Abstract
Electrocardiography imaging (ECGI) is a new non invasive technology used for heart diagnosis. It allows to construct the electrical potential on the heart surface only from measurement on the body surface and some geometrical informations of the torso. The purpose of this work is twofold: First, we propose a new formulation to calculate the distribution of the electric potential on the heart, from measurements on the torso surface. Second, we study the influence of the errors and uncertainties on the conductivity parameters, on the ECGI solution. We use an optimal control formulation for the mathematical formulation of the problem with a stochastic diffusion equation as a constraint. The descretization is done using stochastic Galerkin method allowing to separate random and deterministic variables. The optimal control problem is solved using a conjugate gradient method where the gradient of the cost function is computed with an adjoint technique. The efficiency of this approach to solve the inverse problem and the usability to quantify the effect of conductivity uncertainties in the torso are demonstrated through a number of numerical simulations on a 2D geometrical model. Our results show that adding \(\pm 50\,\%\) uncertainties in the fat conductivity does not alter the inverse solution, whereas adding \(\pm 50\,\%\) uncertainties in the lung conductivity affects the reconstructed heart potential by almost \(50\,\%\).
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References
Shah, A.J., Lim, H.S., Yamashita, S., Zellerhoff, S., Berte, B., Mahida, S., Hooks, D., Aljefairi, N., Derval, N., Denis, A., et al.: Non invasive ecg mapping to guide catheter ablation. JAFIB: J. Atrial Fibrillation 7(3) (2014)
Hadamard, J.: Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Yale University Press, New Haven (1923)
Ghosh, S., Rudy, Y.: Application of l1-norm regularization to epicardial potential solution of the inverse electrocardiography problem. Ann. Biomed. Eng. 37(5), 902–912 (2009)
Zakharov, E., Kalinin, A.: Algorithms and numerical analysis of dc fields in a piecewise-homogeneous medium by the boundary integral equation method. Comput. Math. Model. 20(3), 247–257 (2009)
Li, G., He, B.: Localization of the site of origin of cardiac activation by means of a heart-model-based electrocardiographic imaging approach. Biomed. Eng. IEEE Trans. 48(6), 660–669 (2001)
Doessel, O., Jiang, Y., Schulze, W.H.: Localization of the origin of premature beats using an integral method. Int. J. Bioelectromagnetism 13, 178–183 (2011)
Zemzemi, N., Dubois, R., Coudiere, Y., Bernus, O., Haissaguerre, M.: A machine learning regularization of the inverse problem in electrocardiography imaging. In: Computing in Cardiology Conference (CinC) 2013, 1135–1138 (2013)
Hansen, P.C., O’Leary, D.P.: The use of the l-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14(6), 1487–1503 (1993)
Foster, K.R., Schwan, H.P.: Dielectric properties of tissues and biological materials: a critical review. Crit. Rev. Biomed. Eng. 17(1), 25–104 (1988)
Faes, T., Van Der Meij, H., De Munck, J., Heethaar, R.: The electric resistivity of human tissues (100 hz-10 mhz): a meta-analysis of review studies. Physiol. Meas. 20(4), R1 (1999)
Gabriel, S., Lau, R., Gabriel, C.: The dielectric properties of biological tissues: Ii. measurements in the frequency range 10 hz to 20 ghz. Phys. Med. Biol. 41(11), 2251 (1996)
Van Oosterom, A., Huiskamp, G.: The effect of torso inhomogeneities on body surface potentials quantified using tailored geometry. J. Electrocardiol. 22(1), 53–72 (1989)
Geneser, S.E., Kirby, R.M., MacLeod, R.S.: Application of stochastic finite element methods to study the sensitivity of ecg forward modeling to organ conductivity. Biomed. Eng. IEEE Trans. 55(1), 31–40 (2008)
Weber, F.M., Keller, D.U., Bauer, S., Seemann, G., Lorenz, C., Dossel, O.: Predicting tissue conductivity influences on body surface potentialsan efficient approach based on principal component analysis. Biomed. Eng. IEEE Trans. 58(2), 265–273 (2011)
Aboula\(\ddot{\iota }\)ch, R., Abda, A.B., Kallel, M., Bal, G., Jollivet, A., Bresson, X., Chan, T.F., Flenner, A., Hewer, G.A., Kenney, C.S., et al.: Missing boundary data reconstruction via an approximate optimal control. Inverse Prob. Imaging 2(4), 411–426 (2008)
Le Maître, O.P., Reagan, M.T., Najm, H.N., Ghanem, R.G., Knio, O.M.: A stochastic projection method for fluid flow: Ii. random process. J. Comput. Phys. 181(1), 9–44 (2002)
Andrieux, S., Baranger, T., Abda, A.B.: Solving cauchy problems by minimizing an energy-like functional. Inverse Probl. 22(1), 115 (2006)
Acknowledgments
We would like to thank the LIRIMA Laboratory which financially supported the teams ANO and EPICARD to perform this work.
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Zemzemi, N., Aboulaich, R., Fikal, N., Guarmah, E.E. (2015). Sensitivity of the Electrocardiography Inverse Solution to the Torso Conductivity Uncertainties. In: van Assen, H., Bovendeerd, P., Delhaas, T. (eds) Functional Imaging and Modeling of the Heart. FIMH 2015. Lecture Notes in Computer Science(), vol 9126. Springer, Cham. https://doi.org/10.1007/978-3-319-20309-6_54
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DOI: https://doi.org/10.1007/978-3-319-20309-6_54
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