Model Of Carotid Artery Bifurcation Research Articles

Vortical Structures Promote Atheroprotective Wall Shear Stress Distributions in a Carotid Artery Bifurcation Model.

Carotid artery diseases, such as atherosclerosis, are a major cause of death in the United States. Wall shear stresses are known to prompt plaque formation, but there is limited understanding of the complex flow structures underlying these stresses and how they differ in a pre-disposed high-risk patient cohort. A 'healthy' and a novel 'pre-disposed' carotid artery bifurcation model was determined based on patient-averaged clinical data, where the 'pre-disposed' model represents a pathological anatomy. Computational fluid dynamic simulations were performed using a physiological flow based on healthy human subjects. A main hairpin vortical structure in the internal carotid artery sinus was observed, which locally increased instantaneous wall shear stress. In the pre-disposed geometry, this vortical structure starts at an earlier instance in the cardiac flow cycle and persists over a much shorter period, where the second half of the cardiac cycle is dominated by perturbed secondary flow structures and vortices. This coincides with weaker favorable axial pressure gradient peaks over the sinus for the 'pre-disposed' geometry. The findings reveal a strong correlation between vortical structures and wall shear stress and imply that an intact internal carotid artery sinus hairpin vortical structure has a physiologically beneficial role by increasing local wall shear stresses. The deterioration of this beneficial vortical structure is expected to play a significant role in atherosclerotic plaque formation.

Optimization of 4D Flow MRI Spatial and Temporal Resolution for Examining Complex Hemodynamics in the Carotid Artery Bifurcation.

Three-dimensional, ECG-gated, time-resolved, three-directional, velocity-encoded phase-contrast MRI (4D flow MRI) has been applied extensively to measure blood velocity in great vessels but has been much less used in diseased carotid arteries. Carotid artery webs (CaW) are non-inflammatory intraluminal shelf-like projections into the internal carotid artery (ICA) bulb that are associated with complex flow and cryptogenic stroke. Optimize 4D flow MRI for measuring the velocity field of complex flow in the carotid artery bifurcation model that contains a CaW. A 3D printed phantom model created from computed tomography angiography (CTA) of a subject with CaW was placed in a pulsatile flow loop within the MRI scanner. 4D Flow MRI images of the phantom were acquired with five different spatial resolutions (0.50-2.00 mm3) and four different temporal resolutions (23-96ms) and compared to a computational fluid dynamics (CFD) solution of the flow field as a reference. We examined four planes perpendicular to the vessel centerline, one in the common carotid artery (CCA) and three in the internal carotid artery (ICA) where complex flow was expected. At these four planes pixel-by-pixel velocity values, flow, and time average wall shear stress (TAWSS) were compared between 4D flow MRI and CFD. An optimized 4D flow MRI protocol will provide a good correlation with CFD velocity and TAWSS values in areas of complex flow within a clinically feasible scan time (~ 10min). Spatial resolution affected the velocity values, time average flow, and TAWSS measurements. Qualitatively, a spatial resolution of 0.50 mm3 resulted in higher noise, while a lower spatial resolution of 1.50-2.00 mm3 did not adequately resolve the velocity profile. Isotropic spatial resolutions of 0.50-1.00 mm3 showed no significant difference in total flow compared to CFD. Pixel-by-pixel velocity correlation coefficients between 4D flow MRI and CFD were > 0.75 for 0.50-1.00 mm3 but were < 0.5 for 1.50 and 2.00 mm3. Regional TAWSS values determined from 4D flow MRI were generally lower than CFD and decreased at lower spatial resolutions (larger pixel sizes). TAWSS differences between 4D flow and CFD were not statistically significant at spatial resolutions of 0.50-1.00 mm3 but were different at 1.50 and 2.00 mm3. Differences in temporal resolution only affected the flow values when temporal resolution was > 48.4ms; temporal resolution did not affect TAWSS values. A spatial resolution of 0.74-1.00 mm3 and a temporal resolution of 23-48ms (1-2k-space segments) provides a 4D flow MRI protocol capable of imaging velocity and TAWSS in regions of complex flow within the carotid bifurcation at a clinically acceptable scan time.

