Abstract
The construction of geometry models of heart-torso is critical for solving the forward and inverse problems of magneto- and electro-cardiography (MCG/ECG). Boundary element method (BEM) is a commonly used numerical approach for the solution of these problems and it requires the modeling of interfaces between various tissue regions. In this study, a new BEM (h-adaptive type) has been applied to the ECG forward/inverse problems. Compared with those traditional BEMs, the adaptive BEM can self-adjust the number and size of the boundary element (BE) meshes according to an error indicator, and thus can save a lot of computational time and also improve the accuracy of the forward and inverse solutions. In this paper, the procedure of the adaptive triangular mesh generation is detailed and the algorithm is tested using a concentric sphere model and a realistic heart-torso model. For the realistic torso model, to improve the numerical accuracy, a number of new nodes are added on the basis of initial torso BE meshes, and the corresponding node coordinates are determined using an approach called Parametric Fourier Representation (PFR) of closed polygons. The simulation results show that the adaptive BEM is more accurate and efficient than traditional BEMs and therefore it is a very promising numerical scheme for ECG forward/inverse problems.
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References
Gulrajani, R.M.: The Forward and Inverse problems of Electrocardiography. IEEE. Eng. Med. Bio. 17(122 ), 84–101 (1998)
Dössel, O.: Inverse Problem of Electro- and Magnetocardiography: Review and Recent Progress. Int. J. Bioelectromagnetism 2(2) (2000)
Michel, C.M., Murray, M.M., Lantza, G., Gonzaleza, S., Spinellib, L., Peralta, R.G.: EEG source imaging. Clin. Nerophysiol. 115, 2195–2222 (2004)
Seger, M., Fischer, G., Modre, R., Messnarz, B., Hanser, F., Tilg, B.: Lead field computation for the electrocardiographic inverse problem-finite elements versus boundary elements. Comp. Meth. Prog. Biomed. 77(3), 241–252 (2005)
Johnson, C.R.: Computational and numerical methods for bioelectric field problems. Crit. Rev. Biomed. Eng. 25(1), 1–81 (1997)
Johnson, C.R.: Adaptive Finite Element and Local Regularization Methods for the Inverse ECG Problem. In: Inverse Problems in Electrocardiology, Advances in Computational Biomedicine, Edited by Peter Johnston, WIT Press vol. 5, pp. 51–88 (2001), http://www.cmp.co.uk/
Nixon, J.B., Rasser, P.E., Teubner, M.D., Clark, C.R., Bottema, M.J.: Numerical model of electrical potential within the human head. Int. J. Numer. Methods Eng. 56, 2353–2366 (2003)
Harrild, D.M., Henriquez, C.S.: A finite volume model of cardiac propagation. Ann. Biomed. Eng. 25(2), 315–334 (1997)
Ghosh, S., Rudy, Y.: Accuracy of quadratic versus linear interpolation in noninvasive electrocardiographic imaging (ECGI). Ann. Biomed. Eng. 33, 1187–1201 (2005)
Akalm-Acar, Z., Gençer, N.G.: An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging. Phys. Med. Biol. 49, 5011–5028 (2004)
Fischer, G., Tilg, B., Wach, P., Modre, R., Leder, U., Nowak, H.: Application of high-order boundary elements to the electrocardiographic inverse problem. Comput. Meth. Pro. Biomed. 58, 119–131 (1999)
Buist, M., Pullan, A.: Torso Coupling Techniques for the Forward Problem of Electrocardiography. Ann. Biomed. Eng. 30, 1187–1201 (2002)
Ferguson, A.S., Stroink, G.: Factors affecting the accuracy of the boundary element method in the forward problem - I: Calculating surface potentials. IEEE Trans. Biomed. Eng. 44, 1139–1155 (1997)
Fuchs, M., Jörn, K., Wagner, M., Hawes, S., Ebersole, S., Ebersole, J.S.: A standardized boundary element method volume conductor model. Clin. Nerophysiol. 113, 702–712 (2002)
Kita, E., Kamiya, N.: Error estimation and adaptive mesh refinement in boundary element method, an overview. Eng. Anal. Bound. Elem. 25, 479–495 (2001)
Bächtold, M., Emmenegger, M., Korvink, J.G., Baltes, H.: An error indicator and automatic adaptive meshing for electrostatic boundary element simulations. IEEE Trans.Computer-Aided Design. 16, 1439–1446 (1997)
Hren, R., Stroink, G.: Application of the surface harmonic expansions for modeling the human torso. IEEE Trans. Biomed. Eng. 42, 521–524 (1995)
Zilkowski, M., Brauer, H.: Methods of mesh generation for biomagnetic problems. IEEE Trans. Magn. 32, 1345–13487 (1996)
Lindholm, D.A.: Automatic triangular Mesh Generation Surfaces of Polyhedra. IEEE Trans. Mag. 6, 2539–2542 (1983)
Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM, Philadelphia, 199
Shou, G.F., Jiang, M.F., Xia, L., Wei, Q., Liu, F., Crozier, S.: A comparision of different choices for the regularization parameter in inverse electrocardiography problem. IEEE Eng. Med. Biol. Soc. 28th Ann. Int. Conf. 28, 3903–3906 (2006)
Xia, L., Huo, M., Wei, Q., Liu, F., Crozier, S.: Electrodynamic Heart Model Construction and ECG Simulation. Methods Inf. Med. 45, 564–573 (2006)
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Shou, G., Xia, L., Jiang, M., Liu, F., Crozier, S. (2007). Forward and Inverse Solutions of Electrocardiography Problem Using an Adaptive BEM Method. In: Sachse, F.B., Seemann, G. (eds) Functional Imaging and Modeling of the Heart. FIMH 2007. Lecture Notes in Computer Science, vol 4466. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72907-5_30
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DOI: https://doi.org/10.1007/978-3-540-72907-5_30
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