Relative Residence Time Can Account for Half of the Anatomical Variation in Fatty Streak Prevalence Within the Right Coronary Artery.

PURPOSE: The patchy anatomical distribution of atherosclerosis has been attributed to variation in haemodynamic wall shear stress (WSS). The consensus is that low WSS and a high Oscillatory Shear Index (OSI) trigger the disease. We found that atherosclerosis at aortic branch sites correlates threefold better with transverse WSS (transWSS), a metric which quantifies multidirectional near-wall flow. Coronary artery disease has greater clinical significance than aortic disease but computation of WSS metrics is complicated by the substantial vessel motion occurring during each cardiac cycle. Here we present the first comparison of the distribution of atherosclerosis with WSS metrics computed for moving coronary arteries. METHODS: Maps of WSS metrics were computed using dynamic geometries reconstructed from angiograms of ten non-stenosed human right coronary arteries (RCAs). They were compared with maps of fatty streak prevalence derived from a previous study of 1852 RCAs. RESULTS: Time average WSS (TAWSS), OSI, transWSS and the cross-flow index (CFI), a non-dimensional form of the transWSS, gave non-significant or significant but low spatial correlations with lesion prevalence. The highest correlation coefficient (0.71) was for the relative residence time (RRT), a metric that decreases with TAWSS and increases with OSI. The coefficient was not changed if RRT was calculated using CFI, which captures multidirectional WSS only, rather than OSI, which encompasses both multidirectional and oscillatory WSS. CONCLUSION: Contrary to our earlier findings in the aorta, low WSS in combination with highly multidirectional flow correlates best with lesion location in the RCA, explaining approximately half of its anatomical variation.

Modification of the swirling well cell culture model to alter shear stress metrics.

Effects of hemodynamic shear stress on endothelial cells have been extensively investigated using the "swirling well" method, in which cells are cultured in dishes or multiwell plates placed on an orbital shaker. A wave rotates around the well, producing complex patterns of shear. The method allows chronic exposure to flow with high throughput at low cost but has two disadvantages: a number of shear stress characteristics change in a broadly similar way from the center to the edge of the well, and cells at one location in the well may release mediators into the medium that affect the behavior of cells at other locations, exposed to different shears. These properties make it challenging to correlate cell properties with shear. The present study investigated simple alterations to ameliorate these issues. Flows were obtained by numerical simulation. Increasing the volume of fluid in the well-altered dimensional but not dimensionless shear metrics. Adding a central cylinder to the base of the well-forced fluid to flow in a square toroidal channel and reduced multidirectionality. Conversely, suspending a cylinder above the base of the well made the flow highly multidirectional. Increasing viscosity in the latter model increased the magnitude of dimensional but not dimensionless metrics. Finally, tilting the well changed the patterns of different wall shear stress metrics in different ways. Collectively, these methods allow similar flows over most of the cells cultured and/or allow the separation of different shear metrics. A combination of the methods overcomes the limitations of the baseline model.

Influence of right coronary artery motion, flow pulsatility and non-Newtonian rheology on wall shear stress metrics.

The patchy distribution of atherosclerosis within the arterial system is consistent with a controlling influence of hemodynamic wall shear stress (WSS). Patterns of low, oscillatory and transverse WSS have been invoked to explain the distribution of disease in the aorta. Disease of coronary arteries has greater clinical importance but blood flow in these vessels may be complicated by their movement during the cardiac cycle. Previous studies have shown that time average WSS is little affected by the dynamic geometry, and that oscillatory shear is influenced more. Here we additionally investigate effects on transverse WSS. We also investigate the influence of non-Newtonian blood rheology as it can influence vortical structure, on which transverse WSS depends; Carreau-Yasuda models were used. WSS metrics were derived from numerical simulations of blood flow in a model of a moving right coronary artery which, together with a subject-specific inflow waveform, was obtained by MR imaging of a healthy human subject in a previous study. The results confirmed that time average WSS was little affected by dynamic motion and that oscillatory WSS was more affected. They additionally showed that transverse WSS and its non-dimensional analogue, the Cross Flow Index, were affected still further. This appeared to reflect time-varying vortical structures caused by the changes in curvature. The influence of non-Newtonian rheology was significant with some physiologically realistic parameter values, and hence may be important in certain subjects. Dynamic geometry and non-Newtonian rheology should be incorporated into models designed to produce maps of transverse WSS in coronary arteries.

