occur almost exclusively on the aortic surfaces of AV leaflets, it has been hypothesized that adverse patterns of fluid shear stress on the aortic surface of AV leaflets promote calcification. The current study characterizes AV leaflet aortic surface fluid shear stresses using Laser Doppler velocimetry and an in vitro pulsatile flow loop. The valve model used was a native porcine valve mounted on a suturing ring and preserved using 0.15% glutaraldehyde solution. This valve model was inserted in a mounting chamber with sinus geometries, which is made of clear acrylic to provide optical access for measurements. To understand the effects of hemodynamics on fluid shear stress, shear stress was measured across a range of conditions: varying stroke volumes at the same heart rate and varying heart rates at the same stroke volume. Systolic shear stress magnitude was found to be much higher than diastolic shear stress magnitude due to the stronger flow in the sinuses during systole, reaching up to 20 dyn/cm² at mid-systole. Upon increasing stroke volume, fluid shear stresses increased due to stronger sinus fluid motion. Upon increasing heart rate, fluid shear stresses decreased due to reduced systolic duration that restricted the formation of strong sinus flow. Significant changes in the shear stress waveform were observed at 90 beats/min, most likely due to altered leaflet dynamics at this higher heart rate. Overall, this study represents the most well-resolved shear stress measurements to date across a range of conditions on the aortic side of the AV. The data presented can be used for further investigation to understand AV biological response to shear stresses.     

A Eulerian method to analyze wall shear stress fixed points and manifolds in cardiovascular flows

Biomechanics and Modeling in Mechanobiology - Based upon dynamical systems theory, a fixed point of a vector field such as the wall shear stress (WSS) at the luminal surface of a vessel is a point...     

Experimental technique of measuring dynamic fluid shear stress on the aortic surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. The exact cause and mechanism of the progression of AV calcification is unknown, although mechanical forces have been known to play a role. It is thus important to characterize the mechanical environment of the AV. In the current study, we establish a methodology of measuring shear stresses experienced by the aortic surface of the AV leaflets using an in vitro valve model and adapting the laser Doppler velocimetry (LDV) technique. The valve model was constructed from a fresh porcine aortic valve, which was trimmed and sutured onto a plastic stented ring, and inserted into an idealized three-lobed sinus acrylic chamber. Valve leaflet location was measured by obtaining the location of highest back-scattered LDV laser light intensity. The technique of performing LDV measurements near to biological surfaces as well as the leaflet locating technique was first validated in two phantom flow systems: (1) steady flow within a straight tube with AV leaflet adhered to the wall, and (2) steady flow within the actual valve model. Dynamic shear stresses were then obtained by applying the techniques on the valve model in a physiologic pulsatile flow loop. Results show that aortic surface shear stresses are low during early systole (<5 dyn/cm2) but elevated to its peak during mid to late systole at about 18-20 dyn/cm2. Low magnitude shear stress (<5 dyn/cm2) was observed during early diastole and dissipated to zero over the diastolic duration. Systolic shear stress was observed to elevate only with the formation of sinus vortex flow. The presented technique can also be used on other in vitro valve models such as congenitally geometrically malformed valves, or to investigate effects of hemodynamics on valve shear stress. Shear stress data can be used for further experiments investigating effects of fluid shear stress on valve biology, for conditioning tissue engineered AV, and to validate numerical simulations.     

Unsteady wall shear stress in a distensible tube

An asymptotic expression of the wall shear stress (WSS) in an elastic tube is deduced for small values of the Womersley parameter. In the case of a rigid tube this asymptotic expression is shown to compare better with the exact solution than Poiseuille's or Lambossy's approximations. Its integration in a one-dimensional model of the internal carotid artery blood flow predicts more marked systolic and less marked diastolic WSS than those predicted by the commonly used Poiseuille's approximation.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part I--steady flow hemodynamics

Numerical predictions of blood flow patterns and hemodynamic stresses in Abdominal Aortic Aneurysms (AAAs) are performed in a two-aneurysm, axisymmetric, rigid wall model using the spectral element method. Homogeneous, Newtonian blood flow is simulated under steady conditions for the range of Reynolds numbers 10 < or =Re < or =2265. Flow hemodynamics are quantified by calculating the distributions of wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG). A correlation between maximum values of hemodynamic stresses and Reynolds number is established, and the spatial distribution of WSSG is considered as a hemodynamic force that may cause damage to the arterial wall at an intermediate stage of AAA growth. The temporal distribution of hemodynamic stresses in pulsatile flow and their physical implications in AAA rupture are discussed in Part II of this paper.     