Shear stress metrics associated with pro-atherogenic high-risk anatomical features in a carotid artery bifurcation model

BackgroundDiseases associated with atherosclerotic plaques in the carotid artery are a major cause of deaths in the United States. Blood-flow-induced shear-stresses are known to trigger plaque formation. Prior literature suggests that the internal carotid artery sinus is prone to atherosclerosis, but there is limited understanding of why only certain patients are predisposed towards plaque formation. MethodsWe computationally investigate the effect of vessel geometry on wall-shear-stress distribution by comparing flowfields and wall-shear-stress-metrics between a low-risk and a novel predisposed high-risk carotid artery bifurcation anatomy. Both models were developed based on clinical risk estimations and patient-averaged anatomical features. The high-risk geometry has a larger internal carotid artery branching angle and a lower internal-to-carotid-artery-diameter-ratio. A patient-averaged physiological carotid artery inflow waveform is used. FindingsThe high-risk geometry experiences stronger flow separation in the sinus. Furthermore, it experiences a more equal flow split at the bifurcation, thereby reducing internal carotid artery flowrate and increasing atherosclerosis-prone low-velocity areas. Lowest time-averaged-wall-shear-stresses are present at the sinus outer wall, where plaques are often found, for both geometries. The high-risk geometry has significantly high, unfavorable oscillatory-shear-index values not found in the low-risk geometry. High oscillatory-shear-index areas are located at the vessels outside walls distal to the bifurcation and on the sinus wall. InterpretationThese results highlight the effectiveness of oscillatory-shear-index, to augment classical time-averaged-wall-shear-stress, in evaluating pro-atherogenic geometry features. Furthermore, the flow split at the bifurcation is a promising clinical indicator for atherosclerosis risk as it can be directly accessed using clinical imaging, whereas shear-stress-metrics cannot.

Comparison of blood flow analysis in stenosed and stented carotid artery bifurcation models

Comparison of blood flow analysis in stenosed and stented carotid artery bifurcation models

Embolus Transport Simulations with Fully Resolved Particle Surfaces.

There has been interest in recent work in using computational fluid dynamics with Lagrangian analysis to calculate the trajectory of emboli-like particles in the vasculature. While previous studies have provided an understanding of the hemodynamic factors determining the fates of such particles and their relationship to risk of stroke, most analyses have relied on a particle equation of motion that assumes the particle is "small" e.g., much less than the diameter of the vessel. This work quantifies the limit when a particle can no longer be considered "small". The motion of embolus-like particles are simulated using an overset mesh technique. This allows the fluid stresses on the particle surface to be fully resolved. Consequently, the particles can be of arbitrary size or shape. The trajectory of resolved particles and "small" particles are simulated through a patient-specific carotid artery bifurcation model with particles 500, 1000, and 2000μm in diameter. The proportions of particles entering the internal carotid artery are treated as the outcome of the particle fate, and statistical comparisons are made to ascertain the importance of non-small particle effects. For the 2000μm embolus, the proportion of particles traveling to the internal carotid artery is 74.7 ± 1.3% (mean±95% confidence margin) for the "small" particle model and is 85.7±5.4% for a resolved particle model. The difference is statistically significant, [Formula: see text], based on the binomial test for the particle outcomes. No statistically discernible differences are found for the smaller diameter particles. Quantitative differences are observable for the 2000μm trajectories between the "small" and resolved particle models which is a particle diameter 27% relative to the common carotid artery diameter. A fully resolved particle model ought to be considered for emboli trajectory simulations when the particle size ratio is ≳20%.

CFD Analysis of Haemodynamics in Carotid Artery Bifurcation Model of Healthy and Atherosclerotic Blood Vessel

CFD Analysis of Haemodynamics in Carotid Artery Bifurcation Model of Healthy and Atherosclerotic Blood Vessel

Experimental measurements and visualisation of a viscous fluid flow in Y-branching modelling the common carotid artery bifurcation with MR and Doppler ultrasound velocimetry

In our experiments, we investigate a flow of a viscous fluid in the model of the common carotid artery bifurcation. The studies are carried out using three hardware equipments: two magnetic resonance scanners by Philips and Bruker, and intravascular guidewire ComboWire. The flux is generated by a special pump CompuFlow that is designed to reproduce a flow similar to the one in the blood vessels. A verification of the obtained data is carried out. Conducted research shows the capabilities of the measurement instruments and reflects the character of fluid flow inside the model.

