Flow field and oscillatory shear stress in a tuning-fork-shaped model of the average human carotid bifurcation

The oscillatory shear index (OSI) was developed based on the hypothesis that intimal hyperplasia was correlated with oscillatory shear stresses. However, the validity of the OSI was in question since the correlation between intimal thickness and the OSI at the side walls of the sinus in the Y-shaped model of the average human carotid bifurcation (Y-AHCB) was weak. The objectives of this paper are to examine whether the reason for the weak correlation lies in the deviation in geometry of Y-AHCB from real human carotid bifurcation, and whether this correlation is clearly improved in the tuning-fork-shaped model of the average human carotid bifurcation (TF-AHCB). The geometry of the TF-AHCB model was based on observation and statistical analysis of specimens from 74 cadavers. The flow fields in both models were studied and compared by using flow visualization methods under steady flow conditions and by using laser Doppler anemometer (LDA) under pulsatile flow conditions. The TF-shaped geometry leads to a more complex flow field than the Y-shaped geometry. This added complexity includes strengthened helical movements in the sinus, new flow separation zone, and directional changes in the secondary flow patterns. The results show that the OSI-values at the side walls of the sinus in the TF-shaped model were more than two times as large as those in the Y-shaped model. This study confirmed the stronger correlation between the OSI and intimal thickness in the tuning-fork geometry of human carotid bifurcation, and the TF-AHCB model is a significant improvement over the traditional Y-shaped model.     

Construction of a physical model of the human carotid artery based upon in vivo magnetic resonance images

A method is described for construction of an in vitro flow model based on in vivo measurements of the lumen geometry of the human carotid bifurcation. A large-scale physical model of the vessel lumen was constructed using fused deposition modeling (a rapid prototyping technique) based on magnetic resonance (MR) images of the carotid bifurcation acquired in a healthy volunteer. The lumen negative was then used to construct a flow model for experimental studies that examined the hemodynamic environment of subject-specific geometry and flow conditions. The physical model also supplements physician insight into the three-dimensional geometry of the arterial segment, complementing the two-dimensional images obtained by MR. Study of the specific geometry and flow conditions in patients with vascular disease may contribute to our understanding of the relationship between their hemodvnamic environment and conditions that lead to the development and progression of arterial disease.     

Computational modeling of the mechanical behavior of the cerebrospinal fluid system

A computational fluid dynamics (CFD) model of the cerebrospinal fluid system was constructed based on a simplified geometry of the brain ventricles and their connecting pathways. The flow is driven by a prescribed sinusoidal motion of the third ventricle lateral walls, with all other boundaries being rigid. The pressure propagation between the third and lateral ventricles was examined and compared to data obtained from a similar geometry with a stenosed aqueduct. It could be shown that the pressure amplitude in the lateral ventricles increases in the presence of aqueduct stenosis. No difference in phase shift between the motion of the third ventricle walls and the pressure in the lateral ventricles because of the aqueduct stenosis could be observed. It is deduced that CFD can be used to analyze the pressure propagation and its phase shift relative to the ventricle wall motion. It is further deduced that only models that take into account the coupling between ventricles, which feature a representation of the original geometry that is as accurate as possible and which represent the ventricle boundary motion realistically, should be used to make quantitative statements on flow and pressure in the ventricular space.     

Modeling the effect of blood vessel bifurcation ratio on occlusive thrombus formation

Vascular geometry is a major determinant of the hemodynamics that promote or prevent unnecessary vessel occlusion from thrombus formation. Bifurcations in the vascular geometry are repeating structures that introduce flow separation between parent and daughter vessels. We modelled the blood flow and shear rate in a bifurcation during thrombus formation and show that blood vessel bifurcation ratios determine the maximum shear rate on the surface of a growing thrombus. We built an analytical model that may aid in predicting microvascular bifurcation ratios that are prone to occlusive thrombus formation. We also observed that bifurcation ratios that adhere to Murray’s law of bifurcations may be protected from occlusive thrombus formation. These results may be useful in the rational design of diagnostic microfluidic devices and microfluidic blood oxygenators.     

