Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements.

We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.

Inferring gene networks: dream or nightmare?

We describe several algorithms with winning performance in the Dialogue for Reverse Engineering Assessments and Methods (DREAM2) Reverse Engineering Competition 2007. After the gold standards for the challenges were released, the performance of the algorithms could be thoroughly evaluated under different parameters or alternative ways of solving systems of equations. For the analysis of Challenge 4, the "In-silico" challenges, we employed methods to explicitly deal with perturbation data and time-series data. We show that original methods used to produce winning submissions could easily be altered to substantially improve performance. For Challenge 5, the genome-scale Escherichia coli network, we evaluated a variety of measures of association. These data are troublesome, and no good solutions could be produced, either by us or by any other teams. Our best results were obtained when analyzing subdatasets instead of considering the dataset as a whole.

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

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 next-generation 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.