Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery

The endothelial cells (ECs) lining a blood vessel wall are exposed to both the wall shear stress (WSS) of blood flow and the circumferential strain (CS) of pulsing artery wall motion. These two forces and their interaction are believed to play a role in determining remodeling of the vessel wall and development of arterial disease (atherosclerosis). This study focused on the WSS and CS dynamic behavior in a compliant model of a coronary artery taking into account the curvature of the bending artery and physiological radial wall motion. A three-dimensional finite element model with transient flow and moving boundaries was set up to simulate pulsatile flow with physiological pressure and flow wave forms characteristic of the coronary arteries. The characteristic coronary artery curvature and flow conditions applied to the simulation were: aspect ratio (lambda) = 10, diameter variation (DV) = 6 percent, mean Reynolds number (Re) = 150, and unsteadiness parameter (alpha) = 3. The results show that mean WSS is about 50 percent lower on the inside wall than the outside wall while WSS oscillation is stronger on the inside wall. The stress phase angle (SPA) between CS and WSS, which characterizes the dynamics of the mechanical force pattern applied to the endothelial cell layer, shows that CS and WSS are more out of phase in the coronaries than in any other region of the circulation (-220 deg on the outside wall, -250 deg on the inside wall). This suggests that in addition to WSS, SPA may play a role in localization of coronary atherosclerosis.     

A mechanical model for morphological response of endothelial cells under combined wall shear stress and cyclic stretch loadings

The shape and morphology of endothelial cells (ECs) lining the blood vessels are a good indicator for atheroprone and atheroprotected sites. ECs of blood vessels experience both wall shear stress (WSS) and cyclic stretch (CS). These mechanical stimuli influence the shape and morphology of ECs. A few models have been proposed for predicting the morphology of ECs under WSS or CS. In the present study, a mathematical cell population model is developed to simulate the morphology of ECs under combined WSS and CS conditions. The model considers the cytoskeletal filaments, cell–cell interactions, and cell–extracellular matrix interactions. In addition, the reorientation and polymerization of microfilaments are implemented in the model. The simulations are performed for different conditions: without mechanical stimuli, under pure WSS, under pure CS, and under combined WSS and CS. The results are represented as shape and morphology of ECs, shape index, and angle of orientation. The model is validated qualitatively and quantitatively with several experimental studies, and good agreement with experimental studies is achieved. To the best of our knowledge, it is the first model for predicting the morphology of ECs under combined WSS and CS condition. The model can be used to indicate the atheroprone regions of a patient’s artery.     

Large Negative Stress Phase Angle (SPA) attenuates nitric oxide production in bovine aortic endothelial cells

Hemodynamics plays an important role in cardiovascular physiology and pathology. Pulsatile flow (Q), pressure (P), and diameter (D) waveforms exert wall shear stress (WSS), normal stress, and circumferential strain (CS) on blood vessels. Most in vitro studies to date have focused on either WSS or CS but not their interaction. Recently, we have shown that concomitant WSS and CS affect EC biochemical response modulated by the temporal phase angle between WSS and CS (stress phase angle, SPA). Large negative SPA has been shown to occur in regions of the circulation where atherosclerosis and intimal hyperplasia are prevalent. Here, we report that nitric oxide (NO) biochemical secretion was significantly decreased in response to a large negative SPA of -180 deg with respect to an SPA of 0 degrees in bovine aortic endothelial cells (BAEC) at 5 h. A new hemodynamic simulator for the study of the physiologic SPA was used to provide the hemodynamic conditions of pro-atherogenic (SPA = -180 deg) and normopathic (SPA = 0 deg) states. The role of complex hemodynamics in vascular remodeling, homeostasis, and pathogenesis can be advanced by further assessment of the hypothesis that a large negative SPA is pro-atherogenic.     