Flow-induced wall shear stress in abdominal aortic aneurysms: Part II--pulsatile flow hemodynamics

In continuing the investigation of AAA hemodynamics, unsteady flow-induced stresses are presented for pulsatile blood flow through the double-aneurysm model described in Part I. Physiologically realistic aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50< or =Re(m) < or =300. Hemodynamic disturbance is evaluated for a modified set of indicator functions which include wall pressure (p(w)), wall shear stress (tau(w)), Wall Shear Stress Gradient (WSSG), time-average wall shear stress (tau(w)*), and time-average Wall Shear Stress Gradient WSSG*. At peak flow, the highest shear stress and WSSG levels are obtained at the distal end of both aneurysms, in a pattern similar to that of steady flow. The maximum values of wall shear stresses and wall shear stress gradients are evaluated as a function of the time-average Reynolds number resulting in a fourth order polynomial correlation. A comparison between numerical predictions for steady and pulsatile flow is presented, illustrating the importance of considering time-dependent flow for the evaluation of hemodynamic indicators.     

Aortic valve leaflet wall shear stress characterization revisited: impact of coronary flow

Computational characterizations of aortic valve hemodynamics have typically discarded the effects of coronary flow. The objective of this study was to complement our previous fluid–structure interaction aortic valve model with a physiologic coronary circulation model to quantify the impact of coronary flow on aortic sinus hemodynamics and leaflet wall shear stress (WSS). Coronary flow suppressed vortex development in the two coronary sinuses and altered WSS magnitude and directionality on the three leaflets, with the most substantial differences occurring in the belly and tip regions.     

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.     

A boundary layer model for wall shear stress in arterial stenosis

This paper proposes a model for wall shear stress in arterial stenosis based on boundary layer theory. Wall shear stress estimates are obtained by solving the momentum integral equation using the method proposed by Walz and applying this method to various stenosis geometries for Reynolds numbers (Re) of Re = 59-1000. Elevated wall shear stress may be of importance when considering thrombosis and vascular erosion in stenosis, as well as the potential for debris from the stenotic area to 'break away' and cause further pathology. The values of shear stress obtained using the model in this study agree well with published values of wall shear stress. When compared to a previously published boundary layer model utilizing the Thwaites method (Reese and Thompson, 1998), the model proposed herein performs better at higher Re while the model utilizing the Thwaites method performs better at lower Re. Wall shear stresses are shown to increase with increasing stenosis (increased area reduction) for a given stenosis length, increase with increasing Re for a given stenosis geometry, and increase for steeper stenosis of the same constriction. The boundary layer model proposed can be easily implemented by clinical researchers to provide in vivo estimates of wall shear stress through arterial stenoses.     

Experimental measurement of dynamic fluid shear stress on the ventricular surface of the aortic valve leaflet

Aortic valve (AV) calcification is a highly prevalent disease with serious impact on mortality and morbidity. The exact causes and mechanisms of AV calcification are unclear, although previous studies suggest that mechanical forces play a role. It has been clinically demonstrated that calcification preferentially occurs on the aortic surface of the AV. This is hypothesized to be due to differences in the mechanical environments on the two sides of the valve. It is thus necessary to characterize fluid shear forces acting on both sides of the leaflet to test this hypothesis. The current study is one of two studies characterizing dynamic shear stress on both sides of the AV leaflets. In the current study, shear stresses on the ventricular surface of the AV leaflets were measured experimentally on two prosthetic AV models with transparent leaflets in an in vitro pulsatile flow loop using two-component Laser Doppler Velocimetry (LDV). Experimental measurements were utilized to validate a theoretical model of AV ventricular surface shear stress based on the Womersley profile in a straight tube, with corrections for the opening angle of the valve leaflets. This theoretical model was applied to in vivo data based on MRI-derived volumetric flow rates and valve dimension obtained from the literature. Experimental results showed that ventricular surface shear stress was dominated by the streamwise component. The systolic shear stress waveform resembled a half-sinusoid during systole and peaks at 64–71 dyn/cm², and reversed in direction at the end of systole for 15–25?ms, and reached a significant negative magnitude of 40–51 dyn/cm². Shear stresses from the theoretical model applied to in vivo data showed that shear stresses peaked at 77–92 dyn/cm² and reversed in direction for substantial period of time (108–110?ms) during late systole with peak negative shear stress of 35–38 dyn/cm².     

颈动脉血管壁切应力的分析

动脉中管壁的脉动低切应力在动脉粥样硬化形成中起始动和主要的决定作用。本文比较了几种计算血管壁切应力的方法,认为采用有约束的弹性管模型计算获得的动脉壁切应力更适合于临床应用。根据检测得到的正常人和动脉硬化性脑血管病患者的颈动脉血流速度、血管管径等数据,计算两者的颈动脉壁面切应力。研究发现动脉硬化性脑血管病患者的壁面切应力比正常人显著减小。这表明,颈动脉的壁面切应力可以作为动脉硬化性脑血管疾病的早期诊断的重要参考指标。