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.     

Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?

The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention.     

Dependence of red blood cell dynamics in microvessel bifurcations on the endothelial surface layer’s resistance to flow and compression

Red blood cells (RBCs) make up 40–45% of blood and play an important role in oxygen transport. That transport depends on the RBC distribution throughout the body, which is highly heterogeneous. That distribution, in turn, depends on how RBCs are distributed or partitioned at diverging vessel bifurcations where blood flows from one vessel into two. Several studies have used mathematical modeling to consider RBC partitioning at such bifurcations in order to produce useful insights. These studies, however, assume that the vessel wall is a flat impenetrable homogeneous surface. While this is a good first approximation, especially for larger vessels, the vessel wall is typically coated by a flexible, porous endothelial glycocalyx or endothelial surface layer (ESL) that is on the order of 0.5–1 µm thick. To better understand the possible effects of this layer on RBC partitioning, a diverging capillary bifurcation is analyzed using a flexible, two-dimensional model. In addition, the model is also used to investigate RBC deformation and RBC penetration of the ESL region when ESL properties are varied. The RBC is represented using interconnected viscoelastic elements. Stokes flow equations (viscous flow) model the surrounding fluid. The flow in the ESL is modeled using the Brinkman approximation for porous media with a corresponding hydraulic resistivity. The ESL’s resistance to compression is modeled using an osmotic pressure difference. One cell passes through the bifurcation at a time, so there are no cell–cell interactions. A range of physiologically relevant hydraulic resistivities and osmotic pressure differences are explored. Decreasing hydraulic resistivity and/or decreasing osmotic pressure differences (ESL resistance to compression) produced four behaviors: (1) RBC partitioning nonuniformity increased slightly; (2) RBC deformation decreased; (3) RBC velocity decreased relative to blood flow velocity; and (4) RBCs penetrated more deeply into the ESL. Decreasing the ESL’s resistance to flow and/or compression to pathological levels could lead to more frequent cell adhesion and clotting as well as impaired vascular regulation due to weaker ATP and nitric oxide release. Potential mechanisms that can contribute to these behaviors are also discussed.

     

Convection-diffusion interaction for oscillatory flow in a tapered tube

Transport of soluble material is analyzed for volume-cycle oscillatory flow in a tapered tube. The equations of motion are solved using a regular perturbation method for small taper angle and order unity amplitude over a range of the Womersley parameter. The transport equation is also solved by a regular perturbation method where uniform end concentrations and no wall flux are assumed. The time-averaged axial transport of solute is calculated for several tapered tubes. There is substantial modification of transport compared to the straight tube case and the results are interpreted with respect to pulmonary gas exchange.     

Healthy and diseased coronary bifurcation geometries influence near-wall and intravascular flow: A computational exploration of the hemodynamic risk

Local hemodynamics has been identified as one main determinant in the onset and progression of atherosclerotic lesions at coronary bifurcations. Starting from the observation that atherosensitive hemodynamic conditions in arterial bifurcation are majorly determined by the underlying anatomy, the aim of the present study is to investigate how peculiar coronary bifurcation anatomical features influence near-wall and intravascular flow patterns. Different bifurcation angles and cardiac curvatures were varied in population-based, idealized models of both stenosed and unstenosed bifurcations, representing the left anterior descending (LAD) coronary artery with its diagonal branch. Local hemodynamics was analyzed in terms of helical flow and exposure to low/oscillatory shear stress by performing computational fluid dynamics simulations.Results show that bifurcation angle impacts lowly hemodynamics in both stenosed and unstenosed cases. Instead, curvature radius influences the generation and transport of helical flow structures, with smaller cardiac curvature radius associated to higher helicity intensity. Stenosed bifurcation models exhibit helicity intensity values one order of magnitude higher than the corresponding unstenosed cases. Cardiac curvature radius moderately affects near-wall hemodynamics of the stenosed cases, with smaller curvature radius leading to higher exposure to low shear stress and lower exposure to oscillatory shear stress. In conclusion, the proposed controlled benchmark allows investigating the effect of various geometrical features on local hemodynamics at the LAD/diagonal bifurcation, highlighting that cardiac curvature influences near wall and intravascular hemodynamics, while bifurcation angle has a minor effect.     