Covered Stent Membrane Design for Treatment of Atheroembolic Disease at Carotid Artery Bifurcation and Prevention of Thromboembolic Stroke: An In Vitro Experimental Study

In this study, a polymeric membrane has been designed and developed for carotid stents to prevent detachment of emboli from the arterial wall and subsequent stroke, while maintaining side-branch flow. Prototypes of different geometrical design parameters have been fabricated and their performance has been evaluated in vitro under physiological pulsatile flow condition in a life-size silicone anastomotic model of carotid artery bifurcation. These evaluations include both quantitative and qualitative experimental (in vitro) assessments of emboli prevention capability, side-branch flow preservation, and flow visualization. The covered stents with the novel membrane demonstrated significantly higher emboli prevention capability than the corresponding bare nitinol stent as well as some earlier related designs, while preserving more than 93% of the original flow of the external carotid artery (ECA). Flow in the ECA through these covered stents was uniform without evidence of undesirable flow recirculation or retrograde flow that might predispose the vessel wall to intimal thickening and atherosclerotic plaque formation. This study demonstrated the potential of these novel covered stent designs for the treatment of carotid atherosclerotic stenosis and prevention of late embolic stroke. However, further in vivo investigations of biological effects and mechanical performance of this covered stent design (e.g., its thrombogenicity potential and biocompatibility) are warranted.

Turbulence intensity measurements using particle image velocimetry in diseased carotid artery models: Effect of stenosis severity, plaque eccentricity, and ulceration

Clinical decision-making for the treatment of patients with diseased carotid artery is mainly based on the severity of the stenosis. However, stenosis severity alone is not a sensitive indicator, and other local factors for the assessment of stroke risk are required. Flow disturbance is of particular interest due to its proven association with increased thromboembolic activities. The objective of this study was to investigate the level of turbulence intensity (TI) with regards to certain geometrical features of the plaque – namely stenosis severity, eccentricity, and ulceration. A family of eight carotid-artery bifurcation models was examined using particle image velocimetry. Results showed a marked difference in turbulence intensity among these models; increasing degree of stenosis severity resulted in increased turbulence intensity, going from 0.12m/s for mild stenosis to 0.37m/s for severe stenosis (with concentric geometry). Moreover, independent of stenosis severity, eccentricity led to further elevations in turbulence intensity, increasing TI by 0.05–0.10m/s over the counterpart concentric plaque. The presence of ulceration (in a 50% eccentric plaque) produced a larger portion of moderate turbulence intensity (~0.10m/s) compared to the non-ulcerated model, more proximal to the bifurcation apex in the post-stenotic recirculation zone. The effect of plaque eccentricity and ulceration in enhancing the downstream turbulence has potential clinical implications for a more sensitive assessment of stroke risk beyond stenosis severity alone.

Transitional flow analysis in the carotid artery bifurcation by proper orthogonal decomposition and particle image velocimetry

Blood flow instabilities in the carotid artery bifurcation have been highly correlated to clot formation and mobilization resulting in ischemic stroke. In this work, PIV-measured flow velocities in normal and stenosed carotid artery bifurcation models were analyzed by means of proper orthogonal decomposition (POD). Through POD analysis, transition to more complex flow was visualized and quantified for increasing stenosis severity. While no evidence of transitional flow was seen in the normal model, the 50%-stenosed model started to show characteristics of transitional flow, which became highly evident in the 70% model, with greatest manifestation during the systolic phase of the cardiac cycle. By means of a model comparison, we demonstrate two quantitative measures of the flow complexity through the power-law decay slope of the energy spectrum and the global entropy. The more complex flow in the 70%-stenosed model showed a flatter slope of energy decay (−0.91 compared to −1.34 for 50% stenosis) and higher entropy values (0.26 compared to 0.17). Finally, the minimum temporal resolution required for POD analysis of carotid artery flow was found to be 100Hz when determined through a more typical energy-mode convergence test, as compared to 400Hz based on global entropy values.

Tomographic particle image velocimetry investigation of the flow in a modeled human carotid artery bifurcation

