Advertisement

A Support Vector Laplacian Distance Kernel Approach to the Inverse Problem in Intracardiac Electrophysiology

  • Raúl Caulier-CisternaEmail author
  • Margarita Sanromán-Junquera
  • José Luis Rojo-Álvarez
  • Arcadio García-Alberola
Conference paper
Part of the IFMBE Proceedings book series (IFMBE, volume 57)

Abstract

The accurate estimation of the intracardiac electrical sources from a reduced set of electrodes at some distance from the heart chamber is known as the inverse problem in electrophysiology, and it can provide with relevant knowledge on a number of arrhythmia mechanisms in the clinical practice. Methods based on Singular Value Decomposition and Least Squares require a matrix inversion and exhibit limited resolution, due to the low-pass filter effect of the Tikhonov regularization techniques. We propose to use a Dual Problem Signal Model formulation of the ν -Support Vector Regression (ν -SVR) algorithm, with a Mercer Kernel given by Laplacian of the distance function accounting for quasielectrostatic field conditions. This new approach avoids the matrix inversion while providing with high resolution and improved generalization properties. Simulations on simple one-dimensional synthetic examples show the performance in terms of improved resolution and boundary region detection. Also, the choice of the free parameters in the ν - SVR algorithm is related to several bioelectric properties of the problem. Results suggest that ν -SVR with a Laplacian distance kernel can be a suitable alternative for improved resolution in current and emerging non-contact cardiac imaging systems.

Keywords

Inverse problem Electrophysiology Mercer kernel Laplacian Support Vector Machine Dual signal model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Liu Z., Jia P., Biblo L., Taccardi B.. Rudy Y.. Endocardial potential mapping from a noncontact nonexpandable catheter: a feasibility study AniUlls of biomedical engineering. 1998;26:994-1009.Google Scholar
  2. 2.
    Gonzalez Torrecilla E.. Los sistemas navegadores en la electrofisiologfa actual Revista Espanola de Cardiologfa. 2004;57:722-24.Google Scholar
  3. 3.
    Paul T., Windhagen-Mahnert B., Kriebel T., et al. Atrial reentrant tachycardia after surgery for congenital heart disease endocardial map- ping and radiofrequency catheter ablation using a novel, noncontact mapping system Circulation. 2001;103:2266-71.Google Scholar
  4. 4.
    Rudy Y.. Noninvasive electrocardiographic imaging of arrhythmogenic substrates in humans Circulation research. 2013;112:863-74.Google Scholar
  5. 5.
    Vapnik V.. The IUlture of statistical learning theory. Springer Science & Business Media 2013.Google Scholar
  6. 6.
    Camps-Valls G., Rojo-Al.varez J.L.,Martinez-Ram6n M.. Kernel methods in bioengineering, sigl11ll and image processing. Igi Global2007.Google Scholar
  7. 7.
    Rojo-Al.varez J. L., Martfnez-Ram6n M., Muiloz-Marf J., Camps-Valls G.. A unified SVM framework for signal estimation Digital Sigl11ll Processin. 2014;26:1-20.Google Scholar
  8. 8.
    Rojo-Alvarez J. L., Martfnez-Ram6n M., Muiloz-Marf J., Camps-Valls G., Cruz C., Figueiras-Vidal A.. Sparse deconvolution using support vector machines 2008.Google Scholar
  9. 9.
    Figuera C., Rojo-Al.varez J. L., Martfnez-Ram6n M., Guerrero-Curieses A., Caamailo A.. Spectrally adapted Mercer kernels for support vector signal interpolation in Signal Processing Conference, 2011 19th European:961-5 2011.Google Scholar
  10. 10.
    Skouibine K., Trayanova N., Moore P.. A numerically efficient model for simulation of defibrillation in an active bidomain sheet of my- ocardium Mathematical biosciences. 2000;166:85-100.Google Scholar
  11. 11.
    Rudy Y., Messinger-Rapport B. The inverse problem in electrocardio- graphy: solutions in terms of epicardial potentials. Critical reviews in biomedical engineering. 1987;16:215-68.Google Scholar
  12. 12.
    Tikhonov A. Nikolaevitch. Numerical methods for the solution of ill-posed problems;328. Springer 1995.Google Scholar
  13. 13.
    SchOlkopf B., Smola A., Williamson R., Bartlett P.. New support vector algorithms Neural computation. 2000;12:1207-45.Google Scholar
  14. 14.
    Chang C-C., Lin C-J.. Training v-support vector regression: theory and algorithms Neural Computation. 2002;14:1959-77.Google Scholar
  15. 15.
    Luo C-h., Rudy Y.. A model of the ventricular cardiac action poten- tial. Depolarization, repolarization, and their interaction. Circulation research. 1991;68:1501-26.Google Scholar
  16. 16.
    Dud a R., Hart P., Stork D.. Pattern classification. John Wiley & Sons 2012.Google Scholar
  17. 17.
    Jiang M., Lv J., Wang Ch., Huang W., Xia L., Shou G.. A hybrid model of maximum margin clustering method and support vector re- gression for solving the inverse ECG problem in Computing in Cardi- ology, 2011:457-60 2011.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Raúl Caulier-Cisterna
    • 1
    Email author
  • Margarita Sanromán-Junquera
    • 1
  • José Luis Rojo-Álvarez
    • 1
  • Arcadio García-Alberola
    • 2
  1. 1.Department of Signal Theory and Communications, Telematics and ComputingRey Juan Carlos UniversityMadridSpain
  2. 2.Arrhythmia UnitHospital Universitario Virgen de la ArrixacaMurciaSpain

Personalised recommendations