Development of a general method for designing microvascular networks using distribution of wall shear stress

In the present study, theoretical formulations for calculation of optimal bifurcation angle and relationship between the diameters of mother and daughter vessels using the power law model for non-Newtonian fluids are developed. The method is based on the distribution of wall shear stress in the mother and daughter vessels. Also, the effect of distribution of wall shear stress on the minimization of energy loss and flow resistance is considered. It is shown that constant wall shear stress in the mother and daughter vessels provides the minimum flow resistance and energy loss of biological flows. Moreover, the effects of different wall shear stresses in the mother and daughter branches, different lengths of daughter branches in the asymmetric bifurcations and non-Newtonian effect of biological fluid flows on the bifurcation angle and the relationship between the diameters of mother and daughter branches are considered. Using numerical simulations for non-Newtonian models such as power law and Carreau models, the effects of optimal bifurcation angle on the pressure drop and flow resistance of blood flow in the symmetric bifurcation are investigated. Numerical simulations show that optimal bifurcation angle decreases the pressure drop and flow resistance especially for bifurcations at large Reynolds number.     

Pulsatile flow effects on the hemodynamics of intracranial aneurysms

High-resolution numerical simulations are carried out to systematically investigate the effect of the incoming flow waveform on the hemodynamics and wall shear stress patterns of an anatomic sidewall intracranial aneurysm model. Various wave forms are constructed by appropriately scaling a typical human waveform such that the waveform maximum and time-averaged Reynolds numbers, the Womersley number (α), and the pulsatility index (PI) are systematically varied within the human physiologic range. We show that the waveform PI is the key parameter that governs the vortex dynamics across the aneurysm neck and the flow patterns within the dome. At low PI, the flow in the dome is similar to a driven cavity flow and is characterized by a quasi-stationary shear layer that delineates the parent artery flow from the recirculating flow within the dome. At high PI, on the other hand, the flow is dominated by vortex ring formation, transport across the neck, and impingement and breakdown at the distal wall of the aneurysm dome. We further show that the spatial and temporal characteristics of the wall shear stress field on the aneurysm dome are strongly correlated with the vortex dynamics across the neck. We finally argue that the ratio between the characteristic time scale of transport by the mean flow across the neck and the time scale of vortex ring formation can be used to predict for a given sidewall aneurysm model the critical value of the waveform PI for which the hemodynamics will transition from the cavity mode to the vortex ring mode.     

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.     

Vortex generation in pulsatile flow through arterial bifurcation models including the human carotid artery

Visualization experiments were performed to elucidate the complicated flow pattern in pulsatile flow through arterial bifurcations. Human common carotid arteries, which were made transparent, and glass-models simulating Y- and T-shaped bifurcations were used. Pulsatile flow with wave forms similar to those of arterial flow was generated with a piston pump, elastic tube, airchamber, and valves controlling the outflow resistance. Helically recirculating flow with a pattern similar to that of the horseshoe vortex produced around wall-based protuberances in circular tubes was observed in pulsatile flow through all the bifurcations used in the present study. This flow type, which we shall refer to as the horseshoe vortex, has also been demonstrated to occur at the human common carotid bifurcation in steady flow with Reynolds numbers above 100. Time-varying flows also produced the horseshoe vortex mostly during the decelerating phase. Fluid particles of dye solution approaching the bifurcation apex diverged, divided into two directions perpendicularly, and then showed helical motion representing the horseshoe vortex formation. While this helical flow was produced, the stagnation points appeared on the wall upstream of the apex. Their position was dependent upon the flow distribution ratio between the branches in the individual arteries. The region affected by the horseshoe vortex was smaller during pulsatile flow than during steady flow. Lowering the Reynolds number together with the Womersley number weakened the intensity of helical flow. A separation bubble, resulting from the divergence or wall roughness, was observed at the outer or inner wall of the branch vessels and made the flow more complicated.     

