A bilayer model of human atria: mathematical background, construction, and assessment

Europace. 2014 Nov;16 Suppl 4:iv21-iv29. doi: 10.1093/europace/euu256.


Aims: Atrial numerical modelling has generally represented the organ as either a surface or tissue with thickness. While surface models have significant computational advantages over tissue models, they cannot fully capture propagation patterns seen in vivo, such as dissociation of activity between endo- and epicardium. We introduce an intermediate representation, a bilayer model of the human atria, which is capable of recreating recorded activation patterns.

Methods and results: We simultaneously solved two surface monodomain problems by formalizing an optimization method to set a coupling term between them. Two different asymptotically equivalent numerical implementations of the model are presented. We then built a geometrically and electrophysiologically detailed model of the human atria based on CT data, including two layers of fibre directions, major muscle bundles, and discrete atrial coupling. We adjusted parameters to recreate clinically measured activation times. Activation was compared with a monolayer model. Activation was fit to the physiological range measured over the entire atria. The crista terminalis and pectinate muscles were important for local right atrial activation, but did not significantly affect total activation time. Propagation in the bilayer model was similar to that of a monolayer, but with noticeable difference, due to three-dimensional propagation where fibre direction changed abruptly across the wall, resulting in a slight dissociation of activity.

Conclusion: Atrial structure plays the dominant role in determining activation. A bilayer model is able to take into account transmural heterogeneities, while maintaining the low computational load associated with surface models.

Keywords: Atrial numerical modelling.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials
  • Arrhythmias, Cardiac / diagnostic imaging
  • Arrhythmias, Cardiac / physiopathology*
  • Atrial Function, Left*
  • Atrial Function, Right*
  • Atrial Remodeling
  • Computer Simulation*
  • Heart Atria / diagnostic imaging
  • Heart Atria / physiopathology*
  • Humans
  • Kinetics
  • Models, Cardiovascular*
  • Numerical Analysis, Computer-Assisted
  • Tomography, X-Ray Computed