## Two-scale asymptotic analysis for modeling activation of periodic cardiac strand

This work explores the applicability of two-scale asymptotic analysis to model the excitable cardiac strand with periodic discontinuities. The strand is composed of 60 cells connected by junctions. The membrane excitability is modeled using Ebihara-Johnson equations. The problem is described by a non-linear parabolic equation with one parameter, intracellular conductivity, changing periodically in space. Using two-scale asymptotic analysis, the transmembrane potential is given as a two-scale expansion in powers of the period length. The series converges rapidly, and the solution containing only zero- and first-order terms has a negligible error. Each term of the expansion is found by solving the differential equation derived by decomposing the original problem. The periodic, first-order term is given by a linear elliptic equation and has a closed-form solution. The aperiodic, zero-order term is the solution of a non-linear parabolic equation corresponding to the cardiac strand with homogenized intracellular conductivity; this equation is solved numerically using the Crank-Nicolson method modified to account for the presence of the periodic term. The use of the two-scale asymptotic analysis permits a substantial saving in computer resources over the solution from a purely numerical approach: the problem can be solved with a three times coarser discretization step, requires ten times less memory, and uses about half the computation time. © 1992.

### Duke Scholars

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Numerical & Computational Mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics

### Citation

*Mathematical and Computer Modelling*,

*16*(3), 121–130. https://doi.org/10.1016/0895-7177(92)90053-N

*Mathematical and Computer Modelling*16, no. 3 (January 1, 1992): 121–30. https://doi.org/10.1016/0895-7177(92)90053-N.

*Mathematical and Computer Modelling*, vol. 16, no. 3, Jan. 1992, pp. 121–30.

*Scopus*, doi:10.1016/0895-7177(92)90053-N.

## Published In

## DOI

## ISSN

## Publication Date

## Volume

## Issue

## Start / End Page

## Related Subject Headings

- Numerical & Computational Mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics