Impact of aortic repair based on flow field computer simulation within the thoracic aorta

Purpose of this computational study is to examine the hemodynamic parameters of velocity fields and shear stress in the thoracic aorta with and without aneurysm, based on an individual patient case and virtual surgical intervention. These two cases, case I (with aneurysm) and II (without aneurysm), are analyzed by computational fluid dynamics. The 3D Navier-Stokes equations and the continuity equation are solved with an unsteady stabilized finite element method. The vascular geometries are reconstructed based on computed tomography angiography images to generate a patient-specific 3D finite element mesh. The input data for the flow waveforms are derived from MR phase contrast flow measurements of a patient before surgical intervention.The computed results show velocity profiles skewed towards the inner aortic wall for both cases in the ascending aorta and in the aortic arch, while in the descending aorta these velocity profiles are skewed towards the outer aortic wall. Computed streamlines indicate that flow separation occurs at the proximal edge of the aneurysm, i.e. computed flow enters the aneurysm in the distal region, and that there is essentially a single, slowly rotating, vortex within the aneurysm during most of the systole.In summary, after virtual surgical intervention in case II higher shear stress distribution along the descending aorta could be found, which may produce more healthy reactions in the endothelium and benefit of vascular reconstruction of an aortic aneurysm at this particular location.     

Automated adaptive cardiovascular flow simulations

We present an automatic adaptive procedure to perform blood flow simulations in the cardiovascular system. The procedure allows the user to start with subject-specific data collected through clinical measurements, like magnetic resonance imaging (MRI) data, and evaluate physiological parameters of interest, like flow distribution, pressure variations, wall shear stress, in an automatic and efficient manner. The process involves construction of geometric models of blood vessels, specification of flow conditions and application of an adaptive flow solver. The latter is based on incompressible Navier–Stokes equations using adaptive spatial discretization (meshing) techniques. In this article, we demonstrate the method on a model of a human abdominal aorta of a normal subject with geometry and flow rates assimilated from MRI data. The results obtained show that boundary layer mesh adaptivity offers a better alternative leading to more accurate predictions, especially for key physiological quantities like wall shear stress.     

Simulating cyclic artery compression using a 3D unsteady model with fluid–structure interactions

High pulsating blood pressure and severe stenosis make fluid–structure interaction (FSI) an important role in simulating blood flow in stenotic arteries. A three-dimensional nonlinear model with FSI and a numerical method using GFD are introduced to study unsteady viscous flow in stenotic tubes with cyclic wall collapse simulating blood flow in stenotic carotid arteries. The Navier–Stokes equations are used as the governing equations for the fluid. A thin-shell model is used for the tube wall. Interaction between fluid and tube wall is treated by an incremental boundary iteration method. Elastic properties of the tube wall are determined experimentally using a polyvinyl alcohol hydrogel artery stenosis model. Cyclic tube compression and collapse, negative pressure and high shear stress at the throat of the stenosis, flow recirculation and low shear stress just distal to the stenoses were observed under physiological conditions. These critical flow and mechanical conditions may be related to platelet aggregation, thrombus formation, excessive artery fatigue and possible plaque cap rupture. Computational and experimental results are compared and reasonable agreement is found.     

Hemodynamics in Aneurysm

A numerical simulation of hemodynamics in blood vessels with 0–75% dilation is made. A transient UVP finite element method (FEM) and a stable time integration scheme, based on a predictor–corrector strategy, with constant error monitoring are employed in the flow analysis. The pulsatile flow is analyzed without any assumptions in nonlinear terms and is characterized by thoroughly analyzing the flow, pressure, and stress fields. The central axis velocity, central axis and wall pressures, pressure gradient history, and wall shear stress are influenced by the presence of aneurysm. Time-dependent recirculation regions which are sensitive to the degree of dilation of the vessel are seen in the concavity of the dilation. The transverse velocities and their variations with time are found to be too significant to be neglected. The effects of nonlinear convective terms and the nonlinear geometry of the vessel are clearly depicted through the transverse velocity and pressure profiles.     

