[Show abstract][Hide abstract] ABSTRACT: Atherosclerosis may be triggered by an elevated net transport of lipid-carrying macromolecules from plasma into the arterial wall. We hypothesised that whether lesions are of the thin-cap fibroatheroma (TCFA) type or are less fatty and more fibrous depends on the degree of elevation of transport, with greater uptake leading to the former. We further hypothesised that the degree of elevation can depend on haemodynamic wall shear stress characteristics and nitric oxide synthesis. Placing a tapered cuff around the carotid artery of apolipoprotein E -/- mice modifies patterns of shear stress and eNOS expression, and triggers lesion development at the upstream and downstream cuff margins; upstream but not downstream lesions resemble the TCFA. We measured wall uptake of a macromolecular tracer in the carotid artery of C57bl/6 mice after cuff placement. Uptake was elevated in the regions that develop lesions in hyperlipidaemic mice and was significantly more elevated where plaques of the TCFA type develop. Computational simulations and effects of reversing the cuff orientation indicated a role for solid as well as fluid mechanical stresses. Inhibiting NO synthesis abolished the difference in uptake between the upstream and downstream sites. The data support the hypothesis that excessively elevated wall uptake of plasma macromolecules initiates the development of the TCFA, suggest that such uptake can result from solid and fluid mechanical stresses, and are consistent with a role for NO synthesis. Modification of wall transport properties might form the basis of novel methods for reducing plaque rupture.
[Show abstract][Hide abstract] ABSTRACT: Atherosclerotic lesions have a characteristic spatial distribution within the arterial system, particularly near branches. This distribution has been attributed to elevated uptake of plasma macromolecules by the wall, and to pro-atherogenic influences of disturbed blood flow. We investigated whether there is a significant association of elevated permeability with a novel index of multidirectional disturbed flow termed transverse WSS (transWSS).
Endothelial permeability was mapped around branch ostia in thoracic aortas of 2-month-old rabbits (n=7) by administering fluorescent macromolecular tracers in vivo and measuring their uptake in fixed, excised vessels with quantitative confocal microscopy. TransWSS maps were created by applying computational fluid dynamics to geometric reconstructions obtained using microCT of vascular corrosion casts. Spatial correlations were assessed by novel techniques of surrogate data analysis.
Endothelial permeability was greater downstream of ostia than upstream (141±7% vs 87±7% of mean region intensity, p<0.001), as was transWSS. Both were elevated in strikingly similar arrowhead shaped regions surrounding the distal half of the branch mouth, and were spatially correlated (p<0.05).
These preliminary results are consistent with an influence on endothelial permeability of multidirectional disturbed flow, characterised by the transWSS index. This metric has a different spatial distribution from standard indices of the low and oscillatory flow commonly assumed to trigger atherosclerosis. Confirmation is required in studies at other locations and in other models, but the data suggest that current views of mechanical triggers involved in arterial disease may need re-examination. This study was funded by the BHF and the BHF Centre of Research Excellence.
[Show abstract][Hide abstract] ABSTRACT: Spatial variation of the haemodynamic stresses acting on the arterial wall is commonly assumed to explain the focal development of atherosclerosis. Disturbed flow in particular is thought to play a key role. However, widely-used metrics developed to quantify its extent are unable to distinguish between uniaxial and multidirectional flows. We analysed pulsatile flow fields obtained in idealised and anatomically-realistic arterial geometries using computational fluid dynamics techniques, and in particular investigated the multidirectionality of the flow fields, capturing this aspect of near-wall blood flow with a new metric - the transverse wall shear stress (transWSS) - calculated as the time-average of wall shear stress components perpendicular to the mean flow direction. In the idealised branching geometry, multidirectional flow was observed downstream of the branch ostium, a region of flow stagnation, and to the sides of the ostium. The distribution of the transWSS was different from the pattern of traditional haemodynamic metrics and more dependent on the velocity waveform imposed at the branch outlet. In rabbit aortas, transWSS patterns were again different from patterns of traditional metrics. The near-branch pattern varied between intercostal ostia, as is the case for lesion distribution; for some branches there were striking resemblances to the age-dependent patterns of disease seen in rabbit and human aortas. The new metric may lead to improved understanding of atherogenesis.
