Heart Vector Research Articles

Polarcardiography

Polar coordinates, rather than rectangular coordinates, are more appropriate to the study of the heart vector—hence the term polarcardiography. A display illustrating the value of polar coordinates is the spherocardiogram for which two simple criteria indicate infarction. The lead vector concept has permitted the derivation of a 12-lead electrocardiogram that resembles the conventional ECG yet has the xyz coordinates of the heart vector as its only input. The clinical validity of the resemblance was demonstrated by a comparison study in which the ECGs and their derived equivalents (ECGDs) were interpreted by the Telemed program—with results favorable to the ECGD. The ECGD has significant practical value because of the reduction of raw data to only the three signals, x, y, and z. This makes polarcardiography practical on a routine basis—which might not be the case if double electrode systems had to be used for xyz and ECG. The ECGD is also of value in exercise testing because of noise-reduction techniques that can be applied. The techniques described have been clinically implemented.

Comprehensive analysis of exertional ECG changes before and after oral propranolol

In 12 patients with symptomatic coronary heart disease and three normal persons, comprehensive analyses of the electrocardiographic changes associated with symptom-limited upright exercise are made by computer analysis of the electrocardiogram recorded using a Frank XYZ lead system. This analysis provided a display of the 12 lead ECG, vectorcardiogram, polarcardiogram, and spatial cardiogram and measurements of spatial magnitudes of heart vectors. The effect of 40 mg of oral propranolol was assessed by repeating the exercise protocol 60--90 min later. There is evidence that propranolol reduces the electrocardiographic features of myocardial ischemia. This reduction in myocardial ischemia correlates with reductions in pressure rate product and heart rate. The presence of infarct criteria with exercise is variable and not apparently influenced by propranolol.

The normal electrocardiogram of the conscious beagle dog

The relationships between sex, age, and bodyweight of animals and the parameters heart rate and durations of PQ-interval, QRS-complex, and QT-interval (leads I, II, III) were investigated in 432 male and female beagle dogs (Chbb: Beagle strain; age, 187–646 days; weight, 5.8–18.5 kg). The dogs, kept under standard conditions, were considered clinically healthy at the time of recording and were not treated with drugs or conditioned. The statistical methods applied consisted of: analyses of linear correlation, polynomial regression, and linear covariance. No dependence of heart rate and ECG parameters on sex, age, or weight was evident. The following ranges were observed: heart rate, 45–220 beats/min (mean, 112 beats/min); PQ-interval, 0.080–0.160 sec (mean, 0.107 sec); QRS-complex, 0.030–0.060 sec (mean, 0.042 sec); QT-interval, 0.140–0.240 sec (mean, 0.188 sec). The frequency distributions for heart rate and the ECG parameters were almost symmetrical. A negative correlation between heart rate and QT-interval was shown to be statistically significant and biologically useful. Upper and lower tolerance limits for the regression line for a given heart rate and the dependent QT-interval were determined. Furthermore, tolerance values were calculated for all mentioned ECG parameters including 95% of the population. A slight negative correlation also existed between heart rate and PQ-interval. No further correlations could be detected. Heart vectors (using the leads I, II, III, and aVR, aVL, aVF) were determined in 44 other beagles by means of a hexaaxial system. The values were between +30 and +90 with a mean of 58.3°. Physiological ECG variations can be observed in healthy untreated beagle dogs.

Clinical importance of directional statistics for electrocardiographic differentiation of smoking habits

Statistical methods for the analysis of directional data are of relatively recent origin and have not been generally applied in clinical investigations where they are appropriate. This study compares spherical means and standard deviations for directional polarcardiographic variables with the linear means and standard deviations of the same variables for a typical industrial cohort of male white collar workers. Normal subjects were classified by smoking status and by independent clinical evidence of the presence of CHD, and both directional and linear statistics are applied to compare the PCG variables in these groups. Directional statistics more accurately define the spherical means and variances of heart vectors and thereby permit more reliable differentiation of directions, or angles to aid diagnosis.

Measurement of the Human Magnetic Heart Vector

A unipositional lead system has been developed to record the human magnetic heart vector and to permit comparison with the electric heart vector recorded with a conventional Frank lead system. Recordings made in five normal subjects showed a remarkably consistent relation between the electric and magnetic heart vectors. However, the angle between electric heart vector R and T waves was markedly different from the magnetic heart vector R-T angle. In addition, recordings made in two patients with bundle branch block showed a different relation between the electric and magnetic heart vectors compared to normal subjects. These data support the hypothesis that magnetic measurements have a different sensitivity to some components of cardiac activation compared with body surface potential measurements.