Flow shear stress regulates endothelial barrier function and expression of angiogenic factors in a 3D microfluidic tumor vascular model

Endothelial cells lining blood vessels are exposed to various hemodynamic forces associated with blood flow. These include fluid shear, the tangential force derived from the friction of blood flowing across the luminal cell surface, tensile stress due to deformation of the vessel wall by transvascular flow, and normal stress caused by the hydrodynamic pressure differential across the vessel wall. While it is well known that these fluid forces induce changes in endothelial morphology, cytoskeletal remodeling, and altered gene expression, the effect of flow on endothelial organization within the context of the tumor microenvironment is largely unknown. Using a previously established microfluidic tumor vascular model, the objective of this study was to investigate the effect of normal (4 dyn/cm²), low (1 dyn/cm²), and high (10 dyn/cm²) microvascular wall shear stress (WSS) on tumor-endothelial paracrine signaling associated with angiogenesis. It is hypothesized that high WSS will alter the endothelial phenotype such that vascular permeability and tumor-expressed angiogenic factors are reduced. Results demonstrate that endothelial permeability decreases as a function of increasing WSS, while co-culture with tumor cells increases permeability relative to mono-cultures. This response is likely due to shear stress-mediated endothelial cell alignment and tumor-VEGF-induced permeability. In addition, gene expression analysis revealed that high WSS (10 dyn/cm²) significantly down-regulates tumor-expressed MMP9, HIF1, VEGFA, ANG1, and ANG2, all of which are important factors implicated in tumor angiogenesis. This result was not observed in tumor mono-cultures or static conditioned media experiments, suggesting a flow-mediated paracrine signaling mechanism exists with surrounding tumor cells that elicits a change in expression of angiogenic factors. Findings from this work have significant implications regarding low blood velocities commonly seen in the tumor vasculature, suggesting high shear stress-regulation of angiogenic activity is lacking in many vessels, thereby driving tumor angiogenesis.     

The role of endothelial calcium and nitric oxide in the localisation of atherosclerosis

A mathematical model of endothelial cell calcium signalling and nitric oxide synthesis under flow conditions is presented. The model is coupled to two important environmental stimuli for endothelial cells: the frictional shear stress exerted on the cell membrane by the blood flow; and the binding of adenosine triphosphate in the bloodstream to cell surface receptors. These stimuli are closely linked to haemodynamic flow conditions and are, in general, spatially varying, allowing the cellular response in different regions of the endothelium to be evaluated. This is used to indicate which areas of the artery wall experience reduced bioavailability of nitric oxide, which is a major factor in the onset of atherosclerosis. The model thus directly addresses the key issue of the causative link, and its underlying biochemical mechanisms, between incidence of atherosclerosis and regions of low wall shear stress (WSS). Model results show that intracellular levels of free calcium and endothelial nitric oxide synthase are lower in endothelial cells adjacent to a region of recirculating flow than in cells adjacent to regions of fully developed arterial flow. This will lead to deficient levels of nitric oxide in the recirculation zone and hence a potentially elevated risk of developing atherosclerotic plaque. This is consistent with the observed spatial correlation between atherosclerosis and regions of disturbed blood flow and low WSS, and provides a mechanism for the localisation of the disease to sites such as arterial bifurcations and bends.     

Differentiation of stem/progenitor cells into vascular cells in response to fluid mechanical forces

Vascular functions are regulated not only by chemical mediators, such as hormones, cytokines, and neurotransmitters, but by mechanical hemodynamic forces generated by blood flow and blood pressure. The mechanical force-mediated regulation is based on the ability of vascular cells, including endothelial cells and smooth muscle cells, to recognize fluid mechanical forces, i.e., the shear stress produced by flowing blood and the cyclic strain generated by blood pressure, and to transmit the signals into the cell interior, where they trigger cell responses that involve changes in cell morphology, cell function, and gene expression. Recent studies have revealed that immature cells, such as endothelial progenitor cells (EPCs) and embryonic stem (ES) cells, as well as adult vascular cells, respond to fluid mechanical forces. Shear stress and cyclic strain promote the proliferation and differentiation of EPCs and ES cells into vascular cells and enhance their ability to form new vessels. Even more recently, attempts have been made to apply fluid mechanical forces to EPCs and ES cells cultured on polymer tubes and develop tissue-engineered blood vessel grafts that have a structure and function similar to that of blood vessels in vivo. This review summarizes the current state of knowledge concerning the mechanobiological responses of stem/progenitor cells and its potential applications to tissue engineering.     

