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Atrial Rotor Dynamics Under Complex Fractional Order Diffusion.

Juan P Ugarte1, Catalina Tobón2, António M Lopes3

  • 1Grupo de Investigación en Modelamiento y Simulación Computacional, Facultad de Ingenierías, Universidad de San Buenaventura, Medellín, Colombia.

Frontiers in Physiology
|August 9, 2018
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Summary
This summary is machine-generated.

This study introduces a new fractal model for atrial fibrillation (AF) dynamics. It reveals that structural heterogeneity, quantified by complex fractional derivatives, significantly impacts rotor stability and propagation in cardiac tissue.

Keywords:
atrial fibrillationcomplex order diffusionelectrical remodelingrotor dynamicsstructural heterogeneity

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Area of Science:

  • Computational biology
  • Cardiac electrophysiology
  • Mathematical modeling

Background:

  • Atrial fibrillation (AF) mechanisms are complex, with rotor dynamics playing a key role.
  • Current models often use standard diffusion equations, neglecting cardiac tissue's discrete and heterogeneous nature.
  • Understanding structural heterogeneity's impact on AF is crucial for developing effective treatments.

Purpose of the Study:

  • To develop and apply a novel computational model using complex fractional order derivatives to simulate atrial fibrillation dynamics.
  • To investigate the role of myocardial fractal characteristics and structural heterogeneity on rotor behavior.
  • To analyze how varying degrees of heterogeneity influence action potential propagation and rotor stability.

Main Methods:

  • A new mathematical model based on complex fractional order derivatives (γ = α + jβ) was developed to represent fractal myocardial properties.
  • The model was used to simulate action potential propagation in a 2D atrial tissue model with electrical remodeling.
  • Variations in the complex order derivative (α from 1.1 to 2, β from 0 to 0.28) were tested to quantify structural heterogeneity.

Main Results:

  • The complex fractional order derivative model successfully simulated rotor dynamics in atrial fibrillation.
  • Structural heterogeneity, represented by γ, was shown to modulate rotor stability, core size, and meandering.
  • Increased structural heterogeneity (lower α, higher β) led to a wider vulnerable window and increased rotor tip meandering.

Conclusions:

  • Myocardial structural heterogeneity, when modeled using complex fractional derivatives, significantly influences atrial fibrillation dynamics.
  • The model provides a novel way to link fractal properties of cardiac tissue to the stability and behavior of reentrant rotors.
  • This computational approach offers insights into AF mechanisms and potential therapeutic targets by quantifying heterogeneity's role.