Measurements of wall shear stress with the lattice Boltzmann method and staircase approximation of boundaries

We analyze the accuracy of wall shear stress measurements in lattice Boltzmann simulations that are based on a voxel representation of the geometry and staircase approximation of boundaries. Such approximations are commonly used in the context of lattice Boltzmann simulations, because they favor the use of simple and highly efficient data structures. We show on several two- and three-dimensional simulations that this low-order approximation of the boundary affects the accuracy of wall shear stress measurements in areas directly adjacent to the wall. A few lattice nodes apart from the wall, the accuracy is however largely improved, and can be considered to be compatible with the overall accuracy of a simulation at a given coarseness level of the grid. This result is interpreted as a justification for the use of walls with staircase shape, even in simulations with high expectations regarding the level of accuracy. Furthermore, we propose a novel method for establishing the direction of the wall normal, a quantity which is required for the computation of the wall shear stress. With this method, the wall normal is computed from local data that is extracted from the results of the fluid flow simulation. Owing to the nature of the flow dynamics, which tends to smooth out the asperities of the wall, the information on the wall orientation obtained in this way is observed to be of high quality.     

A mathematical model for the study of interstitial fluid movement vis-a-vis the non-newtonian behaviour of blood in a constricted artery

A mathematical model is developed with an aim to study the transport of interstitial fluid in the wall of a constricted artery by taking into account the microrotation of the erythrocytes of blood. The movement of the interstitial fluid has been described by the Debye-Brinkman equation. Exact solutions are obtained for the displacement of the solid matrix of the porous interstitial space, the velocity of the interstitial fluid movement, and the pressure distribution in the constricted arterial segment, for large and small consolidation times. Expression for the wall shear stress is also obtained for the constricted segment of the artery. Theoretical estimates of the distributions of the axial velocity of blood in the stenosed zone, rotational velocity of the erythrocytes, wall shear stress, and wall displacement, as well as the pressure and velocity profiles for the interstitial fluid movement, have been presented in the form of graphs.     

Effect of sidewall boundary conditions on unsteady high speed cavity flow and acoustics

The effect of sidewall boundary conditions on the computed unsteady flow and sound pressure level is investigated in a transonic open cavity. The hybrid approach used for modeling turbulence combines a Reynolds averaged mode in the boundary layer, and a large eddy simulation mode in the massively separated flow region within the cavity to resolve the wide dynamic range involved. Computational results are presented for the instantaneous vorticity and for the sound pressure level spectra. Comparison of the results obtained using inviscid and periodic sidewall boundary conditions show the sensitivity of the computed SPL spectra and autocorrelation to the conditions enforced at the sidewalls. The computed SPL spectra are also compared with available experimental results, with LES computational results, and with prior investigations based on the same hybrid turbulence model without the wall function used in the current investigation. The comparisons show that the current results obtained using inviscid sidewall boundary conditions are closest to the experimental sound pressure level spectra and that agreement is achieved at considerable saving in required computational resources.     

Analysis of flow patterns in a patient-specific thoracic aortic aneurysm model

In this study, a newly developed two-equation transitional model was employed for the prediction of blood flow patterns in a thoracic aortic aneurysm (TAA) where the growth and progression are closely linked to low and oscillating wall shear stresses. Laminar–turbulent transition in the dilated vessel can alter the flow structure, shear stress and pressure distribution within the aneurysm. A patient-specific TAA model was reconstructed from magnetic-resonance (MR) images and measured velocity waveform was used as the inflow condition. Laminar flow and a correlation-based transitional version of Menter’s hybrid k ? ?/k ? ω Shear Stress Transport (SST Tran) model were implemented in pulsatile simulations from which WSS distribution was obtained throughout a cardiac cycle and velocity profiles were compared with MR measurements. The correlation-based transitional model was found to produce results in closer agreement with the MR data than the laminar flow simulation.     

Mathematical modelling for pulsatile flow of Casson fluid along with magnetic nanoparticles in a stenosed artery under external magnetic field and body acceleration

In the present paper, the magnetohydrodynamics effects on flow parameters of blood carrying magnetic nanoparticles flowing through a stenosed artery under the influence of periodic body acceleration are investigated. Blood is assumed to behave as a Casson fluid. The governing equations are nonlinear and solved numerically using finite difference schemes. The effects of stenotic height, yield stress, magnetic field, particle concentration and mass parameters on wall shear stress, flow resistance and velocity distribution are analysed. It is found that wall shear stress and flow resistance values are considerably enhanced when an external magnetic field is applied. The velocity values of fluid and particles are appreciably reduced when a magnetic field is applied on the model. It is significant to note that the presence of nanoparticles, magnetic field and yield stress tend to increase the plug core radius. Increased wall shear stress and flow resistance affects the circulation of blood in the human cardiovascular system. The results obtained from the study can be used in normalizing the values of the model parameters and hence can be used for medical applications. The presence of magnetic field helps to slow down the flow of fluid and magnetic particles associated with it. The magnetic particles of nanosize developed in recent days are biodegradable and used in biomedical applications. Biomagnetic principles and biomagnetic particles as drug carriers are used in cancer treatments.

