Adriaan van Oosterom

Model Studies with the Inversely Calculated lsochrones of Ventricular Depolarization

This paper describes experimental studies on the influence of inhomogeneities in the volume conductor, and model errors and measurement errors on the inversely calculated isochrones of ventricular depolarization. The results indicate that in the inverse problem the use of inhomogeneous models is essential, that knowledge of the exact heart geometry (shape and orientation) is important, and that signal error (noise) as encountered in normal ECG recordings is not critical. The number of (measurement) leads required is found to be on the order of 64.

Brain symmetry and topographic analysis of lateralized event-related potentials.

OBJECTIVE We investigated the influence of symmetry assumptions implicit in the derivation and the use of event-related lateralized potentials (ERLs), such as the lateralized readiness potential (LRP). We describe these assumptions and demonstrate several alternative computational methods. METHODS Using analytical methods and forward simulations, we computed the error in the ERL topography that results from deviations in symmetry between homologous brain areas. Based on analytical considerations we show that, for source analysis, the ERL derivation provides no benefits compared to a single subtraction of the two (left-lateralized and right-lateralized) conditions underlying the ERL. RESULTS Relative errors of 10% in the ERL topography are found if the location of an active region in one hemisphere differs by 10 mm from the symmetric location as compared to the other hemisphere A difference of 30 degrees in orientation results in a relative error of the ERL of 40%. Differences in source strength between hemispheres result in an ERL error that is half the size of the relative strength difference. CONCLUSIONS We estimate that, due to violations of the symmetry assumption underlying the ERL, errors in the ERL topography of 10-40% can be expected. Source analysis does not benefit from the ERL. In topographic mapping and source analysis, the double subtraction of the ERL should be approached with caution and the single subtraction of the ERPs of two lateralized conditions should be first analyzed whenever possible. We suggest that analyses based on the topography of the ERL should only be performed after the assumption of symmetry has been validated.

Data Reduction of Body Surface Potential Maps by Means of Orthogonal Expansions

The electrical activity of the heart is reflected at the body surface by a potential distnbution which continuously changes in time throughout the cardiac cycle. Sampled versions of the potential data can be considered either as vectors or as matrices. From this conception, two different methods for data reduction can be developed within the frame of the Karhunen-Loeve expansion: a one-step method which implies an expansion into one set of eigenvectors, and a two-step method implying an expansion into two sets of eigenvectors. The set of eigen-vectors for the one-step method and the two sets of eigenvectors (space and time) for the two-step method were derived from the recorded body surface potentials of 136 subjects, used for the representation of the data of this group of subjects (design set), and also applied to a group of 135 subjects (test set). The rms error of the representation using 36 eigenvectors following the one-step method was 47 AV for the design set and 73 AV for the test set. When the two-step method was applied using six eigenvectors in space and six eigenvectors in time (also having 36 coefficients), the error was found to-be 77 , uV for the design set and 80 , uV for the test set. It is concluded that the one-step method is to be preferred for the representation of body surface potential data within a given group.

Atrial Excitation Assuming Uniform Propagation

Introduction: We investigated the spread of the excitation wave over the atria following initiation in a given focus in an atrial model containing its overall geometry only, i.e., without atrial bundles.

The Dominant T Wave and Its Significance

Introduction: The shapes of the T waves as observed in different leads placed on the thorax are very similar. The dominant T wave is introduced as a means to characterize this general signal shape. Its relationship to the transmembrane potentials of cardiac myocytes is discussed.

The inverse problem of bioelectricity: an evaluation.

This invited paper presents a personal view on the current status of the solution to the inverse problem of bioelectricity. Its focus lies on applications in the field of electrocardiography. The topic discussed is also relevant in other medical domains, such as electroencephalography, electroneurography and electromyography. In such domains the methodology involved rests on the same basic principles of physics and electrophysiology as well as on the applied techniques of signal analysis and numerical analysis.This invited paper presents a personal view on the current status of the solution to the inverse problem of bioelectricity. Its focus lies on applications in the field of electrocardiography. The topic discussed is also relevant in other medical domains, such as electroencephalography, electroneurography and electromyography. In such domains the methodology involved rests on the same basic principles of physics and electrophysiology as well as on the applied techniques of signal analysis and numerical analysis.