Fluid shear stress and sphingosine 1-phosphate activate calpain to promote membrane type 1 matrix metalloproteinase (MT1-MMP) membrane translocation and endothelial invasion into three-dimensional collagen matrices

The vascular endothelium continually senses and responds to biochemical and mechanical stimuli to appropriately initiate angiogenesis. We have shown previously that fluid wall shear stress (WSS) and sphingosine 1-phosphate (S1P) cooperatively initiate the invasion of human umbilical vein endothelial cells into collagen matrices (Kang, H., Bayless, K. J., and Kaunas, R. (2008) Am. J. Physiol. Heart Circ. Physiol. 295, H2087-2097). Here, we investigated the role of calpains in the regulation of endothelial cell invasion in response to WSS and S1P. Calpain inhibition significantly decreased S1P- and WSS-induced invasion. Short hairpin RNA-mediated gene silencing demonstrated that calpain 1 and 2 were required for WSS and S1P-induced invasion. Also, S1P synergized with WSS to induce invasion and to activate calpains and promote calpain membrane localization. Calpain inhibition results in a cell morphology consistent with reduced matrix proteolysis. Membrane type 1-matrix metalloproteinase (MT1-MMP) has been shown by others to regulate endothelial cell invasion, prompting us to test whether calpain acted upstream of MT1-MMP. S1P and WSS synergistically activated MT1-MMP and induced cell membrane localization of MT1-MMP in a calpain-dependent manner. Calpain activation, MT1-MMP activation and MT1-MMP membrane localization were all maximal with 5.3 dynes/cm(2) WSS and S1P treatment, which correlated with maximal invasion responses. Our data show for the first time that 5.3 dynes/cm(2) WSS in the presence of S1P combine to activate calpains, which direct MT1-MMP membrane localization to initiate endothelial sprouting into three-dimensional collagen matrices.     

Fluid shear stress modulates endothelial cell invasion into three-dimensional collagen matrices

Endothelial cells are subjected to biochemical and mechanical stimuli, which regulate their angiogenic potential. We determined the synergistic effects of sphingosine-1-phosphate (S1P) and fluid wall shear stress (WSS) on a previously established model of human umbilical vein endothelial cell invasion into three-dimensional collagen matrices. Collagen matrices were incorporated into a parallel-plate flow chamber to apply controlled WSS to the surface of endothelial monolayers over a period of 24 h. Cell invasion required the presence of S1P, with the effects of S1P being enhanced by shear stress to an extent comparable with S1P combined with angiogenic growth factor stimulation. The number of invading cells depended on the magnitude of shear stress, with a maximal induction at a shear stress of approximately 5 dyn/cm2, whereas the invasion distance was proportional to the magnitude of shear stress. The enhancement of invasion by 5.3 dyn/cm2 shear stress coincided with elevated phosphorylation of Akt and matrix metalloproteinase (MMP)-2 activation. Furthermore, invasion induced by the combined application of WSS and S1P was attenuated by inhibitors of MMPs (GM6001) and the phosphatidylinositol 3-kinase/Akt signaling pathway (wortmannin). These results provide evidence that shear stress is a positive modulator of S1P-induced endothelial cell invasion into collagen matrices through enhanced Akt and MMP-2 activation.     

