Realistic non-Newtonian viscosity modelling highlights hemodynamic differences between intracranial aneurysms with and without surface blebs

Most computational fluid dynamic (CFD) simulations of aneurysm hemodynamics assume constant (Newtonian) viscosity, even though blood demonstrates shear-thinning (non-Newtonian) behavior. We sought to evaluate the effect of this simplifying assumption on hemodynamic forces within cerebral aneurysms, especially in regions of low wall shear stress, which are associated with rupture. CFD analysis was performed for both viscosity models using 3D rotational angiography volumes obtained for 26 sidewall aneurysms (12 with blebs, 12 ruptured), and parametric models incorporating blebs at different locations (inflow/outflow zone). Mean and lowest 5% values of time averaged wall shear stress (TAWSS) computed over the dome were compared using Wilcoxon rank-sum test. Newtonian modeling not only resulted in higher aneurysmal TAWSS, specifically in areas of low flow and blebs, but also showed no difference between aneurysms with or without blebs. In contrast, for non-Newtonian analysis, bleb-bearing aneurysms showed significantly lower 5% TAWSS compared to those without (p=0.005), despite no significant difference in mean dome TAWSS (p=0.32). Non-Newtonian modeling also accentuated the differences in dome TAWSS between ruptured and unruptured aneurysms (p<0.001). Parametric models further confirmed that realistic non-Newtonian viscosity resulted in lower bleb TAWSS and higher focal viscosity, especially when located in the outflow zone. The results show that adopting shear-thinning non-Newtonian blood viscosity in CFD simulations of intracranial aneurysms uncovered hemodynamic differences induced by bleb presence on aneurysmal surfaces, and significantly improved discriminant statistics used in risk stratification. These findings underline the possible implications of using a realistic model of blood viscosity in predictive computational hemodynamics.     

Stratification of a population of intracranial aneurysms using blood flow metrics

Indices of the intra-aneurysm hemodynamic environment have been proposed as potentially indicative of their longitudinal outcome. To be useful, the indices need to be used to stratify large study populations and tested against known outcomes. The first objective was to compile the diverse hemodynamic indices reported in the literature. Furthermore, as morphology is often the only patient-specific information available in large population studies, the second objective was to assess how the ranking of aneurysms in a population is affected by the use of steady flow simulation as an approximation to pulsatile flow simulation, even though the former is clearly non-physiological. Sixteen indices of aneurysmal hemodynamics reported in the literature were compiled and refined where needed. It was noted that, in the literature, these global indices of flow were always time-averaged over the cardiac cycle. Steady and pulsatile flow simulations were performed on a population of 198 patient-specific and 30 idealised aneurysm models. All proposed hemodynamic indices were estimated and compared between the two simulations. It was found that steady and pulsatile flow simulations had a strong linear dependence (r ≥ 0.99 for 14 indices; r ≥ 0.97 for 2 others) and rank the aneurysms in an almost identical fashion (ρ ≥ 0.99 for 14 indices; ρ ≥ 0.96 for other 2). When geometry is the only measured piece of information available, stratification of aneurysms based on hemodynamic indices reduces to being a physically grounded substitute for stratification of aneurysms based on morphology. Under such circumstances, steady flow simulations may be just as effective as pulsatile flow simulation for estimating most key indices currently reported in the literature.     

Newtonian and non-Newtonian blood flow in coiled cerebral aneurysms

Endovascular coiling aims to isolate the aneurysm from blood circulation by altering hemodynamics inside the aneurysm and triggering blood coagulation. Computational fluid dynamics (CFD) techniques have the potential to predict the post-operative hemodynamics and to investigate the complex interaction between blood flow and coils. The purpose of this work is to study the influence of blood viscosity on hemodynamics in coiled aneurysms. Three image-based aneurysm models were used. Each case was virtually coiled with a packing density of around 30%. CFD simulations were performed in coiled and untreated aneurysm geometries using a Newtonian and a Non-Newtonian fluid models. Newtonian fluid slightly overestimates the intra-aneurysmal velocity inside the aneurysm before and after coiling. There were numerical differences between fluid models on velocity magnitudes in coiled simulations. Moreover, the non-Newtonian fluid model produces high viscosity (>0.007$>0.007$ [Pa s]) at aneurysm fundus after coiling. Nonetheless, these local differences and high-viscous regions were not sufficient to alter the main flow patterns and velocity magnitudes before and after coiling. To evaluate the influence of coiling on intra-aneurysmal hemodynamics, the assumption of a Newtonian fluid can be used.     

Approximating hemodynamics of cerebral aneurysms with steady flow simulations

Computational fluid dynamics (CFD) simulations can be employed to gain a better understanding of hemodynamics in cerebral aneurysms and improve diagnosis and treatment. However, introduction of CFD techniques into clinical practice would require faster simulation times. The aim of this study was to evaluate the use of computationally inexpensive steady flow simulations to approximate the aneurysm's wall shear stress (WSS) field. Two experiments were conducted. Experiment 1 compared for two cases the time-averaged (TA), peak systole (PS) and end diastole (ED) WSS field between steady and pulsatile flow simulations. The flow rate waveform imposed at the inlet was varied to account for variations in heart rate, pulsatility index, and TA flow rate. Consistently across all flow rate waveforms, steady flow simulations accurately approximated the TA, but not the PS and ED, WSS field. Following up on experiment 1, experiment 2 tested the result for the TA WSS field in a larger population of 20 cases covering a wide range of aneurysm volumes and shapes. Steady flow simulations approximated the space-averaged WSS with a mean error of 4.3%. WSS fields were locally compared by calculating the absolute error per node of the surface mesh. The coefficient of variation of the root-mean-square error over these nodes was on average 7.1%. In conclusion, steady flow simulations can accurately approximate the TA WSS field of an aneurysm. The fast computation time of 6 min per simulation (on 64 processors) could help facilitate the introduction of CFD into clinical practice.     

Aortic valve leaflet wall shear stress characterization revisited: impact of coronary flow

Computational characterizations of aortic valve hemodynamics have typically discarded the effects of coronary flow. The objective of this study was to complement our previous fluid–structure interaction aortic valve model with a physiologic coronary circulation model to quantify the impact of coronary flow on aortic sinus hemodynamics and leaflet wall shear stress (WSS). Coronary flow suppressed vortex development in the two coronary sinuses and altered WSS magnitude and directionality on the three leaflets, with the most substantial differences occurring in the belly and tip regions.     

On the influence of variation in haemodynamic conditions on the generation and growth of cerebral aneurysms and atherogenesis: a computational model

A risk-factor criterion, based on near-wall haemodynamic conditions, for the assessment of vascular pathology risk is developed and tested. This criterion has its foundation on experimentally observed vascular wall responses to oscillatory and swirling wall shear stress patterns and is applied to the results of computational simulations. We test this model on two anatomically accurate vascular segments, where pathologies are either commonplace or have already been developed, i.e. a healthy carotid bifurcation and a cerebral fusiform aneurysm. In the case of the former, the risk-assessment criterion predicts the emergence of atherosclerosis of the same locations that the disease is usually encountered. In the case of the latter, the risk factor shows increased probability for the appearance of secondary, “baby”, aneurysms at certain locations.     

Three-dimensional macro-scale assessment of regional and temporal wall shear stress characteristics on aortic valve leaflets

The aortic valve (AV) achieves unidirectional blood flow between the left ventricle and the aorta. Although hemodynamic stresses have been shown to regulate valvular biology, the native wall shear stress (WSS) experienced by AV leaflets remains largely unknown. The objective of this study was to quantify computationally the macro-scale leaflet WSS environment using fluid–structure interaction modeling. An arbitrary Lagrangian–Eulerian approach was implemented to predict valvular flow and leaflet dynamics in a three-dimensional AV geometry subjected to physiologic transvalvular pressure. Local WSS characteristics were quantified in terms of temporal shear magnitude (TSM), oscillatory shear index (OSI) and temporal shear gradient (TSG). The dominant radial WSS predicted on the leaflets exhibited high amplitude and unidirectionality on the ventricularis (TSM>7.50 dyn/cm², OSI < 0.17, TSG>325.54 dyn/cm² s) but low amplitude and bidirectionality on the fibrosa (TSM < 2.73 dyn/cm², OSI>0.38, TSG < 191.17 dyn/cm² s). The radial WSS component computed in the leaflet base, belly and tip demonstrated strong regional variability (ventricularis TSM: 7.50–22.32 dyn/cm², fibrosa TSM: 1.26–2.73 dyn/cm²). While the circumferential WSS exhibited similar spatially dependent magnitude (ventricularis TSM: 1.41–3.40 dyn/cm², fibrosa TSM: 0.42–0.76 dyn/cm²) and side-specific amplitude (ventricularis TSG: 101.73–184.43 dyn/cm² s, fibrosa TSG: 41.92–54.10 dyn/cm² s), its temporal variations were consistently bidirectional (OSI>0.25). This study provides new insights into the role played by leaflet–blood flow interactions in valvular function and critical hemodynamic stress data for the assessment of the hemodynamic theory of AV disease.     

