Numerical simulation of steady flow in a model of the aortic bifurcation.

The governing equations of steady flow of an incompressible viscous fluid through a 3-D model of the aortic bifurcation are solved with the finite element method. The effect of Reynolds number on the flow was studied for a range including the physiological values (200 < or = Re < or = 1600). The symmetrical bifurcation, with a branch angle of 70 degrees and an area ratio of 0.8, includes a tapered transition zone. Secondary flows induced by the tube curvature are observed in the daughter tubes. Transverse currents in the transition zone are generated by the combined effect of diverging and converging walls. Flow separation depends on both the Reynolds number and the inlet wall shear.     

Characteristics of secondary flow in steady and pulsatile flows through a symmetrical bifurcation

Steady and pulsatile flow in a glass model simulating an arterial bifurcation was investigated by flow visualization techniques. Secondary flow generated at the bifurcation has a similar pattern to a vortex, called the horseshoe vortex, produced around a wall-based protuberance in a circular tube. The same flow disturbance was clearly observed during the decelerating phase of pulsatile flow. The vortex produces a stagnation point on the top and bottom wall just upstream from the bifurcation apex. When aluminium dust was suspended in the test fluid perfusing the blood vessel model, particles deposited over an area spreading from the stagnation point to the lateral corners of the bifurcation. Comparison between the present results and topographical patterns of atherosclerosis reported in the literature suggests that it is in such low shear regions that lipid deposition tends to occur most.     

Numerical simulations of steady flow inside a three dimensional aortic bifurcation model

A finite element formulation of the Navier-Stokes equations for three dimensional flow is presented. The equations are solved using the finite element method. The model is constructed from a cast of a human aortic bifurcation. The numerical problems introduced by solving the equation system are discussed and special attention is paid to the selection of the linear equation solver. The simulations of the steady blood flow patterns in an aortic bifurcation is shown. The results of the numerical analysis are presented as three dimensional plots of velocity vectors, wall shear vectors, streamlines and pressure isobars. The flow simulations are done for Reynolds number 10. The flow patterns found in the bifurcation model are discussed in connection with proposed theories to explain the event of early atherosclerosis.     

Finite element analysis of two dimensional steady flow in model arterial bifurcation

The purpose of the investigation reported in this paper is to determine theoretically the fluid dynamic field in models of common iliac arterial bifurcation and to identify the flow features which might influence the predominant occurrence of atherosclerotic lesions at such sites. This has been accomplished by numerically simulating fluid flow through 90 degrees symmetric bifurcations with branch-to-trunk area ratios of 0.8-1.414 and for Reynolds numbers ranging from 100 to 400. The analysis predicts flow reversal along the outer wall in models with area ratios over unity for high Reynolds number range, while no flow reversal occurred in models with area ratio below unity; a low shear zone along the outer wall and high shear stresses at the divider lip. Adverse pressure gradients are observed along the outer wall downstream of the corner point, the magnitudes increased with Reynolds number for a given branch to area ratio. Biological implication of the results is discussed with specific reference to the sites of atherosclerotic lesions found in man for these geometries.     

外加稳恒直流电场对兔腹主动脉周围电势差的影响

目的:观察外加稳恒直流电场对兔腹主动脉周围电势差的影响.方法:在兔腹主动脉两侧腰大肌埋置刺激电极,在血管外膜、血管内外膜间安置测量电极,给予稳恒直流电场刺激,电场强度采用3V或4V,记录电场刺激前后血管周围电势差的变化情况.结果:①通电后即刻,血管周围电势差与通电前相比无变化(P>0.05).②通电后30min,血管外膜间和血管内外膜间电势差均明显增加,4V组增加更为明显.③断电后30min,两外膜间电势差基本恢复至通电前水平,而血管内外膜间电势差仍高于通电前,两刺激电极间仍有较高电势差存在.结论:将铂电极置入兔腰大肌,连接稳恒直流电源后构成的是一个RC电路,应用3V电压或者4V电压刺激都可以引起血管周围电势的变化.     

