Assessment of boundary conditions for CFD simulation in human carotid artery

Computational fluid dynamics (CFD) is an increasingly used method for investigation of hemodynamic parameters and their alterations under pathological conditions, which are important indicators for diagnosis of cardiovascular disease. In hemodynamic simulation models, the employment of appropriate boundary conditions (BCs) determines the computational accuracy of the CFD simulation in comparison with pressure and velocity measurements. In this study, we have first assessed the influence of inlet boundary conditions on hemodynamic CFD simulations. We selected two typical patients suspected of carotid artery disease, with mild stenosis and severe stenosis. Both patients underwent digital subtraction angiography (DSA), magnetic resonance angiography, and the invasive pressure guide wire measured pressure profile. We have performed computational experiments to (1) study the hemodynamic simulation outcomes of distributions of wall shear stress, pressure, pressure gradient and (2) determine the differences in hemodynamic performances caused by inlet BCs derived from DSA and Womersley analytical solution. Our study has found that the difference is related to the severity of the stenosis; the greater the stenosis, the more the difference ensues. Further, in our study, the two typical subjects with invasively measured pressure profile and thirty subjects with ultrasound Doppler velocimeter (UDV) measurement served as the criteria to evaluate the hemodynamic outcomes of wall shear stress, pressure, pressure gradient and velocity due to different outlet BCs based on the Windkessel model, structured-tree model, and fully developed flow model. According to the pressure profiles, the fully developed model appeared to have more fluctuations compared with the other two models. The Windkessel model had more singularities before convergence. The three outlet BCs models also showed good correlation with the UDV measurement, while the Windkessel model appeared to be slightly better (\( R^{2} = 0.942 \)). The structured-tree model was seen to have the best performance in terms of available computational cost and accuracy. The results of our numerical simulation and the good correlation with the computed pressure and velocity with their measurements have highlighted the effectiveness of CFD simulation in patient-specific human carotid artery with suspected stenosis.     

Shear stress gradient over endothelial cells in a curved microchannel system.

Our purpose was to test a scale model of the microcirculation by measuring the shear forces to which endothelial cells were exposed, and comparing this to computer simulations. In vitro experiments were performed to measure the 2-dimensional projected velocity profile along endothelial cell lined microchannels (D-shaped, 10-30 microns radius, n = 15), or in microchannels without endothelial cells (n = 18). Microchannels were perfused with fluorescently labeled microspheres (0.5 micron dia., < 1%) suspended in cell culture media. The velocity of individual microspheres was obtained off-line (videorecording), using an interactive software program; velocity was determined as the distance traveled in one video field (1/60 s). Mass balance was verified in the microchannels by comparing the microsphere velocities to the perfusion pump rate. In confluent endothelial cell lined microchannels, a velocity profile was obtained as microspheres passed an endothelial cell nucleus (identified by fluorescent dye), and again, for a paired region 100 microns away without nuclei (cytoplasm region). The velocity profile was significantly shifted and sharpened by the endothelial cell nucleus, as anticipated. Over the nucleus, data are consistent with a normal sized nucleus extending into the lumen, further confirming that this scale model can be used to determine the wall shear stress to which endothelial cells are exposed. Using the experimental bulk phase fluid parameters as boundary conditions, we used computational fluid dynamics (CFD) to predict the expected wall shear stress gradient along an endothelial cell lined D-shaped tube. The wall shear stress gradient over the nucleus was 2-fold greater in the radial versus axial directions, and was sensitive to lateral versus midline positioned nuclei.     

Tissue-fluid interface analysis using biphasic finite element method

Numerical studies on fluid-structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid-structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue-fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.     

