Roger C. Barr

The discontinuous nature of propagation in normal canine cardiac muscle. Evidence for recurrent discontinuities of intracellular resistance that affect the membrane currents.

When the propagation velocity of action potentials is modified by changing the internal resistance of a cell, cable theory predicts that the shape of the action potential upstroke should not change; changes in velocity associated with changes in the upstroke usually are attributed to changes in membrane properties. However, we observed, in normal cardiac muscle, that changes in the upstroke with velocity occur under conditions in which the membrane properties could not have changed. Propagation in atrial and ventricular muscle was studied, in which the velocity of propagation was different at different angles with respect to the cell orientation. Fast upstrokes were associated with low propagation velocities (in a direction transverse to the long cell axis) and slower upstrokes were associated with high propagation velocities (in the direction of the long cell axis). Such changes in the shape of depolarization can be accounted for by the discrete cellular nature of cardiac muscle. The recurrent discontinuities in intracellular resistance cause propagation to be discontinuous on a microscopic scale. The presence of discontinuities in intracellular resistance reverses the usual association of high velocity and high safety factor for propagation: propagation at a low velocity is actually more resistant to disturbances in membrane properties than is propagation at a higher velocity. This inverted relationship suggested that propagation could continue in a direction transverse to the long axis of the cells when block occurs in the longitudinal direction, with resultant reentrant propagation. Such prediction was confirmed in the study of the propagation of premature action potentials in atrial muscle. Circ Res 48: 39-54, 1981

Electrophysiological Effects of Remodeling Cardiac Gap Junctions and Cell Size Experimental and Model Studies of Normal Cardiac Growth

The increased incidence of arrhythmias in structural heart disease is accompanied by remodeling of the cellular distribution of gap junctions to a diffuse pattern like that of neonatal cardiomyocytes. Accordingly, it has become important to know how remodeling of gap junctions due to normal growth hypertrophy alters anisotropic propagation at a cellular level (V(max)) in relation to conduction velocities measured at a macroscopic level. To this end, morphological studies of gap junctions (connexin43) and in vitro electrical measurements were performed in neonatal and adult canine ventricular muscle. When cells enlarged, gap junctions shifted from the sides to the ends of ventricular myocytes. Electrically, normal growth produced different patterns of change at a macroscopic and microscopic level. Although the longitudinal and transverse conduction velocities were greater in adult than neonatal muscle, the anisotropic velocity ratios were the same. In the neonate, mean V(max) was not different during longitudinal (LP) and transverse (TP) propagation. However, growth hypertrophy produced a selective increase in mean TP V(max) (P<0.001), with no significant change in mean LP V(max). Two-dimensional neonatal and adult cellular computational models show that the observed increases in cell size and changes in the distribution of gap junctions are sufficient to account for the experimental results. Unexpectedly, the results show that cellular scaling (cell size) is as important (or more so) as changes in gap junction distribution in determining TP properties. As the cells enlarged, both mean TP V(max) and lateral cell-to-cell delay increased. V(max) increased because increases in cell-to-cell delay reduced the electric current flowing downstream up to the time of V(max), thus enhancing V(max). The results suggest that in pathological substrates that are arrhythmogenic, maintaining cell size during remodeling of gap junctions is important in sustaining a maximum rate of depolarization.

Ventricular intramural and epicardial potential distributions during ventricular activation and repolarization in the intact dog.

Ventricular intramural and epicardial potential distributions were measured during normal excitation and repolarization in intact dogs. Potential distributions were chosen because they can be unambiguously measured, are useful in understanding the shapes of wave forms at many specific sites, and provide a direct measure of repolarization. Unipolar wave forms were recorded from intramural and epicardial electrodes and converted into potential distributions. Well-known shapes of wave forms recorded at the inner and outer layers of the ventricles as well as peak-to-peak voltages were shown by the potential distributions to be determined primarily by superposition effects of distant excitation waves. These effects were most prominent before epicardial breakthrough and then receded during the last half of the QRS complex. However, the potential distributions became more complex as excitation waves merged, collided, and terminated. During terminal depolarization, there were scattered positive repolarization potentials intramurally. Normal repolarization was characterized by positive potentials over the ventricular epicardium while there were changes intramurally and on the atrium. Throughout the T wave, there was a predominant transmural unidirectional gradient with the inner wall being more negative than the outer wall. This finding confirms that the sequence of repolarization is from the epicardium to the endocardium with the middle layers having an intermediate time.

