Fluid-structure interaction modeling of aneurysmal arteries under steady-state and pulsatile blood flow: a stability analysis

Tortuous aneurysmal arteries are often associated with a higher risk of rupture but the mechanism remains unclear. The goal of this study was to analyze the buckling and post-buckling behaviors of aneurysmal arteries under pulsatile flow. To accomplish this goal, we analyzed the buckling behavior of model carotid and abdominal aorta with aneurysms by utilizing fluid-structure interaction (FSI) method with realistic waveforms boundary conditions. FSI simulations were done under steady-state and pulsatile flow for normal (1.5) and reduced (1.3) axial stretch ratios to investigate the influence of aneurysm, pulsatile lumen pressure and axial tension on stability. Our results indicated that aneurysmal artery buckled at the critical buckling pressure and its deflection nonlinearly increased with increasing lumen pressure. Buckling elevates the peak stress (up to 118%). The maximum aneurysm wall stress at pulsatile FSI flow was (29%) higher than under static pressure at the peak lumen pressure of 130 mmHg. Buckling results show an increase in lumen shear stress at the inner side of the maximum deflection. Vortex flow was dramatically enlarged with increasing lumen pressure and artery diameter. Aneurysmal arteries are more susceptible than normal arteries to mechanical instability which causes high stresses in the aneurysm wall that could lead to aneurysm rupture.     

Hemodynamic stress in lateral saccular aneurysms

The flow velocities in glass and silastic lateral aneurysm models were quantitatively measured with the non-invasive laser Doppler method. The influences of the elasticity of the wall, the pulse wave and the properties of the perfusion medium on the intra-aneurysmal circulation were investigated. As shown previously, the inflow into the aneurysm arose from the downstream lip and was directed toward the center of the fundus. Backflow to the parent vessel took place along the walls of the fundus. With non-pulsatile perfusion, flow velocities in the center of the standardized aneurysms varied between 0.4 and 2% of the maximum velocity in the parent vessel. With pulsatile perfusion, flow velocities in the center of the fundus ranged between 8 and 13% of the flow velocity in the axis of the parent vessel. Flow velocities in the aneurysms were slower with a polymer suspension with blood-like properties compared to a glycerol/water solution. Flow velocity measurements near the aneurysmal wall allowed the estimation of the shear stresses at critical locations. The maximum shear stresses at the downstream lip of the aneurysm were in the range of the stresses measured at the flow divider of an arterial bifurcation. The present results suggest that in human saccular aneurysms intra-aneurysmal flow and shear stress on the wall are directly related to the pulsatility of perfusion, i.e. the systolic/diastolic pressure difference and that the tendency to spontaneous thrombosis depends on the viscoelastic properties of the blood, namely the hematocrit.     

PIV-measured versus CFD-predicted flow dynamics in anatomically realistic cerebral aneurysm models

Computational fluid dynamics (CFD) modeling of nominally patient-specific cerebral aneurysms is increasingly being used as a research tool to further understand the development, prognosis, and treatment of brain aneurysms. We have previously developed virtual angiography to indirectly validate CFD-predicted gross flow dynamics against the routinely acquired digital subtraction angiograms. Toward a more direct validation, here we compare detailed, CFD-predicted velocity fields against those measured using particle imaging velocimetry (PIV). Two anatomically realistic flow-through phantoms, one a giant internal carotid artery (ICA) aneurysm and the other a basilar artery (BA) tip aneurysm, were constructed of a clear silicone elastomer. The phantoms were placed within a computer-controlled flow loop, programed with representative flow rate waveforms. PIV images were collected on several anterior-posterior (AP) and lateral (LAT) planes. CFD simulations were then carried out using a well-validated, in-house solver, based on micro-CT reconstructions of the geometries of the flow-through phantoms and inlet/outlet boundary conditions derived from flow rates measured during the PIV experiments. PIV and CFD results from the central AP plane of the ICA aneurysm showed a large stable vortex throughout the cardiac cycle. Complex vortex dynamics, captured by PIV and CFD, persisted throughout the cardiac cycle on the central LAT plane. Velocity vector fields showed good overall agreement. For the BA, aneurysm agreement was more compelling, with both PIV and CFD similarly resolving the dynamics of counter-rotating vortices on both AP and LAT planes. Despite the imposition of periodic flow boundary conditions for the CFD simulations, cycle-to-cycle fluctuations were evident in the BA aneurysm simulations, which agreed well, in terms of both amplitudes and spatial distributions, with cycle-to-cycle fluctuations measured by PIV in the same geometry. The overall good agreement between PIV and CFD suggests that CFD can reliably predict the details of the intra-aneurysmal flow dynamics observed in anatomically realistic in vitro models. Nevertheless, given the various modeling assumptions, this does not prove that they are mimicking the actual in vivo hemodynamics, and so validations against in vivo data are encouraged whenever possible.     

