A Method for Normal Direction Judge Applied in Electrocardiographic Problem

Chengcheng Tang,Jian Wu,Riqing Chen

doi:10.4236/jbm.2018.61001

Abstract

Boundary Element Method (BEM) is widely used in electrocardiographic (ECG) problem. Formulations of these problems based on mathematical and numerical approximations of the known source in heart and the volume conductor that can transfer voltages on the surface of the body. To analyze the electric potentials on body surface or epicardial surface, a set of discrete equations derived from a boundary integral equations need to be solved. Solving these equations means to get the potential distribution eventually. In the process of solving, transfer matrix of discrete equations has received considerable attention, how to get an appropriate transfer matrix is an important issue. This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem. Several simulations have been carried out to verify the accurate results with the correct direction of normal vector using new method within a torso model given simultaneous epicardial and body surface potential recordings.

Highlights

This paper found that the direction of normal vector could affect the results when calculating the transfer matrix and presents a method analogous to Mesh Current Method to deal with this direction problem
Electrocardiographic problem, namely given the potential distribution at epicardial surface to calculate the distribution at body surface (Forward Problem), or vice versa (Inverse Problem), draws lots of attentions in biomedical area these years, as electrocardiography can be a powerful tool for diagnosis in clinic [1] [2] [3]
Data of epicardial surface potential distributions include a number of different sequences of cardiac excitation and repolarization, along with the geometric location (x, y, z coordinates) of each body and heart electrode

Summary

Introduction

Electrocardiographic problem, namely given the potential distribution at epicardial surface to calculate the distribution at body surface (Forward Problem), or vice versa (Inverse Problem), draws lots of attentions in biomedical area these years, as electrocardiography can be a powerful tool for diagnosis in clinic [1] [2] [3]. The potential distribution at epicardial surface and body surface are linked by a transfer matrix determined by the shape of heart and torso. Both forward and inverse problem need to calculate the transfer matrix elements deter-. The boundary element method (BEM) is often an appropriate way to compute the transfer matrix, despite the different inner physical properties of the conductor medium when the medium is isotropic [4]. Horácek et al calculate transfer coefficients based on triangle-to-triangle discretization [6] [7], rather than node-to-node discretization used by Barr et al to construct appropriate matrices, these matrices are consisted of coefficients that relate to the potentials and their gradients on the epicardial surface of the conductor and the potential on the body surface [8] [9]. Munck et al uses analytically integrated elements to discretize the boundary integral equation linearly [12] [13]

Methods

Results

Conclusion