Local and global geometric influence on steady flow in distal anastomoses of peripheral bypass grafts

We consider the effect of geometrical configuration on the steady flow field of representative geometries from an in vivo anatomical data set of end-to-side distal anastomoses constructed as part of a peripheral bypass graft. Using a geometrical classification technique, we select the anastomoses of three representative patients according to the angle between the graft and proximal host vessels (GPA) and the planarity of the anastomotic configuration. The geometries considered include two surgically tunneled grafts with shallow GPAs which are relatively planar but have different lumen characteristics, one case exhibiting a local restriction at the perianastomotic graft and proximal host whilst the other case has a relatively uniform cross section. The third case is nonplanar and characterized by a wide GPA resulting from the graft being constructed superficially from an in situ vein. In all three models the same peripheral resistance was imposed at the computational outflows of the distal and proximal host vessels and this condition, combined with the effect of the anastomotic geometry, has been observed to reasonably reproduce the in vivo flow split. By analyzing the flow fields we demonstrate how the local and global geometric characteristics influences the distribution of wall shear stress and the steady transport of fluid particles. Specifically, in vessels that have a global geometric characteristic we observe that the wall shear stress depends on large scale geometrical factors, e.g., the curvature and planarity of blood vessels. In contrast, the wall shear stress distribution and local mixing is significantly influenced by morphology and location of restrictions, particular when there is a shallow GPA. A combination of local and global effects are also possible as demonstrated in our third study of an anastomosis with a larger GPA. These relatively simple observations highlight the need to distinguish between local and global geometric influences for a given reconstruction. We further present the geometrical evolution of the anastomoses over a series of follow-up studies and observe how the lumen progresses towards the faster bulk flow of the velocity in the original geometry. This mechanism is consistent with the luminal changes in recirculation regions that experience low wall shear stress. In the shallow GPA anastomoses the proximal part of the native host vessel occludes or stenoses earlier than in the case with wide GPA. A potential contribution to this behavior is suggested by the stronger mixing that characterizes anastomoses with large GPA.     

Computational model of particle deposition in the nasal cavity under steady and dynamic flow

A computational model for flow and particle deposition in a three-dimensional representation of the human nasal cavity is developed. Simulations of steady state and dynamic airflow during inhalation are performed at flow rates of 9–60 l/min. Depositions for particles of size 0.5–20 μm are determined and compared with experimental and simulation results from the literature in terms of deposition efficiencies. The nasal model is validated by comparison with experimental and simulation results from the literature for particle deposition under steady-state flow. The distribution of deposited particles in the nasal cavity is presented in terms of an axial deposition distribution as well as a bivariate axial deposition and particle size distribution. Simulations of dynamic airflow and particle deposition during an inhalation cycle are performed for different nasal cavity outlet pressure variations and different particle injections. The total particle deposition efficiency under dynamic flow is found to depend strongly on the dynamics of airflow as well as the type of particle injection.     

Pressure drop and flow rate measurements in a human aortic bifurcation cast for steady and pulsatile flow

Pressure drop and flow rate measurements in a rigid cast of a human aortic bifurcation under both steady and physiological pulsatile flow conditions are reported. Integral momentum and mechanical energy balances are used to calculate impedance, spatially averaged wall shear stress and viscous dissipation rate from the data. In the daughter branches, steady flow impedance is within 30% of the Poiseuille flow prediction, while pulsatile flow impedance is within a factor of 2 of fully developed, oscillatory, straight tube flow theory (Womersley theory). Estimates of wall shear stress are in accord with measurements obtained from velocity profiles. Mean pressure drop and viscous dissipation rate are elevated in pulsatile flow relative to steady flow at the mean flow rate, and the exponents of their Reynolds number dependence are in accord with available theory.     

