Field stimulation of 2-D sheets of excitable tissue.

This paper develops equations for the transmembrane potentials (Vm) that occur in two-dimensional (2-D) sheets of tissue in response to field stimulation from an electrode near but not on the surface of the tissue. Comparison of results with those for one dimension shows that an additional term is present in the 2-D equations that influences the evolution of Vm in the interval between the end of the stimulus and the active propagation that may follow. The results provide an analytical framework for understanding Vm in response to field stimulation in two dimensions, both during the tissue's critical linear phase and thereafter.

Electrode systems for measuring cardiac impedances using optical transmembrane potential sensors and interstitial electrodes--theoretical design.

The cardiac electrical substrate is a challenge to direct measurement of its properties. Optical technology together with the capability to fabricate small electrodes at close spacings opens new possibilities. Here, those possibilities are explored from a theoretical viewpoint.

Membrane current from transmembrane potentials in complex core-conductor models.

Core-conductor models, used to integrate the behavior of the longitudinal currents with the distributed voltages of electrically active tissue, have evolved for over a century. A critical step in the use of such models is the computation of membrane current from the set of distributed transmembrane potential values that exist at a given moment, where the potentials are obtained either experimentally or computationally. Over time, interest has developed in a number of substantial extensions of the original model to include such features as nonuniform spatial resistances, loop instead of linear structure, and multiple sites of extracellular stimulation.

Propagation in cardiac tissue adjacent to connective tissue: two-dimensional modeling studies.

The conditions for activation transmission across a region of extracellular space was demonstrated in two-dimensional preparations with results consistent with those previously seen in the one-dimensional fiber studies. In addition, one sees changes in action potential morphology which occur in the tissue nearest the connective-tissue border as well as changes in conduction velocity along the border. These results hinge on an adequate representation of the connective-tissue region achieved by careful implementation of the boundary conditions in the intracellular and interstitial spaces and the expansion of the connective-tissue discretization to a "double-tier network" description.

Statistical analysis of signals from an intracavitary probe in a diseased heart.

A model study introduces the use of statistical signal processing to analyse the signals from an intracavitary probe. A complete derivation is given for the detection of one type of arrhythmogenic substrate, myocardial infarctions (MIs). Both the use of statistical signal processing and the detection of VT substrates, as opposed to activation maps, are unique.

Computer model analysis of the relationship of ST-segment and ST-segment/heart rate slope response to the constituents of the ischemic injury source.

The objective of the study was to investigate a proposed linear relationship between the extent of myocardial ischemic injury and the ST-segment/heart rate (ST/HR) slope by computer simulation of the injury sources arising in exercise electrocardiographic (ECG) tests. The extent and location of the ischemic injury were simulated for both single- and multivessel coronary artery disease by use of an accurate source-volume conductor model which assumes a linear relationship between heart rate and extent of ischemia. The results indicated that in some cases the ST/HR slope in leads II, aVF, and especially V5 may be related to the extent of ischemia.

Threshold variability in fibers with field stimulation of excitable membranes.

The central focus of this report is the evolution of transmembrane potentials following initiation of a point-source field stimulus, particularly when the stimulus is short and the stimulating electrode is close to the fiber. The transmembrane voltage threshold in response to a point-source field stimulus was determined in a numerical model of a single unmyelinated fiber. Both nerve (Hodgkin-Huxley) and cardiac (Ebihara-Johnson [1]) models of the fiber membrane were evaluated.

Epicardial cardiac source-field behavior.

The accurate determination of the spatial distribution of cardiac electrophysiological state is essential for the mechanistic assessment of cardiac arrhythmias in both clinical and experimental cardiac electrophysiological laboratories. This paper describes three fundamental cardiac source-field relationships: 1) activation fields, 2) electrotonic fields, and 3) volume conductor fields. The three cases are described analytically and illustrated with experimentally obtained canine cardiac recordings that capitalize on a recently formulated technique for in vivo cardiac transmembrane current estimation.

Electric field stimulation of excitable tissue.

This paper examines the transmembrane voltage response of an unmyelinated fiber to a stimulating electric field from a point current source. For subthreshold conditions, analytic expressions for the transmembrane potential, vm, are developed that include the specific effects of fiber-source distance, h, and time from the onset of the stimulus, T. Suprathreshold effects are determined for two examples by extending the analytical results with a numerical model.

Significance of inwardly directed transmembrane current in determination of local myocardial electrical activation during ventricular fibrillation.

Ventricular fibrillation (VF) is the principle cardiac rhythm disorder responsible for sudden cardiac death in humans. The accurate determination of local cardiac activation during VF is essential for its mechanistic elucidation. This has been hampered by the rapidly changing and markedly heterogeneous electrophysiological nature of VF.

