Chris D. Cantwell

Nektar++: An open-source spectral/hp element framework

Nektar++ is an open-source software framework designed to support the development of high-performance 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 obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland No. of lines in distributed program, including test data, etc.: 1052456 No. of bytes in distributed program, including test data, etc.: 42851367 External routines: Boost, PFTW, MPI, BLAS, LAPACK and METIS (www.cs.umn.edu) Nature of problem: The Nektar++ framework is designed to enable the discretisation and solution of time-independent or time-dependent partial differential equations. Running time: The tests provided take a few minutes to run. Runtime in general depends on mesh size and total integration time.

Techniques for automated local activation time annotation and conduction velocity estimation in cardiac mapping

Measurements of cardiac conduction velocity provide valuable functional and structural insight into the initiation and perpetuation of cardiac arrhythmias, in both a clinical and laboratory context. The interpretation of activation wavefronts and their propagation can identify mechanistic properties of a broad range of electrophysiological pathologies. However, the sparsity, distribution and uncertainty of recorded data make accurate conduction velocity calculation difficult. A wide range of mathematical approaches have been proposed for addressing this challenge, often targeted towards specific data modalities, species or recording environments. Many of these algorithms require identification of activation times from electrogram recordings which themselves may have complex morphology or low signal-to-noise ratio. This paper surveys algorithms designed for identifying local activation times and computing conduction direction and speed. Their suitability for use in different recording contexts and applications is assessed.

Spatial Resolution Requirements for Accurate Identification of Drivers of Atrial Fibrillation

Background— Recent studies have demonstrated conflicting mechanisms underlying atrial fibrillation (AF), with the spatial resolution of data often cited as a potential reason for the disagreement. The purpose of this study was to investigate whether the variation in spatial resolution of mapping may lead to misinterpretation of the underlying mechanism in persistent AF. Methods and Results— Simulations of rotors and focal sources were performed to estimate the minimum number of recording points required to correctly identify the underlying AF mechanism. The effects of different data types (action potentials and unipolar or bipolar electrograms) and rotor stability on resolution requirements were investigated. We also determined the ability of clinically used endocardial catheters to identify AF mechanisms using clinically recorded and simulated data. The spatial resolution required for correct identification of rotors and focal sources is a linear function of spatial wavelength (the distance between wavefronts) of the arrhythmia. Rotor localization errors are larger for electrogram data than for action potential data. Stationary rotors are more reliably identified compared with meandering trajectories, for any given spatial resolution. All clinical high-resolution multipolar catheters are of sufficient resolution to accurately detect and track rotors when placed over the rotor core although the low-resolution basket catheter is prone to false detections and may incorrectly identify rotors that are not present. Conclusions— The spatial resolution of AF data can significantly affect the interpretation of the underlying AF mechanism. Therefore, the interpretation of human AF data must be taken in the context of the spatial resolution of the recordings.

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.

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.

From h to p efficiently: optimal implementation strategies for explicit time‐dependent problems using the spectral/hp element method

We investigate the relative performance of a second-order Adams–Bashforth scheme and second-order and fourth-order Runge–Kutta schemes when time stepping a 2D linear advection problem discretised using a spectral/hp element technique for a range of different mesh sizes and polynomial orders. Numerical experiments explore the effects of short (two wavelengths) and long (32 wavelengths) time integration for sets of uniform and non-uniform meshes. The choice of time-integration scheme and discretisation together fixes a CFL limit that imposes a restriction on the maximum time step, which can be taken to ensure numerical stability. The number of steps, together with the order of the scheme, affects not only the runtime but also the accuracy of the solution. Through numerical experiments, we systematically highlight the relative effects of spatial resolution and choice of time integration on performance and provide general guidelines on how best to achieve the minimal execution time in order to obtain a prescribed solution accuracy. The significant role played by higher polynomial orders in reducing CPU time while preserving accuracy becomes more evident, especially for uniform meshes, compared with what has been typically considered when studying this type of problem.© 2014. The Authors. International Journal for Numerical Methods in Fluids published by John Wiley & Sons, Ltd.

Nekkloud: A software environment for high-order finite element analysis on clusters and clouds

As the capabilities and diversity of computational platforms continue to grow, scientific software is becoming ever more complex in order to target resources effectively. In the libhpc project we are developing a suite of tools and services to simplify job description and execution on heterogeneous infrastructures. This paper presents Nekkloud, a web-based software environment, built on aspects of the libhpc framework, for running the Nektar++ high-order finite element code on both cluster and cloud platforms, while improving the accessibility of the software for end-users and improving the user experience. Nektar++ provides a suite of solvers which span a range of scientific domains, ensuring that Nekkloud has a broad range of use cases. We describe the Nekkloud environment, its use and its ability to target both local campus cluster infrastructure and cloud computing resources, enabling users to make better use of the facilities available to them.

A technique for visualising three-dimensional left atrial cardiac activation data in two dimensions with minimal distance distortion.

Electro-anatomic mapping and medical imaging systems, used during clinical procedures for treatment of atrial arrhythmias, frequently record and display measurements on an anatomical surface of the left atrium. As such, obtaining a complete picture of activation necessitates simultaneous views from multiple angles. In addition, post-processing of three-dimensional surface data is challenging, since algorithms are typically applicable to planar or volumetric data. We applied a surface flattening methodology to medical imaging data and electro-anatomic mapping data to generate a two-dimensional representation that best preserves distances, since the calculation of many clinically relevant metrics, including conduction velocity and rotor trajectory identification require an accurate representation of distance. Distance distortions were small and improved upon exclusion of the pulmonary veins. The technique is demonstrated using maps of local activation time, based on clinical data, and plotting rotor-core trajectories, using simulated data.

Influence of left atrial geometry on rotor core trajectories in a model of atrial fibrillation

Left atrial anatomy and myocardial architecture are known to influence rotor initiation and maintenance. However, identifying their relative contribution clinically is challenging. The present study aims to investigate in silico the effect of left atrial geometry in isolation on rotor generation and evolution through the spatiotemporal tracking of phase singularities. After meandering for a short period of time, rotors are attracted to specific areas of the chamber where there is high curvature, primarily near the base of the left atrial appendage and the junctions of the pulmonary veins. This suggests that the left atrial anatomy could play a key role in the perpetuation of fibrillatory activity.

Repolarization abnormalities unmasked with exercise in sudden cardiac death survivors with structurally normal hearts

Models of cardiac arrhythmogenesis predict that nonuniformity in repolarization and/or depolarization promotes ventricular fibrillation and is modulated by autonomic tone, but this is difficult to evaluate in patients. We hypothesize that such spatial heterogeneities would be detected by noninvasive ECG imaging (ECGi) in sudden cardiac death (SCD) survivors with structurally normal hearts under physiological stress.