An equivalent body surface charge model representing three-dimensional bioelectrical activity

Localization of endocardial ectopic activity by means of noninvasive endocardial surface current density reconstruction

Localization of the source of cardiac ectopic activity has direct clinical benefits for determining the location of the corresponding ectopic focus. In this study, a recently developed current-density (CD)-based localization approach was experimentally evaluated in noninvasively localizing the origin of the cardiac ectopic activity from body-surface potential maps (BSPMs) in a well-controlled experimental setting. The cardiac ectopic activities were induced in four well-controlled intact pigs by single-site pacing at various sites within the left ventricle (LV). In each pacing study, the origin of the induced ectopic activity was localized by reconstructing the CD distribution on the endocardial surface of the LV from the measured BSPMs and compared with the estimated single moving dipole (SMD) solution and precise pacing site (PS). Over the 60 analyzed beats corresponding to ten pacing sites (six for each), the mean and standard deviation of the distance between the locations of maximum CD value and the corresponding PSs were 16.9 mm and 4.6 mm, respectively. In comparison, the averaged distance between the SMD locations and the corresponding PSs was slightly larger (18.4 ± 3.4 mm). The obtained CD distribution of activated sources extending from the stimulus site also showed high consistency with the endocardial potential maps estimated by a minimally invasive endocardial mapping system. The present experimental results suggest that the CD method is able to locate the approximate site of the origin of a cardiac ectopic activity, and that the distribution of the CD can portray the propagation of early activation of an ectopic beat.

High-resolution electroencephalogram (EEG) mapping: scalp charge layer

The neural electrical signal related to the human brain function is one of the tracks to understanding ourselves. Various electroencephalogram imaging techniques have been developed to reveal spatial information on neural activities in the brain from scalp recordings, such as Laplacian, equivalent source layer and potential. Physically, these methods may be classified into two categories: scalp surface or cortical surface based techniques. In this work, the focus is on the scalp surface based equivalent charge layer (ECL), with a comparison to the scalp potential with different references and scalp Laplacian (SL). The contents include theoretical analysis and numeric evaluation of simulated data and real alpha (8-12 Hz) data. The results confirm the fact that SL and ECL are of higher spatial resolution than various scalp potential maps, and for SL and ECL, SL is of higher resolution but more sensitive to noise.

Equivalent physical models and formulation of equivalent source layer in high-resolution EEG imaging

In high-resolution EEG imaging, both equivalent dipole layer (EDL) and equivalent charge layer (ECL) assumed to be located just above the cortical surface have been proposed as high-resolution imaging modalities or as intermediate steps to estimate the epicortical potential. Presented here are the equivalent physical models of these two equivalent source layers (ESL) which show that the strength of EDL is proportional to the surface potential of the layer when the outside of the layer is filled with an insulator, and that the strength of ECL is the normal current of the layer when the outside is filled with a perfect conductor. Based on these equivalent physical models, closed solutions of ECL and EDL corresponding to a dipole enclosed by a spherical layer are given. These results provide the theoretical basis of ESL applications in high-resolution EEG mapping.

Body surface Laplacian mapping of atrial depolarization in healthy human subjects

In the present study, we report body surface Laplacian mapping of atrial depolarization under sinus rhythm in 8 healthy male subjects. For each subject, 95 unipolar disk electrodes with inter-electrode distance of 2 cm were used to record simultaneously potential ECGs over the anterior chest. The Laplacian ECG was then estimated during the P wave using a novel spline Laplacian technique. The body surface potential map (BSPM) and body surface Laplacian map (BSLM) at different time instants or time intervals of the P wave were constructed and compared. The present results showed that the BSPMs during the P wave were characterized by the rotation of a pair of positive/negative potential distribution from right to left around the anterior torso. On the other hand, the corresponding BSLMs revealed more spatial details, including two positive activities (denoted as P1 and P2, appeared in all 8 subjects), and three negative activities (denoted as N1, N2, and N3, appeared in 7, 7, and 4 subjects, respectively). The separation of these activities and their evolving patterns were also compared and confirmed by computer simulation using a realistic geometry heart-torso model. The above findings may be directly related to the underlying activation sequence during atrial depolarization in healthy subjects, suggesting the potential clinical applications of the Laplacian ECG technique.