A numerical analysis of steady flow in a three-dimensional model of the carotid artery bifurcation

A finite element approximation of steady flow in a rigid three-dimensional model of the carotid artery bifurcation is presented. A Reynolds number of 640 and a flow division ratio of about 50/50, simulating systolic flow, was used. To limit the CPU- and I/O-times needed for solving the systems of equations, a mesh-generator was developed, which gives full control over the number of elements into which the bifurcation is divided. A mini-supercomputer, based on parallel and vector processing techniques, was used to solve the system of equations. The numerical results of axial and secondary flow compare favorably with those obtained from previously performed laser-Doppler velocity measurements. Also, the influence of the Reynolds number, the flow division ratio, and the bifurcation angle on axial and secondary flow in the carotid sinus were studied in the three-dimensional model. The influence of the interventions is limited to a relatively small variation in the region with reversed axial flow, more or less pronounced C-shaped axial velocity contours, and increasing or decreasing axial velocity maxima.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: steady flow in a carotid bifurcation model.

Laser Doppler anemometry experiments and finite element simulations of steady flow in a three dimensional model of the carotid bifurcation were performed to investigate the influence of non-Newtonian properties of blood on the velocity distribution. The axial velocity distribution was measured for two fluids: a non-Newtonian blood analog fluid and a Newtonian reference fluid. Striking differences between the measured flow fields were found. The axial velocity field of the non-Newtonian fluid was flattened, had lower velocity gradients at the divider wall, and higher velocity gradients at the non-divider wall. The flow separation, as found with the Newtonian fluid, was absent. In the computations, the shear thinning behavior of the analog blood fluid was incorporated through the Carreau-Yasuda model. The viscoelastic properties of the fluid were not included. A comparison between the experimental and numerical results showed good agreement, both for the Newtonian and the non-Newtonian fluid. Since only shear thinning was included, this seems to be the dominant non-Newtonian property of the blood analog fluid under steady flow conditions.     

Computational fluid dynamics in abdominal aorta bifurcation: non-Newtonian versus Newtonian blood flow in a real case study

Hemodynamic in abdominal aorta bifurcation was investigated in a real case using computational fluid dynamics. A Newtonian and non-Newtonian (Walburn-Schneck) viscosity models were compared. The geometrical model was obtained by 3D reconstruction from CT-scan and hemodynamic parameters obtained by laser-Doppler. Blood was assumed incompressible fluid, laminar flow in transient regime and rigid vessel wall. Finite volume-based was used to study the velocity, pressure, wall shear stress (WSS) and viscosity throughout cardiac cycle. Results obtained with Walburn-Schneck’s model, during systole, present lower viscosity due to shear thinning behavior. Furthermore, there is a significant difference between the results obtained by the two models for a specific patient. During the systole, differences are more pronounced and are preferably located in the tortuous regions of the artery. Throughout the cardiac cycle, the WSS amplitude between the systole and diastole is greater for the Walburn-Schneck’s model than for the Newtonian model. However, the average viscosity along the artery is always greater for the non-Newtonian model, except in the systolic peak. The hemodynamic model is crucial to validate results obtained with CFD and to explore clinical potential.     

Computational analysis of flow structure and particle deposition in a single asthmatic human airway bifurcation

This paper aims to improve current understanding of flow structure and particle deposition in asthmatic human airways. A single, symmetric airway bifurcation, corresponding to generations 10–11 of Weibel’s model, is investigated through validated numerical simulations. The parent airway segment is modelled as a smooth circular tube. The child segments are considered asthmatic and their cross-section is modelled as a constricted tube with sinusoidal folds uniformly distributed along the circumference. The flow structure and particle deposition pattern for normal (i.e., healthy) and asthmatic airway bifurcations are compared and discussed. The numerical results reveal that the secondary flow in the asthmatic airway bifurcation is much stronger than in the healthy one, resulting in higher particle deposition. The effects of size of the lumen area and number of folds on particle deposition and pressure drop are also investigated. It is found that particle deposition efficiency is significantly affected by lumen area of the asthmatic segment (the smaller the lumen area, the higher the particle deposition efficiency). The effect of number of folds is small. Particle deposition efficiency also increases with Reynolds number. The pressure drop in the asthmatic airway bifurcation depends mainly on size of the lumen area. The effect of number of folds becomes important for strongly collapsed airways.     