壁剪应力变化对动脉重建影响的在体研究

为探讨动脉血流受阻后壁剪应力（Wall shear stress,WSS)变化对动脉适应性重建的影响,在60只实验兔建立动脉血流减小模型,术后0－30天8个不同时相点,检测动脉样本的壁厚及内径,单位面积（mm^2),动脉内皮细胞（Artereial endothelial cell,AEC）核数目和平滑肌细胞核数目。结果显示WSS变化通过调节动脉的舒缩而致使动脉管径适应性缩减,动脉壁腔比（WT／LD）保持恒定。动脉壁细胞成分中AEC受WSS变化的影响,而平滑肌细胞则不受影响。在术后3天、7天、AEC密度较正常对照显著降低（P＜0．01）;而在术后14天、30天,AEC密度显著增高（P＜0．01）。说明WSS对动脉适应性重建的影响,是通过调节动脉的舒缩所致,而非壁腔比的改变,WSS的变化在AEC的适应性重建过程中可能起着重要调节作用。     

A biphasic endothelial stress-survival mechanism regulates the cellular response to vascular endothelial growth factor A

Vascular endothelial growth factor A (VEGF-A) is an essential cytokine that regulates endothelial function and angiogenesis. VEGF-A binding to endothelial receptor tyrosine kinases such as VEGFR1 and VEGFR2 triggers cellular responses including survival, proliferation and new blood vessel sprouting. Increased levels of a soluble VEGFR1 splice variant (sFlt-1) correlate with endothelial dysfunction in pathologies such as pre-eclampsia; however the cellular mechanism(s) underlying the regulation and function of sFlt-1 are unclear. Here, we demonstrate the existence of a biphasic stress response in endothelial cells, using serum deprivation as a model of endothelial dysfunction. The early phase is characterized by a high VEGFR2:sFlt-1 ratio, which is reversed in the late phase. A functional consequence is a short-term increase in VEGF-A-stimulated intracellular signaling. In the late phase, sFlt-1 is secreted and deposited at the extracellular matrix. We hypothesized that under stress, increased endothelial sFlt-1 levels reduce VEGF-A bioavailability: VEGF-A treatment induces sFlt-1 expression at the cell surface and VEGF-A silencing inhibits sFlt-1 anchorage to the extracellular matrix. Treatment with recombinant sFlt-1 inhibits VEGF-A-stimulated in vitro angiogenesis and sFlt-1 silencing enhances this process. In this response, increased VEGFR2 levels are regulated by the phosphatidylinositol-3-kinase and PKB/Akt signaling pathways and increased sFlt-1 levels by the ERK1/2 signaling pathway. We conclude that during serum withdrawal, cellular sensing of environmental stress modulates sFlt-1 and VEGFR2 levels, regulating VEGF-A bioavailability and ensuring cell survival takes precedence over cell proliferation and migration. These findings may underpin an important mechanism contributing to endothelial dysfunction in pathological states.     

Effects of polycythemia on systemic endothelial function in chronic hypoxic lung disease

Chronic obstructive pulmonary disease (COPD) is a major risk factor for cardiovascular disease. Polycythemia, a common complication of hypoxic COPD, may affect systemic vascular function by altering blood viscosity, vessel wall shear stress (WSS), and endothelium-derived nitric oxide (NO) release. Here, we evaluated the effects of hypoxia-related polycythemia on systemic endothelial function in patients with COPD. We investigated blood viscosity, WSS, and endothelial function in 15 polycythemic and 13 normocythemic patients with COPD of equal severity, by recording brachial artery diameter variations in response to hyperemia and by using venous occlusion plethysmography (VOP) to measure forearm blood flow (FBF) responses to a brachial artery infusion of acetylcholine (ACh), bradykinin (BK), sodium nitroprusside (SNP), substance P (SP), isoptin, and N-monomethyl-L-arginine (L-NMMA). At baseline, polycythemic patients had higher blood viscosity and larger brachial artery diameter than normocythemic patients but similar calculated WSS. Flow-mediated brachial artery vasodilation was increased in the polycythemic patients, in proportion to the hemoglobin levels. ACh-induced vasodilation was markedly impaired in the polycythemic patients and negatively correlated with hemoglobin levels. FBF responses to endothelium- (BK, SP) and non-endothelium-dependent (SNP, isoptin) vasodilators were not significantly different between the two groups. L-NMMA infusion induced a similar vasoconstrictor response in both groups, in accordance with their similar baseline WSS. In conclusion, systemic arteries in polycythemic patients adjust appropriately to chronic or acute WSS elevations by appropriate basal and stimulated NO release. Overall, our results suggest that moderate polycythemia has no adverse effect on vascular function in COPD.     

