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Statistical assessment and calibration of numerical ECG models. (English) Zbl 1428.92065

Summary: In this paper, we propose a statistical method to assess and enhance the quality of electrocardiograms (ECGs) produced by deterministic mathematical models that are used to study the physical mechanisms of electrophysiology and related pathologies. We consider a reference dataset of real ECGs and use the notion of functional data depths and quantiles to formulate a family of statistical calibration problems where the deterministic model targets selected functional quantiles of the real, reference population, properly accounting for inter-subject variability of ECG signals. The method is successfully applied to two very different models: a phenomenological model based on ordinary differential equations, and a complex biophysical model based on partial differential equations set on a three-dimensional geometry of the heart and the torso.

MSC:

92C55 Biomedical imaging and signal processing
35Q92 PDEs in connection with biology, chemistry and other natural sciences
34C60 Qualitative investigation and simulation of ordinary differential equation models
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

R; fda (R)
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References:

[1] M. Boulakia, S. Cazeau, M. Fernández, J.-F. Gerbeau and N. Zemzemi, Mathematical modeling of electrocardiograms: a numerical study, Annals of Biomedical Engineering 38 (2010), 1071-1097.
[2] M. Boulakia, E. Schenone and J.-F. Gerbeau, Reduced-order modeling for cardiac electrophysiology, Application to parameter identification, International Journal for Numerical Methods in Biomedical Engineering 28 (2012), 727-744.
[3] A. Bueno-Orovio, E. Cherry and F. Fenton, Minimal model for human ventricular action potentials in tissue, Journal of Theoretical Biology 253 (2008), 544-560. · Zbl 1398.92052
[4] M. Buist and A. Pullan, The effect of torso impedance on epicardial and body surface potentials: A modeling study, IEEE Transactions on Biomedical Engineering 50 (2003), 816-824.
[5] A. Chakraborty and P. Chaudhuri, The spatial distribution in infinite dimensional spaces and related quantiles and depths, The Annals of Statistics 42 (2014), 1203- 1231. · Zbl 1305.62141
[6] D. Chapelle, A. Collin and J.-F. Gerbeau, A surface-based electrophysiology model relying on asymptotic analysis and motivated by cardiac atria modeling, Mathematical Models and Methods in Applied Sciences 23 (2013), 2749-2776. · Zbl 1277.92004
[7] P. Chaudhuri, On a geometric notion of quantiles for multivariate data, Journal of the American Statistical Association 91 (1996), 862-872. · Zbl 0869.62040
[8] G. Clifford, A. Shoeb, P. McSharry and B. Janz, Model-based filtering, compression and classification of the ecg, International Journal of Bioelectromagnetism 7 (2005), 158-161.
[9] A. Collin, J.-F. Gerbeau, M. Hocini, M. Haïssaguerre and D. Chapelle, Surfacebased electrophysiology modeling and assessment of physiological simulations in atria, FIMH 2013, 7945 (2013), 352-359.
[10] C. Corrado, J.-F. Gerbeau and P. Moireau, Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography, Journal of Computational Physics 283 (2015), 271-298. · Zbl 1352.92086
[11] M. Courtemanche, R. Ramirez and S. Nattel, Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model, American Journal of Physiology 275 (1998), H301-H321.
[12] J. Kemperman, The median of a finite measure on a Banach space, Statistical Data Analysis Based on the L1-Norm and Related Methods, Elsevier Science Publishers, North Holland, 1987, pp. 217-230.
[13] V. Koltchinskii, M-estimation, convexity and quantiles, The Annals of Statistics 25 (1997), 435-477. · Zbl 0878.62037
[14] S. Lopez-Pintado and J. Romo, Depth-based inference for functional data, Computational Statistics & Data Analysis 51 (2007), 4957-4968. · Zbl 1162.62359
[15] S. Lopez-Pintado and J. Romo, On the concept of depth for functional data, Journal of the American Statistical Association 104 (2009), 718-734. · Zbl 1388.62139
[16] J. Malmivuo and R. Plonsey, Bioelectromagnetism - Principles and Applications of Bioelectric and Biomagnetic Fields, Oxford University Press, 1995.
[17] V. Martin, A. Drochon, O. Fokapu and J.-F. Gerbeau, Magnetohemodynamics in the aorta and electrocardiograms, Physics in Medicine and Biology 57 (2012), 3177-3195.
[18] P. E. McSharry, G. D. Clifford, L. Tarassenko and L. A. Smith, A dynamical model for generating synthetic electrocardiogram signals, IEEE Transactions on Biomedical Engineering 50 (2003), 289-294.
[19] M. Potse, B. Dubé and R. Gulrajani, ECG simulations with realistic human membrane, heart, and torso models, Engineering in Medicine and Biology Society, 2003, Proceedings of the 25th Annual International Conference of the IEEE, vol. 1, 2003, pp. 70-73.
[20] M. Potse, B. Dubé and A. Vinet, Cardiac anisotropy in boundary-element models for the electrocardiogram, Med. Biol. Eng. Comput. 47 (2009), 719-729.
[21] M. Potse, D. Krause, W. Kroon, R. Murzilli, S. Muzzarelli, F. Regoli, E. Caiani, F. Prinzen, R. Krause and A. Auricchio, Patient-specific modeling of cardiac electrophysiology in heart-failure patients, Europace 16 (2014), iv56-iv61.
[22] R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2014.
[23] J. O. Ramsay and B. Silverman, Functional Data Analysis, Springer, New York, second ed., 2005. · Zbl 1079.62006
[24] A. Rincon, M. Bendahmane and B. Ainseba, Computing the electrical activity of the heart with a dynamic inverse monodomain operator, in 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), IEEE, 2013, pp. 3797-3800.
[25] F. Sachse, Computational Cardiology: Modeling of Anatomy, Electrophysiology and Mechanics, Springer-Verlag, 2004. · Zbl 1051.92025
[26] E. Schenone, A. Collin and J.-F. Gerbeau, Numerical simulation of electrocardiograms for full cardiac cycles in healthy and pathological conditions, International Journal for Numerical Methods in Biomedical Engineering 32 (2015).
[27] J. Sundnes, G. Lines, X. Cai, B. Nielsen, K. Mardal and A. Tveito, Computing the Electrical Activity in the Heart, vol. 1 of Monographs in Computational Science and Engineering, Springer-Verlag, 2006. · Zbl 1182.92020
[28] M.-C. Trudel, B. Dubé, M. Potse, R. Gulrajani and L. Leon, Simulation of QRST integral maps with a membrane-based computer heart model employing parallel processing, IEEE Transactions on Biomedical Engineering 51 (2004), 1319-1329.
[29] D. Wei, O. Okazaki, K. Harumi, E. Harasawa and H. Hosaka, Comparative simulation of excitation and body surface electrocardiogram with isotropic and anisotropic computer heart models, IEEE Transactions on Biomedical Engineering 42 (1995), 343-357.
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