Selection of the Number and Positions of Measuring Locations for Electrocardiography

This paper considers how many and which locations on the body surface must be measured (by taking ECGs at these positions) to be able to determine consistently the total-body QRS surface-potential distribution as it varies in time. The answers to these questions have implications about the complexity of models of heart electrical activity in addition to their experimental value. An advantage of using the ability to compute the total-body potential distribution as a criterion of quality is that untestable assumptions about the nature of heart electrical activity are avoided. The accuracy of computed potential distributions with respect to corresponding experimental ones is specified by the mean-square difference between them. Acceptable maps had an average relative mean square error of less than 4 percent in the presence of about 1 percent noise, since inspection of the surface maps showed this to be the maximum error allowable for the same clinical or physiological interpretation of the surface maps analyzed.

Inverse calculation of QRS-T epicardial potentials from body surface potential distributions for normal and ectopic beats in the intact dog.

Inverse epicardial potential distributions were calculated from potential distributions measured from the body surface in 12 intact dogs, divided into six pairs. The calculation procedure made use of measurements from the initial dog of each pair, giving the geometric location of each epicardial and body surface electrode and the approximate variance of the epicardial potentials and of the body surface noise. The same calculation procedure subsequently was applied to the other dog of the pair. For all dogs, inverse solutions were calculated throughout QRS-T for several sequences of excitation and repolarization which were produced by stimulating singly and in pairs any of eight ventricular sites. All calculated inverse results were checked by detailed quantitative comparison to the corresponding measured epicardial potential distributions, which were obtained from chronically implanted epicardial electrodes. The root mean square (RMS) numerical differences between the inverse computed and the measured epicardial distributions were a substantial fraction of the RMS measured epicardial voltages, often 0.7 or more, and the correlation coefficients between measured and computed epicardial distributions were in the range 0.6-0.8. Nonetheless, the major epicardial electrical events of excitation and repolarization easily were seen in all of the inverse maps in the initial dogs of each pair, and with only slightly less clarity in the subsequent dogs. Events readily observed included the initial minimum around the stimulus site as excitation began, the movement of the zero contour line across the epicardium as excitation progressed, and the characteristic pattern of repolarization with a maximum near the stimulus site. The results demonstrated that specific physical features of epicardial potential distributions can be determined from body surface measurements and can be verified by comparison with direct epicardial measurements.

Determining Surface Potentials from Current Dipoles, with Application to Electrocardiography

This paper presents a method for determining the potentials over the surface of a three-dimensional volume due to internal current sources. The volume may be inhomogeneous and irregularly shaped. The method for determining the potentials uses N simultaneous equations which when solved produce the potentials at N different surface points. The N simultaneous equations are solved by an iterative technique on an IBM computer.

Extracellular Potentials Related to Intracellular Action Potentials in the Dog Purkinje System

Simultaneous extracellular and intracellular recordings of normal action potentials, action potentials initiated at a time when the membrane was partially depolarized (by premature beats or elevated extracellular potassium), and action potentials at reduced temperature were made for Purkinje strands from the left ventricle of the dog with a 50μ tungsten extracellur electrode and a special guarded intracellular microelectrode. The peak-to-peak amplitude of the extracellular wave form was proportional to the maximum rate of rise of the intracellular action potential, and the duration of the extracellular wave form was proportional of the duration of the upstroke of the intracellular potential. Wave forms of extracellular potentials were computed from the recorded intracellular potentials with an equation which included the effects of membrane currents away from the point of observation. The computed wave forms accurately reproduced the recorded extracellular wave forms in all cases, and the wave forms were not directly porportional to the second spatial derivative or the second temporal derivative of the intracellular potential. Extracellular potentials are shown to be directly related to the spatial distribution of the intracellular potential and as such are a sensitive index of propagation and a source of information of the kind previously thought to be obtainable only with an intracllular electrode.

