a b s t r a c tNektar++ is an open-source software framework designed to support the development of highperformance scalable solvers for partial differential equations using the spectral/hp element method. High-order methods are gaining prominence in several engineering and biomedical applications due to their improved accuracy over low-order techniques at reduced computational cost for a given number of degrees of freedom. However, their proliferation is often limited by their complexity, which makes these methods challenging to implement and use. Nektar++ is an initiative to overcome this limitation by encapsulating the mathematical complexities of the underlying method within an efficient C++ framework, making the techniques more accessible to the broader scientific and industrial communities. The software supports a variety of discretisation techniques and implementation strategies, supporting methods research as well as application-focused computation, and the multi-layered structure of the framework allows the user to embrace as much or as little of the complexity as they need. The libraries capture the mathematical constructs of spectral/hp element methods, while the associated collection of pre-written PDE solvers provides out-of-the-box application-level functionality and a template for users who wish to develop solutions for addressing questions in their own scientific domains. Program summaryProgram title: Nektar++ Catalogue identifier: AEVV_v1_0Program summary URL:

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.

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.

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.

We review some of the latest approaches to analysing cardiac electrophysiology data using machine learning and predictive modelling. Cardiac arrhythmias, particularly atrial fibrillation, are a major global healthcare challenge. Treatment is often through catheter ablation, which involves the targeted localised destruction of regions of the myocardium responsible for initiating or perpetuating the arrhythmia. Ablation targets are either anatomically defined, or identified based on their functional properties as determined through the analysis of contact intracardiac electrograms acquired with increasing spatial density by modern electroanatomic mapping systems. While numerous quantitative approaches have been investigated over the past decades for identifying these critical curative sites, few have provided a reliable and reproducible advance in success rates. Machine learning techniques, including recent deep-learning approaches, offer a potential route to gaining new insight from this wealth of highly complex spatio-temporal information that existing methods struggle to analyse. Coupled with predictive modelling, these techniques offer exciting opportunities to advance the field and produce more accurate diagnoses and robust personalised treatment. We outline some of these methods and illustrate their use in making predictions from the contact electrogram and augmenting predictive modelling tools, both by more rapidly predicting future states of the system and by inferring the parameters of these models from experimental observations.