Evaluation of multivariate adaptive non-parametric reduced-order model for solving the inverse electrocardiography problem: a simulation study

  • Önder Nazım OnakEmail author
  • Yesim Serinagaoglu Dogrusoz
  • Gerhard Wilhelm Weber


In the inverse electrocardiography (ECG) problem, the goal is to reconstruct the heart’s electrical activity from multichannel body surface potentials and a mathematical model of the torso. Over the years, researchers have employed various approaches to solve this ill-posed problem including regularization, optimization, and statistical estimation. It is still a topic of interest especially for researchers and clinicians whose goal is to adopt this technique in clinical applications. Among the wide range of mathematical tools available in the fields of operational research, inverse problems, optimization, and parameter estimation, spline-based techniques have been applied to inverse problems in several areas. If proper spline bases are chosen, the complexity of the problem can be significantly reduced while increasing estimation accuracy. However, there are few studies within the context of the inverse ECG problem that take advantage of this property of the spline-based approaches. In this paper, we evaluate the performance of Multivariate Adaptive Regression Splines (MARS)-based method for the solution of the inverse ECG problem using two different collections of simulated data. The results show that the MARS-based method improves the inverse ECG solutions and is “robust” to modeling errors, especially in terms of localizing the arrhythmia sources.

Graphical Abstract

Multivariate adaptive non-parametric model for inverse ECG problem.


Inverse problem Inverse electrocardiography Multivariate adaptive regression splines (MARS) Regularization 



The authors would like to thank Dr. Robert S. MacLeod from University of Utah, Nora Eccles Harrison Cardiovascular Research and Training Institute for the data used in this study. The qualitative assessments in this work became possible by software, Map3d, which was supported by the National Institute of General Medical Sciences of the National Institutes of Health under grant number P41 GM103545-18. The authors also would like to thank Karlsruhe Institute of Technology (KIT) and Walther H. W. Schulze and his colleagues for the data used in this study, and the Consortium of ECGI for facilitating data sharing for all researchers.


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Copyright information

© International Federation for Medical and Biological Engineering 2018

Authors and Affiliations

  1. 1.Institute of Applied MathematicsMiddle East Technical UniversityÇankaya/AnkaraTurkey
  2. 2.Department of Electrical and Electronics EngineeringMiddle East Technical UniversityÇankaya/AnkaraTurkey
  3. 3.Faculty of Engineering ManagementPoznan University of TechnologyPoznanPoland

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