Effect of spatial gradient in fluid shear stress on morphological changes in endothelial cells in response to flow

Arterial bifurcations are common sites for development of cerebral aneurysms. Although this localization of aneurysms suggests that high shear stress (SS) and high spatial SS gradient (SSG) occurring at the bifurcations may be crucial factors for endothelial dysfunction involved in aneurysm formation, the details of the relationship between the hemodynamic environment and endothelial cell (EC) responses remain unclear. In the present study, we sought morphological responses of ECs under high-SS and high-SSG conditions using a T-shaped flow chamber. Confluent ECs were exposed to SS of 2-10 Pa with SSG of up to 34 Pa/mm for 24 and 72 h. ECs exposed to SS without spatial gradient elongated and oriented to the direction of flow at 72 h through different processes depending on the magnitude of SS. In contrast, cells did not exhibit preferred orientation and elongation under the combination of SS and SSG. Unlike cells aligned to the flow by exposure to only SS, development of actin stress fibers was not observed in ECs exposed to SS with SSG. These results indicate that SSG suppresses morphological changes of ECs in response to flow.     

A mechanism for heterogeneous endothelial responses to flow in vivo and in vitro

Exposure of endothelium to a nominally uniform flow field in vivo and in vitrofrequently results in a heterogeneous distribution of individual cell responses. Extremes in response levels are often noted in neighboring cells. Such variations are important for the spatial interpretation of vascular responses to flow and for an understanding of mechanotransduction mechanisms at the level of single cells. We propose that variations of local forces defined by the cell surface geometry contribute to these differences. Atomic force microscopy measurements of cell surface topography in living endothelium both in vitro and in situ combined with computational fluid dynamics demonstrated large cell-to-cell variations in the distribution of flow-generated shear stresses at the endothelial luminal surface. The distribution of forces throughout the surface of individual cells of the monolayer was also found to vary considerably and to be defined by the surface geometry. We conclude that the endothelial three-dimensional surface geometry defines the detailed distribution of shear stresses and gradients at the single cell level, and that there are large variations in force magnitude and distribution between neighboring cells. The measurements support a topographic basis for differential endothelial responses to flow observed in vivo and in vitro. Included in these studies are the first preliminary measurements of the living endothelial cell surface in an intact artery.     

Spatial and temporal resolution of shear in an orbiting petri dish

It is well documented that physiological and morphological properties of anchored cells are influenced by fluid shear stress. Common orbital shakers provide a means of simultaneously applying shear stress to cells for tens to hundreds of cases by loading the shaker with multiple dishes. However, the complex flow in orbiting dishes is amenable to analytical solution for resolving shear created by the fluid motion only for simplified conditions. The only existing quantification of shear in this flow is an equation that estimates a constant scalar value of shear for the entire surface of the dish. In practice, wall shear stress (WSS) will be oscillatory rather than steady due to the travelling waveform and will vary across the surface of the dish at any instant in time. This article presents a computational model that provides complete spatial and temporal resolution of WSS over the bottom surface of a dish throughout the orbital cycle. The model is reasonably well validated by the analytical solution, with resultant WSS magnitudes that are within 0.99 ± 0.42 dyne/cm(2) . The model results were compared to tangential WSS magnitudes obtained using one-dimensional optical velocimetry at discreet locations on the bottom of an orbiting dish. The experimental minimum and maximum WSS at 1 mm from the center of the dish were 6 and 7 dyne/cm(2) , respectively, whereas WSS generated from the computational model ranged from 0.5 to 8.5 dyne/cm(2) . The experimental minimum and maximum WSS at 12 mm from the center of the dish were 6 and 16 dyne/cm(2) , respectively, whereas WSS generated from the computational model ranged from 0.5 to 14 dyne/cm(2) . Discrepancies between the experimental and computational data may be attributed to a sparse sampling rate for the experimental probe, a sharp gradient at the sample area which could cause the unidirectional probe to be inaccurate if its location were not precise, and too few particles to track and a scattering of the signal by the free surface when the liquid is shallow.     

