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 JBM  Vol.6 No.1 , January 2018
A Method for Normal Direction Judge Applied in Electrocardiographic Problem
Abstract:
Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conductor that can transfer voltages on the surface of the body. To analyze the electric potentials on body surface or epicardial surface, a set of discrete equations derived from a boundary integral equations need to be solved. Solving these equations means to get the potential distribution eventually. In the process of solving, transfer matrix of discrete equations has received considerable attention, how to get an appropriate transfer matrix is an important issue. This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem. Several simulations have been carried out to verify the accurate results with the correct direction of normal vector using new method within a torso model given simultaneous epicardial and body surface potential recordings.
Cite this paper: Tang, C. , Wu, J. and Chen, R. (2018) A Method for Normal Direction Judge Applied in Electrocardiographic Problem. Journal of Biosciences and Medicines, 6, 1-8. doi: 10.4236/jbm.2018.61001.
References

[1]   Coll-Font, J., et al. (2014) New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment. Computing in Cardiology Conference, Cambridge, MA, 2014, 213-216.

[2]   Bear, L.R., Cheng, L.K., LeGrice, I.J., Sands, G.B., Lever, N.A., Paterson, D.J. and Smaill, B.H. (2015) Forward Problem of Electrocardiography. Arrhythmia and Electrophysiology, 8, 677-684. https://doi.org/10.1161/CIRCEP.114.001573

[3]   MacLeod, R. and Buist, M. (2010) The Forward Problem of Electrocardiography. In: Macfarlane, P.W., van Oosterom, A., Pahlm, O., Kligfield, P., Janse, M. and Camm, J., Eds., Comprehensive Electrocardiology, Springer Science & Business Media, 247-298.

[4]   Bear, L., Dubois, R. and Zemzemi, N. (2016) Optimization of Organ Conductivity for the Forward Problem of Electrocardiography. Computing in Cardiology Conference, IEEE, Vancouver, BC, 2016, 385-388.

[5]   Barr, R.C. and Spach, M.S. (1977) Relating Epicardial to Body Surface Potential Distributions by Means of Transfer Coefficients Based on Geometry Measurements. Biomedical Engineering, IEEE Transactions on BME, 24, 1-11. https://doi.org/10.1109/TBME.1977.326201

[6]   Horácek, B.M. and Clements, J.C. (1997) The Inverse Problem of Electrocardiography: A Solution in Terms of Single- and Double-Layer Sources on the Epicardial Surface. Mathematical Biosciences, 144, 119-154. https://doi.org/10.1016/S0025-5564(97)00024-2

[7]   Van Oosterom, A. and Strackee, J. (1983) The Solid Angle of a Plane Triangle. IEEE Trans Biomed Eng., BME, 30, 125-126. https://doi.org/10.1109/TBME.1983.325207

[8]   Tikhonov, A.N. and Arsenin, V.Y. (1977) Solutions of Ill-Posed Problems. V.H. Winston & Sons, Washington DC.

[9]   Hansen, P.C. and O’Leary, D.P. (1993) The Use of the l-Curve in the Regularization of Discrete Ill-Posed Problems. Siam Journal on Scientific Computing, 14, 1487-1503. https://doi.org/10.1137/0914086

[10]   Assecondi, S., Hallez, H., D’Asseler, Y. and Lemahieu, I. (2007) Comparison of Different Auto-Solid Angle Approximations in BEM for EEG Dipole Source Localization. Joint Meeting of the International Symposium on Noninvasive Functional Source Imaging of the Brain and Heart and the International Conference on Functional Biomedical Imaging, Nfsi-Icfbi IEEE, 2007, 70-73.

[11]   Yao, B., Pei, S. and Yang, H. (2016) Mesh Resolution Impacts the accuracy of Inverse and Forward ECG Problems. 38th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Orlando, FL, 4047-4050.

[12]   de Munck, J.C. (1992) A Linear Discretization of the Volume Conductor Boundary Integral Equation Using Analytically Integrated Elements. IEEE Transactions on Biomedical Engineering, 39, 986-990. https://doi.org/10.1109/10.256433

[13]   Friston, K.J. (2006) Statistical Parametric Mapping: The Analysis of Functional Brain Images. Science Press, Beijing.

 
 
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