Bradley, Chris; Pullan, Andrew Application of the BEM in biopotential problems. (English) Zbl 0996.92003 Eng. Anal. Bound. Elem. 26, No. 5, 391-403 (2002). Summary: We describe how the boundary element method (BEM) can be used in the general field of biopotential problems. We present here a cubic Hermite boundary element procedure for this purpose and show how this approach is computationally more efficient than traditional BEM procedures for solving potential-related problems. We also show how these \(C^1\) interpolation functions can be used to model the complex domains that are present in many biopotential problems. Illustrative biopotential results for two different clinically important areas are given. The first area deals with potentials generated by the heart (electrocardiography) while the second field is related to potentials arising from brain activity (electroencephalography). Cited in 2 Documents MSC: 92C05 Biophysics 92C55 Biomedical imaging and signal processing 65N38 Boundary element methods for boundary value problems involving PDEs Keywords:electroencephalography; high-order BEM; ECG modelling; EEG modelling; electrocardiography; biopotential problems Software:NPSOL PDFBibTeX XMLCite \textit{C. Bradley} and \textit{A. Pullan}, Eng. Anal. Bound. Elem. 26, No. 5, 391--403 (2002; Zbl 0996.92003) Full Text: DOI References: [1] Plonsey, R., Bioelectric phenomena (1969), McGraw Hill: McGraw Hill New York [2] Nielsen, P. M.F.; Le Grice, I. J.; Smaill, B. H.; Hunter, P. J., Mathematical model of geometry and fibrous structure of the heart, Am J Physiol, 260, H1365-H1378 (1991), Heart Circ Physiol 29 [3] Bradley, C. P.; Pullan, A. J.; Hunter, P. J., Geometric modeling of the human torso using cubic Hermite elements, Ann Biomed Engng, 25, 96-111 (1997) [4] Gill PE, Murray W, Saunders MA, Wright MH. User’s guide for NPSOL (version 4.0): a fortran package for nonlinear programming. Technical Report SOL 86-2, Department of Operations Research, Stanford University, 1986.; Gill PE, Murray W, Saunders MA, Wright MH. User’s guide for NPSOL (version 4.0): a fortran package for nonlinear programming. Technical Report SOL 86-2, Department of Operations Research, Stanford University, 1986. [5] Young, A. A.; Hunter, P. J.; Smaill, B. H., Epicardial surface estimation from coronary angiograms, Comput Vision Graphics Image Process, 47, 111-127 (1989) [6] Bradley, C. P.; Nash, M. P.; Cheng, L. K.; Pullan, A. J.; Paterson, D. J., Electrocardiographic inverse validation study: model development and methodology, FASEB J, 14, 4, A442 (2000) [7] Pullan, A. J., A high-order coupled finite element/boundary element torso model, IEEE Trans Biomed Engng, 43, 3, 292-298 (1996) [8] Pullan, A. J.; Bradley, C. P., A coupled cubic Hermite finite element/boundary element procedure for electrocardiographic problems, Comput Mech, 18, 5, 356-368 (1996) · Zbl 0883.92013 [9] Tomlinson, K. A.; Bradley, C. P.; Pullan, A. J., On the choice of a derivative boundary element formulation using Hermite interpolation, Int J Numer Methods Engng, 39, 451-468 (1996) · Zbl 0865.73074 [10] Durodola, J. F.; Fenner, R. T., Hermitian cubic boundary element for two dimensional potential problems, Int J Numer Methods Engng, 30, 1051-1062 (1990) · Zbl 0728.73080 [11] Bradley, C. P.; Harris, G. M.; Pullan, A. J., The computational performance of a high-order coupled fem/bem procedure in electropotential problems, IEEE Trans Biomed Engng, 48, 11, 1238-1250 (2001) [12] Meijs, J. W.H.; Weier, O. W.; Peters, M. J.; van Oosterom, A., On the numerical accuracy of the boundary element method, IEEE Trans Biomed Engng, 36, 10, 1038-1049 (1989) [13] Ary, J. P.; Klein, S. A.; Fender, D. H., Location of sources of evoked scalp potentials: corrections for skull and scalp thicknesses, IEEE Trans Biomed Engng, 28, 6, 447-452 (1981) [14] Bradley, C. P.; Pullan, A. J.; Hunter, P. J., Effects of material properties and geometry on electrocardiographic forward simulations, Ann Biomed Engng, 28, 7, 721-741 (2000) [15] Harris GM. Modelling the auditory brainstem response using an anatomically accurate model of the human head. Master’s Thesis, The University of Auckland, New Zealand, 1996.; Harris GM. Modelling the auditory brainstem response using an anatomically accurate model of the human head. Master’s Thesis, The University of Auckland, New Zealand, 1996. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.