Wave intensity in the ascending aorta: effects of arterial occlusion

We examine the effects of arterial occlusion on the pressure, velocity and the reflected waves in the ascending aorta using wave intensity analysis. In 11 anaesthetised, open-chested dogs, snares were used to produce total arterial occlusion at 4 sites: the upper descending aorta at the level of the aortic valve (thoracic); the lower thoracic aorta at the level of the diaphragm (diaphragm); the abdominal aorta between the renal arteries (abdominal) and the left iliac artery, 2 cm downstream from the aorta iliac bifurcation (iliac). Pressure and flow in the ascending aorta were measured, and data were collected before and during the occlusion. During thoracic and diaphragm occlusions a significant increase in mean aortic pressure (46% and 23%) and in wave speed (25% and 10%) was observed, while mean flow rate decreased significantly (23% and 17%). Also, the reflected compression wave arrived significantly earlier (45% and 15%) and its peak intensity was significantly greater (257% and 125%), all compared with control. Aortic occlusion distal to the renal arteries, however, caused an indiscernible change in the pressure and velocity waveforms, and in the intensities and timing of the waves in the forward and backward directions. The measured pressure and velocity waveforms are the result of the interaction between the heart and the arterial system. The separated pressure, velocity and wave intensity are required to provide information about arterial hemodynamic such as the timing and magnitude of the forward and backward waves. The net wave intensity is simpler to calculate but provides information only about the predominant direction of the waves and can be misleading when forward and backward waves of comparable magnitudes are present simultaneously.     

Numerical study on the effect of secondary flow in the human aorta on local shear stresses in abdominal aortic branches

Flow in the aortic arch is characterized primarily by the presence of a strong secondary flow superimposed over the axial flow, skewed axial velocity profiles and diastolic flow reversals. A significant amount of helical flow has also been observed in the descending aorta of humans and in models. In this study a computational model of the abdominal aorta complete with two sets of outflow arteries was adapted for three-dimensional steady flow simulations. The flow through the model was predicted using the Navier-Stokes equations to study the effect that a rotational component of flow has on the general flow dynamics in this vascular segment. The helical velocity profile introduced at the inlet was developed from magnetic resonance velocity mappings taken from a plane transaxial to the aortic arch. Results showed that flow division ratios increased in the first set of branches and decreased in the second set with the addition of rotational flow. Shear stress varied in magnitude with the addition of rotational flow, but the shear stress distribution did not change. No regions of flow separation were observed in the iliac arteries for either case. Helical flow may have a stabilizing effect on the flow patterns in branches in general, as evidenced by the decreased difference in shear stress between the inner and outer walls in the iliac arteries.     

Unsteady and three-dimensional simulation of blood flow in the human aortic arch

A three-dimensional and pulsatile blood flow in a human aortic arch and its three major branches has been studied numerically for a peak Reynolds number of 2500 and a frequency (or Womersley) parameter of 10. The simulation geometry was derived from the three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo using CAT scan imaging on a human aorta. The numerical simulations were obtained using a projection method, and a finite-volume formulation of the Navier-Stokes equations was used on a system of overset grids. Our results demonstrate that the primary flow velocity is skewed towards the inner aortic wall in the ascending aorta, but this skewness shifts to the outer wall in the descending thoracic aorta. Within the arch branches, the flow velocities were skewed to the distal walls with flow reversal along the proximal walls. Extensive secondary flow motion was observed in the aorta, and the structure of these secondary flows was influenced considerably by the presence of the branches. Within the aorta, wall shear stresses were highly dynamic, but were generally high along the outer wall in the vicinity of the branches and low along the inner wall, particularly in the descending thoracic aorta. Within the branches, the shear stresses were considerably higher along the distal walls than along the proximal walls. Wall pressure was low along the inner aortic wall and high around the branches and along the outer wall in the ascending thoracic aorta. Comparison of our numerical results with the localization of early atherosclerotic lesions broadly suggests preferential development of these lesions in regions of extrema (either maxima or minima) in wall shear stress and pressure.     

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.     