Ultrastructural localization of nitric oxide synthase and endothelin in coronary and pulmonary arteries of newborn rats

This is the first report on the ultrastructural distribution of nitric oxide synthase and endothelin immunoreactivities in the coronary and pulmonary arteries of newborn Wistar rats. The distribution of nitric oxide synthase and endothelin was investigated using pre-embedding peroxidase-antiperoxidase immunocytochemistry. In both arteries examined, positive labelling for nitric oxide synthase was localized both in the endothelium and smooth muscle, whereas positive labelling for endothelin was localized in the endothelium exclusively. In the coronary artery, approximately 80% and 55% of the endothelial cells examined were positive for nitric oxide synthase and endothelin, respectively, whereas in the pulmonary artery, 77% and 60% of the endothelial cells were positive for nitric oxide synthase and endothelin, respectively. These findings indicate that nitric oxide synthase and endothelin are colocalized in some of the endothelial cells of the newborn rat. In the endothelium, nitric oxide synthase and endothelin immunoreactivities were distributed throughout the cell cytoplasm and in association with the membranes of intracellular organelles. In smooth muscle, a relationship of nitric oxide synthase immunoreactivity to endoplasmic reticulum was observed in the pulmonary artery. In summary, in the newborn rat, endothelial cells of the coronary and pulmonary artery are rich in nitric oxide synthase (neuronal isoform) and endothelin, and it is suggested therefore that they may be substantially involved in vasomotor control of the cardiac and pulmonary circulation during early stages of postnatal development.     

Periodic flow at airway bifurcations. III. Energy dissipation

We measured the energy dissipation associated with large-amplitude periodic flow through airway bifurcation models. Each model consisted of a single asymmetric bifurcation with a different branching angle and area ratio, with each branch terminated into an identical elastic load. Sinusoidal volumetric oscillations were applied at the parent duct so that the upstream Reynolds number (Re) varied from 30 to 77,000 and the Womersley parameter (alpha) from 4 to 30. Pressures were measured continuously at the parent duct and at both terminals, and instantaneous branch flow rates were calculated. Time-averaged energy dissipation in the bifurcation was computed from an energy budget over a control volume integrated over a cycle and was expressed as a friction factor, F. We found that when tidal volume was small [ratio of tidal volume to resident (dead space) volume, VT/VD less than 1], F was independent of branching angle and fell with increasing alpha and VT/VD. When tidal volume was large (VT/VD greater than 1), F increased with increasing branching angle and varied less strongly with alpha and VT/VD. No simple benchmark flow represented the data well over the entire experimental range. This study demonstrates that only two nondimensional parameters, alpha and VT/VD, are necessary and are sufficient to describe time-averaged energy dissipation in a given bifurcation geometry during sinusoidal flow.     

Theoretical analysis of biochemical pathways of nitric oxide release from vascular endothelial cells

Vascular endothelium expressing endothelial nitric oxide synthase (eNOS) produces nitric oxide (NO), which has a number of important physiological functions in the microvasculature. The rate of NO production by the endothelium is a critical determinant of NO distribution in the vascular wall. We have analyzed the biochemical pathways of NO synthesis and formulated a model to estimate NO production by the microvascular endothelium under physiological conditions. The model quantifies the NO produced by eNOS based on the kinetics of NO synthesis and the availability of eNOS and its intracellular substrates. The predicted NO production from microvessels was in the range of 0.005-0.1 microM/s. This range of predicted values is in agreement with some experimental values but is much lower than other rates previously measured or estimated from experimental data with the help of mathematical modeling. Paradoxical discrepancies between the model predictions and previously reported results based on experimental measurements of NO concentration in the vicinity of the arteriolar wall suggest that NO can also be released through eNOS-independent mechanisms, such as catalysis by neuronal NOS (nNOS). We also used our model to test the sensitivity of NO production to substrate availability, eNOS concentration, and potential rate-limiting factors. The results indicated that the predicted low level of NO production can be attributed primarily to a low expression of eNOS in the microvascular endothelial cells.     