Mechanical instability of normal and aneurysmal arteries

Tortuous arteries associated with aneurysms have been observed in aged patients with atherosclerosis and hypertension. However, the underlying mechanism is poorly understood. The objective of this study was to determine the effect of aneurysms on arterial buckling instability and the effect of buckling on aneurysm wall stress. We investigated the mechanical buckling and post-buckling behavior of normal and aneurysmal carotid arteries and aorta’s using computational simulations and experimental measurements to elucidate the interrelationship between artery buckling and aneurysms. Buckling tests were done in porcine carotid arteries with small aneurysms created using elastase treatment. Parametric studies were done for model aneurysms with orthotropic nonlinear elastic walls using finite element simulations. Our results demonstrated that arteries buckled at a critical buckling pressure and the post-buckling deflection increased nonlinearly with increasing pressure. The presence of an aneurysm can reduce the critical buckling pressure of arteries, although the effect depends on the aneurysm’s dimensions. Buckled aneurysms demonstrated a higher peak wall stress compared to unbuckled aneurysms under the same lumen pressure. We conclude that aneurysmal arteries are vulnerable to mechanical buckling and mechanical buckling could lead to high stresses in the aneurysm wall. Buckling could be a possible mechanism for the development of tortuous aneurysmal arteries such as in the Loeys–Dietz syndrome.     

Blood flow dynamics in saccular aneurysm models of the basilar artery

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture, and surgical treatment of intracranial aneurysms. The temporal and spatial variations of wall pressure and wall shear stress in the aneurysm are hypothesized to be correlated with its continuous expansion and eventual rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This paper describes the flow dynamics in two representative models of a terminal aneurysm of the basilar artery under Newtonian and non-Newtonian fluid assumptions, and compares their hemodynamics with that of a healthy basilar artery. Virtual aneurysm models are investigated numerically, with geometric features defined by beta = 0 deg and beta = 23.2 deg, where beta is the tilt angle of the aneurysm dome with respect to the basilar artery. The intra-aneurysmal pulsatile flow shows complex ring vortex structures for beta = 0 deg and single recirculation regions for beta = 23.2 deg during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations for both models. When compared to a non-Newtonian fluid, the symmetric aneurysm model (beta = 0 deg) exhibits a more unstable Newtonian flow dynamics, although with a lower peak wall shear stress than the asymmetric model (beta = 23.2 deg). The non-Newtonian fluid assumption yields more stable flows than a Newtonian fluid, for the same inlet flow rate. Both fluid modeling assumptions, however, lead to asymmetric oscillatory flows inside the aneurysm dome.     

Validation of CFD simulations of cerebral aneurysms with implication of geometric variations

BACKGROUND: Computational fluid dynamics (CFD) simulations using medical-image-based anatomical vascular geometry are now gaining clinical relevance. This study aimed at validating the CFD methodology for studying cerebral aneurysms by using particle image velocimetry (PIV) measurements, with a focus on the effects of small geometric variations in aneurysm models on the flow dynamics obtained with CFD. METHOD OF APPROACH: An experimental phantom was fabricated out of silicone elastomer to best mimic a spherical aneurysm model. PIV measurements were obtained from the phantom and compared with the CFD results from an ideal spherical aneurysm model (S1). These measurements were also compared with CFD results, based on the geometry reconstructed from three-dimensional images of the experimental phantom. We further performed CFD analysis on two geometric variations, S2 and S3, of the phantom to investigate the effects of small geometric variations on the aneurysmal flow field. Results. We found poor agreement between the CFD results from the ideal spherical aneurysm model and the PIV measurements from the phantom, including inconsistent secondary flow patterns. The CFD results based on the actual phantom geometry, however, matched well with the PIV measurements. CFD of models S2 and S3 produced qualitatively similar flow fields to that of the phantom but quantitatively significant changes in key hemodynamic parameters such as vorticity, positive circulation, and wall shear stress. CONCLUSION: CFD simulation results can closely match experimental measurements as long as both are performed on the same model geometry. Small geometric variations on the aneurysm model can significantly alter the flow-field and key hemodynamic parameters. Since medical images are subjected to geometric uncertainties, image-based patient-specific CFD results must be carefully scrutinized before providing clinical feedback.     