A computational fluid dynamics (CFD) based method for assessing the hydrodynamic impact of animal borne data loggers on host marine mammals

Animal‐borne data loggers (ABDLs) or “tags” are regularly used to elucidate animal ecology and physiology, but current literature highlights the need to assess associated deleterious impacts including increased resistive force to motion. Previous studies have used computational fluid dynamics (CFD) to estimate this impact, but many suffer limitations (e.g., inaccurate turbulence modeling, neglecting boundary layer transition, neglecting added mass effects, and analyzing the ABDL in isolation from the animal). A novel CFD‐based method is presented in which a “tag impact envelope” is defined utilizing simulations with and without transition modeling to define upper and lower drag limits, respectively, and added mass coefficients are found via simulations with sinusoidally varying inlet velocity, with modified Navier‐Stokes conservation of momentum equations enforcing a shift to the animal's noninertial reference frame. The method generates coefficients for calculating total resistive force for any velocity and acceleration combination, and is validated against theory for a prolate spheroid. An example case shows ABDL drag impact on a harp seal of 11.21%–16.24%, with negligible influence on added mass. By considering the effects of added mass and boundary layer transition, the approach presented is an enhancement to the CFD‐based ABDL impact assessment methods previously applied by researchers.     

Comparison of 4D Phase-Contrast MRI Flow Measurements to Computational Fluid Dynamics Simulations of Cerebrospinal Fluid Motion in the Cervical Spine

Cerebrospinal fluid (CSF) dynamics in the cervical spinal subarachnoid space (SSS) have been thought to be important to help diagnose and assess craniospinal disorders such as Chiari I malformation (CM). In this study we obtained time-resolved three directional velocity encoded phase-contrast MRI (4D PC MRI) in three healthy volunteers and four CM patients and compared the 4D PC MRI measurements to subject-specific 3D computational fluid dynamics (CFD) simulations. The CFD simulations considered the geometry to be rigid-walled and did not include small anatomical structures such as nerve roots, denticulate ligaments and arachnoid trabeculae. Results were compared at nine axial planes along the cervical SSS in terms of peak CSF velocities in both the cranial and caudal direction and visual interpretation of thru-plane velocity profiles. 4D PC MRI peak CSF velocities were consistently greater than the CFD peak velocities and these differences were more pronounced in CM patients than in healthy subjects. In the upper cervical SSS of CM patients the 4D PC MRI quantified stronger fluid jets than the CFD. Visual interpretation of the 4D PC MRI thru-plane velocity profiles showed greater pulsatile movement of CSF in the anterior SSS in comparison to the posterior and reduction in local CSF velocities near nerve roots. CFD velocity profiles were relatively uniform around the spinal cord for all subjects. This study represents the first comparison of 4D PC MRI measurements to CFD of CSF flow in the cervical SSS. The results highlight the utility of 4D PC MRI for evaluation of complex CSF dynamics and the need for improvement of CFD methodology. Future studies are needed to investigate whether integration of fine anatomical structures and gross motion of the brain and/or spinal cord into the computational model will lead to a better agreement between the two techniques.     

Quantitative comparison of CFD predicted and MRI measured velocity fields in a carotid bifurcation phantom

Steady flow of a blood mimicking fluid in a physiologically realistic model of the human carotid bifurcation was studied using both magnetic resonance imaging (MRI) and computational fluid dynamics (CFD) modelling techniques. Quantitative comparisons of the 3D velocity field in the bifurcation phantom were made between phase contrast MRI measurements and CFD predictions. The geometry for the CFD model was reconstructed from T(1) weighted MR imaging of the test phantom. It was found that the predicted velocity fields were in fair agreement with MR measured velocities. In both the internal and external carotid arteries, the agreement between CFD predictions and MRI measurements was better along the inner-outer wall axis with a correlation factor C>0.897 (average 0.939) where the velocity profiles were skewed, than along the anterior-posterior axis (average correlation factor 0.876) where the velocity profiles were in M-shape.     