Endothelial function and coronary artery disease

The endothelium produces a number of vasodilator and vasoconstrictor substances that not only regulate vasomotor tone, but also the recruitment and activity of inflammatory cells and the propensity towards thrombosis. Endothelial vasomotor function is a convenient way to assess these other functions, and is related to the long-term risk of cardiovascular disease. Lipids (particularly low density lipoprotein cholesterol) and oxidant stress play a major role in impairing these functions, by reducing the bioavailability of nitric oxide and activating pro-inflammatory signalling pathways such as nuclear factor kappa B. Biomechanical forces on the endothelium, including low shear stress from disturbed blood flow, also activate the endothelium increasing vasomotor dysfunction and promoting inflammation by upregulating pro-atherogenic genes. In contrast, normal laminar shear stress promotes the expression of genes that may protect against atherosclerosis. The sub-cellular structure of endothelial cells includes caveolae that play an integral part in regulating the activity of endothelial nitric oxide synthase. Low density lipoprotein cholesterol and oxidant stress impair caveolae structure and function and adversely affect endothelial function. Lipid-independent pathways of endothelial cell activation are increasingly recognized, and may provide new therapeutic targets. Endothelial vasoconstrictors, such as endothelin, antagonize endothelium-derived vasodilators and contribute to endothelial dysfunction. Some but not all studies have linked certain genetic polymorphisms of the nitric oxide synthase enzyme to vascular disease and impaired endothelial function. Such genetic heterogeneity may nonetheless offer new insights into the variability of endothelial function.     

Angiotensin II stimulates nitric oxide production in pulmonary artery endothelium via the type 2 receptor

We previously reported that angiotensin II stimulates an increase in nitric oxide production in pulmonary artery endothelial cells. The aims of this study were to determine which receptor subtype mediates the angiotensin II-dependent increase in nitric oxide production and to investigate the roles of the angiotensin type 1 and type 2 receptors in modulating angiotensin II-dependent vasoconstriction in pulmonary arteries. Pulmonary artery endothelial cells express both angiotensin II type 1 and type 2 receptors as assessed by RT-PCR, Western blot analysis, and flow cytometry. Treatment of the endothelial cells with PD-123319, a type 2 receptor antagonist, prevented the angiotensin II-dependent increase in nitric oxide synthase mRNA, protein levels, and nitric oxide production. In contrast, the type 1 receptor antagonist losartan enhanced nitric oxide synthase mRNA levels, protein expression, and nitric oxide production. Pretreatment of the endothelial cells with either PD-123319 or an anti-angiotensin II antibody prevented this losartan enhancement of nitric oxide production. Angiotensin II-dependent enhanced hypoxic contractions in pulmonary arteries were blocked by the type 1 receptor antagonist candesartan; however, PD-123319 enhanced hypoxic contractions in angiotensin II-treated endothelium-intact vessels. These data demonstrate that angiotensin II stimulates an increase in nitric oxide synthase mRNA, protein expression, and nitric oxide production via the type 2 receptor, whereas signaling via the type 1 receptor negatively regulates nitric oxide production in the pulmonary endothelium. This endothelial, type 2 receptor-dependent increase in nitric oxide may serve to counterbalance the angiotensin II-dependent vasoconstriction in smooth muscle cells, ultimately regulating pulmonary vascular tone.     

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.     

The influence of radial RBC distribution, blood velocity profiles, and glycocalyx on coupled NO/O2 transport.

The purpose of this investigation was to study the effect of the presence of red blood cells (RBCs) in the plasma layer near the arteriole wall on nitric oxide (NO) and oxygen (O2) transport. To this end, we extended a coupled NO and O2 diffusion-reaction model in the arteriole, developed by our group, to include the effect of the presence of RBCs in the plasma layer and the effect of convection. Two blood flow velocity profiles (plug and parabolic) were tested. The average hematocrit in the bloodstream was assumed to be constant in the central core and decreasing to zero in the boundary layer next to the endothelial surface layer. The effect of the presence or absence of RBCs near the endothelium was studied while varying the endothelial surface layer and boundary layer thickness. With RBCs present in the boundary layer, the model predicts that 1) NO decreases significantly in the endothelium and vascular wall; 2) there is a very small increase in endothelial and vascular wall Po2; 3) scavenging of NO by hemoglobin decreases with increasing thickness of the boundary layer; 4) the shape of the velocity profile influences both NO and Po2 gradients in the bloodstream; and 5) the presence of RBCs in the boundary layer near the endothelium has a much larger effect on NO than on O2 transport.     