Hemodynamic forces within the human carotid artery are well known to play a key role in the initiation and progression of vascular diseases such as atherosclerosis. The degree and extent of the disease largely depends on the prevailing three-dimensional flow structure and wall shear stress (WSS) distribution. This work presents tomographic PIV (Tomo-PIV) measurements of the flow structure and WSS in a physiologically accurate model of the human carotid artery bifurcation. The vascular geometry is reconstructed from patient-specific data and reproduced in a transparent flow phantom to demonstrate the feasibility of Tomo-PIV in a complex three-dimensional geometry. Tomographic reconstruction is performed with the multiplicative line-of-sight (MLOS) estimation and simultaneous multiplicative algebraic reconstruction (SMART) technique. The implemented methodology is validated by comparing the results with Stereo-PIV measurements in the same facility. Using a steady flow assumption, the measurement error and RMS uncertainty are directly inferred from the measured velocity field. It is shown that the measurement uncertainty increases for increasing light sheet thickness and increasing velocity gradients, which are largest near the vessel walls. For a typical volume depth of 6 mm (or 256 pixel), the analysis indicates that the velocity derived from 3D cross-correlation can be measured within ±2% of the maximum velocity (or ±0.2 pixel) near the center of the vessel and within ±5% (±0.6 pixel) near the vessel wall. The technique is then applied to acquire 3D-3C velocity field data at multiple axial locations within the carotid artery model, which are combined to yield the flow field and WSS in a volume of approximately 26 mm × 27 mm × 60 mm. Shear stress is computed from the velocity gradient tensor and a method for inferring the WSS distribution on the vessel wall is presented. The results indicate the presence of a complex and three-dimensional flow structure, with regions of flow separation and strong velocity gradients. The WSS distribution is markedly asymmetric confirming a complex swirling flow structure within the vessel. A comparison of the measured WSS with Stereo-PIV data returns an acceptable agreement with some differences in stress magnitude.

Choice of In Vivo Versus Idealized Velocity Boundary Conditions Influences Physiologically Relevant Flow Patterns in a Subject-Specific Simulation of Flow in the Human Carotid Bifurcation

Accurate fluid mechanics models are important tools for predicting the flow field in the carotid artery bifurcation and for understanding the relationship between hemodynamics and the initiation and progression of atherosclerosis. Clinical imaging modalities can be used to obtain geometry and blood flow data for developing subject-specific human carotid artery bifurcation models. We developed subject-specific computational fluid dynamics models of the human carotid bifurcation from magnetic resonance (MR) geometry data and phase contrast MR velocity data measured in vivo. Two simulations were conducted with identical geometry, flow rates, and fluid parameters: (1) Simulation 1 used in vivo measured velocity distributions as time-varying boundary conditions and (2) Simulation 2 used idealized fully-developed velocity profiles as boundary conditions. The position and extent of negative axial velocity regions (NAVRs) vary between the two simulations at any given point in time, and these regions vary temporally within each simulation. The combination of inlet velocity boundary conditions, geometry, and flow waveforms influences NAVRs. In particular, the combination of flow division and the location of the velocity peak with respect to individual carotid geometry landmarks (bifurcation apex position and the departure angle of the internal carotid) influences the size and location of these reversed flow zones. Average axial wall shear stress (WSS) distributions are qualitatively similar for the two simulations; however, instantaneous WSS values vary with the choice of velocity boundary conditions. By developing subject-specific simulations from in vivo measured geometry and flow data and varying the velocity boundary conditions in otherwise identical models, we isolated the effects of measured versus idealized velocity distributions on blood flow patterns. Choice of velocity distributions at boundary conditions is shown to influence pathophysiologically relevant flow patterns in the human carotid bifurcation. Although mean WSS distributions are qualitatively similar for measured and idealized inlet boundary conditions, instantaneous NAVRs differ and warrant imposing in vivo velocity boundary conditions in computational simulations. A simulation based on in vivo measured velocity distributions is preferred for modeling hemodynamics in subject-specific carotid artery bifurcation models when studying atherosclerosis initiation and development.

Parametric geometry exploration of the human carotid artery bifurcation

A parametric computational model of the human carotid artery bifurcation is employed to demonstrate that it is only necessary to simulate approximately one-half of a single heart pulse when performing a global exploration of the relationships between shear stress and changes in geometry. Using design of experiments and surface fitting techniques, a landscape is generated that graphically depicts these multi-dimensional relationships. Consequently, whilst finely resolved, grid and pulse independent results are traditionally demanded by the computational fluid dynamics (CFD) community, this strategy demonstrates that it is possible to efficiently detect the relative impact of different geometry parameters, and to identify good and bad regions of the landscape by only simulating a fraction of a single pulse. Also, whereas in the past comparisons have been made between the distributions of appropriate shear stress metrics, such as average wall shear stress and oscillatory shear index, this strategy requires a figure of merit to compare different geometries. Here, an area-weighted integral of negative time-averaged shear stress, τ ˜ , is used as the principal objective function, although the discussion reveals that the extent as well as the intensity of reverse flow may be important. Five geometry parameters are considered: the sinus bulb width, the angles and the outflow diameters of the internal carotid artery (ICA) and external carotid artery (ECA). A survey of the landscape confirms that bulb shape has the dominant effect on τ ˜ with maximum τ ˜ occurring for large bulb widths. Also, it is shown that different sets of geometric parameters can produce low values of τ ˜ by either relatively small intense areas, or by larger areas of less intense reverse flow.