Path and significance of heart vector migration during QRS and ST-T complexes of ectopic beats in isolated perfused rabbit hearts.

Path and significance of heart vector migration during QRS and ST-T complexes of ectopic beats in isolated perfused rabbit hearts.

A global display of the heart vector (spherocardiogram). Applicability of vector-and polarcardiographic infarct criteria

The spatial loop of the heart vector can be projected on the Aitoff projection of the globe. The complete information that is contained in the orthogonal leads in displayed on a single graph when the vector magnitudes are indicated by the diameter of circles drawn around the vector projection in short time intervals (spherocardiogram). Diagnostic vector- and polarcardiographic criteria were applied to the spherocardiograms of 68 survivors of inferior myocardial infarction and 30 healthy men. Sensitivity increased from 65% (standard 12-lead ECG) to 87% (VCG criteria) (P less than 0.001) to 94% (VCG and PCG criteria combined), with no false-positive diagnoses. The spherocardiogram can be obtained by use of an "intelligent plotter." In contrast to the vectorcardiogram (VCG) and the polarcardiogram (PCG), it permits the direct visual study of the spatial direction and the spatial magnitude of the heart vector and of their sequential changes during the heart cycle.

A new practical lead system for vector magnetocardiography

This letter describes a new lead system for vector magnetocardiography. Numerical calculations, electrolytic tank studies, and data from normal subjects show that the output of this lead system corresponds closely to the Magnetic Heart Vector described by Baule and McFee, gives good signal quality and is easy to use.

The multipolar content of the human electrocardiogram.

The previously limited dipole or vector concept in electrocardiography may now be extended to the multipole concept, and the extraction of otherwise lost surface reflections of myocardial electrical activity may now be obtained. The geometric form and orientation for each of the 15 components of a three-stage multipole located at the heart's center have been characterized. This permitted determination of the patterns of potential distribution on the chest resulting from the activation of each of the respective components. The 15 leads have been employed to determine dipolar-quadripolar-octapolar moment of instantaneous body surface potentials, first calculated from a 20-dipole model of ventricular depolarization and, second, actually recorded from normal human subjects. The new information in the quadripolar and octapolar leads appears related both to the anatomic displacement of the mean heart vector and to the estimate of opposed simultaneous electrical forces in the myocardium which ordinarily average or “cancel out” in conventional electrocardiographic and vectorcardiographic leads and thus go unreported. Octapolar strength was found to be greatest in mid-QRS in normal subjects but less than quadripolar in early and late QRS. The quadripolar strength remained approximately one-half that of the dipole or heart vector throughout the heart cycle.

A Study on Normal Polarcardiogram by Digital Computer Analysis

Methods using polar coordinates to display heart vector and their clinical usefulness have been reported by many investigators. In the present study, normal findings of polarcardograms, timerelated curves of sequential changes of spatial magnitudes and orientations of heart vector, were studied. Materials and Methods: Thirty healthy men ranging in age from 19 to 45 (average 25.2 years old) were included in this study. In all, simultaneous high-speed recording of the three scalar ECGs of Frank system were obtained by Mingograph Type 81 recorder (1, 000 mm per second and 1 mV=1 cm). These scalar ECGs were digitalized at each 0.002 second interval from the biginning to the end of QRS for the analysis of QRS wave and at each 0.91 second interval from the end of QRS to the end of T for the analysis of ST segment and T wave. About seventy digitalized measurements obtained by this method were used as input signals to the digital computer (Tosbac Type 3400) in order to calculate the instantaneous magnitudes, longitudes and latitudes of QRS wave, ST segment and T wave. The calculated values were printed out in numerical from and the sequential changes were plotted out in curves by automatic plotter. Three polar axes, namely the postero-anterior, infero-superior and right-left axes, were employed in this study. Time-related curves of the sequential changes of the electomotive forces of the heart expressed in polar coordinates were named as below following Dower, namely the spatial magnitude ECG (SM); the frontal, transverse and sagittal magnitude ECG (fm, tm and sm); the alpha-, beta- and gamma-longitude ECG (alpha-, beta- and gamma-long); postero-anterior, infero-superior and right-left latitude ECG (P-A, I-S and R-L lat).