An equivalent current source model and laplacian weighted minimum norm current estimates of brain electrical activity

We have developed a method for estimating the three-dimensional distribution of equivalent current sources inside the brain from scalp potentials. Laplacian weighted minimum norm algorithm has been used in the present study to estimate the inverse solutions. A three-concentric-sphere inhomogeneous head model was used to represent the head volume conductor. A closed-form solution of the electrical potential over the scalp and inside the brain due to a point current source was developed for the three-concentric-sphere inhomogeneous head model. Computer simulation studies were conducted to validate the proposed equivalent current source imaging. Assuming source configurations as either multiple dipoles or point current sources/sinks, in computer simulations we used our method to reconstruct these sources, and compared with the equivalent dipole source imaging. Human experimental studies were also conducted and the equivalent current source imaging was performed on the visual evoked potential data. These results highlight the advantages of the equivalent current source imaging and suggest that it may become an alternative approach to imaging spatially distributed current sources-sinks in the brain and other organ systems.

Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging

Various approaches to the solution to the inverse problem of electrocardiography have been proposed over the years. Recently, the use of inverse algorithms using measured body surface Laplacians has been proposed, and in various studies this technique has been shown to outperform the traditional use of body surface potentials in certain model problems. In this paper, we compare the use of body surface potentials and body surface Laplacians on two model problems with different assumed cardiac sources. For the spherical cap model problems with an anterior source, the epicardial estimates using body surface potentials had smaller average relative errors than when body surface Laplacians were used. For the spherical cap model problems with a posterior source, the epicardial estimates using body surface potential or body surface Laplacian sensors generally produced similar relative errors. For the radial dipole model, the epicardial estimates using body surface Laplacians had smaller errors than when body surface potentials were used. We introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.

On the algorithm for computing body surface Laplacians in an inhomogeneous volume conductor of arbitrary shape

In this short communication, a corrected version of algorithm for calculating the body surface Laplacian (BSL) in an inhomogeneous volume conductor of arbitrary shape is described. The present computer simulation results show that the corrected algorithm can give an accurate numerical solution. This algorithm was then applied to examine the effect of the lung inhomogeneity on the BSL's in a realistically shaped torso model. The simulation results show that the low-conductivity lungs have little effect on both topology and magnitudes of body surface Laplacian maps (BSLM's) for a single dipole source.

A bioelectric inverse imaging technique based on surface Laplacians

A new approach is proposed to solve bioelectric inverse problems by employing the surface Laplacian of the bioelectrical potential. A theoretical investigation was conducted to test the feasibility of epicardial inverse imaging of cardiac electrical activity. A two-sphere homogeneous volume conductor model, where the inner sphere represents the epicardium and the outer sphere the body surface, was used. Radial and tangential current dipoles were used to approximate localized wavefronts propagating from the endocardium to the epicardium, and ectopic myocardial activities. The epicardial potential distribution was reconstructed from the body surface Laplacians with the aid of the Tikhonov zero-order regularization technique, which then was compared with the results obtained from the body surface potentials using the same regularization scheme. The two inverse solutions were compared qualitatively via visual inspection of the reconstructed epicardial potential maps, and quantitatively by examining relative errors and correlation coefficients between the "true" and the reconstructed epicardial potentials. Both qualitative and quantitative results indicate that the surface Laplacians play a positive role in improving the ill-posed nature of the bioelectric inverse problem, which would enhance our capability of reconstructing important epicardial events such as extrema in the epicardial potential distribution. The present theoretical study suggests that the Laplacian-based inverse imaging technique may have important applications to epicardial inverse imaging and other bioelectric inverse imaging.

A comparison of volume conductor effects on body surface Laplacian and potential ECGS: a model study

The objective of this investigation is to study, using a computer model, the torso volume conductor effects on body surface potential electrograms and body surface Laplacian electrograms. A spherical volume conductor model was used to approximate the torso and the heart. Myocardial electrical events were approximated by two distributed dipole-layers representing activation wavefronts propagating from the endocardium to the epicardium. The present computer simulation results indicate that the body surface Laplacian maps provide enhanced performance over the body surface potential maps in resolving the configurations of two activation wavefronts over the anterior wall of the heart.