An LDA and flow visualization study of pulsatile flow in an aortic bifurcation model

The structure of pulsatile flow in a rigid aortic bifurcation model was studied by means of a flow visualization technique and three-dimensional laser-Doppler anemometry. The model was made of glass, having the same shape as that of the average human aortic bifurcation. It was installed into a mock circulatory loop that generated physiological pulsatile flow. Flow separation was observed during accelerated and decelerated flow periods. Double helical flow existed inside the flow separation in the early accelerated flow period. In the decelerated flow period, disturbed flow appeared behind the separation zone. Flow was strongly disturbed during the back flow period, and then was gradually stabilized in the forward flow period. The flow separation and the disturbances released from the flow separation zone greatly influenced near-wall velocities along the lateral wall. The wave form of the near-wall velocity in the flow separation zone was much different from that observed in the aortic portion and behind the separation zone; for example, the magnitude of the negative peak velocity in the direction of the tube axis was larger than that of the positive one, and mean velocity in a cycle was very low. This abnormal phasic change of the near-wall velocity may be associated with atherogenesis. The three-dimensional velocity measurement is very useful for the detailed analysis of near-wall velocity patterns.     

Pulsatile non-newtonian blood flow in three-dimensional carotid bifurcation models: a numerical study of flow phenomena under different bifurcation angles

Flow and stress patterns in human carotid artery bifurcation models, which differ in the bifurcation angle, are analysed numerically under physiologically relevant flow conditions. The governing Navier-Stokes equations describing pulsatile, three-dimensional flow of an incompressible non-Newtonian fluid are approximated using a pressure correction finite element method, which has been developed recently. The non-Newtonian behaviour of blood is modelled using Casson's relation, based on measured dynamic viscosity. The study concentrates on flow and stress characteristics in the carotid sinus. The results show that the complex flow in the sinus is affected by the angle variation. The magnitude of reversed flow, the extension of the recirculation zone in the outer sinus region and the duration of flow separation during the pulse cycle as well as the resulting wall shear stress are clearly different in the small angle and in the large angle bifurcation. The haemodynamic phenomena, which are important in atherogenesis, are more pronounced in the large angle bifurcation.     

Computational fluid dynamics modeling of the upper airway of children with obstructive sleep apnea syndrome in steady flow

Computational fluid dynamic (CFD) analysis was used to model the effect of airway geometry on internal pressure in the upper airway of three children with obstructive sleep apnea syndrome (OSAS), and three controls. Model geometry was reconstructed from magnetic resonance images obtained during quiet tidal breathing, meshed with an unstructured grid, and solved at normative peak resting flow. The unsteady Reynolds-averaged Navier-Stokes equations were solved with steady flow boundary conditions in inspiration and expiration, using a two-equation low-Reynolds number turbulence model. Model results were validated using an in-vitro scale model, unsteady flow simulation, and reported nasal resistance measurements in children. Pharynx pressure drop strongly correlated to airway area restriction. Inspiratory pressure drop was primarily proportional to the square of flow, consistent with pressure losses due to convective acceleration caused by area restriction. On inspiration, in OSAS pressure drop occurred primarily between the choanae and the region where the adenoids overlap the tonsils (overlap region) due to airway narrowing, rather than in the nasal passages; in controls the majority of pressure drop was in the nasal passages. On expiration, in OSAS the majority of pressure drop occurred between the oropharynx (posterior to the tongue) and overlap region, and local minimum pressure in the overlap region was near atmospheric due to pressure recovery in the anterior nasopharynx. The results suggest that pharyngeal airway shape in children with OSAS significantly affects internal pressure distribution compared to nasal resistance. The model may also help explain regional dynamic airway narrowing during expiration.     

