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We have previously proposed an inverse algorithm for fitting potentials due to an arbitrary bio-electrical source to a single equivalent moving dipole (SEMD) model. The algorithm achieves fast identification of the SEMD parameters by employing a SEMD model embedded in an infinite homogeneous volume conductor. However, this may lead to systematic error in the identification of the SEMD parameters. In this paper, we investigate the accuracy of the algorithm in a realistic anatomic geometry torso model (forward problem). Specifically, we investigate the effect of measurement noise, dipole position and electrode configuration in the accuracy of the algorithm. The boundary element method was used to calculate the forward potential distribution at multiple electrode positions on the body surface due to a point dipole in the heart. We have found that the position and not the number of electrodes as well as the site of the origin of the arrhythmia in the heart have a significant effect on the accuracy of the inverse algorithm, while the measurement noise does not. Finally, we have shown that the inverse algorithm preserves the topology of the source distribution in the heart, thus potentially allowing the cardiac electrophysiologist to efficiently and accurately guide the tip of the catheter to the ablation site.

The conductivity of the human skull was measured both in vitro and in vivo. The in vitro measurement was performed on a sample of fresh skull placed within a saline environment. For the in vivo measurement a small current was passed through the head by means of two electrodes placed on the scalp. The potential distribution thus generated on the scalp was measured in two subjects for two locations of the current injecting electrodes. Both methods revealed a skull conductivity of about 0.015 [symbol: see text]/m. For the conductivities of the brain, the skull and the scalp a ratio of 1:1/15:1 was found. This is consistent with some of the reports on conductivities found in the literature, but differs considerably from the ratio 1:1/80:1 commonly used in neural source localization. An explanation is provided for this discrepancy, indicating that the correct ratio is 1:1/15:1.

The problem of obtaining the retinal source distribution that generates the electroretinogram (ERG) from measured skin potentials is addressed. A realistic three-dimensional (3-D) volume conductor model of the head is constructed from magnetic resonance image (MRI) data sets. The skin potential distribution generated in this model by a dipole layer source at the retina is computed by using the boundary element method (BEM). The influence of the various compartments of the complete model on the results was investigated, and a simplified model was defined. An inverse procedure for estimating the source distribution at the retina from ERG's obtained from skin electrodes was developed. The procedure was tested on simulated potentials. A fair correspondence between the original and estimated source distribution was found. Furthermore, the ERG's measured at seven skin electrodes were used to estimate the source distribution at the retina. The ERG potential waveform at an additional skin electrode was computed from this source distribution and compared to the measured potential at this electrode. Again a fair correspondence was obtained. It is concluded that the methods may become a useful tool for clinical applications, i.e., for the assessment of localized defects in retinal function.

The use of the surface Laplacian of the potential (Ls) in bioelectricity is discussed. Different estimates of Ls, in particular the field measured by coaxial electrodes, are compared to that of the true Laplacian. A method to compute Ls on the surface of an inhomogeneous volume conductor of arbitrary shape resulting from assumed electrical sources in introduced. In two applications the sensitivity of the body surface Laplacian is carried to that of body surface potentials. This comparison is carried out for dipolar sources within the human brain as well as for distributed sources within the heart.

In this paper it is demonstrated that the use of a direct matrix inverse in the solution of the forward problem in volume conduction problems greatly facilitates the application of standard, nonlinear parameter estimation procedures for finding the strength as well as the location of current sources inside an inhomogeneous volume conductor of arbitrary shape from potential measurements at the outer surface (inverse procedure). This, in turn, facilitates the inclusion of a priori constraints. Where possible, the performance of the method is compared to that of the Gabor-Nelson method. Applications are in the fields of bioelectricity (e.g., electrocardiography and electroencephalography).