NO在实验性大鼠颈动脉瘤发展中的作用

目的建立一种新的颈动脉动脉瘤模型,观察iNOS在实验性动脉瘤组织局部的表达情况和选择性iNOS抑制剂氨基胍对动脉瘤增大和对血清NO水平的影响。方法50只SD大鼠随机分为3组,应用弹性蛋白酶灌注颈总动脉建立颈动脉梭形动脉瘤模型。A组给予氨基胍干预;B组给予生理盐水;C组为阴性对照。测量颈总动脉直径和血清硝酸盐含量。应用HE、免疫组化和原位杂交评价动脉瘤的病理特征和iNOS的局部表达特点。结果选择性iNOS抑制剂可以明显抑制动脉瘤增大的程度和血清硝酸盐水平。诱导的动脉瘤病理特征和外形与人动脉瘤组织相似,主要表现为动脉瘤壁明显增厚,内弹力膜和弹性膜全部消失,平滑肌细胞层变薄和消失。中膜和外膜管壁大量的炎症细胞浸润,氨基胍明显抑制iNOS的表达。结论应用弹性蛋白酶灌注颈动脉可以在大鼠诱导出梭形动脉瘤。动脉瘤的增大与局部升高的NO有关。     

Pulmonary vascular impedance and wave reflections in the hypoxic calf.

The alterations in pulsatile hemodynamics that occur during hypoxic pulmonary vasoconstriction have not been well characterized. Changes in oscillatory hemodynamics, however, may affect right ventricular-pulmonary vascular coupling and the dissipation of energy within the lung vasculature. To better define hypoxic pulsatile hemodynamics, we measured main pulmonary artery proximal and distal micromanometric pressures and ultrasonic flow in four open-chest calves during progressive hypoxia. Main pulmonary artery impedance and pressure transmission spectra were calculated using spectral analysis methods. Measured pressure and flow signals were separated in the time domain into forward and backward components. Hypoxia increased pulmonary blood pressure and resistance and produced multiple modifications in the impedance and pressure transmission spectra that indicated increased wave reflections and elasticity. The impedance and apparent phase velocity first-harmonic values were increased in amplitude, and the pressure transmission modulus plot showed an increased peak value. In addition, the impedance modulus plot demonstrated a rightward shift and increased oscillation in the mid- to high-frequency range. The time domain analysis also confirmed increased wave reflections and elasticity. Hypoxia produced large backward-traveling (reflected) pressure and flow waves. The initial portions of these waves arrived at the heart during systole, producing characteristic changes in the measured pressure and flow waveforms. With prolonged hypoxia, main pulmonary artery pulse wave velocity increased by 30%. Thus, hypoxia is associated with complex alterations in pulmonary artery elasticity and wave reflections that act to increase the oscillatory afterload of the right ventricle.     

Modelling evolution and the evolving mechanical environment of saccular cerebral aneurysms

A fluid–solid-growth (FSG) model of saccular cerebral aneurysm evolution is developed. It utilises a realistic two-layered structural model of the internal carotid artery and explicitly accounts for the degradation of the elastinous constituents and growth and remodelling (G&R) of the collagen fabric. Aneurysm inception is prescribed: a localised degradation of elastin results in a perturbation in the arterial geometry; the collagen fabric adapts, and the artery achieves a new homeostatic configuration. The perturbation to the geometry creates an altered haemodynamic environment. Subsequent degradation of elastin is explicitly linked to low wall shear stress (WSS) in a confined region of the arterial domain. A sidewall saccular aneurysm develops, the collagen fabric adapts and the aneurysm stabilises in size. A quasi-static analysis is performed to determine the geometry at diastolic pressure. This enables the cyclic stretching of the tissue to be quantified, and we propose a novel index to quantify the degree of biaxial stretching of the tissue. Whilst growth is linked to low WSS from a steady (systolic) flow analysis, a pulsatile flow analysis is performed to compare steady and pulsatile flow parameters during evolution. This model illustrates the evolving mechanical environment for an idealised saccular cerebral aneurysm developing on a cylindrical parent artery and provides the guidance to more sophisticated FSG models of aneurysm evolution which link G&R to the local mechanical stimuli of vascular cells.     

Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm

In experiments turbulence has previously been shown to occur in intracranial aneurysms. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulation in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, before relaminarization occurred during diastole. The turbulent structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5Pa. The recorded frequencies were predominantly in the range of 1-500Hz. The current study confirms, through properly resolved CFD simulations that turbulence can occur in intracranial aneurysms.     

The effect of asymmetry in abdominal aortic aneurysms under physiologically realistic pulsatile flow conditions

In the abdominal segment of the human aorta under a patient's average resting conditions, pulsatile blood flow exhibits complex laminar patterns with secondary flows induced by adjacent branches and irregular vessel geometries. The flow dynamics becomes more complex when there is a pathological condition that causes changes in the normal structural composition of the vessel wall, for example, in the presence of an aneurysm. This work examines the hemodynamics of pulsatile blood flow in hypothetical three-dimensional models of abdominal aortic aneurysms (AAAs). Numerical predictions of blood flow patterns and hemodynamic stresses in AAAs are performed in single-aneurysm, asymmetric, rigid wall models using the finite element method. We characterize pulsatile flow dynamics in AAAs for average resting conditions by means of identifying regions of disturbed flow and quantifying the disturbance by evaluating flow-induced stresses at the aneurysm wall, specifically wall pressure and wall shear stress. Physiologically realistic abdominal aortic blood flow is simulated under pulsatile conditions for the range of time-average Reynolds numbers 50 < or = Rem < or = 300, corresponding to a range of peak Reynolds numbers 262.5 < or = Repeak < or = 1575. The vortex dynamics induced by pulsatile flow in AAAs is depicted by a sequence of four different flow phases in one period of the cardiac pulse. Peak wall shear stress and peak wall pressure are reported as a function of the time-average Reynolds number and aneurysm asymmetry. The effect of asymmetry in hypothetically shaped AAAs is to increase the maximum wall shear stress at peak flow and to induce the appearance of secondary flows in late diastole.     

In vitro evaluation of flow divertors in an elastase-induced saccular aneurysm model in rabbit

Endovascular coiling is an acceptable treatment of intracranial aneurysms, yet long term follow-ups suggest that endovascular coiling fails to achieve complete aneurysm occlusions particularly in wide-neck and giant aneurysms. Placing of a stentlike device across the aneurysm neck may be sufficient to occlude the aneurysm by promoting intra-aneurysmal thrombosis; however, conclusive evidence of its efficacy is still lacking. In this study, we investigate in vitro the efficacy of custom designed flow divertors that will be subsequently implanted in a large cohort of animals. The aim of this study is to provide a detailed database against which in vivo results can be analyzed. Six custom designed flow divertors were fabricated and tested in vitro. The design matrix included three different porosities (75%, 70%, and 65%). For each porosity, there were two divertors with one having a nominal pore density double than that of the other. To quantify efficacy, the divertors were implanted in a compliant elastomeric model of an elastase-induced aneurysm model in rabbit and intra-aneurysmal flow changes were evaluated by particle image velocimetry (PIV). PIV results indicate a marked reduction in intra-aneurysmal flow activity after divertor implantation in the innominate artery across the aneurysm neck. The mean hydrodynamic circulation after divertor implantation was reduced to 14% or less of the mean circulation in the control and the mean intra-aneurysmal kinetic energy was reduced to 29% or less of its value in the control. The intra-aneurysmal wall shear rate in this model is low and implantation of the flow divertor did not change the wall shear rate magnitude appreciably. This in vitro experiment evaluates the characteristics of local flow phenomena such as hydrodynamic circulation, kinetic energy, wall shear rate, perforator flow, and changes of these parameters as a result of implantation of stentlike flow divertors in an elastomeric replica of elastase-induced saccular aneurysm model in rabbit. These initial findings offer a database for evaluation of in vivo implantations of such devices in the animal model and help in further development of cerebral aneurysm bypass devices.     

The Influence of Drag on Nonlinear Oscillatory Flow through Concentric Annulus

A mathematical model has been developed to study the effect of particle drag parameter and frequency parameter on velocity and pressure gradient in nonlinear oscillatory two phase flow. The main purpose is to apply the model to study the combined effect of introduction of the catheter and elastic properties of the arterial wall on the pulsatile nature of the blood flow. We model the artery as an isotropic thin walled elastic tube and the catheter as a coaxial flexible tube. Blood is modeled as an incompressible particulate viscous Newtonian fluid. Perturbation technique has been applied to find the approximations for velocity and pressure gradient up to second order. Numerical solutions are investigated with graphical presentations to understand the effects of drag parameter, frequency parameter and phase angle on velocity along radial direction and pressure gradient along axial directions. As the drag parameter increases, mean pressure gradient and mean velocity will be decreased. As frequency parameter increases mean velocity profile bends near the outer wall. Due to elastic nature of artery wall, a thin catheter experience small oscillations and a thick catheter remains stationary inside the artery. Finally, the effect of catheterization on various physiologically important flow rate characteristics—mean velocity, mean pressure gradient are studied for a range of different catheter sizes, particle drag parameter and frequency parameters.     

