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Efficiency of semi-implicit alternating direction implicit methods for solving cardiac monodomain model.

Youssef Belhamadia1, Zeinab Rammal1

  • 1American University of Sharjah, Department of Mathematics, Sharjah, United Arab Emirates.

Computers in Biology and Medicine
|January 17, 2021
PubMed
Summary

New operator-splitting alternating direction implicit (ADI) schemes efficiently solve cardiac monodomain models. These methods reduce computational time and memory for electrocardiology simulations, offering a significant improvement over standard numerical techniques.

Keywords:
Aliev–panfilov modelAlternating direction implicit (ADI) methodCardiac monodomain modelFinite differenceMitchell–schaeffer modelScroll waveSpiral wave

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Area of Science:

  • Computational biology
  • Biomedical engineering
  • Numerical analysis

Background:

  • Numerical simulations of cardiac monodomain models demand high mesh resolution, leading to substantial computational costs.
  • Efficiently solving these complex electrocardiology models is crucial for advancing cardiac research.

Purpose of the Study:

  • To develop and present three novel operator-splitting alternating direction implicit (ADI) schemes.
  • To significantly reduce computational time and memory requirements for cardiac monodomain model simulations.

Main Methods:

  • Construction of three operator-splitting ADI schemes for the nonlinear cardiac monodomain model.
  • Evaluation of the schemes' accuracy (second-order in space and time) and computational efficiency.
  • Comparison with the standard semi-implicit Crank-Nicolson/Adams-Bashforth method.

Main Results:

  • The proposed ADI methods demonstrate reduced computational time and memory usage compared to standard methods.
  • Simulations involving regular waves, spiral wave reentry, and nonsymmetrical scroll waves validate the efficiency.
  • The methods achieve second-order accuracy in both spatial and temporal domains.

Conclusions:

  • The developed operator-splitting ADI schemes offer an efficient and accurate approach for solving cardiac monodomain models.
  • These methods provide a valuable tool for large-scale two- and three-dimensional electrocardiology simulations.
  • The study highlights a significant advancement in computational efficiency for cardiac modeling.