Deriving macroscopic myocardial conductivities by homogenization of microscopic models

Paul E. Hand, Boyce E. Griffith, Charles Peskin

Research output: Contribution to journalArticle

Abstract

We derive the values for the intracellular and extracellular conductivities needed for bidomain simulations of cardiac electrophysiology using homogenization of partial differential equations. In our model, cardiac myocytes are rectangular prisms and gap junctions appear in a distributed manner as flux boundary conditions for Laplace's equation. Using directly measurable microproperties such as cellular dimensions and end-to-end and side-to-side gap junction coupling strengths, we inexpensively obtain effective conductivities close to those given by simulations with a detailed cyto-architecture (Stinstra et al. in Ann. Biomed. Eng. 33:1743-1751, 2005). This model provides a convenient framework for studying the effect on conductivities of aligned vs. brick-like arrangements of cells and the effect of different distributions of gap junctions along the myocyte membranes.

Original languageEnglish (US)
Pages (from-to)1707-1726
Number of pages20
JournalBulletin of Mathematical Biology
Volume71
Issue number7
DOIs
StatePublished - Oct 2009

Fingerprint

Gap Junction
gap junctions
Gap Junctions
homogenization
Homogenization
Conductivity
conductivity
Laplace equation
Brick
Prisms
Cardiac Myocytes
Cardiac Electrophysiology
Partial differential equations
Myocytes
Cuboid
Effective Conductivity
electrophysiology
bricks
Boundary conditions
Fluxes

Keywords

  • Bidomain
  • Cardiac modeling
  • Effective conductivity
  • Homogenization
  • Syncytium

ASJC Scopus subject areas

  • Neuroscience(all)
  • Computational Theory and Mathematics
  • Mathematics(all)
  • Pharmacology
  • Immunology
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Environmental Science(all)

Cite this

Deriving macroscopic myocardial conductivities by homogenization of microscopic models. / Hand, Paul E.; Griffith, Boyce E.; Peskin, Charles.

In: Bulletin of Mathematical Biology, Vol. 71, No. 7, 10.2009, p. 1707-1726.

Research output: Contribution to journalArticle

Hand, Paul E. ; Griffith, Boyce E. ; Peskin, Charles. / Deriving macroscopic myocardial conductivities by homogenization of microscopic models. In: Bulletin of Mathematical Biology. 2009 ; Vol. 71, No. 7. pp. 1707-1726.
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