A decoupled fluid structure approach for estimating wall stress in abdominal aortic aneurysms

Abdominal aortic aneurysm (AAA) is a localized dilatation of the aortic wall. The lack of an accurate AAA rupture risk index remains an important problem in the clinical management of the disease. To accurately estimate AAA rupture risk, detailed information on patient-specific wall stress distribution and aortic wall tissue yield stress is required. A complete fluid structure interaction (FSI) study is currently impractical and thus of limited clinical value. On the other hand, isolated static structural stress analysis based on a uniform wall loading is a widely used approach for AAA rupture risk estimation that, however, neglects the flow-induced wall stress variation. The aim of this study was to assess the merit of a decoupled fluid structure analysis of AAA wall stress. Anatomically correct, patient specific AAA wall models were created by 3D reconstruction of computed tomography images. Flow simulations were carried out with inflow and outflow boundary conditions obtained from patient extracted data. Static structural stress analysis was performed applying both a uniform pressure wall loading and a flow induced non-uniform pressure distribution obtained during early systolic deceleration. For the structural analysis, a hyperelastic arterial wall model and an elastic intraluminal thrombus model were assumed. The results of this study demonstrate that although the isolated static structural stress analysis approach captures the gross features of the stress distribution it underestimates the magnitude of the peak wall stress by as much as 12.5% compared to the proposed decoupled fluid structure approach. Furthermore, the decoupled approach provides potentially useful information on the nature of the aneurysmal sac flow.     

Numerical and experimental studies on pulsatile flow in aneurysms arising laterally from a curved parent vessel at various angles

Both numerical and experimental studies have been performed to characterize the fluid flow inside the lateral aneurysms arising from the curved parent vessels at various angles gamma. The implicit solver was based on the time-dependent Navier-Stokes equations of incompressible laminar flow. Solutions were generated by a cell-center finite-volume method that used second order upwind and second order center flux difference splitting for the convection and diffusion term, respectively. The second order Crank-Nicolson method was used in the time integration term while the SIMPLEC algorithm was adopted to handle the pressure-velocity coupling. Complementarily, the particle tracking velocimetry (PTV) was used to measure the velocity fields. The conditions selected were to simulate an internal carotid artery with a diameter of 5 mm by similarity rules. The values of gamma explored were 0 degrees, 45 degrees, 90 degrees, and 135 degrees. Pulsatile flow with Wormersley number 3.9 and Reynolds numbers varying from 350 to 850 was considered. The computed results are firstly verified by the PTV measured ones. Discussion of the results is in terms of pulsatile main and secondary velocity vector fields, inflow rates into the aneurysm, and the distributions of wall shear stress and static pressure. It is found that among the angles examined gamma=45( composite function) is the riskiest angle from a fluid dynamics point of view and the aneurysmal dome is at risk.     

Visualization and finite element analysis of pulsatile flow in models of the abdominal aortic aneurysm

Pulsatile flows in glass models simulating fusiform and lateral saccular aneurysms were investigated by a flow visualization method. When resting fluid starts to flow, the initial fluid motion is practically irrotational. After a short period of time, the flow began to separate from the proximal wall of the aneurysm. Then the separation bubble or vortex grew rapidly in size and filled the whole area of the aneurysm circumferentially. During this period of time, the center of the vortex moved from the proximal end to the distal point of the aneurysm. The transient reversal flow, for instance, which may occur at the end of the ejection period, passed between the wall of the aneurysm and the centrally located vortex. When the rate and pulsatile frequency of flow were high, the vortex broke down into highly disturbed flow (or turbulence) at the distal portion of the aneurysm. The same effect was observed when the length of the aneurysm was increased. A reduction in pulsatile amplitude made the flow pattern close to that in steady flow. A finite element analysis was made to obtain velocity and pressure fields in pulsatile flow through a tube with an axisymmetric expansion. Calculations were performed with the pulsatile flows used in the visualization experiment in order to study the effects of change in the pulsatile wave form by keeping the time-mean Reynolds number and Womersley's parameter unchanged. Calculated instantaneous patterns of velocity field and stream lines agreed well with the experimental results. The appearance and disappearance of the vortex in the dilated portion and its development resulted in complex distributions of pressure and shear fields. Locally minimum and maximum values of wall shear stress occurred at points just upstream and downstream of the distal end of the expansion when the flow rate reached its peak.     

