Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source

Abstract

Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the chi2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.

Method for guiding the ablation catheter to the ablation site: a simulation and experimental study

“…A spatial criterion was imposed to force solutions to land inside a predefined volume that includes the heart [1][2][3]8]. In prior studies [2,3] we have learned that the algorithm is convergent to a global minimum and hence is terminated, if two solutions that start from two different seeds are found to be closer than 0.5 cm.…”

“…In the inverse algorithm, we used the SEMD model embedded in an infinite homogeneous volume conductor [1,2]. Then, the potential / i at location r i (x i , y i , z i ) on the body surface due to the dipole at r 0 (x 0 , y 0 , z 0 ) with moment p (p x , p y , p z ) in an infinite medium of conductivity g, was given by…”

“…with a few seconds delay). Furthermore, the advantages of using the SEMD model are (1) it is a good model when cardiac electrical activity is localized [2,3], as is the case at the initial activation site one wants to ablate; (2) it permits quantification of the strength of the source in biophysical terms that are independent of volume conductor size (in clinical terms this means that one can obtain an estimate of the initial depolarization wavefront from the strength of the SEMD, that is independent of the size of the heart); and (3) the active equivalent source can be assigned a location [1]. Then, the six dipole parameters (three location and three moment parameters) can be obtained easily [2,3] for a real-time application, such as RCA, from ECG signals recorded e.g.…”

“…In order to satisfy this need, we have introduced a new method to guide the ablative therapy of cardiac arrhythmias, in which we model both cardiac electrical activity (at the exit site of the scar tissue or the site of abnormal automaticity which for purposes of this application we call ''target site'') and current pulses generated from a pair of electrodes at the tip of the ablation catheter with a single equivalent moving dipole (SEMD) [1][2][3]8]. The method employs a three-step approach: (1) models cardiac electrical activity during VT with a SEMD, and from the analysis of the SEMD trajectory identifies the SEMD location corresponding to the target site; (2) models nonexcitatory (high frequency, e.g.…”

The Single Equivalent Moving Dipole Model Does Not Require Spatial Anatomical Information to Determine Cardiac Sources of Activation

“…In subsequent computational studies [12]- [14] in which we estimated the accuracy of the guiding process as the tip of the ablation catheter approaches the target site, we observed that despite differences in the systematic error across the left and the right ventricles, for a target site anywhere on the endocardial ventricular wall, our algorithm has been able to guide the catheter tip very close to the target site, the absolute error is ∼0.2 cm, which is appropriate for RCA procedures.…”