Effect of inlet velocity profiles on patient-specific computational fluid dynamics simulations of the carotid bifurcation

Patient-specific computational fluid dynamics (CFD) is a powerful tool for researching the role of blood flow in disease processes. Modern clinical imaging technology such as MRI and CT can provide high resolution information about vessel geometry, but in many situations, patient-specific inlet velocity information is not available. In these situations, a simplified velocity profile must be selected. We studied how idealized inlet velocity profiles (blunt, parabolic, and Womersley flow) affect patient-specific CFD results when compared to simulations employing a "reference standard" of the patient's own measured velocity profile in the carotid bifurcation. To place the magnitude of these effects in context, we also investigated the effect of geometry and the use of subject-specific flow waveform on the CFD results. We quantified these differences by examining the pointwise percent error of the mean wall shear stress (WSS) and the oscillatory shear index (OSI) and by computing the intra-class correlation coefficient (ICC) between axial profiles of the mean WSS and OSI in the internal carotid artery bulb. The parabolic inlet velocity profile produced the most similar mean WSS and OSI to simulations employing the real patient-specific inlet velocity profile. However, anatomic variation in vessel geometry and the use of a nonpatient-specific flow waveform both affected the WSS and OSI results more than did the choice of inlet velocity profile. Although careful selection of boundary conditions is essential for all CFD analysis, accurate patient-specific geometry reconstruction and measurement of vessel flow rate waveform are more important than the choice of velocity profile. A parabolic velocity profile provided results most similar to the patient-specific velocity profile.     

Anatomically based finite element models of the human pulmonary arterial and venous trees including supernumerary vessels.

Studies of the origin of pulmonary blood flow heterogeneity have highlighted the significant role of vessel branching structure on flow distribution. To enable more detailed investigation of structure-function relationships in the pulmonary circulation, an anatomically based finite element model of the arterial and venous networks has been developed to more accurately reflect the geometry found in vivo. Geometric models of the arterial and venous tree structures are created using a combination of multidetector row X-ray computed tomography imaging to define around 2,500 vessels from each tree, a volume-filling branching algorithm to generate the remaining accompanying conducting vessels, and an empirically based algorithm to generate the supernumerary vessel geometry. The explicit generation of supernumerary vessels is a unique feature of the computational model. Analysis of branching properties and geometric parameters demonstrates close correlation between the model geometry and anatomical measures of human pulmonary blood vessels. A total of 12 Strahler orders for the arterial system and 10 Strahler orders for the venous system are generated, down to the equivalent level of the terminal bronchioles in the bronchial tree. A simple Poiseuille flow solution, assuming rigid vessels, is obtained within the arterial geometry of the left lung, demonstrating a large amount of heterogeneity in the flow distribution, especially with inclusion of supernumerary vessels. This model has been constructed to accurately represent available morphometric data derived from the complex asymmetric branching structure of the human pulmonary vasculature in a form that will be suitable for application in functional simulations.     

Toward the modeling of mucus draining from the human lung: role of the geometry of the airway tree

Mucociliary clearance and cough are the two main natural mucus draining methods in the bronchial tree. If they are affected by a pathology, they can become insufficient or even ineffective, then therapeutic draining of mucus plays a critical role to keep mucus levels in the lungs acceptable. The manipulations of physical therapists are known to be very efficient clinically but they are mostly empirical since the biophysical mechanisms involved in these manipulations have never been studied. We develop in this work a model of mucus clearance in idealized rigid human bronchial trees and focus our study on the interaction between (1) tree geometry, (2) mucus physical properties and (3) amplitude of flow rate in the tree. The mucus is considered as a Bingham fluid (gel-like) which is moved upward in the tree thanks to its viscous interaction with air flow. Our studies point out the important roles played both by the geometry and by the physical properties of mucus (yield stress and viscosity). More particularly, the yield stress has to be overcome to make mucus flow. Air flow rate and yield stress determine the maximal possible mucus thickness in each branch of the tree at equilibrium. This forms a specific distribution of mucus in the tree whose characteristics are strongly related to the multi-scaled structure of the tree. The behavior of any mucus distribution is then dependent on this distribution. Finally, our results indicate that increasing air flow rates ought to be more efficient to drain mucus out of the bronchial tree while minimizing patient discomfort.     