Determination of the locus of the heart vector from body surface measurements: Model experiments

Based on the Gabor-Nelson equations a technique is described for measuring the location of the resultant heart dipole (locus-cardiogram). The technique uses three rows of eight electrodes, a head and a foot lead. Experiments with a male and a female human torso model showed good agreement between actual andmeasured dipole locations. The presence of intrathoracic electricla inhomogeneities shifts theapparetn locus of the dipole toward the highly conductive mass. The conductivity of the volume conductor and the dipole monent value do not introduce any error into the computed locus of the dipole. It is concluded that the technique is accurate and simple enough to be used for experimental and clinical observation.

Localization of heart vectors produced by epicardial burns and ectopic stimuli; validation of a dipole ranging method.

Location of the equivalent cardiac dipole has been estimated but not fully verified in several laboratories. To test the accuracy of such a procedure, injury vectors were produced in 14 isolated, perfused rabbit hearts by epicardial searing. Strongly dipolar excitation fronts were produced in 6 additional hearts by left ventricular pacing. Twenty computer-processed signals, derived from surface electrodes on a spherical electrolyte-filled tank containing the test preparation, were optimally fitted with a locatable cardiac dipole that accounted for over 99% of the root-mean-square surface potential. For the 14 burns (mean radius 5.0 mm), the S-T injury dipole was located 3.4 plus or minus 0.7 (SD) mm from the burn center. For the 6 paced hearts, the dipole early in the ectopic beat was located 3.7 mm (range 2.6 to 4.6 mm) from the stimulating electrode. Phase inhomogeneities within the chamber appeared to have a small but predictable effect on dipole site determination. The study demonstrates that equivalent dipole location can be determined with acceptable accuracy from potential measurements of the external cardiac field.

Some parameters associated with the normal atrial electrocardiogram

Summary o 1. Corrected axial system orthogonal leads and leads aV L , II, V 1 , and V 2 were collected for 106 normal subjects. The atrial portions were subjected to digitized signal processing to reduce noise. 2. The relationships between the scalar leads and the orthogonal leads were explored, using linear prediction methods. Linear prediction of the scalar leads left little residual error when each subject was fitted individually. However, large residuals were present when the subjects were fitted as a group. 3. Templates for the normal time-course of spatial magnitude, heart vector direction and scalar lead voltage were calculated, and their potential applications discussed. 4. The interrelations between various parameters associated with deviation of the atrial electrocardiogram from central values and their possible physical significance were explored using the techniques of factor analysis. The purpose of this paper is to provide information on the atrial electrocardiogram. Specifically the relationship between the orthogonal and scalar leads will be presented, as well as templates for the average time-course of the heart vector and scalar leads.

Optimal synthesis of the sixth frontal-plane lead from data of the other five leads

When one of the six frontal-plane leads is missing, there are still ten possible solutions for a heart vector in this plane. The missing lead can be optimally reconstructed by projecting the centroidal vector of these ten solutions on the missing-lead axis. Analytical expressions as well as a graphical method for such synthesized leads are presented in this paper.

Anatomical level of X and Z electrodes in the Frank VCG lead system

Summary In the Frank lead system, the electrodes used to derive the X and Z components are intended to be at the transverse level of the electrical center of ventricular depolarization. This level is defined functionally; anatomically, it varies from subject to subject. A three-step technique to determine the level for X- and Z-lead electrodes was devised by Frank, and both fourth and fifth intercostal spaces have been recommended for routine use. o 1. Application of the Frank technique in 13 infants indicated a level in only one case. 2. Evaluation of Frank's technique by computer simulation indicated that this technique is based on incorrect reasoning and only by chance indicates the correct level. 3. To avoid problems inherent in that method, a technique bassed on crosscorrelation analysis of Y and precordial leads was devised, and was validated by computer simulation. 4. Application of the Y-precordial technique in 44 healthy adult males indicated (a) widely diverse levels, below the fourth intercostal space in most subjects whether upright or supine, with relatively small beat-to-beat variation in the level; and (b) no consistent difference in relation to the supine or upright position. The findings indicate that, in most cases, the X- and Z-lead electrodes should be below the fourth intercostal space. In an appendix to his original description of a system of spatial vectorcardiography 1 , Frank described a simple method to determine the correct level for electrodes used to derive the X and Z components of the heart vector. This should be the anatomic level of the electrical center of ventricular depolarization. In routine practice this was taken to be the level of the fifth intercostal space at the sternal border 1 . However, Langner et al 2 , who used both the fourth and fifth interspeces in a comparative study of the Frank and three other orthogonal systems, reported similar findings with both interspaces in the majority of cases and, in supine subjects closer similarity when the fourth interspace was used. Since their report appeared, both the fourth and fifth interspace have been used. One of the design objectives of Frank's lead system was to locate the electrodes used to derive the X and Z components in such a way that they would be as insensitive as possible to Y components 1,3 . A small displacement of these electrodes may lead to sizable errors 1,4,5 . However, the anatomic site of this level is still in dispute 6 . The theoretical basis of this technique lies in the properties of the so-called image surface in the region corresponding to the precordium, the image surface being a geometrical representation of the relationship between the heart vector and lead voltage 7 . Since the lead voltage is the dot product of heart vector (H) and lead vector (L), this relationship can be expressed as: lead voltage=H-L=aX + bY + cZ, (I) where X, Y, and Z are the orthogonal components of the heart vector, and a, b, and c are the orthogonal components of the lead vector. If a, b and c are used as coordinates, they can be taken to represent the image of an anatomic point on the body surface in the so-called image space. All points on the body surface have their counterpart in image space, together forming the image surface.

