Skip to main content
SpringerLink
Log in

Spherical harmonic-based finite element meshing scheme for modelling current flow within the heart

  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

Abstract

The paper describes a spherical harmonic-based finite element scheme for solving Poisson-type equations throughout volumes characterised by irregularly shaped inner and outer surfaces. The inner and outer surfaces are defined by spherical harmonics, and the volume in between these surfaces is divided into nested shells that are weighted averages of the inner and outer surfaces. The resulting mesh comprises hexahedral elements, wherein each hexahedral element is defined by inner and outer shells in the radial direction and divisions in the polar and azimuthal directions. The spacing between shells can be set to any desired value. Similarly, the size of the polar and azimuthal divisions can be specified. A test of the scheme on an anisotropic sphere, meshed with 720 nodes, yielded a relative error of 0.78% on the sphere's surface. As a comparison, a previously published combined finite element/boundary element scheme with a 946-node mesh produced a corresponding error of 3.57%.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Colli Franzone, P., Guerri, L., Pennacchio, M., andTaccardi, B. (1998): ‘Spread of excitation in 3-D models of the anisotropic cardiac tissue. III. Effects of ventricular geometry and fibre structure on the potential distribution’,Math. Biosci.,151, pp. 51–98

    Article  MathSciNet  Google Scholar 

  • Fischer, G., Tilg, B., Modre, R., Huiskamp, G. J. M., Fetzer, J., Rucker, W., andWach, P. (2000): ‘A bidomain model based BEM-FEM coupling formulation for anisotropic cardiac tissue’,Ann. Biomed. Eng.,28, pp. 1229–1243

    Article  Google Scholar 

  • Hren, R. (1996): ‘A realistic model of the human ventricular myocardium: application to the study of ectopic activation’. PhD thesis, Dalhousie University

  • Miller, C. E., andHenriquez, C. S. (1990): ‘Finite element analysis of bioelectric phenomena’,Crit. Rev. Biomed. Eng.,18, pp. 207–33

    Google Scholar 

  • Nielsen, P. M. F., Legrice, I. J., Smaill, B. H., andHunter, P. J. (1991): ‘Mathematical model of geometry and fibrous structure of the heart’,Am. J. Physiol.,260, pp. H1365-H1378

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Bioengineering, University of Utah, Salt Lake City, Utah, USA

    B. Hopenfeld

Authors
  1. B. Hopenfeld
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Hopenfeld.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hopenfeld, B. Spherical harmonic-based finite element meshing scheme for modelling current flow within the heart. Med. Biol. Eng. Comput. 42, 847–851 (2004). https://doi.org/10.1007/BF02345219

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02345219

Keywords

Search

Navigation