A model for flow through discontinuities in the tight junction of the endothelial intercellular cleft

A mathematical model for steady flow through a discontinuity in the tight junction of an endothelial intercellular cleft is presented. Subject to plausible assumptions the problem of calculating the flow in the cleft, in either the presence or the absence of a fibre matrix, reduces to the solution of Laplace's equation in a two-dimensional domain. For an idealized geometry representing a discontinuity between two semi-infinite tight junction regions, a general analytic solution is found by means of conformal mappings. The model geometry, unlike those assumed in previous studies, allows the tight junction regions to be out of alignment with each other, and even to overlap, modelling flow through a tortuous, rather than a direct, pathway. Useful asymptotic approximations for the flow rate are derived when the discontinuity is either very small or very large. For small discontinuities, the predicted flow rate is much greater than a naïve estimate based on uniform parallel flow through the discontinuity. For the special case where the tight junction regions are aligned with each other, comparison of our results with those of an approximate treatment due to Tsayet al. [Chem. Engng Commun. 82, 67–102 (1989)] shows generally very close agreement.     

Effects of aortic irregularities on blood flow

Anatomic aortic anomalies are seen in many medical conditions and are known to cause disturbances in blood flow. Turner syndrome (TS) is a genetic disorder occurring only in females where cardiovascular anomalies, particularly of the aorta, are frequently encountered. In this study, numerical simulations are applied to investigate the flow characteristics in four TS patient- related aortic arches (a normal geometry, dilatation, coarctation and elongation of the transverse aorta). The Quemada viscosity model was applied to account for the non-Newtonian behavior of blood. The blood is treated as a mixture consisting of water and red blood cells (RBC) where the RBCs are modeled as a convected scalar. The results show clear geometry effects where the flow structures and RBC distribution are significantly different between the aortas. Transitional flow is observed as a jet is formed due to a constriction in the descending aorta for the coarctation case. RBC dilution is found to vary between the aortas, influencing the WSS. Moreover, the local variations in RBC volume fraction may induce large viscosity variations, stressing the importance of accounting for the non-Newtonian effects.     

A parametric geometry model of the aortic valve for subject-specific blood flow simulations using a resistive approach

Cardiac valves simulation is one of the most complex tasks in cardiovascular modeling. Fluid–structure interaction is not only highly computationally demanding but also requires knowledge of the mechanical properties of the tissue. Therefore, an alternative is to include valves as resistive flow obstacles, prescribing the geometry (and its possible changes) in a simple way, but, at the same time, with a geometry complex enough to reproduce both healthy and pathological configurations. In this work, we present a generalized parametric model of the aortic valve to obtain patient-specific geometries that can be included into blood flow simulations using a resistive immersed implicit surface (RIIS) approach. Numerical tests are presented for geometry generation and flow simulations in aortic stenosis patients whose parameters are extracted from ECG-gated CT images.

     

Flow profiles and wall shear stress distribution at a hemodialysis venous anastomosis: preliminary study

The phasic velocity field in the vicinity of the venous anastomosis in a hemodialysis angioaccess arteriovenous fistula loop graft (AVLG) is investigated employing a laser Doppler anemometer (LDA) system. Detailed LDA velocity profiles are obtained by sectional survey performed in a transparent, elastic flow model which was fabricated to represent the geometry of the AVLG system under physiological pressure and flow waveforms. The geometry of the flow model was based on a silicone rubber cast obtained from an experimental dog model. In the present study, detailed distribution of velocity profiles is obtained. The distribution of wall shear stress in the model is computed from the slope of the local velocity profiles near the wall. The relationship between the results obtained by flow visualization and the LDA measurement is discussed.     

On the physics of CNS memory

The effects of geometry, type of fluid and properties of the desmotubule membrane on the fluid transport in plasmodesma are discussed from a hydrodynamics viewpoint. It is shown that the “necking” of the ends of plasmodesma has a profound effect on the volume flow rates reducing them by several orders of magnitude. Most of the pressure drop occurs across the “neck” regions. There appears to be little significant difference in the volume flow rates if we consider a Newtonian or powerlaw fluid or if we allow the desmotubule membrane to be permeable or slightly flexible, at least in comparison to the dominating feature of plasmodesma geometry.     

