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Quadratic adaptive algorithm for solving cardiac action potential models.

Min-Hung Chen1, Po-Yuan Chen2, Ching-Hsing Luo3

  • 1Department of Mathematics, National Cheng Kung University, 1 University Road, Tainan 701, Taiwan.

Computers in Biology and Medicine
|September 18, 2016
PubMed
Summary
This summary is machine-generated.

A new adaptive integration method enhances cardiac action potential model accuracy and efficiency. It uses adaptive time steps and extremum-locator functions for precise computations, outperforming traditional methods, especially for complex models like the human O'Hara-Rudy dynamic model.

Keywords:
Action potentialAdaptive methodCardiac action potential modelComputer simulationNumerical method

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Area of Science:

  • Computational biology
  • Biophysics
  • Numerical analysis

Background:

  • Cardiac action potential models are crucial for understanding heart function and disease.
  • Traditional numerical methods can struggle with accuracy and stability, particularly for stiff models.
  • Accurate and efficient computation of these models is essential for research and clinical applications.

Purpose of the Study:

  • To develop and evaluate a novel adaptive integration method for cardiac action potential models.
  • To improve the accuracy and efficiency of numerical simulations compared to existing methods.
  • To address limitations of traditional methods, such as abrupt changes and instability with stiff models.

Main Methods:

  • An adaptive time-stepping strategy based on solving a quadratic formula involving derivatives of the membrane potential.
  • Incorporation of an extremum-locator function to enhance accuracy near action potential peaks.
  • Implementation of a time step restriction technique to prevent abrupt potential changes.
  • Validation using established models: Luo-Rudy (LR1, LR2), human O'Hara-Rudy (ORd), and Courtemanche atrial model with a Markov sodium channel.

Main Results:

  • The proposed method demonstrates superior accuracy, particularly near the action potential peak, compared to the traditional Hybrid method.
  • It successfully handles stiff Markov ionic channel models, maintaining stability where the Hybrid method fails.
  • Adaptive time stepping results in smoother action potential profiles closer to reference solutions.
  • The method shows improved performance for action potentials with non-smooth morphologies.

Conclusions:

  • The novel adaptive integration method offers enhanced accuracy and efficiency for cardiac action potential modeling.
  • It provides a more robust and stable alternative to traditional methods, especially for complex and stiff models.
  • Further investigation is warranted to assess its utility in action potential propagation simulations.