Haemodynamics and stresses in abdominal aortic aneurysms: A fluid-structure interaction study into the effect of proximal neck and iliac bifurcation angle

Our knowledge of how geometry influences abdominal aortic aneurysm (AAA) biomechanics is still developing. Both iliac bifurcation angle and proximal neck angle could impact the haemodynamics and stresses within AAA. Recent comparisons of the morphology of ruptured and intact AAA show that cases with large iliac bifurcation angles are less likely to rupture than those with smaller angles. We aimed to perform fluid-structure interaction (FSI) simulations on a range of idealised AAA geometries to conclusively determine the influence of proximal neck and iliac bifurcation angle on AAA wall stress and haemodynamics.Peak wall shear stress (WSS) and time-averaged WSS (TAWSS) in the AAA sac region only increased when the proximal neck angle exceeded 30°. Both peak WSS (p < 0.0001) and peak von Mises wall stress (p = 0.027) increased with iliac bifurcation angle, whereas endothelial cell activation potential (ECAP) decreased with iliac bifurcation angle (p < 0.001) and increased with increasing neck angle.These observations may be important as AAAs have been shown to expand, develop thrombus and rupture in areas of low WSS. Here we show that AAAs with larger iliac bifurcation angles have higher WSS, potentially reducing the likelihood of rupture. Furthermore, ECAP was lower in AAA geometries with larger iliac bifurcation angles, implying less likelihood of thrombus development and wall degeneration. Therefore our findings could help explain the clinical observation of lower rupture rates associated with AAAs with large iliac bifurcation angles.     

Computational mechanical model studies on the spontaneous emergent morphogenesis of the cultured endothelial cells

To address questions concerning why and how the morphology of endothelial cells (ECs) forms under shear stress loading, a computational fluid dynamics (CFD) three-dimensional (3D) model of ECs simulating cell shape was designed. A full 3D non-linear CFD simulation was conducted to estimate the wall shear stress (WSS) distribution. The model cell was capable of random rotation, deformation, migration, and proliferation. Flow was computed after each update of the cell shape with infinitesimal configuration changes. After a finite interval of the flow computation, only the infinitesimal configuration changes that reduced the WSS were allowed to accumulate. As a result of the very long free-run computation experiment, starting with a sub-confluent pattern of cells, the model cells became confluent and were elongated and aligned, with a shape index (SI) very close to that reported for cells in vivo. The average WSS converged to the lowest value at the same time.     

Analysis of early embryonic great-vessel microcirculation in zebrafish using high-speed confocal μPIV

In the developing cardiovascular system, hemodynamic vascular loading is critical for angiogenesis and cardiovascular adaptation. Normal zebrafish embryos with transgenically-labeled endothelial and red blood cells provide an excellent in vivo model for studying the fluid-flow induced vascular loading. To characterize the developmental hemodynamics of early embryonic great-vessel microcirculation in the zebrafish embryo, two complementary studies (experimental and numerical) are presented. Quantitative comparison of the wall shear stress (WSS) at the first aortic arch (AA1) of wild-type zebrafish embryos during two consecutive developmental stages is presented, using time-resolved confocal micro-particle image velocimetry (μPIV). Analysis showed that there was significant WSS difference between 32 and 48 h post-fertilization (hpf) wild-type embryos, which correlates with normal arch morphogenesis. The vascular distensibility of the arch wall at systole and the acceleration/deceleration rates of time-lapse phase-averaged streamwise blood flow curves were also analyzed. To estimate the influence of a novel intermittent red-blood cell (RBC) loading on the endothelium, a numerical two-phase, volume of fluid (VOF) flow model was further developed with realistic in vivo conditions. These studies showed that near-wall effects and cell clustering increased WSS augmentation at a minimum of 15% when the distance of RBC from arch vessel wall was less than 3 μm or when RBC cell-to-cell distance was less than 3 μm. When compared to a smooth wall, the WSS augmentation increased by a factor of ~1.4 due to the roughness of the wall created by the endothelial cell profile. These results quantitatively highlight the contribution of individual RBC flow patterns on endothelial WSS in great-vessel microcirculation and will benefit the quantitative understanding of mechanotransduction in embryonic great vessel biology, including arteriovenous malformations (AVM).     