Epicardial coronary blood flow including the presence of stenoses and aorto-coronary bypasses--I: Model and numerical method

A computer model and numerical method for calculating left epicardial coronary blood flow has been developed. This model employs a finite-branching geometry of the coronary vasculature and the one-dimensional, unsteady equations for flow with friction. The epicardial coronary geometry includes the left main and its bifurcation, the left anterior descending and left circumflex coronary arteries, and a selected number of small branches. Each of the latter terminate in an impedance, whose resistive component is related to intramyocardial compression through a linear dependence on left ventricular pressure. The elastic properties of the epicardial arteries are taken to be non-linear and are prescribed by specifying the local small-disturbance wave speed. The model allows for the incorporation of multiple stenoses as well as aorto-coronary bypasses. Calculations using this model predict pressure and flow waveform development and allow for the systematic investigation of the dependence of coronary flow on various parameters, e.g., peripheral resistance, wall properties, and branching pattern, as well as the presence of stenoses and bypass grafts. Reasonable comparison between calculations and earlier experiments in horses has been obtained.     

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, tau , 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 tau with maximum tau occurring for large bulb widths. Also, it is shown that different sets of geometric parameters can produce low values of tau by either relatively small intense areas, or by larger areas of less intense reverse flow.     

Optimization of shunt placement for the Norwood surgery using multi-domain modeling

An idealized systemic-to-pulmonary shunt anatomy is parameterized and coupled to a closed loop, lumped parameter network (LPN) in a multidomain model of the Norwood surgical anatomy. The LPN approach is essential for obtaining information on global changes in cardiac output and oxygen delivery resulting from changes in local geometry and physiology. The LPN is fully coupled to a custom 3D finite element solver using a semi-implicit approach to model the heart and downstream circulation. This closed loop multidomain model is then integrated with a fully automated derivative-free optimization algorithm to obtain optimal shunt geometries with variable parameters of shunt diameter, anastomosis location, and angles. Three objective functions: (1) systemic; (2) coronary; and (3) combined systemic and coronary oxygen deliveries are maximized. Results show that a smaller shunt diameter with a distal shunt-brachiocephalic anastomosis is optimal for systemic oxygen delivery, whereas a more proximal anastomosis is optimal for coronary oxygen delivery and a shunt between these two anatomies is optimal for both systemic and coronary oxygen deliveries. Results are used to quantify the origin of blood flow going through the shunt and its relationship with shunt geometry. Results show that coronary artery flow is directly related to shunt position.     

Effects of stents under asymmetric inflow conditions

Patient-to-patient variations in artery geometry may determine their susceptibility to stenosis formation. These geometrical variations can be linked to variations in flow characteristics such as wall shear stress through stents, which increases the risk of restenosis. This paper considers computer models of stents in non-symmetric flows and their effects on flow characteristics at the wall. This is a fresh approach from the point of view of identifying a stent design whose performance is insensitive to asymmetric flow. Measures of dissipated energy and power are introduced in order to discriminate between competing designs of stents.     

Theoretical analysis of the flow of cells over villi of the small intestine

The flow of epithelial cells over villi of mouse small intestine is calculated from equations of cell number balance and irrotational flow. The influence of both villus geometry and crypt distribution about the villus base are studied. Specific, experimentally verifiable predictions are made.     

Computation in the rabbit aorta of a new metric – the transverse wall shear stress – to quantify the multidirectional character of disturbed blood flow

Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric – the transverse wall shear stress (transWSS) – calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis.     

Numerical simulations of the blood flow through vertebral arteries

Vertebral arteries are two arteries whose structure and location in human body result in development of special flow conditions. For some of the arteries, one can observe a significant difference between flow rates in the left and the right arteries during ultrasonography diagnosis. Usually the reason of such a difference was connected with pathology of the artery in which a smaller flow rate was detected. Simulations of the flow through the selected type of the vertebral artery geometry for twenty five cases of artery diameters have been carried out. The main aim of the presented experiment was to visualize the flow in the region of vertebral arteries junction in the origin of the basilar artery. It is extremely difficult to examine this part of human circulation system, thus numerical experiments may be helpful in understanding the phenomena occurring when two relatively large arteries join together to form one vessel. The obtained results have shown that an individual configuration and diameters of particular arteries can exert an influence on the flow in them and affect a significant difference between flow rates for vertebral arteries. It has been assumed in the investigations that modelled arteries were absolutely normal, without any pathology. In the numerical experiment, the non-Newtonian model of blood was employed.