Spatial- and frequency-domain ring source models for the single-muscle fibre action potential.

In the paper, single-fibre models for the extracellular action potential are developed that will allow the potential to be evaluated at an arbitrary field point in the extracellular space. Fourier-domain models are restricted in that they evaluate potentials at equidistant points along a line parallel to the fibre axis. Consequently, they cannot easily evaluate the potential at the boundary nodes of a boundary-element electrode model.

Boundary element analysis of the directional sensitivity of the concentric EMG electrode.

Assessment of the motor unit architecture based on concentric electrode motor unit potentials requires a thorough understanding of the recording characteristics of the concentric EMG electrode. Previous simulation studies have attempted to include the effect of EMG electrodes on the recorded waveforms by uniformly averaging the tissue potential at the coordinates of one- or two-dimensional electrode models. By employing the boundary element method, this paper improves earlier models of the concentric EMG electrode by including an accurate geometric representation of the electrode, as well as the mutual electrical influence between the electrode surfaces.

In vivo estimation of cardiac transmembrane current.

The ionic currents that cross the myocardial membrane during cardiac activation have a corresponding return path in the extracellular space. The transmembrane current (Im) during activation of cardiac cells in situ has previously been envisioned only in mathematical models. We have developed a remarkably simple in vivo technique that incorporates an electrode array with cellular dimensions to continuously estimate the extracellular counterparts of cardiac Ims.

Active response of a one-dimensional cardiac model with gap junctions to extracellular stimulation.

To study the response of cardiac tissue to electrical stimulation, a one-dimensional model of cardiac tissue has been developed using linear core-conductor theory and the DiFrancesco-Noble model of Purkinje tissue. The cable lies in a restricted extracellular medium and includes a representation of the junctional resistances known to interconnect cardiac cells. Two electrode geometries are considered: (a) a semi-infinite cable with a monopolar electrode at the end of the cable and (b) a terminated cable with one electrode at each end of the cable.

Electrophysiological interaction through the interstitial space between adjacent unmyelinated parallel fibers.

The influence of interstitial or extracellular potentials on propagation usually has been ignored, often through assuming these potentials to be insignificantly different from zero, presumably because both measurements and calculations become much more complex when interstitial interactions are included. This study arose primarily from an interest in cardiac muscle, where it has been well established that substantial interstitial potentials occur in tightly packed structures, e.g.

The effect of cellular discontinuities on the transient subthreshold response of a one-dimensional cardiac model.

Previous studies have examined the influence of the gap-junction discontinuity on the steady-state response of a cardiac cable to electrical defibrillation. It is important to understand when steady-state conditions may be assumed. For this reason, the transient, subthreshold behavior of a discontinuous cardiac cable is examined in this study.

The transient subthreshold response of spherical and cylindrical cell models to extracellular stimulation.

The effect of extracellular stimulation on excitable tissue is evaluated using analytical models. Primary emphasis is placed on the determination of the rate of rise of the membrane potential in response to subthreshold stimulation. Three models are studied: 1) a spherical cell in a uniform electric field, 2) an infinite cylindrical fiber with a point source stimulus, and 3) a finite length cable with sealed ends and a stimulus electrode at each end.

The Brody effect revisited.

This paper reexamines the Brody effect, both in the far-field and in the near-field approximation. It stresses the fact that near an inhomogeneity the Brody factor is not a constant but a function of space. A full documentation of this function for realistic values of the inhomogeneity as relevant to electrocardiography is included.

One-dimensional model of cardiac defibrillation.

The response of a single strand of cardiac cells to a uniform defibrillatory shock assuming steady-state linear conditions is examined. It is argued that the effect of this current is quantitatively described by the induced transmembrane potential even under passive conditions. The characteristics of the single strand are those that would exist if the heart was a system of equivalent parallel pathways from apex to base.

Implications of macroscopic source strength on cardiac cellular activation models.

This paper compares several cellular-level models of cardiac activation according to the sources that are generated and their macroscopic fields. Since macroscopic field patterns and strengths are well documented, by comparing the models of cardiac activation, the more controversial microscopic processes can be evaluated. The results show that it is most likely that both macroscopic and microscopic activation of cardiac tissue are uniform processes, and in a direction that is transverse to the fiber axis.

The quantitative investigation of the binding process of calcium blocking drugs in a sinoatrial node.

Application of existing models of sinoatrial node pacemaker activity and of channel-drug interaction allow us to reproduce action potential changes as a result of the blocking effect of drugs. Two calcium antagonistic drugs, nifedipine and mesudipine, were investigated and as a result averaged rate constants of binding and unbinding were evaluated. The procedure applied which is based on experimental results and on computer simulations, can be used as an initial step for comparison of different drugs.