Experimental investigation of steady flow through a model of the human aortic arch

Steady flow through a model of the human aortic arch has been studied with hot-film anemometry. A three sensor hot-film velocity probe was inserted into an acrylic flow chamber fabricated from the in situ casting of a human aorta, and the axial, radial and tangential velocity profiles were determined for steady flows in the region of the aortic arch. These studies demonstrated the presence of a potential core throughout the arch region, with a concomitant boundary layer adjacent to the inner wall of curvature of the arch. Trapped secondary flows in this fluid layer along the inner wall were quantitatively determined. Our steady flow studies in the model human aortic arch suggests that a shear-dependent mass transfer mechanism may play a significant role in the development and propagation of atherosclerotic lesions in this segment of the human cardiovascular system.     

Some flow visualization and laser-Doppler-velocity measurements in a true-to-scale elastic model of a human aortic arch--a new model technique.

Flow studies were done in an elastic true-to-scale silicone rubber model of an aortic arch to study further hemodynamic influences on atherosclerosis. The model was prepared from a cast of a young woman. A revised model technique was used. The model had a compliance similar to that of the human aortic arch. Velocity measurements were done in the model with a two component laser-Doppler-anemometer in steady and pulsatile flow using a calcium chloride solution with a viscosity of eta = 3.18 mPas and density of rho = 1.28 kg/m3 at 20 degrees C. The time average Reynolds numbers over a whole cycle in the ascending aorta was Re = 1350. The Womersley parameter for pulsatile flow was a = 20. The pulse wave velocity in the ascending aorta was about c = 5.4 m/sec. The secondary flow behavior was discussed for steady and pulsatile flow. Reverse flows were found, especially along the inner radius of the aortic arch in the descending aorta in steady and pulsatile flow and also in small areas of the ascending aorta and at the branches of the aortic arch. The formation of atherosclerotic plaques at preferred local flow regions is discussed.     

Measurement of wall shear stress distal to a tri-leaflet valve in a rigid model of the aortic arch with branch flows

Flush mounted hot film anemometer probes were used to measure wall shear stress magnitudes on the inside and outside walls of a rigid model of the human aortic arch. The effects of the presence of an Ionescu-Shiley tri-leaflet bioprosthetic heart valve at the entrance of the aortic arch and the side flows through arteries located in the mid-arch region on wall shear stress magnitudes were determined. It was found that the presence of the tri-leaflet valve leads to an elevation of wall shear stress (relative to the same flow without a valve) over the entire aortic arch region by as much as 50 percent. The valve influence extended to about 180 deg from the entrance to the aorta on the inside wall and even further on the outside wall based on extrapolation of available data. Peak wall shear stress magnitudes measured on the outside wall were in the range of 1.5-4.0 N/m2 (15-40 dynes/cm2) over the length of the aortic arch and took on their highest values in the mid-arch region. Inside wall values were of comparable magnitude. It was observed that the presence of the aortic valve and side flow from the top of the aortic arch reduced wall shear stress reversal in the arch region.     

Experimental study of physiological pulsatile flow past valve prosthesis in a model of human aorta--II. Tilting disc valves and the effect of orientation

In Part II of this two paper sequence, pulsatile flow development past a tilting disc valve in a model human aorta has been studied using quantitative laser Doppler techniques. The valve was mounted in three different orientations with respect to the aortic root in this study. Under pulsatile flow, the region of flow reversal induced near the wall of the minor flow orifice extends to more than one tissue annulus diameter downstream from the valve into the ascending aorta. In a plane perpendicular to the tilt axis, a bi-helical secondary flow is induced distal to the valve. This secondary flow is further compounded by the multiple curvatures in the aorta. Hence the valve orientation affects the velocity profiles as far downstream as the mid-arch region as well as in the brachio-cephalic arterial branch. In the mid-arch region, a flow reversal along the entire cross-section is observed in early diastole for all the three orientations of the disc valve.     

Topographical mapping of sites of enhanced HRP permeability in the normal rabbit aorta.

The spatial distribution of sites of enhanced permeability to the macromolecule horseradish peroxidase (HRP) in the normal rabbit aorta after one min circulation was studied using image analysis. These sites, referred to as "HRP spots," exhibit a nonuniform distribution that is qualitatively similar in all rabbits studied. The density of HRP spots is highest in the aortic arch, decreases distally, reaches a minimum in the lower descending thoracic aorta, and then increases again in the abdominal aorta. The region of highest spot density follows a clockwise helical pattern in the aortic arch and outside the arch occurs in streaks largely oriented in the bulk flow direction. The streaks in the abdominal aorta localize along the anatomical right lateral wall and occasionally along the left lateral wall proximal to the celiac artery and along the ventral wall between the celiac and superior mesenteric arteries. The density of spots is high in the immediate vicinity of aortic ostia with the most elevated density being distal to ostia in most cases. At a short distance from the ostium edge of the celiac and superior mesenteric branches the proximal density is comparably high, and no preferred spot orientation is observed around the brachiocephalic vessel. These results are consistent with an influence of localizing factors such as detailed hemodynamic phenomena and/or arterial wall structural and/or functional variations.     