Hemodynamic Analysis in an Idealized Artery Tree: Differences in Wall Shear Stress between Newtonian and Non-Newtonian Blood Models

Development of many conditions and disorders, such as atherosclerosis and stroke, are dependent upon hemodynamic forces. To accurately predict and prevent these conditions and disorders hemodynamic forces must be properly mapped. Here we compare a shear-rate dependent fluid (SDF) constitutive model, based on the works by Yasuda et al in 1981, against a Newtonian model of blood. We verify our stabilized finite element numerical method with the benchmark lid-driven cavity flow problem. Numerical simulations show that the Newtonian model gives similar velocity profiles in the 2-dimensional cavity given different height and width dimensions, given the same Reynolds number. Conversely, the SDF model gave dissimilar velocity profiles, differing from the Newtonian velocity profiles by up to 25% in velocity magnitudes. This difference can affect estimation in platelet distribution within blood vessels or magnetic nanoparticle delivery. Wall shear stress (WSS) is an important quantity involved in vascular remodeling through integrin and adhesion molecule mechanotransduction. The SDF model gave a 7.3-fold greater WSS than the Newtonian model at the top of the 3-dimensional cavity. The SDF model gave a 37.7-fold greater WSS than the Newtonian model at artery walls located immediately after bifurcations in the idealized femoral artery tree. The pressure drop across arteries reveals arterial sections highly resistive to flow which correlates with stenosis formation. Numerical simulations give the pressure drop across the idealized femoral artery tree with the SDF model which is approximately 2.3-fold higher than with the Newtonian model. In atherosclerotic lesion models, the SDF model gives over 1 Pa higher WSS than the Newtonian model, a difference correlated with over twice as many adherent monocytes to endothelial cells from the Newtonian model compared to the SDF model.     

Biorheological views of endothelial cell responses to mechanical stimuli

Vascular endothelial cells are located at the innermost layer of the blood vessel wall and are always exposed to three different mechanical forces: shear stress due to blood flow, hydrostatic pressure due to blood pressure and cyclic stretch due to vessel deformation. It is well known that endothelial cells respond to these mechanical forces and change their shapes, cytoskeletal structures and functions. In this review, we would like to mainly focus on the effects of shear stress and hydrostatic pressure on endothelial cell morphology. After applying fluid shear stress, cultured endothelial cells show marked elongation and orientation in the flow direction. In addition, thick stress fibers of actin filaments appear and align along the cell long axis. Thus, endothelial cell morphology is closely related to the cytoskeletal structure. Further, the dynamic course of the morphological changes is shown and the related events such as changes in mechanical stiffness and functions are also summarized. When endothelial cells were exposed to hydrostatic pressure, they exhibited a marked elongation and orientation in a random direction, together with development of centrally located, thick stress fibers. Pressured endothelial cells also exhibited a multilayered structure with less expression of VE-cadherin unlike under control conditions. Simultaneous loading of hydrostatic pressure and shear stress inhibited endothelial cell multilayering and induced elongation and orientation of endothelial cells with well-developed VE-cadherin in a monolayer, which suggests that for a better understanding of vascular endothelial cell responses one has to take into consideration the combination of the different mechanical forces such as exist under in vivo mechanical conditions.     