     

Adaptive boundary layer meshing for viscous flow simulations

A procedure for anisotropic mesh adaptation accounting for mixed element types and boundary layer meshes is presented. The method allows to automatically construct meshes on domains of interest to accurately and efficiently compute key flow quantities, especially near wall quantities like wall shear stress. The new adaptive approach uses local mesh modification procedures in a manner that maintains layered and graded elements near the walls, which are popularly known as boundary layer or semi-structured meshes, with highly anisotropic elements of mixed topologies. The technique developed is well suited for viscous flow applications where exact knowledge of the mesh resolution over the computational domain required to accurately resolve flow features of interest is unknown a priori. We apply the method to two types of problem cases; the first type, which lies in the field of hemodynamics, involves pulsatile flow in blood vessels including a porcine aorta case with a stenosis bypassed by a graft whereas the other involves high-speed flow through a double throat nozzle encountered in the field of aerodynamics.     

Three-dimensional flow velocity and wall shear stress distribution measurement on a micropillar-arrayed surface using astigmatism PTV to understand the influence of microstructures on the flow field

In this study, the influence of the microstructure in a microchannel on the three-dimensional (3D) flow field and shear stress distribution on the wall was investigated with 3D velocity measurement method. In a micro-total analysis system or a lab-on-a-chip application, the control of the flow is necessary. Thus, microstructures are often applied to the fluidic system for passive flow control. However, the flow field which interacts with microstructures becomes complicated three-dimensionally. The 3D measurement of such microfluidic flow would give insight on the interaction of the flow with the structures and be also useful for other applications. In this study, micropillar array was introduced in a microchannel and we investigated the influence of the micropillar on the 3D flow field by the astigmatism particle tracking velocimetry which enables to determine three-dimensional and three-component velocity by single-viewing. Furthermore, the wall shear stress distribution was also investigated. From measurement results, it was confirmed that the pillar changes the wall shear stress distribution and 3D velocity distribution. Compared to a flat channel (no-pillar array), the wall shear stress in our channel varied spatially in a range of approximately ??80 to +?20%. Moreover, we also conducted a numerical simulation to consolidate the measurement results.     

On a method for direct numerical simulation of shear layer/compression wave interaction for aeroacoustic investigations

Direct numerical simulation (DNS) of a spatially developing mixing layer was performed. The compressible three-dimensional Navier-Stokes equations were solved for pressure, velocities and entropy for this flow using a compact finite-difference scheme of sixth-order accuracy in space, combined with Runge-Kutta three-step time advancement. On one of the transverse boundaries of the box-shaped domain, a compression wave profile was imposed in pressure and velocity components via a wave decomposition of the governing equations, in order to study the interaction of an isolated weak shock wave entering the domain with the mixed subsonic/supersonic shear layer. This flow situation is found along the shear layer of supersonic, imperfectly expanded jets containing a shock cell structure. In the present work, an isolated compression-expansion structure constitutes the model problem. The domain setup and the boundary conditions were chosen such as to allow analysis of the sound field generated by the turbulent flow and the shock-turbulence interaction. The numerical method used to impose the boundary conditions and solve the compressible Navier-Stokes equations, and the choice of numerical parameters, are described in detail. Some results on the two-dimensional and three-dimensional flow field computed are presented as well.     

Eduction of near wall flow structures responsible for large deviations of the momentum-heat transfer analogy and fluctuations of wall transfer rates in turbulent channel flow

In this paper we analyze the flow structures responsible for large local instantaneous deviations of the conventional momentum-heat transfer analogy and large fluctuations of the wall shear stress and the wall heat flux in a forced convection turbulent channel flow at low-Reynolds numbers (Re = 4570, Pr = 0.7). The analysis was carried out using a database obtained from a direct numerical simulation performed with a second-order finite volume code. The ensemble averaged velocity and temperature profiles and profiles of the turbulence intensities and turbulent heat fluxes agree well with direct numerical simulations available in the literature. When the flow was statistically fully developed, we recorded the time evolution of the velocities and temperatures near one wall of the channel. The near wall structures responsible for the extreme values of the deviations were educed by a conditional sampling technique. Results show that extreme values of the wall shear stress and wall heat transfer rates, as well as departures from the conventional analogy between momentum and heat transfer, occur within the high-speed streaks on the wall and are associated with fluctuations of the streamwise pressure gradient. These large fluctuations on the wall are produced by the combined effect of two quasi-parallel counterrotating streamwise vortices.     