Experimental study of physiological pulsatile flow past valve prostheses in a model of human aorta--I. Caged ball valves

Pulsatile flow development past a caged ball valve in a model human aorta was studied using laser Doppler anemometry. Velocity profiles measured in the ascending aorta and in the mid-arch region were strongly influenced by the geometry of the valve at the root of the aorta. Velocity profiles distal to the valve were asymmetric with jet-like flow in the peripheral region having larger velocity magnitudes towards the left lateral wall. In early diastole, a streamwise vortex motion was observed throughout the model aorta with fluid moving towards the downstream direction along the left lateral wall and reversed flow along the right lateral wall. With the caged ball valve at the root of the aorta, no reversed flow was observed along the inner wall of curvature in the mid-arch region.     

Development of wall surface tangent DPIV measurement techniques for arterial branch models.

Experimental techniques for measuring unsteady flow in a glass arterial bifurcation model have been developed to aid in quantifying three-dimensional wall shear fluctuations associated with arterial disease. The unique feature of the current technique is the use of a "curved" laser sheet, which was everywhere tangent to the inner wall of a daughter tube in an arterial bifurcation model. Surface tangent velocity vector field measurements were made to demonstrate the potential of this technique. Ensemble-averaged data showing weak secondary flows as well as statistical distributions of flow angles are presented. Measurements of this type may be used to estimate mean and instantaneous wall shear magnitude and direction, data that are necessary for understanding the importance of circumferential motions on arterial disease.     

Nontraumatic aortic blood flow sensing by use of an ultrasonic esophageal probe.

The measurement of blood velocity fields, volume flow, and arterial wall motion in the descending thoracic aorta provides essential hemodynamic information for both research and clinical diagnosis. The close proximity of the esophagus to the aorta in the dog makes it possible to obtain such data nonsurgically using an ultrasonic esophageal probe; however, the accuracy of such a probe is limited if the angle between the sound beam and the flow axis, known as the Doppler angle, is not precisely known. By use of a pulsed Doppler velocity meter (PUDVM) and a triangulation procedure, accurate empirical measurement of the Doppler angle has been obtained, allowing quantification of blood velocity scans across the aorta. Volume flow is obtained by integration of blood velocity profiles and arterial wall motion is measured with an ultrasonic echo tracking device. Accuracy of the probe was substantiated by comparison with ultrasonic and electromagnetic implanted flow cuff measurements. Use of the probe in measurement of blood velocity, volume flow and arterial wall motion at various locations along the 8- and 10-cm length of the descending thoracic aorta in adult beagle dogs is detailed. The simplicity, accuracy, and nontraumatic aspect of the technique should allow increasing use of such a probe in numerous research and clinical applications.     

Comparison of hinge microflow fields of bileaflet mechanical heart valves implanted in different sinus shape and downstream geometry

The characterization of the bileaflet mechanical heart valves (BMHVs) hinge microflow fields is a crucial step in heart valve engineering. Earlier in vitro studies of BMHV hinge flow at the aorta position in idealized straight pipes have shown that the aortic sinus shapes and sizes may have a direct impact on hinge microflow fields. In this paper, we used a numerical study to look at how different aortic sinus shapes, the downstream aortic arch geometry, and the location of the hinge recess can influence the flow fields in the hinge regions. Two geometric models for sinus were investigated: a simplified axisymmetric sinus and an idealized three-sinus aortic root model, with two different downstream geometries: a straight pipe and a simplified curved aortic arch. The flow fields of a 29-mm St Jude Medical BMHV with its four hinges were investigated. The simulations were performed throughout the entire cardiac cycle. At peak systole, recirculating flows were observed in curved downsteam aortic arch unlike in straight downstream pipe. Highly complex three-dimensional leakage flow through the hinge gap was observed in the simulation results during early diastole with the highest velocity at 4.7 m/s, whose intensity decreased toward late diastole. Also, elevated wall shear stresses were observed in the ventricular regions of the hinge recess with the highest recorded at 1.65 kPa. Different flow patterns were observed between the hinge regions in straight pipe and curved aortic arch models. We compared the four hinge regions at peak systole in an aortic arch downstream model and found that each individual hinge did not vary much in terms of the leakage flow rate through the valves.     