Three-dimensional cerebrospinal fluid flow within the human ventricular system

Cerebrospinal fluid (CSF) is a Newtonian fluid and can, therefore, be modelled using computational fluid dynamics (CFD). Previous modelling of the CSF has been limited to simplified geometric models. This work describes a geometrically accurate three dimensional (3D) computational model of the human ventricular system (HVS) constructed from magnetic resonance images (MRI) of the human brain. It is an accurate and full representation of the HVS and includes appropriately positioned CSF production and drainage locations. It was used to investigate the pulsatile motion of CSF within the human brain. During this investigation CSF flow rate was set at a constant 500 ml/day, to mimic real life secretion of CSF into the system, and a pulsing velocity profile was added to the inlets to incorporate the effect of cardiac pulsations on the choroid plexus and their subsequent influence on CSF motion in the HVS. Boundary conditions for the CSF exits from the ventricles (foramina of Magendie and Lushka) were found using a "nesting" approach, in which a simplified model of the entire central nervous system (CNS) was used to examine the effects of the CSF surrounding the ventricular system (VS). This model provided time varying pressure data for the exits from the VS nested within it. The fastest flow was found in the cerebral aqueduct, where a maximum velocity of 11.38 mm/s was observed over five cycles. The maximum Reynolds number recorded during the simulation was 15 with an average Reynolds number of the order of 0.39, indicating that CSF motion is creeping flow in most of the computational domain and consequently will follow the geometry of the model. CSF pressure also varies with geometry with a maximum pressure drop of 1.14 Pa occurring through the cerebral aqueduct. CSF flow velocity is substantially slower in the areas that are furthest away from the inlets; in some areas flow is nearly stagnant.     

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.     

Diffusive Promotion by Velocity Gradient of Cytoplasmic Streaming (CPS) in Nitella Internodal Cells

Cytoplasmic streaming (CPS) is well known to assist the movement of nutrients, organelles and genetic material by transporting all of the cytoplasmic contents of a cell. CPS is generated by motility organelles that are driven by motor proteins near a membrane surface, where the CPS has been found to have a flat velocity profile in the flow field according to the sliding theory. There is a consistent mixing of contents inside the cell by CPS if the velocity gradient profile is flattened, which is not assisted by advection diffusion but is only supported by Brownian diffusion. Although the precise flow structure of the cytoplasm has an important role for cellular metabolism, the hydrodynamic mechanism of its convection has not been clarified. We conducted an experiment to visualise the flow of cytoplasm in Nitella cells by injecting tracer fluorescent nanoparticles and using a flow visualisation system in order to understand how the flow profile affects their metabolic system. We determined that the velocity field in the cytosol has an obvious velocity gradient, not a flattened gradient, which suggests that the gradient assists cytosolic mixing by Taylor–Aris dispersion more than by Brownian diffusion.     

Flow pattern visualization in a mimic anaerobic digester using CFD

Three-dimensional steady-state computational fluid dynamics (CFD) simulations were performed in mimic anaerobic digesters to visualize their flow pattern and obtain hydrodynamic parameters. The mixing in the digester was provided by sparging gas at three different flow rates. The gas phase was simulated with air and the liquid phase with water. The CFD results were first evaluated using experimental data obtained by computer automated radioactive particle tracking (CARPT). The simulation results in terms of overall flow pattern, location of circulation cells and stagnant regions, trends of liquid velocity profiles, and volume of dead zones agree reasonably well with the experimental data. CFD simulations were also performed on different digester configurations. The effects of changing draft tube size, clearance, and shape of the tank bottoms were calculated to evaluate the effect of digester design on its flow pattern. Changing the draft tube clearance and height had no influence on the flow pattern or dead regions volume. However, increasing the draft tube diameter or incorporating a conical bottom design helped in reducing the volume of the dead zones as compared to a flat-bottom digester. The simulations showed that the gas flow rate sparged by a single point (0.5 cm diameter) sparger does not have an appreciable effect on the flow pattern of the digesters at the range of gas flow rates used.     

Effect of asymmetry of concentration-response curves on the results obtained by the receptorial responsiveness method (RRM): an in silico study

The receptorial responsiveness method (RRM) was proposed to estimate changes in the concentration of an agonist in the microenvironment of its receptor. Usually, this is done by providing the equieffective concentration of another agonist for the same receptor or for a largely overlapping postreceptorial signaling ("test agonist"). The RRM is a special nonlinear regression algorithm to analyze a concentration-response (E/c) curve that represents the simultaneous actions of a single agonist concentration to be estimated and of increasing concentrations of the test agonist. The aim of this study was to explore whether asymmetry of the E/c curve to be analyzed influences the reliability of the RRM. For this purpose, computer simulation was performed by constructing symmetric and asymmetric E/c curves using the operational model of agonism, and then these curves were analyzed with the RRM. To perform the RRM, 2 types of equations were used: one involving the Hill equation, the simplest model of the E/c relationship, and one containing the Richards equation, an advanced model properly handling E/c curve asymmetry. Results of this study indicate that E/c curve asymmetry does not significantly influence the accuracy of the estimates provided by the RRM. Thus, when using the RRM, it is not necessary to replace the Hill equation with the Richards equation to obtain useful estimates. Furthermore, it was found that estimation of a high concentration of a high-efficacy agonist can fail when the RRM is performed with a low-efficacy test agonist in a system characterized by a small operational slope factor.     