Sex differences in intracranial arterial bifurcations

Background: Subarachnoid hemorrhage (SAH) is a serious condition, occurring more frequently in females than in males. SAH is mainly caused by rupture of an intracranial aneurysm, which is formed by localized dilation of the intracranial arterial vessel wall, usually at the apex of the arterial bifurcation. The female preponderance is usually explained by systemic factors (hormonal influences and intrinsic wall weakness); however, the uneven sex distribution of intracranial aneurysms suggests a possible physiologic factor—a local sex difference in the intracranial arteries.Objective: The aim of this study was to explore sex variation in the bifurcation anatomy of the middle cerebral artery (MCA) and internal carotid artery (ICA), and the subsequent hemodynamic impact.Methods: Vessel radii and bifurcation angles were measured in patients with MCA and ICA bifurcations. Data from a previously published study of 55 patients undergoing diagnostic cerebral digital subtraction angiography at Dalcross Private Hospital in Sydney, Australia, between 2002 and 2003, were available for analysis. The measurements were used to create idealized, averaged bifurcations of the MCA and ICA for females and males. Computational fluid dynamics simulations were performed to calculate hemodynamic forces in the models.Results: The vessel radii and bifurcation angles of 47 MCA and 52 ICA bifurcations in 49 patients (32 females, 17 males; mean age, 53 years; age range, 14–86 years) were measured. Statistically significant sex differences were found in vessel diameter (males larger than females; P < 0.05), but not in bifurcation angle. Computational fluid dynamics simulations revealed higher wall shear stress in the female MCA (19%) and ICA (50%) bifurcations compared with the male bifurcations.Conclusions: This study of MCA and ICA bifurcations in female and male patients suggests that sex differences in vessel size and blood flow velocity result in higher hemodynamic forces acting on the vessel wall in females. This new hypothesis may partly explain why intracranial aneurysms and SAH are more likely to occur in females than in males.     

Nitric oxide-an endothelial cell survival factor

Due to its unique position in the vessel wall, the endothelium acts as a barrier and thereby controls adhesion, aggregation and invasion of immune competent cells. Apoptosis of endothelial cells may critically disturb the integrity of the endothelial monolayer and contribute to the initiation of proinflammatory events. Endothelial cell apoptosis is counteracted by nitric oxide synthesised by the endothelium nitric oxide synthase (eNOS). Thus, nitric oxide inhibits endothelial cell apoptosis induced by proinflammatory cytokines and proatherosclerotic factors including reactive oxygen species and angiotensin II. The apoptosis-suppression may contribute to the profound anti-inflammatory and anti-atherosclerotic effects of endothelial-derived NO. Furthermore, the support of endothelial cell survival by NO may further play a central role for the pro-angiogenic effects of NO.     

Low density lipoprotein inhibits accumulation of nitrites in murine brain endothelial cell cultures.

Endothelial cells produce nitric oxide which is considered to serve as a major source of endothelial derived relaxing factor activity. It has been demonstrated that activation of mouse brain endothelium by TNF-alpha and IFN-gamma led to accumulation of nitrite which is presumably formed by oxidation of nitric oxide. A number of studies suggest that reactive oxygen species produced by cytokine-activated cells are involved in the conversion of nitric oxide to nitrites and nitrates. We investigated whether low density lipoprotein (LDL), acting as a radical scavenger, is able to inhibit nitrite accumulation in mouse brain endothelial cell cultures and in a cell-free system in which sodium nitroprusside was used as a source of nitric oxide. A comparison of these two models indicates the active involvement of LDL in suppressing nitrite accumulation in murine endothelial cultures.