A. Heringa

Solution Methods of Electrical Field Problems in Physiology

The forward problem in electrophysiology¿the computation of the potential distribution due to a known electrical source in a known volume conductor¿is discussed. Three methods of solution are considered: 1) the finite difference method 2) a discretized integral equation method 3) the analytic method.

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.

Calculated potential and electric field distributions around an active nerve fiber

Potential distributions around a model nerve fiber are computed by using analytical methods. The fiber is situated either in a homogeneous isotropic unbounded conductor or in a homogeneous isotropic cylinder. In the latter case the source is placed either centrically or eccentrically. The potential distributions are used to derive the precise electric field distribution. The results are presented in equipotential and field line maps. It is described how the inherent numerical problems in the calculations can be avoided. It is demonstrated that the boundaries of the volume conductor and the nature of the source (potential source, current source) can significantly influence the field, even at large distances from this source.

Limits of reproducibility of mitral pulsed Doppler spectra

The total intrinsic variability of pulsed Doppler spectra of mitral blood flow was evaluated in this study. Doppler examinations were performed in 10 normal volunteers (7 men, 3 women), ages 29 to 57 years (mean 41) with an interval period of 3 months. The recordings were made in the apical 4-chamber view, using a 2.25-MHz transducer. The sample was placed approximately 1 cm proximal (left atrium) and 1 cm distal (left ventricle) from the middle of the anulus of the mitral valve at the onset of diastole. Processing of the raw Doppler spectra was done in a way that avoided subjective manipulation by the investigators. Mitral peak velocities, accelerations and spectral widths were measured in early diastole and late diastole. From the parameters under investigation, maximal velocities showed the best reproducibility with a range of coefficients of variation of 9 to 13%. Peak acceleration in early diastole and spectral widths showed rather large coefficients of variation, ranging from 19 to 30 and 14 to 24%, respectively. Mitral pulsed Doppler spectra in the left atrium were more reproducible than in the left ventricle.

Body surface maps and the conventional 12-lead ECG compared by studying their performances in classification of old myocardial infarction

The performance of body surface potential maps and the 12-lead ECG in the detection of old myocardial infarction has been compared in a two-group (54 normals; 52 infarctions) classification procedure (linear discriminant analysis). Three methods for data reduction of body surface maps were compared: 1) time integration, 2) one-step reduction in eigenvectors and 3) two-step reduction in spatial and temporal eigenvectors. Features were taken from the reduction variables by a stepwise selection procedure. From 90% to 93% correct classifications could be obtained using three features from the map data over the initial 30 ms (Q interval) of the QRS wave for all three methods considered. Using the 100 ms (QRS) interval 86% correct classifications were obtained using method 1, and up to 90% and 87% for methods 2 and 3, respectively. In a further analysis the classification based on body surface maps was compared to the one based on the 12-lead ECG. The 12-lead ECG was treated as a restricted set of the body surface mapping leads, so the same methods of data reduction, feature extraction and classification could be applied to both sets of data. Applying method 1 (time integration) 89% correct classifications were obtained using data taken from the 30 ms interval of the 12-lead ECG and a subsequent reduction to three features. When using the 100 ms interval the result was 79% also using three features. The results of method 2 applied to the 12-lead ECG were 89% (30 ms interval, three features) and 78% (100 ms interval, three features).

The vibratory innocent heart murmur studied by echo-Doppler.

ABSTRACT. So‐called innocent heart murmurs are thought to be originated by a possible physiologic narrowing of the left ventricular outflow tract, accentuated by a higher contractibility of the myocardium in some children. The aim of our studies was to evaluate this theory with pulsed Doppler echocardiography in order to detect possible local bloodstream disturbances. In a study of 20 children, with or without a vibratory innocent heart murmur no statistical difference was found in either peak‐velocity, acceleration or width of the Doppler spectra, read out in an objective computed digital way. The hypothetic location of the origin of the vibratory innocent heart murmur in the lefl ventricular outflow tract has not yet been confirmed with Doppler echocardiography.

Comments on "Potentials Produced by Arbitrary Current Sources in an Infinite-and Finite-Length Circular Conducting Cylinder"

Recently in this TRANSACTIONS, a paper was published1, dealing with the electric potential problem in a circular conducting cylinder. The authors criticize the approach to the same problem as proposed by Okada in 1956. Obviously, an important motive for preparing the paper was the existence of contradictory results from different solution methods found in literature. We want to rehabilitate Okadas paper. We will point to the small error in Okadas paper. Correction of this error removes the confusing difference with other methods.