Transient magneto-peristaltic flow of couple stress biofluids: A magneto-hydro-dynamical study on digestive transport phenomena

Magnetic fields are increasingly being utilized in endoscopy and gastric transport control. In this regard, the present study investigates the influence of a transverse magnetic field in the transient peristaltic rheological transport. An electrically-conducting couple stress non-Newtonian model is employed to accurately simulate physiological fluids in peristaltic flow through a sinusoidally contracting channel of finite length. This model is designed for computing the intra-bolus oesophageal and intestinal pressures during the movement of food bolus in the digestive system under magneto-hydro-dynamic effects. Long wavelength and low Reynolds number approximations have been employed to reduce the governing equations from nonlinear to linear form, this being a valid approach for creeping flows which characterizes physiological dynamics. Analytical approximate solutions for axial velocity, transverse velocity, pressure gradient, local wall shear stress and volumetric flow rate are obtained for the non-dimensional conservation equations subject to appropriate boundary conditions. The effects of couple stress parameter and transverse magnetic field on the velocity profile, pressure distribution, local wall shear stress and the averaged flow rate are discussed with the aid of computational results. The comparative study of non-integral and integral number of waves propagating along the finite length channel is also presented. Magnetic field and non-Newtonian properties are found to strongly influence peristaltic transport.     

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.     

Impact of plaques in the left coronary artery on wall shear stress and pressure gradient in coronary side branches

In this study, we investigate plaques located at the left coronary bifurcation. We focus on the effect that the resulting changes in wall shear stress (WSS) and wall pressure stress gradient (WPSG) have on atherosclerotic progress in coronary artery disease. Coronary plaques were simulated and placed at the left main stem and the left anterior descending to produce >50% narrowing of the coronary lumen. Computational fluid dynamics analysis was carried out, simulating realistic physiological conditions that show the in vivo cardiac haemodynamic. WSS and WPSG in the left coronary artery were calculated and compared in the left coronary models, with and without the presence of plaques during cardiac cycles. Our results showed that WSS decreased while WPSG was increased in coronary side branches due to the presence of plaques. There is a direct correlation between coronary plaques and subsequent WSS and WPSG variations based on the bifurcation plaques simulated in the realistic coronary models.     

A computational study of leukocyte adhesion and its effect on flow pattern in microvessels

Three-dimensional computational modeling and simulation are presented on the adhesive rolling of deformable leukocytes over a P-selectin coated surface in parabolic shear flow in microchannels. The computational model is based on the immersed boundary method for cell deformation and Monte Carlo simulation for receptor/ligand interaction. The simulations are continued for at least 1 s of leukocyte rolling during which the instantaneous quantities such as cell deformation index, cell/substrate contact area, and fluid drag remain statistically stationary. The characteristic ‘stop-and-go’ motion of rolling leukocytes, and the ‘tear-drop’ shape of adherent leukocytes as observed in experiments are reproduced by the simulations. We first consider the role of cell deformation and cell concentration on rolling characteristics. We observe that compliant cells roll slower and more stably than rigid cells. Our simulations agree with previous in vivo observation that the hydrodynamic interactions between nearby leukocytes affect cell rolling, and that the rolling velocity decreases inversely with the separation distance, irrespective of cell deformability. We also find that cell deformation decreases, and the cells roll more stably with reduced velocity fluctuation, as the cell concentration is increased. However, the effect of nearby cells on the rolling characteristics is found to be more significant for rigid cells than compliant cells. We then address the effect of cell deformability and rolling velocity on the flow resistance due to, and the fluid drag on, adherent leukocytes. While several earlier computational works have addressed this problem, two key features of leukocyte adhesion, such as cell deformation and rolling, were often neglected. Our results suggest that neglecting cell deformability and rolling velocity may significantly overpredict the flow resistance and drag force. Increasing the cell concentration is shown to increase the flow resistance and reduce the fluid drag. The reduced drag then results in slower and more stable rolling of the leukocytes with longer pause time and shorter step distance. But the increase/decrease in the flow resistance/fluid drag due to the increase in the cell concentration is observed to be more significant in case of rigid cells than compliant cells.     

Comparative study of flow in right-sided and left-sided aortas: numerical simulations in patient-based models

A right-sided aorta is a rare malformation which may be associated with other various types of congenital heart disease. We utilised haemodynamic, echocardiographic measurements, computerised tomography and image reconstruction software packages that were integrated in a computational fluid dynamics model to determine blood flow patterns in patient-based aortas. In the left-sided aorta, a systolic clockwise rotational component was present, while helical flow was depicted in the aortic arch that was converted in the descending aorta as counter-rotating vortices with accompanying retrograde flow. The right-sided configuration has not altered the orientation of the three-dimensional vortex, but intensification of polymorphic flow patterns, alterations in wall shear stress distribution and development of a lateral pressure gradient at the area of an aneurysmal anomaly was observed. Moreover, increments of Reynolds, Womersley and Dean numbers were evident. These phenomena along with the formation of the aneurysm might influence cardiovascular risk in patients with right-sided aortas.     