Improvement and validation of a computational model of flow in the swirling well cell culture model.

Effects of fluid dynamics on cells are often studied by growing the cells on the base of cylindrical wells or dishes that are swirled on the horizontal platform of an orbital shaker. The swirling culture medium applies a shear stress to the cells that varies in magnitude and directionality from the center to the edge of the vessel. Computational fluid dynamics methods are used to simulate the flow and hence calculate shear stresses at the base of the well. The shear characteristics at each radial location are then compared with cell behavior at the same position. Previous simulations have generally ignored effects of surface tension and wetting, and results have only occasionally been experimentally validated. We investigated whether such idealized simulations are sufficiently accurate, examining a commonly-used swirling well configuration. The breaking wave predicted by earlier simulations was not seen, and the edge-to-center difference in shear magnitude (but not directionality) almost disappeared, when surface tension and wetting were included. Optical measurements of fluid height and velocity agreed well only with the computational model that incorporated surface tension and wetting. These results demonstrate the importance of including accurate fluid properties in computational models of the swirling well method.

Endothelial cells do not align with the mean wall shear stress vector.

The alignment of arterial endothelial cells (ECs) with the mean wall shear stress (WSS) vector is the prototypical example of their responsiveness to flow. However, evidence for this behaviour rests on experiments where many WSS metrics had the same orientation or where they were incompletely characterized. In the present study, we tested the phenomenon more rigorously. Aortic ECs were cultured in cylindrical wells on the platform of an orbital shaker. In this system, orientation would differ depending on the WSS metric to which the cells aligned. Variation in flow features and hence in possible orientations was further enhanced by altering the viscosity of the medium. Orientation of endothelial nuclei was compared with WSS characteristics obtained by computational fluid dynamics. At low mean WSS magnitudes, ECs aligned with the modal WSS vector, while at high mean WSS magnitudes they aligned so as to minimize the shear acting across their long axis (transverse WSS). Their failure to align with the mean WSS vector implies that other aspects of endothelial behaviour attributed to this metric require re-examination. The evolution of a mechanism for minimizing transverse WSS is consistent with it having detrimental effects on the cells and with its putative role in atherogenesis.

Estimating central blood pressure from aortic flow: development and assessment of algorithms.

Central blood pressure (cBP) is a highly prognostic cardiovascular (CV) risk factor whose accurate, invasive assessment is costly and carries risks to patients. We developed and assessed novel algorithms for estimating cBP from noninvasive aortic hemodynamic data and a peripheral blood pressure measurement. These algorithms were created using three blood flow models: the two- and three-element Windkessel (0-D) models and a one-dimensional (1-D) model of the thoracic aorta. We tested new and existing methods for estimating CV parameters (left ventricular ejection time, outflow BP, arterial resistance and compliance, pulse wave velocity, and characteristic impedance) required for the cBP algorithms, using virtual (simulated) subjects (n = 19,646) for which reference CV parameters were known exactly. We then tested the cBP algorithms using virtual subjects (n = 4,064), for which reference cBP were available free of measurement error, and clinical datasets containing invasive (n = 10) and noninvasive (n = 171) reference cBP waves across a wide range of CV conditions. The 1-D algorithm outperformed the 0-D algorithms when the aortic vascular geometry was available, achieving central systolic blood pressure (cSBP) errors ≤ 2.1 ± 9.7 mmHg and root-mean-square errors (RMSEs) ≤ 6.4 ± 2.8 mmHg against invasive reference cBP waves (n = 10). When the aortic geometry was unavailable, the three-element 0-D algorithm achieved cSBP errors ≤ 6.0 ± 4.7 mmHg and RMSEs ≤ 5.9 ± 2.4 mmHg against noninvasive reference cBP waves (n = 171), outperforming the two-element 0-D algorithm. All CV parameters were estimated with mean percentage errors ≤ 8.2%, except for the aortic characteristic impedance (≤13.4%), which affected the three-element 0-D algorithm's performance. The freely available algorithms developed in this work enable fast and accurate calculation of the cBP wave and CV parameters in datasets containing noninvasive ultrasound or magnetic resonance imaging data.NEW & NOTEWORTHY First, our proposed methods for CV parameter estimation and a comprehensive set of methods from the literature were tested using in silico and clinical datasets. Second, optimized algorithms for estimating cBP from aortic flow were developed and tested for a wide range of cBP morphologies, including catheter cBP data. Third, a dataset of simulated cBP waves was created using a three-element Windkessel model. Fourth, the Windkessel model dataset and optimized algorithms are freely available.

