Forward problem of electrocardiography: construction of human torso models and field calculations using finite element method

  • A. Vahld Shahidi
  • P. Savard
Electrocardiographic Modelling

Abstract

Finite element models of the human torso were constructed using anatomical data measured by serial computerised tomography scans in a subject. A first set of three models with a mesh resolution of 5517 nodes and 29810 elements included an homogeneous conductivity, lungs inhomogeneity, and heart, lungs and spinal region inhomogeneities. A second set comprised similar models with a mesh resolution of 12084 nodes and 67045 elements. A cylindrically shaped volume conductor was also constructed to evaluate the convergency and accuracy of the finite element solutions by comparison with the analytical solution. Forward simulations were performed using different excitation sites on the cardiac surface. The inclusion of conductivity inhomogeneities altered the maximum and minimum values of the body surface potentials, but did not substantially modify the pattern of the potential distributions. The greatest effect was due to the inclusion of the lungs. Increasing the mesh resolution from 5517 to 12084 nodes did not change noticeably the shape or amplitude of the simulated body surface potential maps. These models can readily be used for other bioelectromagnetic problems.

Keywords

Finite element method Forward problem of electrocardiography Human torso model 

References

  1. Barr, R. C., Pilkington, T. C., Boineau, J. P., andSpach, M. S. (1966): ‘Determining surface potentials from current dipoles with application to electrocardiography’,IEEE Trans.,BME-13, pp. 88–92Google Scholar
  2. Barr, R. C., Ramsey, M., III, andSpach, M. S. (1977): ‘Effects of geometrical uncertainties on electrocardiography’,IEEE Trans.,BME-28, pp. 325–334Google Scholar
  3. Barr, R. C., andSpach, M. S. (1978): ‘Inverse calculation of QRS-T epicardial potential from body surface potential distributions for normal and ectopic beats in the intact dog’,Circ. Res.,42, pp. 661–675Google Scholar
  4. Brody, D. A. (1956): ‘A theoretical analysis of intracavity blood mass influence on the heart-lead relationship’,Circ. Res.,4, pp. 731–738Google Scholar
  5. Colli-Franzone, P., Guerri, L., Taccardi, B., andViganotti, C. (1985): ‘Finite element approximation of regularized solutions of the inverse potential problem of electrocardiography and applications to experimental data,’Calcolo,12, pp. 91–186MathSciNetGoogle Scholar
  6. Gelernter, H. L., andSwihart, J. C. (1964): ‘A mathematical-physical model of the genesis of the electrocardiogram’,Biophys. J.,4, pp. 285–301CrossRefGoogle Scholar
  7. Gulrajani, R. M., andMailloux, G. E. (1983): ‘A simulation study of the effects of torso inhomogeneities on electrocardiographic potentials, using realistic heart and torso models’,Circ. Res.,52, pp. 45–56Google Scholar
  8. Gulrajani, R. M., Roberge, F. A., and Mailloux, G. E. (1988): ‘The forward problem of electrocardiography,’In Macfarlane, P. W., andLawrie, T. D. V. (Eds.), ‘Comprehensive electrocardiography’ (Pergamon Press) Chap. 8Google Scholar
  9. Johnson, C. R. (1990): ‘The generalized inverse problem in electrocardiography: theoretical, computational, and experimental results’, PhD Thesis, University of Utah, Salt Lake City, USAGoogle Scholar
  10. Kim, Y. (1982): ‘A three-dimensional modifiable computer body model and its applications’, PhD Thesis, University of Wisconsin, Madison, USAGoogle Scholar
  11. Lo, G-C. (1977): ‘Estimation of epicardial electrical potentials from body surface measurements based on a digital simulation of the human thorax’, PhD Thesis, Imperial College of Science and Technology, London, UKGoogle Scholar
  12. Okada, R. (1956): ‘Potentials produced by an eccentric current dipole in a finite-length circular conducting cylinder’,IRE Trans. Med. Electron.,7, pp. 14–19CrossRefGoogle Scholar
  13. van Oosterom, A., andHuiskamp, G. J. (1989): ‘The effect of torso inhomogeneities on body surface potentials quantified using tailored geometry’,J. Electrocardiol.,22, pp. 53–72CrossRefGoogle Scholar
  14. Pilkington, T. C., Morrow, M. N., andStanley, P. C. (1985): ‘A comparison of finite element and integral equation formulations for the calculation of electrocardiographic potentials’,IEEE Trans.,BME-32, pp. 166–173Google Scholar
  15. Pilkington, T. C., Morrow, M. N., andStanley, P. C. (1987): ‘A comparison of finite element and integral equation formulations for the calculation of electrocardiographic potentials. II’-ibid.,,BME-34, p. 258Google Scholar
  16. Plonsey, R. (1969): ‘Bioelectric phenomena’ (McGraw-Hill)Google Scholar
  17. Rudy, Y., andPlonsey, R. (1979): ‘The eccentric spheres models as the basis for a study of the role of geometry and inhomogeneities in electrocardiography’,IEEE Trans.,BME-26, pp. 392–399Google Scholar
  18. Rush, S., Abildskov, J. A., andMcFee, R. (1963): ‘Resisitivity of body tissues at low frequencies’,Circ. Res.,12, pp. 40–50Google Scholar
  19. Silvester, P. P., andFerrari, R. L. (1983): ‘Finite elements for electrical engineers’ (Cambridge University Press)Google Scholar
  20. Silvester, P. P., andTymchyshyn, S. (1974): ‘Finite-element modelling of the inhomogeneous human thorax,’Adv. Cardiol.,10, 46–50Google Scholar
  21. Vahid Shahidi, A. (1991): ‘The inverse problem of electrocardiography: recovery and validation using finite element method in man’, PhD Thesis, Ecole Polytechnique de Montréal, Montréal, CanadaGoogle Scholar
  22. Walker, S. J., andKilpatrick, D. (1987): ‘Forward and inverse electrocardiographic calculations using resistor network models of the human torso,Circ. Res.,61, p. 504Google Scholar
  23. Yamashita, Y., andTakahashi, D. (1980): ‘On the properties of the inverse solution in ECG: determining epicardial from body surface potentials by using the finite element method’in Kaihara, S., andLindberg, D. A. B. (Eds.): MEDINFO 80 (North-Holland) pp. 264–268Google Scholar
  24. Yamashita, Y., andTakahashi, T. (1984): ‘Use of finite element method to determine epicardial from body surface potentials under a realistic torso model’,IEEE Trans.,BME-26, pp. 611–621Google Scholar
  25. Zienkiewicz, O. C. (1977): ‘The finite element method’ (McGraw-Hill)Google Scholar

Copyright information

© IFMBE 1994

Authors and Affiliations

  • A. Vahld Shahidi
    • 1
  • P. Savard
    • 1
  1. 1.Institute of Biomedical EngineeringEcole Polytechnique and Université de MontréalMontréalCanada

Personalised recommendations