Current flow patterns in two-dimensional anisotropic bisyncytia with normal and extreme conductivities.

Cardiac tissue has been shown to function as an electrical syncytium in both intracellular and extracellular (interstitial) domains. Available experimental evidence and qualitative intuition about the complex anatomical structure support the viewpoint that different (average) conductivities are characteristic of the direction along the fiber axis, as compared with the cross-fiber direction, in intracellular as well as extracellular space. This report analyzes two-dimensional anisotropic cardiac tissue and achieves integral equations for finding intracellular and extracellular potentials, longitudinal currents, and membrane currents directly from a given description of the transmembrane voltage. These mathematical results are used as a basis for a numerical model of realistic (though idealized) two-dimensional cardiac tissue. A computer simulation based on the numerical model was executed for conductivity patterns including nominally normal ventricular muscle conductivities and a pattern having the intra- or extracellular conductivity ratio along x, the reciprocal of that along y. The computed results are based on assuming a simple spatial distribution for Vm, usually a circular isochrone, to isolate the effects on currents and potentials of variations in conductivities without confounding propagation differences. The results are in contrast to the many reports that explicity or implicitly assume isotropic conductivity or equal conductivity ratios along x and y. Specifically, with reciprocal conductivities, most current flows in large loops encompassing several millimeters, but only in the resting (polarized) region of the tissue; further, a given current flow path often includes four or more rather than two transmembrane excursions. The nominally normal results showed local currents predominantly with only two transmembrane passages; however, a substantial part of the current flow patterns in two-dimensional anisotropic bisyncytia may have qualitative as well as quantitative properties entirely different from those of one-dimensional strands.

Spread of excitation from the atrium into thoracic veins in human beings and dogs

Abstract Atrial and thoracic vein mapping in patients showed that the earliest site of atrial activity ranged from a low to high position along the sulcus terminalis and that cardiac muscle extended for 2 to 4 cm into all of the thoracic veins except the inferior vena cava. To understand the epicardial wave forms, experiments were carried out in open and closed chest dogs. Atrial muscle extended superiorly into the superior vena cava of the dog to a far greater degree than it extended into this vessel in man. In some dogs, cardiac muscle in the azygous vein extended to the spine, and at this site the heart could be paced; no cardiac electrical activity occurred in the azygous vein of man. The shape of most wave forms (a rapid deflection superimposed on a prolonged negative curve) was due to a superposition of effect of a large excitation wave in the atrium and a smaller excitation wave in the thoracic veins. Ultrastructural studies revealed atrial muscle in the thoracic veins of the dog. The extension of cardiac muscle into the thoracic veins of human embryos was far greater than that found in children and adults. In a patient with a persistent left superior vena cava, cardiac excitation progressed far above the heart to the junction with the innominate vein, a position from which the heart could be paced. The results suggest that the Lewis theory of atrial flutter—that is, that the venae cavae present an obstacle around which excitation waves progress—is untenable since wave fronts propagate in the venous muscle in a manner that quickly renders the tissue refractory by the merging and collision of waves.

Effect of microscopic and macroscopic discontinuities on the response of cardiac tissue to defibrillating (stimulating) currents.

What transmembrane potentials are produced in cardiac tissue in response to the application of defibrillating (or stimulating) currents? Such transmembrane potentials are found here by means of an idealised one-dimensional model of cardiac tissue that incorporates intracellular and extracellular current flow paths and allows variable (intracellular) junction resistance. Markedly different transmembrane potentials were computed near the ends (compared with the centre) of 30- and 60-cell strands. With high junction resistance, periodic positive and negative transmembrane potentials occurred within each cell near the centre of the strand. The results in the aggregate paint a picture quite different from that of uniform depolarisation.