Full-text · Article · Aug 2013 · Journal of Biomechanics
[Show abstract][Hide abstract] ABSTRACT: AIMS: Low and oscillatory wall shear stress is widely assumed to play a key role in the initiation and development of atherosclerosis. Indeed, some studies have relied on the low shear theory when developing diagnostic and treatment strategies for cardiovascular disease. We wished to ascertain if this consensus is justified by published data.Methods and ResultsWe performed a systematic review of papers that compare the localisation of atherosclerotic lesions with the distribution of haemodynamic indicators calculated using computational fluid dynamics. The review showed that although many articles claim their results conform to the theory, it has been interpreted in different ways: a range of metrics has been used to characterise the distribution of disease, and they have been compared to a range of haemodynamic factors. Several studies, including all of those making systematic point-by-point comparisons of shear and disease, failed to find the expected relation. The various pre- and post-processing techniques used by different groups have reduced the range of shears over which correlations were sought, and in some cases are mutually incompatible. Finally, only a subset of the known patterns of disease has been investigated. CONCLUSIONS: The evidence for the low/oscillatory shear theory is less robust than commonly assumed. Longitudinal studies starting from the healthy state, or the collection of average flow metrics derived from large numbers of healthy vessels, both in conjunction with point-by-point comparisons using appropriate statistical techniques, will be necessary to improve our understanding of the relation between blood flow and atherogenesis.
Full-text · Article · Mar 2013 · Cardiovascular Research
[Show abstract][Hide abstract] ABSTRACT: Studies investigating the relation between the focal nature of atherosclerosis and hemodynamic factors are employing increasingly rigorous approaches to map the disease and calculate hemodynamic metrics. However, no standardized methodology exists to quantitatively compare these distributions. We developed a statistical technique that can be used to determine if hemodynamic and lesion maps are significantly correlated. The technique, which is based on a surrogate data analysis, does not require any assumptions (such as linearity) on the nature of the correlation. Randomized sampling was used to ensure the independence of data points, another basic assumption of commonly-used statistical methods that is often disregarded. The novel technique was used to compare previously-obtained maps of lesion prevalence in aortas of immature and mature cholesterol-fed rabbits to corresponding maps of wall shear stress, averaged across several animals in each age group. A significant spatial correlation was found in the proximal descending thoracic aorta, but not further downstream. Around intercostal branch openings the correlation was borderline significant in immature but not in mature animals. The results confirm the need for further investigation of the relation between the localization of atherosclerosis and blood flow, in conjunction with appropriate statistical techniques such as the method proposed here.
No preview · Article · Feb 2013 · Journal of Biomechanical Engineering
[Show abstract][Hide abstract] ABSTRACT: Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.
Full-text · Article · Feb 2013 · Journal of Biomechanical Engineering
[Show abstract][Hide abstract] ABSTRACT: Haemodynamic stresses acting on the arterial wall may play an important role in the initiation and development of atherosclerosis, and in particular are likely to explain its focal occurrence. Computational fluid dynamic (CFD) simulations of blood flow in arteries have been widely used to investigate this relation and a variety of metrics have been derived to link flow characteristics with lesion prevalence . Although the initial focus was on the magnitude of the time-averaged wall shear stress (TAWSS), an oscillatory shear index (OSI) was subsequently introduced “to describe the shear stress acting in directions other than the direction of the temporal mean shear stress vector” . Biological evidence suggests that flow without a definite direction, in contrast to shear with a clear direction (whether resulting from steady or pulsatile flow), causes sustained molecular signaling of pro-inflammatory and proliferative pathways . Although the OSI has frequently been used to quantify the extent of disturbed flow, we emphasise that no singular metric can fully characterise the flow environment; in particular, we and other research groups  note that OSI and other similar metrics are unable to distinguish between simple uniaxial flows (which can be purely forward flowing or reversing) and multi-directional flows, which we term “truly disturbed”. We propose a new method that has this potential, and which complements existing metrics. The new method may help investigations of the importance of flow directionality.
[Show abstract][Hide abstract] ABSTRACT: The BioFlow Group at Imperial College London develops and uses computational and experimental techniques to study fluid dynamics in organisms with the aim of advancing healthcare applications. Within this framework our group applies Computational Fluid Dynamics (CFD) to gain a better understanding of the initiation of atherosclerotic disease. Our in-house spectral element solver has been applied to idealised [1–2] and anatomically realistic  geometries, including the rabbit aorta and its branches .
[Show abstract][Hide abstract] ABSTRACT: The focal occurrence of atherosclerotic lesions around branching points and in curved vessels has led to the hypothesis that haemodynamics plays an important role in the development of the disease. The spatial distribution of atherosclerosis is also age-dependent in humans and rabbits ; detailed maps of disease prevalence in aortas of immature and mature rabbits were presented recently . Vincent et al.  applied computational fluid dynamics to study blood flow in the aorta of a mature rabbit, but they did not investigate age-dependent effects. The purpose of the present study was to quantify differences in aortic haemodynamics between immature and mature rabbits, and to compare averaged distributions of the flow-related wall shear stress with maps of disease prevalence. As blood flow is heavily dependent on vessel geometry, the shapes of the aorta in the two age groups were also compared.
