Theo C. Pilkington

The potential gradient field created by epicardial defibrillation electrodes in dogs.

Knowledge of the potential gradient field created by defibrillation electrodes is important for the understanding and improvement of defibrillation. To obtain this knowledge by direct measurements, potentials were recorded from 60 epicardial, eight septal, and 36 right ventricular transmural electrodes in six open-chest dogs while 1 to 2 V shocks were given through defibrillation electrodes on the right atrium and left ventricular apex (RA. V) and on the right and left ventricles (RV .LV). The potential gradient field across the ventricles was calculated for these low voltages. Ventricular fibrillation was electrically induced, and ventricular activation patterns were recorded after delivering high-voltage shocks just below the defibrillation threshold. With the low-voltage shocks, the potential gradient field was very uneven, with the highest gradient near the epicardial defibrillation electrodes and the weakest gradient distant from the defibrillation electrodes for both RA. V and RV .LV combinations. The mean ratio of the highest to the lowest measured gradient over the entire ventricular epicardium was 19.4 +/- 8.1 SD for the RA. V combination and 14.4 +/- 3.4 for the RV .LV combination. For both defibrillation electrode combinations, the earliest sites of activation after unsuccessful shocks just below the defibrillation threshold were located in areas where the potential gradient was weak for the low-voltage shocks. We conclude that there is a markedly uneven distribution of potential gradients for epicardial defibrillation electrodes with most of the voltage drop occurring near the electrodes, the potential gradient field is significant because it determines where shocks fail to halt fibrillation, and determination of the potential gradient field should lead to the development of improved electrode locations for defibrillation.

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.

Optical measurements of transmembrane potential changes during electric field stimulation of ventricular cells.

We evaluated transmembrane potential changes at the ends of isolated rabbit ventricular myocytes during defibrillation-strength shocks given in the cellular refractory period. The myocytes were stimulated (S1 pulse) to produce an action potential. Then a constant-field shock (S2 pulse) with an electric field of 20 or 40 V/cm was given at an S1-S2 interval of 50 msec. The cells were stained with potentiometric dye (di-4-ANEPPS), and the cell end facing the S2 anode or cathode was illuminated with a laser while the fluorescence was recorded. During S2, the cell end facing the S2 cathode became more positive intracellularly, whereas the cell end facing the S2 anode became more negative intracellularly. The S2-induced transmembrane potential change at the cell end (delta Vm) was determined relative to the amplitude of the S1-induced action potential (APA) in each recording (i.e., delta Vm/APA). In Tyrodes solution containing 4.5 mM potassium, delta Vm/APA for 40-V/cm S2 was 1.36 +/- 0.34 at the cell end facing the S2 cathode and -1.65 +/- 0.61 at the cell end facing the S2 anode (n = 9). For the 20-V/cm S2, delta Vm/APA was 0.61 +/- 0.33 at the cell end facing the S2 cathode and -0.71 +/- 0.33 at the cell end facing the S2 anode (n = 6). The delta Vm/APA was not significantly influenced by 20 mM diacetyl monoxime. These results indicate that large delta Vm values occurred at the ends of the cells during S2. The calculated values of delta Vm, assuming a nominal APA of 130 mV, were 177 and -214 mV for the 40-V/cm S2 and 79 and -93 mV for the 20-V/cm S2. The delta Vm was correlated with cell size (r > or = 0.95) and agreed with values predicted by the S2 electric field strength multiplied by half of the cell length to within 27%. When the potassium concentration was increased to 20 mM, delta Vm/APA for 40 V/cm S2 increased 85% and 67% at the cell ends facing the S2 cathode and anode, respectively (n = 9, p < 0.005 versus 4.5 mM potassium), consistent with reduced APA. Thus, with normal or elevated extracellular potassium, transmembrane potential changes at the ends of cells during defibrillation-type stimulation are large enough to produce activation or recovery of voltage-dependent ion channels and may produce the effects responsible for defibrillation.

Periodic Conductivity as a Mechanism for Cardiac Stimulation and Defibrillation

This study examines the distribution of the transmembrane potential in the periodic strand of cardiac muscle established by configurations of sources similar to those arising during extracellular stimulation and defibrillation, during intracellular stimulation, and during propagation of action potential. The closed-form solution indicates that during extracellular stimulation with large current and during defibrillation, the periodic component of the transmembrane potential is very important. We postulate that this periodic component causes the depolarization or defibrillation in cardiac muscle, which is different from the depolarization mechanism for a continuous fiber. On the other hand, during propagation and intracellular stimulation, the periodic component only slightly modifies the monotonic decrease of the transmembrane potential, which suggests that the mechanism of propagation in discrete structures may be similar to that of the continuous fiber.