Polarcardiographic study of hospital staff—Abnormalities found in smokers

Polarcardiograms, graphs of the polar coordinates of the heart vectors vs time, display information not otherwise apparent, thereby providing a more sensitive test of infarction. Applying the infarction criteria to hospital staff thought to be healthy showed a low prevalence of positive cases among the young adults but markedly increased prevalences among the older subjects; there was a significant correlation with age and smoking habits.

Research in electrocardiography and magnetocardiography

The mathematical, physical, and engineering aspects of electrocardiography and magnetocardiography are reviewed. A brief summary of relevant physiological and clinical information is also given. The aim of the article is to provide a general perspective for engineers new to the area who want to do research. A detailed discussion of difficulties encountered in determining the heart vector and the nondipolar properties of the heart's field is included. Stress is placed on the need for development of practical ECG and MCG systems for use in the clinic. A number of research problems of current interest are pointed out.

Heart vector magnitude. A simple recording system

The clinical application of spatial magnitude (SM) recording, using a specially constructed SM computer, is presented. The method allows routine recording of X, Y, Z and SM vectors and has been applied with success in 45 out of 50 patients. The failures have occurred in cases with atrial fibrillation or high heart rates.

The magnetic heart vector

Records of the magnetic field due to the heart can be obtained in a hospital environment without the use of a magnetically shielded room. It is possible to build a magnetocardiograph sensitive primarily to the tangential components of the heart's EMF's. This is in contrast to ECG's where the radial component is emphasized and usually masks any tangential components. Tangential EMF components lying in frontal planes cause current to circulate around the front-to-back (z) axis, and can be assigned a vector direction along this axis. Similarly, tangential EMF's in sagittal and horizontal planes can be associated with x and y directed vectors. The vector sum of these three components is the spatial “magnetic heart vector.” The magnetic heart vector is conceptually similar to, and can be displayed using the same techniques as, the “heart vector” of electrovectorcardiography but is of radically different interpretation. Ideal magnetocardiographic leads, analogous to ideal electrovectorcardiographic leads, are defined in terms of the lead fields produced. Our present magnetocardiograph, while not specifically designed to implement the ideas of this paper, does give evidence that there are some tangentially oriented EMF components in persons without heart disease, and often much larger tangential EMF's in persons with heart disease.

Temporospatial frequency distribution of P, QRS, and T in normal man and woman

A study of 455 normal individuals divided into four decades and both sexes is presented. The lead system employed is that of Frank. The data are presented as mean and two standard deviation values of the spherical coordinates describing the instantaneous heart vector of P, QRS, and T. Einthoven's angle α and its angle tilt with the frontal plane were selected to describe the heart direction. This set of spherical angles is just as simple to conceive as azimuth and elevation, but has the advantage of correlating with the traditional heart axis orientation. The method may be described as presenting the statistical range of the instantaneous spatial heart axis as a function of time. The areas of narrow scatter in this display correlate well with electrocardiographic experience. Characteristic differences between male and female subjects, particularly in the T wave pattern, are described. The limitations of this method are two-fold: (1) this study is based on the assumption that the cardiac generator can be represented by a single equivalent dipole, and (2) the statistical decision regions employed here are only a first approximation. The advantage, however, is that once statistical envelopes, as presented in this report, are available, this method can be performed by analogue or small digital computer techniques.