The potential distribution generated by the fetal heart at the maternal abdomen

The pathways along which the electrical currents generated by the fetal heart are conducted to the surface of the maternal abdomen are not known. As a consequence, in recording the fetal electrocardiogram (FECG) it is hard to predict where electrodes should be placed in order to obtain an optimal signal. The amplitude of the FECG varies with gestation, and there is a large interindividual variability in the amplitude of the FECG and in the optimal recording site among subjects within the same gestational age. Attempts have been made to explain these phenomena in terms of volume conduction. In this research the complete potential distribution on the maternal abdomen is studied in connection with the geometrical configuration of the electrical source (fetal heart) and the volume conductor (surrounding tissues). For a small group of pregnant women the abdominal FECG is recorded simultaneously in 32 leads during a period of about one minute, once every two weeks from 20 weeks of gestation onwards. A spatial filtering technique which combines information of all 32 leads is used to provide a trigger of the fetal QRS complexes. Using this trigger, an average fetal complex is constructed for each lead by time coherent averaging, after subtraction of the maternal contribution. These average fetal complexes are combined to plot the complete potential distribution generated by the fetal heart at the maternal abdomen (fetal body surface map, FBSM) at any given time instant during the fetal cardiac cycle. At these recording sessions the geometry is carefully quantified by making transverse scans every 2 cm with a compound echo scanner. The contours of fetal head and body, the placenta and the uterus are manually drawn on hardcopies of the video display images. Real time echoscopy is used to support the identification of the geometry. The contours are fed into a computer using a graphics tablet. The three dimensional surfaces of fetus, placenta and uterus are separately represented by a triangulation of the respective contour lines. Figures 5 and 6 show an example of the triangulated representation of the recorded geometry. Figure 7 shows the average fetal complexes of an individual at 26 weeks of gestation, plotted at the site where they have been recorded.(ABSTRACT TRUNCATED AT 400 WORDS)

Closed-form analytical expressions for the potential fields generated by triangular monolayers with linearly distributed source strength

The solution of the mixed boundary value problem of potential theory involves the computation of the potential field generated by monolayer and double layer source distributions on surfaces at which boundary conditions are known. Closed-form analytical expressions have been described in the literature for the potential field generated by double layers having a linearly distributed strength over triangular source elements. This contribution presents the corresponding expression for the linearly distributed monolayer strength. The solution is shown to be valid for all observation points in space, including those on the interior, edges and vertices of the source triangle.The solution of the mixed boundary value problem of potential theory involves the computation of the potential field generated by monolayer and double layer source distributions on surfaces at which boundary conditions are known. Closed-form analytical expressions have been described in the literature for the potential field generated by double layers having a linearly distributed strength over triangular source elements. This contribution presents the corresponding expression for the linearly distributed monolayer strength. The solution is shown to be valid for all observation points in space, including those on the interior, edges and vertices of the source triangle.

Potential applications of the new ECGSIM

This contribution demonstrates some applications of the most recent release of ECGSIM, an interactive simulation program that enables the user to study the relationship between the electric current sources of the heart and the resulting electrocardiographic signals on the body surface as well as those on the surface of the heart. It aims to serve as an educational tool as well as a research tool. The examples are drawn from the topics discussed by the participants of the Magnetic Anatomic and eLectrical Technology meeting in Maastricht, the Netherlands (February 2011), reports of which are to be found in the current issue of the Journal of Electrocardiology. These examples include simulation of the atrial electrocardiogram, improved accessibility of endocardial source locations, and an explanation of ST elevations accompanying true TQ depressions.

The Forward Problem in Electroneurography II: Comparson of Models

We present a comparison of the various model descriptions of the evoked compound action potential (CAP) of a peripheral nerve as have appeared in literature. First, a survey is given of both theoretical and empirical model formulations, concentrating upon the different descriptions of SFAP variation among the active fibers. The relationships between the various model formulations are clarified and the involved assumptions are discussed. Then, using computer calculations of both single fiber and compound action potentials, the differences in signal characteristics as predicted by the different models are studied. It is concluded that the models show distinct differences in the predicted potentials, which are revealed more clearly in near-nerve recordings in pathological nerves. Apart from these differences, however, adequate interpretation of the fiber population-statistics and of volume conductor characteristics prove to be the most essential prerequisites in CAP analysis.