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. It appears that with careful measurements from a well-designed set of electrodes one can obtain structural conductivities, separating intracellular from interstitial values, and longitudinal from transverse. Resting membrane resistance also can be obtained.

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. This paper concisely restates and extends the equations for calculation of transmembrane currents with the systematic inclusion of alternative cases, noting how they reduce to the standard forms. An important issue is how complex the calculation of membrane current has to be. Thus, the paper goes on to show criteria (based on the uniformity of resistance and the presence of stimulation) for deciding when membrane currents can be obtained with a relatively simple calculation with a single equation involving local variables versus with a more complex calculation involving the simultaneous solution of a (possibly large) set of equations.