Wave Intensity Analysis Combined With Machine Learning can Detect Impaired Stroke Volume in Simulations of Heart Failure.

Heart failure is treatable, but in the United Kingdom, the 1-, 5- and 10-year mortality rates are 24.1, 54.5 and 75.5%, respectively. The poor prognosis reflects, in part, the lack of specific, simple and affordable diagnostic techniques; the disease is often advanced by the time a diagnosis is made. Previous studies have demonstrated that certain metrics derived from pressure-velocity-based wave intensity analysis are significantly altered in the presence of impaired heart performance when averaged over groups, but to date, no study has examined the diagnostic potential of wave intensity on an individual basis, and, additionally, the pressure waveform can only be obtained accurately using invasive methods, which has inhibited clinical adoption. Here, we investigate whether a new form of wave intensity based on noninvasive measurements of arterial diameter and velocity can detect impaired heart performance in an individual. To do so, we have generated a virtual population of two-thousand elderly subjects, modelling half as healthy controls and half with an impaired stroke volume. All metrics derived from the diameter-velocity-based wave intensity waveforms in the carotid, brachial and radial arteries showed significant crossover between groups-no one metric in any artery could reliably indicate whether a subject's stroke volume was normal or impaired. However, after applying machine learning to the metrics, we found that a support vector classifier could simultaneously achieve up to 99% recall and 95% precision. We conclude that noninvasive wave intensity analysis has significant potential to improve heart failure screening and diagnosis.

Comparison of arterial wave intensity analysis by pressure-velocity and diameter-velocity methods in a virtual population of adult subjects.

Pressure-velocity-based analysis of arterial wave intensity gives clinically relevant information about the performance of the heart and vessels, but its utility is limited because accurate pressure measurements can only be obtained invasively. Diameter-velocity-based wave intensity can be obtained noninvasively using ultrasound; however, due to the nonlinear relationship between blood pressure and arterial diameter, the two wave intensities might give disparate clinical indications. To test the magnitude of the disagreement, we have generated an age-stratified virtual population to investigate how the two dominant nonlinearities viscoelasticity and strain-stiffening cause the two formulations to differ. We found strong agreement between the pressure-velocity and diameter-velocity methods, particularly for the systolic wave energy, the ratio between systolic and diastolic wave heights, and older subjects. The results are promising regarding the introduction of noninvasive wave intensities in the clinic.

Computational modelling for decision-making: where, why, what, who and how.

In order to deal with an increasingly complex world, we need ever more sophisticated computational models that can help us make decisions wisely and understand the potential consequences of choices. But creating a model requires far more than just raw data and technical skills: it requires a close collaboration between model commissioners, developers, users and reviewers. Good modelling requires its users and commissioners to understand more about the whole process, including the different kinds of purpose a model can have and the different technical bases. This paper offers a guide to the process of commissioning, developing and deploying models across a wide range of domains from public policy to science and engineering. It provides two checklists to help potential modellers, commissioners and users ensure they have considered the most significant factors that will determine success. We conclude there is a need to reinforce modelling as a discipline, so that misconstruction is less likely; to increase understanding of modelling in all domains, so that the misuse of models is reduced; and to bring commissioners closer to modelling, so that the results are more useful.

