A mathematical model of the unidirectional block caused by the pulmonary veins for anatomically induced atrial reentry

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Abstract

It is widely believed that the pulmonary veins (PVs) of the left atrium play the central role in the generation of anatomically induced atrial reentry but its mechanism has not been analytically explained. To understand this mechanism, a new analytic approach is proposed by adapting the geometric relative acceleration analysis from spacetime physics based on the hypothesis that a large relative acceleration can translate to a dramatic increase in the curvature of a wavefront and subsequently to conduction failure. By verifying the strong dependency of the propagational direction and the magnitude of anisotropy for conduction failure, this analytic method reveals that a unidirectional block can be generated by asymmetric propagation toward the PVs. This model is validated by computational tests in a T-shaped domain, computational simulations for three-dimensional atrial reentry and previous in-silico reports for anatomically induced atrial reentry.

Original languageEnglish
Pages (from-to)219-258
Number of pages40
JournalJournal of Biological Physics
Volume40
Issue number3
DOIs
Publication statusPublished - 2014 Jun

Bibliographical note

Funding Information:
Acknowledgements Thanks are due to various readers who pointed out desirable modifications, but especially to Dr. Martins Bruveris (EPFL) and Dr. Emma Coutts (Durham University) for kind reading and suggestions. This paper is partially supported by the British Heart Foundation (BHF) who initiated the Car-dioMath group lead by Professor Darryl D. Holm (Imperial College London) and Professor Nicholas S. Peters (Imperial College London). The use of Nektar++ for computational simulation was kindly advised and supported by Professor Spencer J. Sherwin (Imperial College London) and Robert M. Kirby (University of Utah) who were also members of the group.

All Science Journal Classification (ASJC) codes

  • Biophysics
  • Atomic and Molecular Physics, and Optics
  • Molecular Biology
  • Cell Biology

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