[Show abstract][Hide abstract] ABSTRACT: The distribution of atherosclerotic lesions changes with age in human and rabbit aortas. We investigated if this can be explained by changes in patterns of blood flow and wall shear stress.
The luminal geometry of thoracic aortas from immature and mature rabbits was obtained by micro-CT of vascular corrosion casts. Blood flow was computed and average maps of wall shear stress were derived.
The branch anatomy of the aortic arch varied widely between animals. Wall shear was increased downstream and to a lesser extent upstream of intercostal branch ostia, and a stripe of high shear was located on the dorsal descending aortic wall. The stripe was associated with two vortices generated by aortic arch curvature; their persistence into the descending aorta depended on aortic taper and was more pronounced in mature geometries. These results were not sensitive to the modelling assumptions.
Blood flow characteristics in the rabbit aorta were affected by the degree of taper, which tends to increase with age in the aortic arch and strengthens secondary flows into the descending aorta. Previously-observed lesion distributions correlated better with high than low shear, and age-related changes around branch ostia were not explained by the flow patterns.
[Show abstract][Hide abstract] ABSTRACT: Three-dimensional simulations of blood flow usually produce such large quantities of data that they are unlikely to be of clinical use unless methods are available to simplify our understanding of the flow dynamics. We present a new method to investigate the mechanisms by which vascular curvature and torsion affect blood flow, and we apply it to the steady-state flow in single bends, helices, double bends, and a rabbit thoracic aorta based on image data. By calculating forces and accelerations in an orthogonal coordinate system following the centreline of each vessel, we obtain the inertial forces (centrifugal, Coriolis, and torsional) explicitly, which directly depend on vascular curvature and torsion. We then analyse the individual roles of the inertial, pressure gradient, and viscous forces on the patterns of primary and secondary velocities, vortical structures, and wall stresses in each cross section. We also consider cross-sectional averages of the in-plane components of these forces, which can be thought of as reducing the dynamics of secondary flows onto the vessel centreline. At Reynolds numbers between 50 and 500, secondary motions in the directions of the local normals and binormals behave as two underdamped oscillators. These oscillate around the fully developed state and are coupled by torsional forces that break the symmetry of the flow. Secondary flows are driven by the centrifugal and torsional forces, and these are counterbalanced by the in-plane pressure gradients generated by the wall reaction. The viscous force primarily opposes the pressure gradient, rather than the inertial forces. In the axial direction, and depending on the secondary motion, the curvature-dependent Coriolis force can either enhance or oppose the bulk of the axial flow, and this shapes the velocity profile. For bends with little or no torsion, the Coriolis force tends to restore flow axisymmetry. The maximum circumferential and axial wall shear stresses along the centreline correlate well with the averaged in-plane pressure gradient and the radial displacement of the peak axial velocity, respectively. We conclude with a discussion of the physiological implications of these results.
Full-text · Article · Mar 2012 · Physics of Fluids
[Show abstract][Hide abstract] ABSTRACT: Although risk factors for atherosclerosis such as genetic predisposition and diet are systemic, the disease develops non-uniformly throughout the arterial system. Lesions preferentially occur in curved arteries and branching regions and their distribution has been observed to change with age in both humans and rabbits . If local blood flow patterns play a role in the initiation of atherosclerosis, the age-related differences may be a consequence of changes in the flow characteristics.
[Show abstract][Hide abstract] ABSTRACT: Bone fracture healing is a complex process in which angiogenesis or the development of a blood vessel network plays a crucial role. In this paper, a mathematical model is presented that simulates the biological aspects of fracture healing including the formation of individual blood vessels. The model consists of partial differential equations, several of which describe the evolution in density of the most important cell types, growth factors, tissues and nutrients. The other equations determine the growth of blood vessels as a result of the movement of leading endothelial (tip) cells. Branching and anastomoses are accounted for in the model. The model is applied to a normal fracture healing case and subjected to a sensitivity analysis. The spatiotemporal evolution of soft tissues and bone, as well as the development of a blood vessel network are corroborated by comparison with experimental data. Moreover, this study shows that the proposed mathematical framework can be a useful tool in the research of impaired healing and the design of treatment strategies.
No preview · Article · Jun 2011 · Biomechanics and Modeling in Mechanobiology