Visualization of three pathways for macromolecule transport across cultured endothelium and their modification by flow.

Transport of macromolecules across vascular endothelium and its modification by fluid mechanical forces are important for normal tissue function and in the development of atherosclerosis. However, the routes by which macromolecules cross endothelium, the hemodynamic stresses that maintain endothelial physiology or trigger disease, and the dependence of transendothelial transport on hemodynamic stresses are controversial. We visualized pathways for macromolecule transport and determined the effect on these pathways of different types of flow. Endothelial monolayers were cultured under static conditions or on an orbital shaker producing different flow profiles in different parts of the wells. Fluorescent tracers that bound to the substrate after crossing the endothelium were used to identify transport pathways. Maps of tracer distribution were compared with numerical simulations of flow to determine effects of different shear stress metrics on permeability. Albumin-sized tracers dominantly crossed the cultured endothelium via junctions between neighboring cells, high-density lipoprotein-sized tracers crossed at tricellular junctions, and low-density lipoprotein-sized tracers crossed through cells. Cells aligned close to the angle that minimized shear stresses across their long axis. The rate of paracellular transport under flow correlated with the magnitude of these minimized transverse stresses, whereas transport across cells was uniformly reduced by all types of flow. These results contradict the long-standing two-pore theory of solute transport across microvessel walls and the consensus view that endothelial cells align with the mean shear vector. They suggest that endothelial cells minimize transverse shear, supporting its postulated proatherogenic role. Preliminary data show that similar tracer techniques are practicable in vivo.NEW & NOTEWORTHY Solutes of increasing size crossed cultured endothelium through intercellular junctions, through tricellular junctions, or transcellularly. Cells aligned to minimize the shear stress acting across their long axis. Paracellular transport correlated with the level of this minimized shear, but transcellular transport was reduced uniformly by flow regardless of the shear profile.

Understanding the fluid mechanics behind transverse wall shear stress.

The patchy distribution of atherosclerosis within arteries is widely attributed to local variation in haemodynamic wall shear stress (WSS). A recently-introduced metric, the transverse wall shear stress (transWSS), which is the average over the cardiac cycle of WSS components perpendicular to the temporal mean WSS vector, correlates particularly well with the pattern of lesions around aortic branch ostia. Here we use numerical methods to investigate the nature of the arterial flows captured by transWSS and the sensitivity of transWSS to inflow waveform and aortic geometry. TransWSS developed chiefly in the acceleration, peak systolic and deceleration phases of the cardiac cycle; the reverse flow phase was too short, and WSS in diastole was too low, for these periods to have a significant influence. Most of the spatial variation in transWSS arose from variation in the angle by which instantaneous WSS vectors deviated from the mean WSS vector rather than from variation in the magnitude of the vectors. The pattern of transWSS was insensitive to inflow waveform; only unphysiologically high Womersley numbers produced substantial changes. However, transWSS was sensitive to changes in geometry. The curvature of the arch and proximal descending aorta were responsible for the principal features, the non-planar nature of the aorta produced asymmetries in the location and position of streaks of high transWSS, and taper determined the persistence of the streaks down the aorta. These results reflect the importance of the fluctuating strength of Dean vortices in generating transWSS.

Zebrafish Model for Functional Screening of Flow-Responsive Genes.