Ancient life and moving fluids

Over 3.7 billion years of Earth history, life has evolved complex adaptations to help navigate and interact with the fluid environment. Consequently, fluid dynamics has become a powerful tool for studying ancient fossils, providing insights into the palaeobiology and palaeoecology of extinct organisms from across the tree of life. In recent years, this approach has been extended to the Ediacara biota, an enigmatic assemblage of Neoproterozoic soft-bodied organisms that represent the first major radiation of macroscopic eukaryotes. Reconstructing the ways in which Ediacaran organisms interacted with the fluids provides new insights into how these organisms fed, moved, and interacted within communities. Here, we provide an in-depth review of fluid physics aimed at palaeobiologists, in which we dispel misconceptions related to the Reynolds number and associated flow conditions, and specify the governing equations of fluid dynamics. We then review recent advances in Ediacaran palaeobiology resulting from the application of computational fluid dynamics (CFD). We provide a worked example and account of best practice in CFD analyses of fossils, including the first large eddy simulation (LES) experiment performed on extinct organisms. Lastly, we identify key questions, barriers, and emerging techniques in fluid dynamics, which will not only allow us to understand the earliest animal ecosystems better, but will also help to develop new palaeobiological tools for studying ancient life.     

MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models

Pulsatile flow was studied in physiologically realistic models of a normal and a moderately stenosed (30% diameter reduction) human carotid bifurcation. Time-resolved velocity measurements were made using magnetic resonance imaging, from which wall shear stress (WSS) vectors were calculated. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for a computational fluid dynamics (CFD) model. Experimental flow patterns and derived WSS vectors were compared qualitatively with the corresponding CFD predictions. In the stenosed phantom, flow in the bulb region of the "internal carotid artery" was concentrated along the outer wall, with a region of low and recirculating flow near the inner wall. In the normal phantom, the converse was found, with a low flow region near the outer wall of the bulb. Time-averaged WSS and oscillatory shear index were also markedly different for the two phantoms.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Effects of Geometric Parameters on Swimming of Micro Organisms with Single Helical Flagellum in Circular Channels

We present a computational fluid dynamics (CFD) model for the swimming of micro organisms with a single helical flagellum in circular channels. The CFD model is developed to obtain numerical solutions of Stokes equations in three dimensions, validated with experiments reported in literature, and used to analyze the effects of geometric parameters, such as the helical radius, wavelength, radii of the channel and the tail and the tail length on forward and lateral swimming velocities, rotation rates, and the efficiency of the swimmer. Optimal shapes for the speed and the power efficiency are reported. Effects of Brownian motion and electrostatic interactions are excluded to emphasize the role of hydrodynamic forces on lateral velocities and rotations on the trajectory of swimmers. For thin flagella, as the channel radius decreases, forward velocity and the power efficiency of the swimmer decreases as well; however, for thick flagella, there is an optimal radius of the channel that maximizes the velocity and the efficiency depending on other geometric parameters. Lateral motion of the swimmer is suppressed as the channel is constricted below a critical radius, for which the magnitude of the lateral velocity reaches a maximum. Results contribute significantly to the understanding of the swimming of bacteria in micro channels and capillary tubes.     

Using a CFD model to understand the fluid dynamics promoting E. coli breakage in a high-pressure homogenizer