Flow Characteristics in an Anatomically Realistic Compliant Carotid Artery Bifurcation Model

A numerical model for the pulsatile blood flow in an anatomically realistic compliant model of the human carotid artery bifurcation has been developed. The geometric model has been generated on the basis of an optically digitized arterial cast. The effects of the geometrically realistic flow domain and of the wall distensibility on the flow characteristics are investigated. The description of the blood flow uses the time-dependent, three-dimensional, incompressible Navier-Stokes equations for non-Newtonian inelastic fluids. The calculation of the wall displacement uses geometrically non-linear shell theory. In an iteratively coupled approach the flow equations and the shell equations are numerically solved using the finite element method. The results show strongly skewed velocity profiles with high gradients at the internal and external divider walls downstream of the bifurcation. Flow separation and recirculation occur in the regions at the outer walls of the branching during systolic flow deceleration and at the diastolic flow minimum. Further the results show complex non-symmetric secondary motion in the carotid sinus due to the slightly non-planar branching of the geometrically realistic model. At the internal divider wall high shear stress can be observed, whereas at the outer internal wall low and oscillating shear stress occurs. The comparison of the results in the realistic model with results in a geometrically idealized model primarily points out differences concerning the flow recirculation and the secondary flow pattern. Comparing the results with results of a corresponding rigid wall model demonstrates a decrease of wall shear stress magnitude and a slight reduction of flow separation and recirculation at the outer sinus wall in the distensible model. The relative decrease of the axial wall shear stress maximum is 17% at the internal divider wall. At the outer sinus wall where the shear stress is low the decrease is in the range of up to 50%.

Analysis of the axial flow field in stenosed carotid artery bifurcation models—LDA experiments

Laser Doppler anemometer (LDA) experiments were performed to gain quantitative information on the differences between the large-scale flow phenomena in a non-stenosed and a stenosed model of the carotid artery bifurcation. The influence of the presence of the stenosis was compared to the effect of flow pulse variation to evaluate the feasibility of early detection of stenosis in clinical practice. Three-dimensional Plexiglass models of a non-stenosed and a 25% stenosed carotid artery bifurcation were perfused with a Newtonian fluid. The flow conditions approximated physiological flow. The results of the velocity measurements in the non-stenosed model agreed with the results from previous hydrogen-bubble visualization. A shear layer separated the low-velocity area near the non-divider wall from the high-velocity area near the divider wall. In this shear layer, vortex formation occurred during the deceleration phase of the flow pulse. The instability of this shear layer dictated the flow disturbances. The influences of the mild stenosis, located at the non-divider wall, was mainly limited to the stability of the shear layer. No disturbances were found downstream of the stenosis near the non-divider wall. Using a pulse wave with an increased systolic deceleration time, the velocity distribution showed an extended region with reversed flow, a more pronounced shear layer and increased vortex strength. From these measurements it is obvious that the influence of the presence of a mild stenosis, mainly limited to the stability of the shear layer, can hardly be distinguished from the effects of a variation of the flow pulse. From this it can be concluded that methods for detection of mild stenosis, using solely the large-scale flow phenomena, as can be measured by ultrasound or MRI techniques, will hardly have any clinical relevance.

Full-field flow visualization and velocity measurement with a photochromic grid method

A novel approach to full-field velocity measurement with the photochromic method of flow visualization is described. A photochromic grid is constructed by superimposing many individual dye traces that are measured at different instants in time. By tracking the points of intersection, the velocity field can be estimated. Since this approach is applicable under a wide range of conditions including pulsatile flows, it is well-suited to in vitro haemodynamic investigations. The potential of this new approach is demonstrated by its application to the measurement of steady flow in a life-sized model of a human carotid artery bifurcation.