OBJECTIVE: Atherosclerosis is initiated at branches and bends of arteries exposed to disturbed blood flow that generates low shear stress. This mechanical environment promotes lesions by inducing endothelial cell (EC) apoptosis and dysfunction via mechanisms that are incompletely understood. Although transcriptome-based studies have identified multiple shear-responsive genes, most of them have an unknown function. To address this, we investigated whether zebrafish embryos can be used for functional screening of mechanosensitive genes that regulate EC apoptosis in mammalian arteries. APPROACH AND RESULTS: First, we demonstrated that flow regulates EC apoptosis in developing zebrafish vasculature. Specifically, suppression of blood flow in zebrafish embryos (by targeting cardiac troponin) enhanced that rate of EC apoptosis (≈10%) compared with controls exposed to flow (≈1%). A panel of candidate regulators of apoptosis were identified by transcriptome profiling of ECs from high and low shear stress regions of the porcine aorta. Genes that displayed the greatest differential expression and possessed 1 to 2 zebrafish orthologues were screened for the regulation of apoptosis in zebrafish vasculature exposed to flow or no-flow conditions using a knockdown approach. A phenotypic change was observed in 4 genes; p53-related protein (PERP) and programmed cell death 2-like protein functioned as positive regulators of apoptosis, whereas angiopoietin-like 4 and cadherin 13 were negative regulators. The regulation of perp, cdh13, angptl4, and pdcd2l by shear stress and the effects of perp and cdh13 on EC apoptosis were confirmed by studies of cultured EC exposed to flow. CONCLUSIONS: We conclude that a zebrafish model of flow manipulation coupled to gene knockdown can be used for functional screening of mechanosensitive genes in vascular ECs, thus providing potential therapeutic targets to prevent or treat endothelial injury at atheroprone sites.

Automated fiducial point selection for reducing registration error in the co-localisation of left atrium electroanatomic and imaging data.

Registration of electroanatomic surfaces and segmented images for the co-localisation of structural and functional data typically requires the manual selection of fiducial points, which are used to initialise automated surface registration. The identification of equivalent points on geometric features by the human eye is heavily subjective, and error in their selection may lead to distortion of the transformed surface and subsequently limit the accuracy of data co-localisation. We propose that the manual trimming of the pulmonary veins through the region of greatest geometrical curvature, coupled with an automated angle-based fiducial-point selection algorithm, significantly reduces target registration error compared with direct manual selection of fiducial points.

Change of direction in the biomechanics of atherosclerosis.

The non-uniform distribution of atherosclerosis within the arterial system has been attributed to pro-atherogenic influences of low, oscillatory haemodynamic wall shear stress (WSS) on endothelial cells (EC). This theory is challenged by the changes in lesion location that occur with age in human and rabbit aortas. Furthermore, a number of point-wise comparisons of lesion prevalence and WSS have failed to support it. Here we investigate the hypothesis that multidirectional flow-characterized as the average magnitude of WSS components acting transversely to the mean vector (transWSS)-plays a key role. Maps of lesion prevalence around aortic branch ostia in immature and mature rabbits were compared with equivalent maps of time average WSS, the OSI (an index characterizing oscillatory flow) and transWSS, obtained from computational simulations; Spearman's rank correlation coefficients were calculated for aggregated data and 95% confidence intervals were obtained by bootstrapping methods. Lesion prevalence correlated positively, strongly and significantly with transWSS at both ages. Correlations of lesion prevalence with the other shear metrics were not significant or were significantly lower than those obtained for transWSS. No correlation supported the low, oscillatory WSS theory. The data are consistent with the view that multidirectional near-wall flow is highly pro-atherogenic. Effects of multidirectional flow on EC, and methods for investigating them, are reviewed. The finding that oscillatory flow has pro-inflammatory effects when acting perpendicularly to the long axis of EC but anti-inflammatory effects when acting parallel to it may explain the stronger correlation of lesion prevalence with transWSS than with the OSI.

Elevated uptake of plasma macromolecules by regions of arterial wall predisposed to plaque instability in a mouse model.

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.

High-order spectral/hp element discretisation for reaction-diffusion problems on surfaces: Application to cardiac electrophysiology.

