Measurement of the conductivity of skull, temporarily removed during epilepsy surgery.

The conductivity of the human skull plays an important role in source localization of brain activity, because it is low as compared to other tissues in the head. The value usually taken for the conductivity of skull is questionable. In a carefully chosen procedure, in which sterility, a stable temperature, and relative humidity were guaranteed, we measured the (lumped, homogeneous) conductivity of the skull in five patients undergoing epilepsy surgery, using an extended four-point method. Twenty-eight current configurations were used, in each of which the potential due to an applied current was measured. A finite difference model, incorporating the geometry of the skull and the electrode locations, derived from CT data, was used to mimic the measurements. The conductivity values found were ranging from 32 mS/m to 80 mS/m, which is much higher than the values reported in other studies. Causes for these higher conductivity values are discussed.

Conversion of left ventricular endocardial positions from patient-independent co-ordinates into biplane fluoroscopic projections.

Electrocardiographic body surface mapping is used clinically to guide catheter ablation of cardiac arrhythmias by providing an estimate of the site of origin of an arrhythmia. The localisation methods used in our group produce results in left-ventricular cylinder co-ordinates (LVCCs), which are patient-independent but hard to interpret during catheterisation in the electrophysiology laboratory. It is preferable to provide these results as three-dimensional (3D) co-ordinates which can be presented as projections in the biplane fluoroscopic views that are used routinely to monitor the catheter position. Investigations were carried out into how well LVCCs can be converted into fluoroscopic projections with the limited anatomical data available in contemporary clinical practice. Endocardial surfaces from magnetic resonance imaging (MRI) scans of 24 healthy volunteers were used to create an appropriate model of the left-ventricular endocardial wall. Methods for estimation of model parameters from biplane fluoroscopic images were evaluated using simulated biplane data created from these surfaces. In addition, the conversion method was evaluated, using 107 catheter positions obtained from eight patients, by computing LVCCs from biplane fluoroscopic images and reconstructing the 3D positions using the model. The median 3D distance between reconstructed positions and measured positions was 4.3mm.

Geometrical aspects of the interindividual variability of multilead ECG recordings.

The electrocardiogram (ECG) as measured from healthy subjects shows a considerable interindividual variability. This variability is caused by geometrical as well as by physiological factors. In this study, the relative contribution of the geometrical factors is estimated. In addition a method aimed at correcting for these factors is described. First, a measure (RV) for quantifying the overall variability is presented, and for healthy individuals its value is estimated as 0.52. Next, based on a simulation study using the individual (heart-lung-torso) geometry of 25 subjects, the variability caused by geometrical factors is estimated as 0.40, indicating that in healthy subjects the RV for healthy individuals resulting from electrophysiology is of the order of 0.33. In an evaluation of the correction procedure, applied to realistic, simulated body surface potentials, it is shown that RV caused by geometrical factors can be reduced from 0.40 to 0.06. When applying the correction procedure to measured ECG data no reduction of the RV value could be demonstrated. These results indicate that the involved procedure of the inverse computation of a cardiac equivalent source, at the present time, is of insufficient quality to cash in on the substantial reduction of RV values from 0.52 down to 0.33 that might be obtainable.

Localization of implanted EEG electrodes in a virtual-reality environment.

In the planning of epilepsy surgery procedures, intracranial electrodes are implanted in a significant fraction of the patients. Accurate localization of the individual electrode contacts with respect to the brain cortex is imperative. Because the manual tracking of an EEG electrode in a CT scan in a slice-by-slice fashion is cumbersome and subjective, the goal of this study was to develop an easier and more accurate way to localize implanted EEG electrodes. In this paper, we present our solution in the form of a virtual-reality environment with interactive tools to assist the clinician with EEG localization. With the help of a high-quality and fast volume renderer, a view is created of the inside of the patient's skull to obtain an overview of the electrodes in relation to the cortical structures. Depth, grid, and reed electrodes are characterized semi-interactively using different methods. For depth electrodes, the contacts (which are not visible in the CT scan) are derived by measuring off the theoretical distance between the contact and the end of the electrode from the central axis produced by a three-dimensional (3D) line tracker. For grid electrodes, the contacts are visible in a CT, so the 3D view is merely used to find the contacts and to resolve the overlap of grids with other grids, tail wires, or bone ridges. For reed electrodes, the contacts, which are again not visible in this case, are calculated from a line model fitted to the positions of lead markers. After letting the user place artificial spheres on the lead markers and wire, a B-spline is fitted to the spheres' centers to estimate the positions of the contacts. The approach was evaluated by applying it to CT scans of seven patients. It appeared that the method is generally applicable (even crossing electrodes or electrodes with gaps were correctly characterized), and that the display via 3D views and slices is so good that manual placement of spheres performed as well as semi-automatic placement. From computer experiments, it appeared that the final localization error in the position of EEG contacts could be estimated to lie in the order of the dimensions of one voxel.

Geometrical factors affecting the interindividual variability of the ECG and the VCG.