Turbulent boundary layer structure of flow over a smooth-curved ramp

The effects of a convex-curved wall followed by a recovery over a flat surface on a turbulent boundary layer structure are addressed via large-eddy simulation (LES). The curved wall constitutes a smooth ramp formed by a portion of circular arc. The statistically two-dimensional upstream boundary layer flow is realistically fed by an injected inflow boundary condition. The inflow is extracted from a simultaneously simulated flat-plate boundary layer which is computed based on a compressible rescaling method. After flowing over the curved surface the flow is allowed to recover its realistic condition by passing over a downstream flat surface. The Reynolds number introduced at the inlet section of the computational domain which starts 4 times the ramp length (L_r) upstream of the curved surface is Re_δo=U_∞δ_o/ν=9907. The Reynolds number is based on the inflow boundary layer thickness δ_o, the free-stream velocity U_∞ and the kinematic viscosity ν.Mean flow predictions obtained using the present LES with the rescaling–recycling inflow condition agree well with the available experimental data from literature. The Reynolds stress components match the experimental one. However, small deviation occurs due to the smaller-domain height used in the present simulation. The experiments showed that there is a generated pressure gradient on the upper wall and this in return affects the turbulence energy on the other wall. The numerical data as well as the experiments show an enhancement of the turbulent stresses in the adverse pressure gradient region. The increased level of turbulent stresses is accompanied with large peaks aligned with the inflection point of the velocity profiles. The high stress levels are nearly unchanged by reattachment process, decaying only after the mean velocity recovered and the high production of turbulence near the outer layer drops. The recovery of the outer layer is due to the turbulent eddies generated by the separation region. Numerical visualizations show strong elongation and lifting of eddies in the region of the adverse pressure gradient generated by the curved wall. Computations of two-point correlations are also performed to represent the formation and deformation of the turbulent eddies before, over and after the curved wall. Different effects on the eddy size and its structure angle are presented.     

Simulation of media behaviour in vibration assisted abrasive flow machining

Abrasive flow machining (AFM) is an abrasive-based precision finishing process used for achieving surface finish in micro and nano-level. The AFM polishes surfaces by extruding a visco-elastic media in contact with the workpiece. The media, also called a ‘flexible tool’, plays a key role in the performance of the process. Ultrasonic assisted abrasive flow machining (UAAFM) is a new variant of the AFM process in which the workpiece is subjected to mechanical vibration orthogonal to the media flow direction. In this process a high frequency, in the range of about 5–20 kHz, is given to the workpiece with the help of a piezo actuator and a specially designed fixture. The present work highlights on the possible behaviour of the tool (media) during UAAFM and its effect on the machining process through a computation based approach. Commercially available simulation tool was used to study the effect of the media in response to different set of machining conditions. The responses were evaluated in terms of changes in the fluid pressure, velocity profile of the fluid, temperature distribution in the working fluid and the possible wall shear on the work surface. A three-dimensional model was constructed for simulating the UAAFM process. The simulation shows that the abrasive particles tend to hit the target surface at an angle ‘θ’ which significantly affects the basic mechanisms involved and enhances the effectiveness of the process. The computed wall shear explains that the process will have higher finishing rate and hence the performance. The enhanced interaction of abrasive media in UAAFM while compared to simple AFM could be explained by the resultant pressure–velocity phenomena. Results show that while changes in the amplitude of applied vibration (10 μm and 50 μm) significantly affect the wall shear, the media velocity and pressure profiles are only marginally sensitive to this parameter. The simulation results also confirm that the rise in temperature during the process will not affect the media stability. Results have been discussed vis-a-vis the basic mechanism of the process through suitable illustrations.     

Application of the method of integral relations to boundary layer flows over blunt bodies

Calculations of boundary layer flows past blunt bodies at angles of incidence are presented. Using the method of integral relations together with the method of lines, the full three-dimensional boundary layer equations are reduced to a system of first order ordinary differential equations. The streamwise shear stress function θ and the cross-flow velocity component V are represented as suitable functions of the streamwise velocity component U. The role of the zone of dependence is automatically satisfied by the choice of differencing in the method of lines. Solutions correct to the second order are obtained in the positive shear region for flow over an ellipsoid at 30° incidence. The results are compared with corresponding finite difference solutions.     