The Effects of Thoracic Inhomogeneities on the Relationship Between Epicardial and Torso Potentials

This study examines the effects of the lungs, spine, sternum, and the anisotropic skeletal muscle layer on the relationship between torso and epicardial potentials. Boundary integral equations representing potentials on the epicardial surface, the torso surface, and the internal conductivity interfaces were solved yielding a set of transfer coefficients valid for any source inside the epicardium and for any conductivity configuration outside the epicardial surface. These transfer coefficients relate potentials on the torso to potentials on the epicardial surface. Calculated torso potentials are generated via the transfer coefficients and measured epicardial potentials for comparison to measured torso potentials. This comparison indicates whether including the thoracic inhomogeneities improves attainable accuracy in calculations relating torso potentials to epicardial potentials.

Unconstrained Inverse Electrocardiography: Epicardial Potentials

The inverse problem in electrocardiography is attacked via the development of a model appropriate for the computation of epicardial potentials from a knowledge of heart and torso geometry as well as surface potentials. The model takes the form of an integral equation of the first kind in which the kernel is interpreted as a Greens function. A theoretical investigation of system independence in the presence of error is developed, and two techniques for the theoretical consideration of system independence are examined. Application of these two techniques to concentric spherical systems indicates that spheres with ratios of inner-to-outer radii less than 0.5 contain less than twenty independent parameters in the presence of realistic noise levels. The number of independent parameters deteriorates rapidly as this ratio falls below 0.5. These results suggest that it is not feasible to determine epicardial potentials from torso potentials by using unconstrained solutions.

Potential distribution in three-dimensional periodic myocardium. II. Application to extracellular stimulation

For pt.I see ibid., vol.37, no.3, p.252-66 (1990). Modeling potential distribution in the myocardium treated as a periodic structure implies that activation from high-current stimulation with extracellular electrodes is caused by the spatially oscillating components of the transmembrane potential. This hypothesis is tested by comparing the results of the model with experimental data. The conductivity, fiber orientation, extent of the region, location of the pacing site, and stimulus strength determined from experiments are components of the model used to predict the distributions of potential, potential gradient, and transmembrane potential throughout the region. Assuming that a specific value of the transmembrane potential is necessary and sufficient to activate fully repolarized myocardium, the model provides an analytical relation between large-scale field parameters, such as gradient and current density, and small-scale parameters, such as transmembrane potential.<<ETX>>

A volume conductor model of the thorax for the study of defibrillation fields

The authors develop a physiologically realistic volume conductor model for calculating epicardial potentials during transthoracic stimulation. The objective of the study is to measure cardiac potentials during a transthoracic stimulus and compare the measurements to calculated epicardial potentials obtained from the model. The results for all four stimulus configurations (anterior-posterior, neck-waist, precordial, and right-left) on the torso consistently yield correlation coefficients of about 0.90 and RMS errors of 47% between calculated and measured epicardial potentials for a homogeneous torso. Incorporating the effects of the skeletal muscle layer improves the agreement, i.e., correlation coefficients increase to about 0.914 and RMS errors decrease to about 42%. At the same time, the lungs and heart have little influence on the agreement between measured and calculated epicardial potentials. The results of the study demonstrate the importance of the skeletal muscle layer in physiologically realistic volume conductor models.<<ETX>>

Relationship between Body Surface Potential and Ventricular Excitation in the Dog

The distribution of body surface potential was studied in normal dogs by time normalization of nonsimuitaneously recorded voltages from 200 thoracic electrocardiograms using a digital computer technique. In addition, ventricular excitation data were obtained in the same animals using Scher myo-cardial plunge electrodes. Subsequently, the external surface voltage distribution was correlated spatially and temporally with the process of ventricular activation. It was noted that “dipolar” and “nondipolar” surface voltage patterns were related to the configuration of the instantaneous activation distribution in the ventricles. The reproducibility of the data obtained from the body surface and within the ventricles, and the observed consistent correlations between these two events indicate that there is a predictable relationship between major “inside-outside” activities.

The Closed Forn Solution to the Periodic Core-Conductor Model Using Asymptotic Analysis

The distribution of the transmembrane potential along an infinite strand of cardiac cells generated by a point source under steady-state conditions has been calculated using the asymptotic analysis method. With the intracellular conductivity changing periodically in space, the problem can be treated as dependent upon two variables: the large scale variable x covering the whole strand, and the small scale variable y defined on the unit cell. The solution is given as a two-scale expansion in powers of the period length. Each term of the expansion can be determined by solving the differential equations derived by decomposing the original problem. These equations do not have to be solved simultaneously; moreover, the linearity of the problem allows the separation of the x and y dependence in the higher order terms. The series converges quickly, and for all practical purposes, the solution containing zero-, first-, and second-order terms has a negligible truncation error. The subsequent terms of the solution have the following physiological interpretation: The zero-order term is the solution to the classical core-conductor model obtained by the homogenization of the periodic model, the first-order term acts as the dipole sources located at junctions, and finally, the second-order term resembles the monopole sources arising at junctions.