Mechanotransduction of shear stress occurs through changes in VE-cadherin and PECAM-1 tension: Implications for cell migration

Recent work has shown that cadherins at cell-cell junctions bear tensile forces. Using novel FRET-based tension sensors, we showed first that in response to shear stress, endothelial cells rapidly reduce mechanical tension on vascular endothelial (VE)-cadherin. Second, we observed a simultaneous increase in tension on platelet endothelial cell adhesion molecule (PECAM)-1, induced by an interaction with vimentin. In this commentary, we discuss how our results fit with existing data on cadherins as important mediators of mechanotransduction, in particular, in cell migration where mechanical tension across cadherins may communicate the direction of movement. The ability of PECAM-1 to bear mechanical tension may also be important in other PECAM-1 functions, such as leukocyte transmigration through the endothelium. Additionally, our observation that vimentin expression was required for PECAM-1 tension and mechanotransduction of fluid flow suggests that intermediate filaments are capable of transmitting tension. Overall, our results argue against models where an external force is passively transferred across the cytoskeleton, and instead suggest that cells actively respond to extracellular forces by modulating tension across junctional proteins.     

Changes in glutamate dehydrogenase activity of Chlamydomonas reinhardtii under different trophic and stress conditions

Abstract. Under stress conditions (darkness, nitrogen starvation, high ammonium concentrations, glutamine synthetase and glutamate synthase inhibition) glutamate dehydrogenase animating activity levels of Chlamydomonas cells varied inversely to those of glutamine synthetase. Nitrogen and carbon sources also influenced glutamate dehydrogenase levels in Chlamydomonas , the highest values being found in cells cultured mixotrophically with ammonium, under which conditions glutamate dehydrogenase and glutamine synthetase levels were likewise inversely related. These facts, together with the analysis of internal fluctuations of ammonium, 2-oxoglutarate, and the amino acid pool as well as the variations of certain enzymes involved in carbon metabolism indicate that glutamate dehydrogenase animating activity is adaptative, being involved in the maintenance of intracellular levels of L-glutamate when they cannot be maintained by the GS-GOGAT cycle, and probably more connected with carbon than nitrogen metabolism.     

DNA microarray study on gene expression profiles in co-cultured endothelial and smooth muscle cells in response to 4- and 24-h shear stress

Shear stress, a major hemodynamic force acting on the vessel wall, plays an important role in physiological processes such as cell growth, differentiation, remodelling, metabolism, morphology, and gene expression. We investigated the effect of shear stress on gene expression profiles in co-cultured vascular endothelial cells (ECs) and smooth muscle cells (SMCs). Human aortic ECs were cultured as a confluent monolayer on top of confluent human aortic SMCs, and the EC side of the co-culture was exposed to a laminar shear stress of 12 dyn/cm² for 4 or 24 h. After shearing, the ECs and SMCs were separated and RNA was extracted from the cells. The RNA samples were labelled and hybridized with cDNA array slides that contained 8694 genes. Statistical analysis showed that shear stress caused the differential expression (p ≤ 0.05) of a total of 1151 genes in ECs and SMCs. In the co-cultured ECs, shear stress caused the up-regulation of 403 genes and down-regulation of 470. In the co-cultured SMCs, shear stress caused the up-regulation of 152 genes and down-regulation of 126 genes. These results provide new information on the gene expression profile and its potential functional consequences in co-cultured ECs and SMCs exposed to a physiological level of laminar shear stress. Although the effects of shear stress on gene expression in monocultured and co-cultured EC are generally similar, the response of some genes to shear stress is opposite between these two types of culture (e.g., ICAM-1 is up-regulated in monoculture and down-regulated in co-culture), which strongly indicates that EC–SMC interactions affect EC responses to shear stress.     

Experimental characterization of flow conditions in 2- and 20-L bioreactors with wave-induced motion

Quantifying the influence of flow conditions on cell viability is essential for a successful control of cell growth and cell damage in major biotechnological applications, such as in recombinant protein and antibody production or vaccine manufacturing. In the last decade, new bioreactor types have been developed. In particular, bioreactors with wave‐induced motion show interesting properties (e.g., disposable bags suitable for cGMP manufacturing, no requirement for cleaning and sterilization of cultivation vessels, and fast setup of new production lines) and are considered in this study. As an additional advantage, it is expected that cultivations in such bioreactors result in lower shear stress compared with conventional stirred tanks. As a consequence, cell damage would be reduced as cell viability is highly sensitive to hydrodynamic conditions. To check these assumptions, an experimental setup was developed to measure the most important flow parameters (liquid surface level, liquid velocity, and liquid and wall shear stress) in two cellbag sizes (2 and 20 L) of Wave Bioreactors®. The measurements confirm in particular low shear stress values in both cellbags, indicating favorable hydrodynamic conditions for cell cultivation. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011