Computational study on effect of stenosis on primary thrombus formation

The purpose of this study was to evaluate the effects of stenosis geometry on primary thrombogenesis with respect to the dynamics of the blood flow. A two-dimensional computer simulation was carried out to simulate the formation of a primary thrombus under blood flow in two geometrically different blood vessels: one straight and the other stenosed. In the simulation, blood was modeled by particles that have characteristics of plasma and of platelets. Plasma and platelet flow was analyzed using the Moving Particle Semi-implicit (MPS) method, while the motion of adhered and aggregated platelets was expressed by mechanical spring forces. With these models, platelet motion in the flowing blood and platelet aggregation and adhesion were successfully coupled with viscous blood flow. The results of the simulation demonstrated that the presence of a stenosis induced changes in blood flow and thereby altered the formation, growth, and destruction of a thrombus. In particular, whereas in the absence of stenosis, the thrombus evenly covered the injured site, in the presence of a stenosis, thrombus formation was skewed to the downstream side. The number of platelets that adhered to the injured site increased earlier as the stenosis became more severe. These results suggest that dynamic changes in blood flow due to the presence of a stenosis affect primary thrombogenesis.     

Computational study of the Trp-cage miniprotein based on the ECEPP/3 force field

Using a newly developed Monte Carlo global optimization method called basin paving, we have performed an ab initio computation for the structure of Trp-cage based on the ECEPP/3 force field in vacuo. The lowest energy minimum has been located. Its corresponding configuration is comparable to the native structure of Trp-cage (PDB code 1L2Y) with a backbone root mean square deviation of 2.24 A.     

The effect of different sample collection methods on rabbit blood parameters

Nowadays great deal of research is physiological field is conducted on experimental animals and there is a lot of criticism from the wide public on methods used. Therefore, recently there is a lot of effort focused on the welfare of the animals. Main aim of this study is to determine the effect of experimental sample collection method on the selected parameters of stress. In the experiment two sample collections of rabbit blood from marginal ear vein were realized – first using standard method with one person fixing the animal and other collecting the blood using gently fixating the animal. In the second groups experimental method of inserting the experimental animal into a sack and further collection in dark was realized. During the experiment the levels of cortisol – main stress indicator in organism and other health parameters of animals including mineral profile and haematological parameters were observed. Our results show no significant changes in levels of cortisol but also a decreasing tendency in the sample from the second (dark) collection. Haematological parameters were generally in the reference values and any significant changes except levels of lymphocytes and percent of lymphocytes which shown significant increase in the second collection period were found. Also the levels of mean corpuscular haemoglobin and percent of neutrophils unveiled a significant decrease in values. Values of mineral profile parameters have indicated no significant changes except the levels of phosphorus. Based on the result we can state that the experimental sample collection has no effect on blood parameters of the animals but we spectated a statistically insignificant decrease in the levels of cortisol which can suggest that the dark collection is possibly less stressful to the animals.     

The effects of non-Newtonian viscoelasticity and wall elasticity on flow at a 90 degrees bifurcation

To study the fundamentals of hemodynamics in arteries, the flow parameters: pulsatility, elasticity and non-Newtonian viscoelasticity were considered in detail in a 90 degrees-T-bifurcation of a rigid and elastic model. The velocity distribution 2.5 mm behind the bifurcation in the straight tube was measured with a laser-Doppler-anemometer. The fluid used was an aqueous glycerine solution and a viscoelastic Separan mixture. Flow visualization studies were done with a sheet of laser light in the plane of the bifurcation. The velocity distribution was measured for both steady and pulsatile flows with a laser-Doppler-anemometer in a backward scattered way. From the velocity measurements the shear gradients were calculated. Substantial differences were found in the flow behavior of Newtonian and non-Newtonian fluids, especially behind the bifurcation in the main tube, where secondary flows and flow separation started. Also, differences due to the elastic and rigid wall could be seen. Very high shear gradients were found in the flow between main flow and the separation zone which can lead to a damage of the blood cells.