Effects of stent porosity on hemodynamics in a sidewall aneurysm model

Computation and experiment have been complementarily performed to study the fluid flow inside a stented lateral aneurysm anchored on the straight parent vessel. The implicit solver was based on the time-dependent incompressible Navier-Stokes equations of laminar flow. Solutions were generated by a cell-center finite-volume method that used second-order upwind and second-order center flux difference splitting for the convection and diffusion term, respectively. The second-order Crank-Nicolson method was used in the time integration term. Experimental techniques used were flow visualization (FV) and particle tracking velocimetry (PTV). Experimentally, the straight afferent vessel had an inner diameter 10mm. The diameters of the aneurysmal orifice, neck, and fundus were 14, 10, and 15 mm, respectively, and the distance between the orifice and dome measured 20mm. A 30 mm long helix-shaped stent was tested. Four stent porosities of 100%, 70%, 50%, and 25% were examined. Volume-flow rate waveform of a cerebral artery was considered with a maximum Reynolds number of 250 and Womersley number of 3.9. Results are presented in terms of the pulsatile main and secondary flow velocity vector fields, the volume inflow rates into the aneurysm, and the wall shear stress (WSS) and wall pressure at the aneurysm dome. Some comparisons of computed results with the present FV and PTV results and with the data available from the literature are also made. The maximum flow velocity inside the aneurysm ostium and the WSS in the dome region at the peak flow can, respectively, be suppressed to less than 5% of the parent vessel bulk velocity (or 20% of the unstented case) and 8% of the unstented case if the stent porosity is smaller than 40% (about the porosity of the two-layer stents). In general, the three-layer stents seem not as effective as the two-layer stents in reducing the magnitude of aneurysm inflow rate and WSS.     

Pulsatile flow effects on the hemodynamics of intracranial aneurysms

High-resolution numerical simulations are carried out to systematically investigate the effect of the incoming flow waveform on the hemodynamics and wall shear stress patterns of an anatomic sidewall intracranial aneurysm model. Various wave forms are constructed by appropriately scaling a typical human waveform such that the waveform maximum and time-averaged Reynolds numbers, the Womersley number (α), and the pulsatility index (PI) are systematically varied within the human physiologic range. We show that the waveform PI is the key parameter that governs the vortex dynamics across the aneurysm neck and the flow patterns within the dome. At low PI, the flow in the dome is similar to a driven cavity flow and is characterized by a quasi-stationary shear layer that delineates the parent artery flow from the recirculating flow within the dome. At high PI, on the other hand, the flow is dominated by vortex ring formation, transport across the neck, and impingement and breakdown at the distal wall of the aneurysm dome. We further show that the spatial and temporal characteristics of the wall shear stress field on the aneurysm dome are strongly correlated with the vortex dynamics across the neck. We finally argue that the ratio between the characteristic time scale of transport by the mean flow across the neck and the time scale of vortex ring formation can be used to predict for a given sidewall aneurysm model the critical value of the waveform PI for which the hemodynamics will transition from the cavity mode to the vortex ring mode.     

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.     

Effects of elastic property of the wall on flow characteristics through arterial stenoses

Hemodynamic characteristics of blood flow through arterial stenoses are numerically investigated in this work. The blood is assumed as a Newtonian fluid and the pulsatile nature of flow is modeled by using measured values of the flowrate and pressure for the canine femoral artery. An isotropic elastic and incompressible material is assumed for the wall at each axial section, but a non-uniform distribution of the shear modulus in axial direction is used to model the high stiffness of the wall at the stenosis location. Full Navier equations for a thick wall are used as the governing equations for the wall displacements. A continuous grid extending over the flow field and the wall is considered and governing equations are transformed for use in the computational domain. Discretized forms of the transformed wall and flow equations, which are coupled through the boundary conditions at their interface, are obtained by control volume method and simultaneously solved using the well-known SIMPLER algorithm. To study the effects of wall deformability, solutions are obtained for both rigid and elastic walls. The results indicate that deformability of the wall causes an increase in the time average of pressure drop, but a decrease in the maximum wall shear stress. Displacement and stress distributions in the wall are presented.