Simulation of cardiac electrophysiology on next-generation high-performance computers

Abstract

Models of cardiac electrophysiology consist of a system of partial differential equations (PDEs) coupled with a system of ordinary differential equations representing cell membrane dynamics. Current software to solve such models does not provide the required computational speed for practical applications. One reason for this is that little use is made of recent developments in adaptive numerical algorithms for solving systems of PDEs. Studies have suggested that a speedup of up to two orders of magnitude is possible by using adaptive methods. The challenge lies in the efficient implementation of adaptive algorithms on massively parallel computers. The finite-element (FE) method is often used in heart simulators as it can encapsulate the complex geometry and small-scale details of the human heart. An alternative is the spectral element (SE) method, a high-order technique that provides the flexibility and accuracy of FE, but with a reduced number of degrees of freedom. The feasibility of implementing a parallel SE algorithm based on fully unstructured all-hexahedra meshes is discussed. A major computational task is solution of the large algebraic system resulting from FE or SE discretization. Choice of linear solver and preconditioner has a substantial effect on efficiency. A fully parallel implementation based on dynamic partitioning that accounts for load balance, communication and data movement costs is required. Each of these methods must be implemented on nextgeneration supercomputers in order to realize the necessary speedup. The problems that this may cause, and some of the techniques that are beginning to be developed to overcome these issues, are described.

Verification of cardiac tissue electrophysiology simulators using an N -version benchmark

“…Distinct from the development of new models is the corresponding development of simulation codes that solve numerically the equations of a given model. These codes have also increased in complexity to represent new models, as well as to incorporate advanced numerical techniques [11,12], and exploit opportunities provided by increasingly complex computer architectures, including graphics processing units [9] and peta-scale systems [10]. These developments in turn have produced a growth in the number of software codes available to perform these simulations.…”

“…The impact of cardiac electrophysiology simulations across an expanded range of applications has seen an increase in model complexity through increasing numbers of equations to describe cellular and sub-cellular functions [8], regionspecific parameter sets for cell models [9,10] and high-resolution meshes to capture anatomical detail [11]. Distinct from the development of new models is the corresponding development of simulation codes that solve numerically the equations of a given model.…”

Chaste: A test-driven approach to software development for biological modelling

“…Since cardiac modelling is such a mature field, the mathematical modelling approach is well established and in Section 2.1 we give only a brief outline together with the equations. Full details of the current state of the art in cardiac electrophysiology modelling can be found in the recent review papers [4,5]. In Section 2.2, however, where we describe the cancer modelling supported by Chaste, the more novel aspects of the underlying models require us to give much more detail of both the biology and the models.…”

The virtual physiological human: tools and applications I

“…First, Linge et al (2009) give an overview of numerical methods developed over the past 10 years for the solution of the governing bidomain equations, concluding that the full potential of modern computational methods is yet to be exploited. Then, Bordas et al (2009) follow on from this by considering how recent developments in adaptive finite-element methods may yield much more computationally efficient solutions to the governing partial differential equations. The paper by van Beek et al (2009) considers the issue of modelling a very complex system (such as animal metabolic systems) when accurate experimental data, quantifying very large numbers of parameters, are lacking.…”