We present a numerical discretisation of an embedded two-dimensional manifold using high-order continuous Galerkin spectral/hp elements, which provide exponential convergence of the solution with increasing polynomial order, while retaining geometric flexibility in the representation of the domain. Our work is motivated by applications in cardiac electrophysiology where sharp gradients in the solution benefit from the high-order discretisation, while the computational cost of anatomically-realistic models can be significantly reduced through the surface representation and use of high-order methods. We describe and validate our discretisation and provide a demonstration of its application to modelling electrochemical propagation across a human left atrium.

Disturbed flow promotes endothelial senescence via a p53-dependent pathway.

OBJECTIVE: Although atherosclerosis is associated with systemic risk factors such as age, high cholesterol, and obesity, plaque formation occurs predominately at branches and bends that are exposed to disturbed patterns of blood flow. The molecular mechanisms that link disturbed flow-generated mechanical forces with arterial injury are uncertain. To illuminate them, we investigated the effects of flow on endothelial cell (EC) senescence. APPROACH AND RESULTS: LDLR(-/-) (low-density lipoprotein receptor(-/-)) mice were exposed to a high-fat diet for 2 to 12 weeks (or to a normal chow diet as a control) before the assessment of cellular senescence in aortic ECs. En face staining revealed that senescence-associated ß-galactosidase activity and p53 expression were elevated in ECs at sites of disturbed flow in response to a high-fat diet. By contrast, ECs exposed to undisturbed flow did not express senescence-associated ß-galactosidase or p53. Studies of aortae from healthy pigs (aged 6 months) also revealed enhanced senescence-associated ß-galactosidase staining at sites of disturbed flow. These data suggest that senescent ECs accumulate at disturbed flow sites during atherogenesis. We used in vitro flow systems to examine whether a causal relationship exists between flow and EC senescence. Exposure of cultured ECs to flow (using either an orbital shaker or a syringe-pump flow bioreactor) revealed that disturbed flow promoted EC senescence compared with static conditions, whereas undisturbed flow reduced senescence. Gene silencing studies demonstrated that disturbed flow induced EC senescence via a p53-p21 signaling pathway. Disturbed flow-induced senescent ECs exhibited reduced migration compared with nonsenescent ECs in a scratch wound closure assay, and thus may be defective for arterial repair. However, pharmacological activation of sirtuin 1 (using resveratrol or SRT1720) protected ECs from disturbed flow-induced senescence. CONCLUSIONS: Disturbed flow promotes endothelial senescence via a p53-p21-dependent pathway which can be inhibited by activation of sirtuin 1. These observations support the principle that pharmacological activation of sirtuin 1 may promote cardiovascular health by suppressing EC senescence at atheroprone sites.

An automated algorithm for determining conduction velocity, wavefront direction and origin of focal cardiac arrhythmias using a multipolar catheter.

Determining locations of focal arrhythmia sources and quantifying myocardial conduction velocity (CV) are two major challenges in clinical catheter ablation cases. CV, wave-front direction and focal source location can be estimated from multipolar catheter data, but currently available methods are time-consuming, limited to specific electrode configurations, and can be inaccurate. We developed automated algorithms to rapidly identify CV from multipolar catheter data with any arrangement of electrodes, whilst providing estimates of wavefront direction and focal source position, which can guide the catheter towards a focal arrhythmic source. We validated our methods using simulations on realistic human left atrial geometry. We subsequently applied them to clinically-acquired intracardiac electrogram data, where CV and wavefront direction were accurately determined in all cases, whilst focal source locations were correctly identified in 2/3 cases. Our novel automated algorithms can potentially be used to guide ablation of focal arrhythmias in real-time in cardiac catheter laboratories.

Computation in the rabbit aorta of a new metric - the transverse wall shear stress - to quantify the multidirectional character of disturbed blood flow.

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.

Variability of computational fluid dynamics solutions for pressure and flow in a giant aneurysm: the ASME 2012 Summer Bioengineering Conference CFD Challenge.

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.