Descending aorta subject-specific one-dimensional model validated against in vivo data

The aorta plays a major role in the cardiovascular system and its function and structure are primarily affected by aging, eating habits, life style and other cardiovascular risk factors, inducing increased stiffness which is associated with cardiovascular and cerebral morbi-mortality. Our objective was to develop and validate a robust subject-specific one-dimensional wave propagation numerical model of the descending aorta. This model with a cross-sectional area, velocity and pressure formulation is built using geometric and hemodynamic data measured on a specific person and is validated against in vivo data acquired on the same subject at three distinct anatomical locations along the thoracic aorta. We studied seven healthy volunteers, who underwent carotid applanation tonometry and aortic cardiovascular magnetic resonance (CMR). Responses of our model in terms of changes in central pressure waveform with arterial alterations were consistent with previously described physiological knowledge. Quantitative validation averaged over the three descending aortic locations and the seven subjects provided low rms errors (given in percentage of the maximal clinical value) between simulated and CMR data, i.e. area: 10±6%, velocity: 11±3%, flow rate: 9±3%. Finally, we also found low rms (5±2%) when comparing simulated pressure in the proximal aortic location against tonometric carotid pressure curves. In conclusion, this simple model performs similar to more complex models of the entire systemic arterial tree at a fraction of the cost, and could be of major usefulness in the non-invasive and local estimation of proximal biomechanical and hemodynamic indices.     

Systolic fluid–structure interaction model of the congenitally bicuspid aortic valve: assessment of modelling requirements

A transient fluid–structure interaction (FSI) model of a congenitally bicuspid aortic valve has been developed which allows simultaneous calculation of fluid flow and structural deformation. The valve is modelled during the systolic phase (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the bicuspid aortic valve in two dimensions. A congenital bicuspid valve is compared within the aortic root only and within the aortic arch. Symmetric and asymmetric cusps were simulated, along with differences in mechanical properties. A moving arbitrary Lagrange–Euler mesh was used to allow FSI. The FSI model requires blood flow to induce valve opening and induced strains in the region of 10%. It was determined that bicuspid aortic valve simulations required the inclusion of the ascending aorta and aortic arch. The flow patterns developed were sensitive to cusp asymmetry and differences in mechanical properties. Stiffening of the valve amplified peak velocities, and recirculation which developed in the ascending aorta. Model predictions demonstrate the need to take into account the category, including any existing cusp asymmetry, of a congenital bicuspid aortic valve when simulating its fluid flow and mechanics.     

Pressure and flow in the systemic arterial system

The dynamic characteristics of the proximal arterial system are studied by solving the nonlinear momentum and mass conservation equations for pressure and flow. The equations are solved for a model systemic arterial system that includes the aorta, common iliacs, and the internal and external iliac arteries. The model includes geometric and elastic taper of the aorta, nonlinearly elastic arteries, side flows, and a complex distal impedance. The model pressure wave shape, inlet and outlet impedance, wave travel, and apparent wave velocity compare favorably with the values measured on humans. Calculations indicate that: (i) reflections are the major factor determining the shape and distal amplification of the pressure wave in the arterial tree; (ii) although important in attenuating the proximal transmission of reflecting waves, geometric taper is not the major cause of the distal pressure wave amplification; (iii) the dicrotic wave is a result of peripheral reflection and is not due to the sudden change in flow at the end of systole; (iv) the elastic taper and nonlinearity of the wall elasticity are of minor significance in determining the flow and pressure profiles; and (v) in spite of numerous nonlinearities, the system behaves in a somewhat linear fashion for the lower frequency components.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.     

Instantaneous blood flow, impedance and elastic properties computed in man from aortic pulse waves

A mathematical model of the pressure-flow relationship in the arterial circulation and its possible use in routine hemodynamics in man are described. The instantaneous blood flow velocity in the ascending aorta can be calculated from two pressure curves simultaneously recorded 5 cm apart. The mechanical aortic input impedance is computed from the recorded pressure and the calculated blood flow velocity curves. Projection of the pulse waves on a time-length plane leads to the determination of the pulse wave velocity and then an estimation of the elastic modulus of the aortic wall.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.