A Computational Fluid Dynamic (CFD) model of flow in a high-pressure homogenizing valve (APV Gaulin model 30CD) was developed with the Fluent software. The 2D model consists of an unstructured hexagonal mesh, dense in the regions of high gradients. The flow (single-phase) was modeled as laminar upstream of and in the channel (gap) and turbulent downstream of the channel exit. Applying a realizable kappa-epsilon turbulence model, the CFD model accurately predicted the effect of gap space on fluid dynamic conditions upstream (inlet pressure and pressure gradient) and downstream (impact pressure) of the channel for a valve with a standard (CD-0) impact distance (0.25 mm) and a 1 cP fluid. This CFD model was then used to estimate the magnitude of the fluid dynamic parameters (except cavitation effects) presumed to be responsible for cell breakage, as a function of gap space, impact distance and fluid viscosity. The CFD models predicted that for a given volumetric flowrate the upstream fluid conditions (inlet pressure gradient, maximum channel strain rate) and the maximum energy dissipation rate in the post-gap jet depend only on the gap space and the fluid viscosity and not on the impact distance. The impact pressure however depends on the gap spacing, the fluid viscosity and especially the impact distance. Experimental results indicate that higher inlet pressures are required to break cells, if the impact distance is increased. By conducting experiments to isolate individual cell breakage mechanisms for a single pass, threshold values were identified for breaking Escherichia coli cells: pressure gradient, 1.2 x 10(12) Pa/m; energy dissipation rate, 1.0 x 10(10) m(3)/s(2); and impact pressure, 160 psig. By isolating the wall impact as the sole mechanism responsible for breaking the E. coli cells between 3000 and 6000 psig inlet pressure, a relationship between E. coli cell breakage rate and maximum wall impact pressure was established (eq 5).     

计算流体力学在古生物学中的应用——以寒武纪始海百合在COMSOL软件中的模拟为例

提要关于古生物生态位和功能形态学方面的研究通常是推测性的,而定量分析工作较少。此外由于缺少现生生物做对比等诸多因素,使得有些假说存在争议。计算流体力学CFD (computational fluid dynamics)在验证这些推测性假说上具有极大的潜力,并为了解古生物的生活环境以及解释生物在进化过程中的形态变化提供了新的契机。COMSOL Multiphysics作为一款多物理场仿真软件,适用于对古生物的CFD模拟,本文以凯里组始海百合Globoeocrinus模型在COMSOL中的流体实验为案例,来论证关于Globoeocrinus螺旋的腕会使附近的水体形成湍性流动进而帮助滤食这一假说的可能性。流体模拟结果表明在水流流速0.01–0.5 m/s的范围内,Globoeocrinus腕周围并没有出现湍性流动的涡,而是形成了低流速域。低流速域的形成有利于增加始海百合滤取食物的概率。同时文章详细介绍了在COMSOL中进行案例研究的操作步骤,以期望帮助更多的古生物研究者理解和应用CFD技术。     

CFD simulation of flow through heart: a perspective review

The heart is an organ which pumps blood around the body by contraction of muscular wall. There is a coupled system in the heart containing the motion of wall and the motion of blood fluid; both motions must be computed simultaneously, which make biological computational fluid dynamics (CFD) difficult. The wall of the heart is not rigid and hence proper boundary conditions are essential for CFD modelling. Fluid-wall interaction is very important for real CFD modelling. There are many assumptions for CFD simulation of the heart that make it far from a real model. A realistic fluid-structure interaction modelling the structure by the finite element method and the fluid flow by CFD use more realistic coupling algorithms. This type of method is very powerful to solve the complex properties of the cardiac structure and the sensitive interaction of fluid and structure. The final goal of heart modelling is to simulate the total heart function by integrating cardiac anatomy, electrical activation, mechanics, metabolism and fluid mechanics together, as in the computational framework.     

Darcian permeability constant as indicator for shear stresses in regular scaffold systems for tissue engineering

The shear stresses in printed scaffold systems for tissue engineering depend on the flow properties and void volume in the scaffold. In this work, computational fluid dynamics (CFD) is used to simulate flow fields within porous scaffolds used for cell growth. From these models the shear stresses acting on the scaffold fibres are calculated. The results led to the conclusion that the Darcian (k ₁) permeability constant is a good predictor for the shear stresses in scaffold systems for tissue engineering. This permeability constant is easy to calculate from the distance between and thickness of the fibres used in a 3D printed scaffold. As a consequence computational effort and specialists for CFD can be circumvented by using this permeability constant to predict the shear stresses. If the permeability constant is below a critical value, cell growth within the specific scaffold design may cause a significant increase in shear stress. Such a design should therefore be avoided when the shear stress experienced by the cells should remain in the same order of magnitude.