Computer simulation of local blood flow and vessel mechanics in a compliant carotid artery bifurcation model

To investigate the effect of the distensible artery wall on the local flow field and to determine the mechanical stresses in the artery wall, a numerical model for the blood flow in the human carotid artery bifurcation has been developed. The wall displacement and stress analysis use geometrically non-linear shell theory where incrementally linearly elastic wall behavior is assumed. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier-Stokes equations for non-Newtonian inelastic fluids. In an iteratively coupled approach the equations of the fluid motion and the transient shell equations are numerically solved using the finite element method. The study shows the occurring characteristics in carotid artery bifurcation flow, such as strongly skewed axial velocity in the carotid sinus with high velocity gradients at the internal divider wall and with flow separation at the outer common-internal carotid wall and at the bifurcation side wall. Flow separation results in locally low oscillating wall shear stress. Further strong secondary motion in the sinus is found. The comparison of the results for a rigid and a distensible wall model demonstrates quantitative influence of the vessel wall motion. With respect to the quantities of main interest, it can be seen, that flow separation and recirculation slightly decrease in the sinus and somewhat increase in the bifurcation side region, and the wall shear stress magnitude decreases by 25% in the distensible model. The global structure of the flow and stress patterns remains unchanged. The deformation analysis shows that the tangential displacements are generally lower by one order of magnitude than the normal directed displacements. The maximum deformation is about 16% of the vessel radius and occurs at the side wall region of the intersection of the two branches. The analysis of the maximum principal stresses at the inner vessel surface shows a complicated stress field with locally high gradients and indicates a stress concentration factor of 6.3 in the apex region.

Analysis of the flow in stenosed carotid artery bifurcation models—Hydrogen-bubble visualisation

This paper deals with the effect of geometric changes of mild stenoses on large-scale flow disturbances in the carotid artery bifurcation. Hydrogen-bubble visualisation experiments have been performed in Plexiglas models of a non-stenosed and a 25% stenosed carotid artery bifurcation. The flow conditions approximate physiological flow. The experiments show that shortly after the onset of the diastolic phase vortex formation occurs in the plane of symmetry. This vortex formation is found in a shear layer, which is formed in the carotid sinus. The shear layer is located between a region with low shear rates at the non-divider wall and a region with high shear rates at the divider wall. In order to gain insight into the parameters that are important with respect to the stability of the shear layer, experiments have been performed in which the influence of the shape of the flow pulse, the Reynolds number ( Re), the Womersley parameter (α) and the flow division ratio (γ) on the flow phenomena is studied. From these experiments it appears that the flow phenomena in the carotid artery bifurcation are significantly influenced by Re, α the systolic acceleration (sa) and deceleration (sd) and the duration of the peak-systolic flow ( T max). With these results a simplified flow pulse is chosen, with which the experiments in the non-stenosed and the 25% stenosed bifurcation are performed. Comparison of the hydrogen-bubble profiles in the 0 and 25% stenosed models with similar flow conditions shows that the geometric change of the 25% stenosis only slightly influences the flow phenomena. The most striking influences are found in the stability of the shear layer. Quantitative experiments by means of laser Doppler anemometry measurements and numerical computations are needed to analyse the influence of the stenosis of the flow field more accurately.

Flow and stress characteristics in rigid walled and compliant carotid artery bifurcation models.

Computer simulation of pulsatile non-Newtonian blood flow has been carried out in different human carotid artery bifurcation models. In the first part of the investigation, two rigid walled models are analysed, differing in the bifurcation angle (wide angle and acute angle bifurcation) and in the shape of both the sinus (narrow and larger sinus width) and the bifurcation region (small and larger rounding of the flow divider), in order to contribute to the study of the geometric factor in atherosclerosis. The results show a significant difference in the wall shear stress and in the flow separation. Flow recirculation in the sinus is much more pronounced in the acute angle carotid. An important factor in flow separation is the sinus width. In the second part of the study, flow velocity and wall shear stress distribution have been analysed in a compliant carotid artery bifurcation model. In the mathematical model, the non-Newtonian flow field and the idealized elastic wall displacement are coupled and calculated iteratively at each time step. Maximum displacement of approximately 6% of the diastolic vessel diameter occurs at the side wall of the bifurcation region. The investigation demonstrates that the wall distensibility alters the flow field and the wall shear stress during the systolic phase. Comparison with corresponding rigid wall results shows that flow separation and wall shear stress are reduced in the distensible wall model.

Numerical analysis of intramural stresses and blood flow in arterial bifurcation models

The study deals with the calculation of the stresses in elastic arterial walls and with the analysis of the interaction of local blood flow and vessel wall motion. While the stress study is primarily carried out in a basic end-to-side bypass anastomosis model incorporating different material properties of the graft and the artery, the flow study is performed in a compliant carotid artery bifurcation model. The displacement and stress analysis uses geometrically non-linear shell theory. The flow analysis applies the time-dependent, three-dimensional, incompressible, Navier-Stokes equations for non-Newtonian inelastic fluids In an iteratively coupled approach the equations of the fluid motion and the transient shell equations are numerically solved using the finite element method.