A simple analytical model of action potential duration profile in electrotonically-coupled cells

Area of Science:

• Computational biology
• Mathematical modeling
• Cardiac electrophysiology

Background:

• Electrotonic coupling between cardiac cells influences action potential duration (APD) dispersion.
• Understanding these interactions is crucial for analyzing cardiac arrhythmias and repolarization abnormalities.

Purpose of the Study:

• To develop a comprehensive mathematical framework for analyzing electrotonic interactions in cardiac cell networks.
• To derive analytical solutions for both forward (predicting APD maps) and inverse (inferring intrinsic APDs) problems.

Main Methods:

• Mathematical analysis of a simplified model with exponential repolarization.
• Derivation of a closed-form algebraic formula for the forward problem.
• Proof of unique solution for the inverse problem and development of a Newton-based solver.
• Analytical expression for a 1D convolution filter.

Main Results:

• A closed-form solution for the forward problem of computing APD maps from intrinsic APDs.
• Demonstration of a unique solution for the inverse problem of inferring intrinsic APDs.
• Development of an efficient Newton-based solver for the inverse problem.
• Derivation of a convolution filter for the 1D forward problem.

Conclusions:

• The study provides a robust mathematical foundation for estimating repolarization parameters in cardiac tissue.
• The derived analytical solutions and solvers facilitate the development of advanced techniques for cardiac modeling and diagnostics.