Observability and Inverse Problems Arising in Electrocardiography

  • I. Iakovidis
  • C. F. Martin
  • S. Xie
Part of the Progress in Systems and Control Theory book series (PSCT, volume 1)


The problem we consider arises in electrocardiography. It is one of a general class of inverse problems in electrocardiography and its goal is the reconstruction of cardiac electrical events from information obtained non-invasively at the body surface. In this paper we formulate the problem as a problem in observability by considering the heart-torso system as a dynamical system governed by the Laplace’s equation with input the electrical potential distribution on the surface of the heart and output the potential distribution on the torso. The problem then becomes the reconstruction of as much information as possible about the state of the system using only a finite number of measurements on the torso. We will present two analytical approaches to the inverse problem under the assumptions of spherical and cylindrical geometry of the heart-torso system. Also, we will point out the dependence of the solution to the problem on the selection of the location of the measurements. We note that the aim of this paper is to describe the problem and suggest reasonable modes of attack.


Inverse Problem Potential Distribution Cubature Formula Body Surface Potential Epicardial Potential 
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Copyright information

© Birkhäuser Boston 1989

Authors and Affiliations

  • I. Iakovidis
    • 1
  • C. F. Martin
    • 1
  • S. Xie
    • 1
  1. 1.Department of MathematicsTexas UniversityLubbockUSA

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