Abstract
Much attention has been drawn to adopt complicated and realistic physiological models for simulating cardiac electrophysiological activities with abundant computing resources for quite a long time. However, to incorporate these physiological meaningful models into the recovery/inverse framework for estimating patient-specific cardiac electrophysiological activities always needs to handle excessive computational loads caused by the complexities of models. Thus, a balance should be found between physiological meaningfulness and computational feasibility for the recovery/inverse framework. In this paper, a novel numerical scheme, combination of meshfree method and BEM (boundary element method), is proposed to simulate intracardiac and extracardiac electrophysiological activities, which is aimed to provide physiological meaningful simulations with feasible computation for our recovery/inverse approaches. In our simulations, intracardiac electrophysiological activities (transmembrane potentials, TMPs) are obtained by solving a modified Fitzhugh-Nagumo (FHN) model using the meshfree method, and then extracardiac electrophysiological activities (body surface potentials, BSPs) are calculated using BEM. Moreover, we demonstrate the ability of our meshfree-BEM framework through favorable results.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Belystchko, T., Krysl, P., Krongauz, Y.: A three-dimensional explicit element-free galerkin method. Int. J. Numer. Meth. Fluids 37, 229–256 (1997)
Belystchko, T., Lu, Y.Y., Gu, L.: Element-free galerkin methods. Int. J. Numer. Meth. Eng. 37, 229–256 (1994)
Dolbow, J., Belytschko, T.: Numerical integration of the galerkin weak form in meshfree methods. Comp. Mech. 23, 219–230 (1990)
Dolbow, J., Belytschko, T.: Numerical integration of galerkin weak form in meshfree methods. Comp. Mech. 23, 219–230 (1999)
Durrer, D., van Dam, R., Freud, G., Janse, M., Meijler, F., Arzbaecher, R.: Total excitation of the isolated human heart. Circulation 41(6), 899–912 (1970)
Lancaster, P., Salkauskas.: Surface generated by moving least squares methods. Math. Comp. 37(155), 141–158 (1982)
Liu, G.R.: Mesh free methods: moving beyond the finite element method. CRC Press, Boca Raton (2003)
Luo, C.H., Rudy, Y.: A dynamic model of the cardiac ventricular action potential - simulations of ionic currents and concentration changes. Circ. Res. 74, 1071–1097 (1994)
MacLeod, R.S., Brooks, D.H.: Recent progress in inverse problems in electrocardiology. IEEE EMBS Magazine 17(1), 73–83 (1998)
MacLeod, R.S., Johnson, C.R., Ershler, P.R.: Construction of an inhomogeneous model of the human torso for use in computational electrocardiography. In: EMBS, pp. 688–689 (1991)
Mulquiney, P.J., Smith, N.P., Clark, K., Hunter, P.J.: Mathematical modelling of the ischaemic heart. Nonlinear Analysis, 47, 235–244 (2001)
Pullan, A.J., Buist, M.L., Cheng, L.K.: Mathematically modelling the electrical activity of the heart: from cell to body surface and back again. World Science Publishing Co. Pte. Ltd, Singapore (2005)
Pullan, A.J., Cheng, L.K., Nash, M.P., Bradley, C.P., Paterson, D.J.: Non-invasive electrical imaging of the heart - theory and model development. In: Annals of Biomedical Eng. pp. 817–836 (2001)
Rogers, J.M., McCulloch, A.D.: A collation-galerkin finite element model of cardiac action potential propagation. IEEE Trans. BioMed. Eng. 41(8), 743–756 (1994)
Sachse, F.B.: Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics. Springer, Heidelberg (2004)
Sanchez-Ortiz, G.I., Sermesant, M., Rhode, K.S., Chandrashekara, R., Razavi, R., Hill, D.L.G., Rueckert, D.: Localization of abnormal conduction pathways for tachyarrhythmia treatment using tagged MRI. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 425–433. Springer, Heidelberg (2005)
Singh, I.V.: Parallel implementation of the EFG method for heat transfer and fluid flow problems. Comp. Mech. 34, 453–463 (2004)
Wang, L.W., Zhang, H.Y., Shi, P.C., Liu, H.F.: Imaging of 3d cardiac electrical activity: A model-based recovery framework. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, Springer, Heidelberg (2006)
Wang, Y., Rudy, Y.: Application of the method of fundamental solutions to potential-based inverse electrocardiography. Ann. Biomed Eng. 34, 1272–1288 (2006)
Zhang, H.Y., Shi, P.C.: A meshfree method for solving cardiac electrical propagation. In: EMBS, pp. 349–352 (2005)
Zhang, H.Y., Wong, K.C.L., Shi, P.C.: Estimation of cardiac electrical propagation from medical image sequence. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 528–535. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Zhang, H., Wang, L., Shi, P. (2007). Simulations of Cardiac Electrophysiological Activities Using a Heart-Torso Model. 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_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-72907-5_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72906-8
Online ISBN: 978-3-540-72907-5
eBook Packages: Computer ScienceComputer Science (R0)