Simulation of fractionated electrograms at low spatial resolution in large-scale heart models.
Mark Potse and Nico H. L. Kuijpers.
Computing in Cardiology 37:849-852, 2010.

Gary and Bill Sanders Poster Award



conference paper


Computation of extracellular potentials from transmembrane potentials is a common problem in cardiac simulation. It is part of some bidomain reaction-diffusion models, and is also used to compute (intracardiac) electrograms from membrane potentials simulated by monodomain models. It consists of solving an elliptic boundary-value problem which, when discretized, becomes a system of linear equations.

Extracellular potentials must be solved at a spatial resolution of 1/5 mm or better to avoid artefacts in the form of large spikes before and after large deflections in the signal. For macroscopic heart models, this leads to linear systems with tens or hundreds of millions of equations.

Artefacts in low-resolution solutions are related to the restriction operator that is used to translate the source data from the high-resolution to the low-resolution. Typically, this restriction is done by injecting transmembrane potentials. We propose to use transmembrane current as a source, with full trilinear weighting rather than simple injection.

We tested this method in a model of the human ventricles, which used 90 million nodes at 0.2-mm resolution. We found that using the proposed scheme, a good visual match could be obtained between electrograms computed at 1-mm and 0.2-mm resolution, even in regions where strong sub-millimeter heterogeneity in tissue conductivity was present. Quantitatively, peak potential values were well reproduced, but the slope of steep deflections was underestimated at low resolution. The solution at low resolution was more than proportionately faster than that at high resolution.

The proposed scheme is easy to implement in an existing bidomain solver, and is useful to rapidly compute electrograms intended for visual inspection at thousands of sites simultaneously. The scheme may also be valuable as a restriction operator in multigrid methods.


Computational resources for this work were provided by the Réseau québécois de calcul de haute performance (RQCHP).

related work

The anatomic model used in this study was prepared by Dr André Linnenbank and Dr Pieter Postema at the Academic Medical Center of the University of Amsterdam. The representation of fibrotic myocardium was developed in collaboration with Dr Mark Hoogendijk, from the same institution. These materials were used in the following studies:

Mechanism of Right Precordial ST-Segment Elevation in Structural Heart Disease: Excitation Failure by Current-to-Load Mismatch
Mark G. Hoogendijk, Mark Potse, et al.,
Heart Rhythm 7:238-248, February 2010

ST-Segment Elevation by Current-to-Load Mismatch: An Experimental and Computational Study
Mark G. Hoogendijk, Mark Potse, Alain Vinet, Jacques M. T. de Bakker, and Ruben Coronel
Heart Rhythm 8:111-118, 2011