Various measures for quantifying the interindividual variability of the electrocardiogram and the vectorcardiogram in healthy subjects are presented. An analysis of factors that may cause this variability is performed, in particular of the geometrical factors of body size, heart size, heart position, and orientation. The results indicate that the variations in the magnitude of the electrocardiogram as observed through leads placed on the anterior thorax are dominated by the solid angle at which the outline of ventricular mass is seen from points on the thorax. Heart size and body size as such play only a secondary role. The limited spatial sampling of the anterior thorax directly overlaying the heart causes the mean values of all measures of amplitudes in women to be lower than in men. The vectorcardiogram magnitude was found to be much less dependent on overall geometry and heart position, and, hence, also to be less dependent on gender.

The number of independent signals in body surface maps.

This paper reports on the number of independent signals in body surface maps measured using a variety of lead systems incorporating 32 up to 219 leads. The number of independent signals is estimated using the minimum description length. It is found that the number of independent signals in body surface maps is of the order of 10. For lead systems incorporating many leads the number of independent signals is only marginally larger than in lead systems incorporating fewer leads. A lead system incorporating 64 leads will suffice for most applications.

On selecting a body surface mapping procedure.

Throughout the world, various procedures related to body surface mapping have evolved. The large differences in these procedures make multicenter studies difficult. This paper discusses the problems involved in selecting the number of leads, lead placement, and map format. Methods are highlighted that have been developed for pooling of the data as obtained by different centers. Recommendations are included to newcomers in the field. (The work stems from an international study, the Noninvasive Evaluation of the Myocardium, a study group sponsored by the European Commission, which has as one of its objectives the standardization of body surface mapping procedures.)

Interindividual variability of multilead electrocardiographic recordings: influence of heart position.

The electrocardiogram (ECG) of normal, healthy subjects shows a large interindividual variability. Part of this variability is due to the heart position and orientation relative to the electrodes. In this report, the interindividual variability is quantified using the relative variability measure, computed as the averaged standard deviation in the ECGs, scaled by the average root mean square of the ECGs. The relative variability in the QRS complex is estimated as 0.52. The heart position and orientation relative to the lead positions is documented in 25 normal subjects. The long axis angle varies considerably among the subjects (27.1+/-8.8 degrees to the transversal plane and 38 degrees +/-5 degrees to the frontal plane). Moving the electrodes in the frontal plane to a position relative to a common reference point at the base of the heart (shift: 0.8+/-0.7 cm leftward and 2.4+/-2.3 cm downward) did not reduce the interindividual variability.

Multigrid solution of the potential field in modeling electrical nerve stimulation.

In this paper, multilevel techniques are introduced as a fast numerical method to compute 3-D potential field in nerve stimulation configurations. It is shown that with these techniques the computing time is reduced significantly compared to conventional methods. Consequently, these techniques greatly enhance the possibilities for parameter studies and electrode design. Following a general description of the model of nerve stimulation configurations, the basic principles of multilevel solvers for the numerical solution of partial differential equations are briefly summarized. Subsequently, some essential elements for successful application are discussed. Finally, results are presented for the potential field in a nerve bundle induced by tripolar stimulation with a cuff electrode surrounding part of the nerve.

Theoretical performance and clinical evaluation of transverse tripolar spinal cord stimulation.

A new type of spinal cord stimulation electrode, providing contact combinations with a transverse orientation, is presented. Electrodes were implanted in the cervical area (C4-C5) of two chronic pain patients and the stimulation results were subsequently simulated with a computer model consisting of a volume conductor model and active nerve fiber models. For various contact combinations a good match was obtained between the modeling results and the measurement data with respect to load resistance (less than 20% difference), perception thresholds (16% difference), asymmetry of paresthesia (significant correlation) and paresthesia distributions (weak correlation). The transversally oriented combinations provided the possibility to select either a preferential dorsal column stimulation, a preferential dorsal root stimulation or a mixed stimulation. The (a)symmetry of paresthesia could largely be affected in a predictable way by the selection of contact combinations as well. The transverse tripolar combination was shown to give a higher selectivity of paresthesia than monopolar and longitudinal dipolar combinations, at the cost of an increased current (more than twice).

Lead system transformation of body surface map data.

Multicenter application of body surface map data (multilead electrocardiographic [ECG] data) is hampered by the fact that the centers involved in body surface mapping use lead systems differing in lead placement as well as in the number of leads. In this study, the performance of two methods for converting multilead ECGs from one lead system to another is evaluated in their application to the major lead systems presently in use throughout the world. The first method is based on Laplacian interpolation, and the second method is derived from the correlations between the signals in an extensive lead system. Through analyzing the representation errors, it was found that, for lead systems incorporating over 60 leads, both methods work well, yielding errors comparable to interbeat differences in individuals. For lead systems incorporating fewer leads, the correlation method is to be preferred.

Lead system transformation for pooling of body surface map data: a surface Laplacian approach.

In this paper, a method is described to transform Body Surface Map (BSM) data from one lead system to that of another. This enables pooling of BSM data between different centres. The transformation tool is based upon Laplacian interpolation. It is evaluated by inspecting transformations from lead systems having few leads to one having many leads.