On the influence of the wall shear stress vector form on hemodynamic indicators

Hemodynamic indicators such as the averaged wall shear stress (AWSS) and the oscillatory shear index (OSI) are well established to characterize areas of arterial walls with respect to the formation and progression of aneurysms. Here, we study two different forms for the wall shear stress vector from which AWSS and OSI are computed. One is commonly used as a generalization from the two-dimensional setting, the latter is derived from the full decomposition of the wall traction force given by the Cauchy stress tensor. We compare the influence of both approaches on hemodynamic indicators by numerical simulations under different computational settings. Namely, different (real and artificial) vessel geometries, and the influence of a physiological periodic inflow profile. The blood is modeled either as a Newtonian fluid or as a generalized Newtonian fluid with a shear rate dependent viscosity. Numerical results are obtained by using a stabilized finite element method. We observe profound differences in hemodynamic indicators computed by these two approaches, mainly at critical areas of the arterial wall.

     

Direct numerical simulation of rarefied turbulent microchannel flow

Direct numerical simulation (DNS) has been carried out to investigate the effect of weak rarefaction on turbulent gas flow and heat transfer characteristics in microchannel. The Reynolds number based on the friction velocity and the channel half width is 150. Grid number is 64 × 128 × 64. Fractional time-step method is employed for the unsteady Navier–Stokes equations, and the governing equations are discretized with finite difference method. Statistical quantities such as turbulent intensity, Reynolds shear stress, turbulent heat flux and temperature variance are obtained under various Knudsen number from 0 to 0.05. The results show that rarefaction can influence the turbulent flow and heat transfer statistics. The streamwise mean velocity and temperature increase with increase of Kn number. In the near-wall-region rarefaction can increase the turbulent intensities and temperature variance. The effects of rarefaction on Reynolds shear stress and wall-normal heat flux are presented. The instantaneous velocity fluctuations in the vicinity of the wall are visualized and the influence of Kn number on the flow structure is discussed.     

Flow through blood vessels under the action of a periodic acceleration field A mathematical analysis

The paper is devoted to an analytical study of flow through blood vessels subjected to a periodic acceleration field. The analysis consists of two parts. In the first case, the wall is treated as a non-linear orthotropic elastic cylindrical membrane and the blood as a Newtonian viscous fluid, while in the second case the experimentally observed material damping properties of the wall tissues and the viscoelasticity of blood have been incorporated in the analysis. In each of these two cases, analytical expressions for the displacement and shear stresses developed in the wall as well as the velocity distribution, fluid acceleration and volume flow rate of blood are derived. The influence of material damping of the wall tissues as well as the viscoelastic properties of blood on the flow and deformation characteristic of a blood vessel has been estimated by using the values of the different material constants (involved in the analysis) determined experimentally for the human abdominal aorta. Numerical results presented in the paper correspond to observed parameters of the circulatory system of living animals.     

Dynamic variation of hemodynamic shear stress on the walls of developing chick hearts: computational models of the heart outflow tract

Heart morphogenesis and growth are influenced by hemodynamic forces (wall shear stress and blood pressure) acting on the walls of the heart. Mechanisms by which hemodynamic forces affect heart development are not well understood, in part because of difficulties involved in measuring these forces in vivo. In this paper, we show how wall shear stress in the heart outflow tract (OFT) of chick embryos at an early developmental stage (HH18) are affected by changes in the geometry and motion of the OFT wall. In particular, we were interested in the effects of cardiac cushions, which are protrusions of the OFT wall toward the lumen and that are located where valves will later form. We developed idealized finite element models (FEM) of the chick OFT with and without cardiac cushions. Geometrical parameters used in these models were estimated from in vivo images obtained using optical coherence tomography (OCT) techniques. The FEMs showed significant reverse blood flow (backflow) in the OFT, consistent with experimental observations in the chick heart at HH18, and revealed that cardiac cushions decrease backflow. In addition, our FEMs showed that the spatial distribution of wall shear stress is affected by cardiac cushions, with larger absolute peak values observed at the cushions. Differences in mechanical stimuli (wall shear stress) that the cells in the cardiac cushions and elsewhere are subjected to may affect valve formation and heart development.