Influence of oxidatively modified LDL on monocyte-macrophage differentiation

Cellular cytoskeletal remodeling reflects alterations in local biochemical and mechanical changes in terms of stress that manifests relocation of signaling molecules within and across the cell. Although stretching due to load and chemical changes by high homocysteine (HHcy) causes cytoskeletal re-arrangement, the synergism between stretch and HHcy is unclear. We investigated the contribution of HHcy in cyclic stretch-induced focal adhesion (FA) protein redistribution leading to cytoskeletal re-arrangement in mouse aortic endothelial cells (MAEC). MAEC were subjected to cyclic stretch (CS) and HHcy alone or in combination. The redistribution of FA protein, and small GTPases were determined by Confocal microscopy and Western blot techniques in membrane and cytosolic compartments. We found that each treatment induces focal adhesion kinase (FAK) phosphorylation and cytoskeletal actin polymerization. In addition, CS activates and membrane translocates small GTPases RhoA with minimal effect on Rac1, whereas HHcy alone is ineffective in both GTPases translocation. However, the combined effect of CS and HHcy activates and membrane translocates both GTPases. Free radical scavenger NAC (N-Acetyl-Cysteine) inhibits CS and HHcy-mediated FAK phosphorylation and actin stress fiber formation. Interestingly, CS also activates and membrane translocates another FA protein, paxillin in HHcy condition. Cytochalasin D, an actin polymerization blocker and PI3-kinase inhibitor Wortmannin inhibited FAK phosphorylation and membrane translocation of paxillin suggesting the involvement of PI3K pathway. Together our results suggest that CS- and HHcy-induced oxidative stress synergistically contribute to small GTPase membrane translocation and focal adhesion protein redistribution leading to endothelial remodeling.     

Effects of biaxial oscillatory shear stress on endothelial cell proliferation and morphology

Wall shear stress (WSS) on anchored cells affects their responses, including cell proliferation and morphology. In this study, the effects of the directionality of pulsatile WSS on endothelial cell proliferation and morphology were investigated for cells grown in a Petri dish orbiting on a shaker platform. Time and location dependent WSS was determined by computational fluid dynamics (CFD). At low orbital speed (50 rpm), WSS was shown to be uniform (0-1 dyne/cm(2)) across the bottom of the dish, while at higher orbital speed (100 and 150 rpm), WSS remained fairly uniform near the center and fluctuated significantly (0-9 dyne/cm(2)) near the side walls of the dish. Since WSS on the bottom of the dish is two-dimensional, a new directional oscillatory shear index (DOSI) was developed to quantify the directionality of oscillating shear. DOSI approached zero for biaxial oscillatory shear of equal magnitudes near the center and approached one for uniaxial pulsatile shear near the wall, where large tangential WSS dominated a much smaller radial component. Near the center (low DOSI), more, smaller and less elongated cells grew, whereas larger cells with greater elongation were observed in the more uniaxial oscillatory shear (high DOSI) near the periphery of the dish. Further, cells aligned with the direction of the largest component of shear but were randomly oriented in low magnitude biaxial shear. Statistical analyses of the individual and interacting effects of multiple factors (DOSI, shear magnitudes and orbital speeds) showed that DOSI significantly affected all the responses, indicating that directionality is an important determinant of cellular responses.     

Carotid geometry effects on blood flow and on risk for vascular disease

It has been widely observed that atherosclerotic diseases occur at sites with complex hemodynamics, such as artery bifurcations, junctions, and regions of high curvature. These regions usually have very low or highly oscillatory wall shear stress (WSS). In the present work, 3D pulsatile blood flow through a model of the carotid artery bifurcation was simulated using a finite volume numerical method. The goal was to quantify the risk of atherogenesis associated with different carotid artery geometries. A risk scale based on the average WSS on the sinus wall of the internal carotid artery was proposed-a scale that can be used to quantify the effect of the carotid geometry on the relative risk for developing vascular disease. It was found that the bifurcation angle and the out-of-plane angle of the internal carotid artery affect the formation of low stress regions on the carotid walls. The main conclusions are: (a) larger internal carotid artery angles (theta(IC)) generally increase the frequency and the area of blood recirculation and lower the WSS on the sinus wall, hence increasing the risk of plaque build-up; (b) off-plane angles were found to lower the WSS on the sinus for geometries with theta(IC)25 degrees . Larger off-plane angles generally increase the danger of plague build-up; (c) for theta(IC) < 25 degrees , the off-plane angle does not have an obvious effect on the hemodynamic WSS; (d) symmetric bifurcations were found to increase the WSS on the sinus wall and ease the risk of vascular disease.