David B. Geselowitz

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

An Application of Electrocardiographic Lead Theory to Impedance Plethysmography

The change in mutual impedance ?Z resulting from a change ?g in the conductivity of a particular region of a volume conductor is shown to be given by ?Z = - ?g?Lt?·L? dv. L? and L? are the lead fields associated with the two ports used to measure ?Z. The integration is over the region where the conductivity has changed. The superscript t indicates that the lead field is to be evaluated following the change in conductivity. An example involving a spherical conductor is provided.

Simulation studies of the electrocardiogram. I. The normal heart.

A digital computer model is presented for the simulation of the body surface electrocardiogram (ECG) during ventricular activation and recovery. The ventricles of the heart are represented in detail by a three-dimensional array of approximately 4000 points which is subdivided into 23 regions. Excitation sequence and cellular action potential data taken from the literature are used to determine the spatial distribution of intracellular potentials at each instant of time during a simulated cardiac cycle. The moment of the single dipole representing each region is determined by summing the spatial gradient of the intracellular potential distribution throughout the region. The resulting set of 23 dipoles is then used to calculate the potentials on the surface of a bounded homogeneous volume conductor with the shape of an adult male torso. Simulated isopotential surface maps during both activation and recovery are in good agreement with data for humans reported in the literature.

Recommendations for Standardization of Leads and of Specifications for Instruments in Electrocardiography and Vectorcardiography

By COMMITTEE MEMBERS: CHARLES E. KOSSMANN, M.D., CHAIRMAN, DANIEL A. BRODY, M.D., GEORGE E. BURCH, M.D., HANs H. HECHT, M.D., FRANKLIN D. JOHNSTON, M.D., CALVIN KAY, M.D., EUGENE LEPESCHKIN, M.D., HUBERT V. PIPBERGER, M.D., AND by MEMBERS OF THE SUBCOMMITTEE ON INSTRUMENTATION: * HUBERT V. PIPBERGER, M.D., CHAIRMAN, GERHARD BAULE, PH.D., ALAN S. BERSON, M.S., STANLEY A. BRILLER, M.D., DAVID B. GESELOWITZ, Ph.D., LEO G. HORAN, M.D., AND OTTO H. SCHMITT, Ph.D.

On Bioelectric Potentials in an Inhomogeneous Volume Conductor

Greens theorem is used to derive two sets of expressions for the quasi-static potential distribution in an inhomogeneous volume conductor. The current density in passive regions is assumed to be linearly related instantaneously to the electric field. Two equations are derived relating potentials to an arbitrary distribution of impressed currents. In one, surfaces of discontinuity in electrical conductivity are replaced by double layers and in the other, by surface charges. A multipole equivalent generator is defined and related both to the potential distribution on the outer surface of the volume conductor and to the current sources. An alternative result involves the electric field at the outer surface rather than the potential. Finally, the impressed currents are related to electrical activity at the membranes of active cells. The normal component of membrane current density is assumed to be equal at both membrane surfaces. One expression is obtained involving the potentials at the inner and outer surfaces of the membrane. A second expression involves the transmembrane potential and the normal component of membrane current.

A bidomain model for anisotropic cardiac muscle

Cardiac muscle is considered to consist of an intracellular domain and an exracellular or interstitial domain. Current passes from one domain to the other through the cell membrane. Electric potentials in interstitial space are shown to be associated with current sources proportional to the spatial gradient of the cellular transmembrane action potential, φm. Hence, given the distribution of φm throughout the myocardium, one can calculate the surface electrocardiogram and extracorporeal magnetocardiogram. The problem is considerably complicated when anisotropy is considered. If interstitial space is approximately isotropic, however, the sources are still proportional to ∇φm. It is shown that the effects of intracellular anisotropy on the surface electrocardiogram may be relatively small. The inverse problem is discussed briefly, with consideration of the relationship of the magnetocardiogram to the electrocardiogram. Finally, it is shown that if the heart can be considered to be bounded by a closed surface, then the value of φm on this surface is uniquely related to the surface electrocardiogram to within a constant, provided there are no internal discontinuities. Such discontinuities, however, would be expected to occur in cases of ischemia and necrosis.

Model Studies of the Magnetocardiogram

A general expression is developed for the quasi-static magnetic field outside an inhomogeneous nonmagnetic volume conductor containing internal electromotive forces. Multipole expansions for both the electric and magnetic fields are derived. It is shown that the external magnetic field vanishes under conditions of axial symmetry. The magnetic field for a dipole current source in a sphere is derived, and the effect of an eccentric spherical inhomogeneity is analyzed. Finally the magnetic dipole moment is calculated for a current dipole in a conducting prolate spheroid.

On the theory of the electrocardiogram

The biophysical basis for understanding the electrocardiogram is set forth. Bioelectric sources arise from electrical activity in the heart at the cellular level. The relation of these sources, which can be formally represented as impressed currents, to potentials involves solution of the volume conductor problem. This solution is based on Greens theorem. Sources are related to the transmembrane action potential through a bidomain model of heart muscle. Microscopic and macroscopic aspects of the bidomain model are developed. Various transformations of the source are considered, including multipoles, multiple dipoles, and replacement of the volume distribution with distributions on the heart surface. Time integrals of the waveform are related to excitation time and action potential duration. The theoretical results form the basis of a computer model of the electrocardiogram that relates skin potentials to the spatial and temporal distribution of action potentials in the heart. >

High-frequency components in the electrocardiograms of normal subjects and of patients with coronary heart disease.

Abstract Through the use of electronic and photographic equipment capable of recording a wide band of frequencies, from 0.01 to 5,000 cycles per second, it has been shown that subjects with clinical evidence of coronary heart disease have a much greater incidence of high-frequency notching and slurring in the electrocardiogram recorded with this high-fidelity equipment than do apparently normal subjects. The diagnostic possibilities of this method are discussed.

LDA Measurements of Mean Velocity and Reynolds Stress Fields Within an Artificial Heart Ventricle

Laser Doppler Anemometry measurements of mean (ensemble average) velocities and turbulent (Reynolds) stresses at 140 locations within the left ventricle of the Penn State 70 cc electric artificial heart/ventricular assist device are reported at 8 times during the cardiac cycle. Mean velocity patterns indicate that the surfaces of the blood sac and valve tracts are exposed to significant levels of wall shear stress (good wall washing) during some portion of the flow cycle, and there is no location where the flow is stagnant over the entire flow cycle. This implies that thrombus deposition within the artificial heart should be suppressed. Turbulent stresses in the main pumping chamber and the outflow tracts of the tilting disk valves do not exceed 2000 dynes/cm2. The highest turbulent stresses (20,000 dynes/cm2) and smallest turbulent microscales (6 microns) are found in the regurgitant jets on the minor orifice side of the aortic valve during diastole and the mitral valve during systole. Taken together, the data suggest that improvements in artificial heart fluid mechanics will come through valve design and pump operating conditions, not pumping chamber design.