Simulations of passive properties and action potential conduction in an idealized bullfrog atrial trabeculum

Mechanistically based mapping of human cardiac fibrillation

The mechanisms underpinning human cardiac fibrillation remain elusive. In his 1913 paper ‘On dynamic equilibrium in the heart’, Mines proposed that an activation wave front could propagate repeatedly in a circle, initiated by a stimulus in the vulnerable period. While the dynamics of activation and recovery are central to cardiac fibrillation, these physiological data are rarely used in clinical mapping. Fibrillation is a rapid irregular rhythm with spatiotemporal disorder resulting from two fundamental mechanisms – sources in preferred cardiac regions or spatially diffuse self‐sustaining activity, i.e. with no preferred source. On close inspection, however, this debate may also reflect mapping technique. Fibrillation is initiated from triggers by regional dispersion in repolarization, slow conduction and wavebreak, then sustained by non‐uniform interactions of these mechanisms. Notably, optical mapping of action potentials in atrial fibrillation (AF) show spiral wave sources (rotors) in nearly all studies including humans, while most traditional electrogram analyses of AF do not. Techniques may diverge in fibrillation because electrograms summate non‐coherent waves within an undefined field whereas optical maps define waves with a visually defined field. Also fibrillation operates at the limits of activation and recovery, which are well represented by action potentials while fibrillatory electrograms poorly represent repolarization. We conclude by suggesting areas for study that may be used, until such time as optical mapping is clinically feasible, to improve mechanistic understanding and therapy of human cardiac fibrillation.

A general approach to modeling conduction and concentration dynamics in excitable cells of concentric cylindrical geometry

This paper discusses mathematical approaches for modeling the propagation of the action potential and ion concentration dynamics in a general class of excitable cells and cell assemblies of concentric cylindrical geometry. Examples include myelinated and unmyelinated axons, single strands of interconnected cardiac cells and outer hair cells. A key feature in some of the cells is the presence of a small working volume such as the periaxonal space between the myelin sheath and the axon in the myelinated axon and the extracisternal space between the plasma membrane and the subsurface cisterna of the outer hair cell. Proper treatment of these cell types requires a modeling approach which can readily address these anatomical properties and the non-uniform biophysical properties of the concentric membranes and the ionic composition of the volumes between the membranes. An electrodiffusion approach is first developed in which the Nernst-Planck equation is used to characterize axial ion fluxes. It is then demonstrated that this "full" model can be stepwise reduced, eventually becoming equivalent to the standard cable equation formulation. This is done in a manner that permits direct comparisons between the full and simplified models by running simulations using a single parameter set. An intermediate approach where the contributions of the axial currents to ion concentration changes and the effect of varying ion concentrations on solution conductivities are ignored is derived and is found adequate in many cases. Two application examples are given: a "cardiac strand" model, for which the intermediate formulation is shown sufficient and a model of the myelinated axon, for which the full electrodiffusion formulation is clearly necessary. The latter finding is due to spatial inhomogeneities in the anatomy and distribution of ion channels and transporters in the myelinated axon and the restricted periaxonal space between the myelin sheath and the axon.

Multiple site optical recording of transmembrane voltage (MSORTV) in patterned growth heart cell cultures: assessing electrical behavior, with microsecond resolution, on a cellular and subcellular scale

We have applied multiple site optical recording of transmembrane voltage (MSORTV) to patterned growth cultures of heart cells to analyze the effect of geometry per se on impulse propagation in excitable tissue, with cellular and subcellular resolution. Extensive dye screening led to the choice of di-8-ANEPPS as the most suitable voltage-sensitive dye for this application; it is internalized slowly and permits optical recording with signal-to-noise ratios as high as 40:1 (measured peak-to-peak) and average fractional fluorescence changes of 15% per 100 mV. Using a x 100 objective and a fast data acquisition system, we could resolve impulse propagation on a microscopic scale (15 microns) with high temporal resolution (uncertainty of +/- 5 microseconds). We could observe the decrease in conduction velocity of an impulse propagating along a narrow cell strand as it enters a region of abrupt expansion, and we could explain this phenomenon in terms of the micro-architecture of the tissue. In contrast with the elongated and aligned cells forming the narrow strands, the cells forming the expansions were aligned at random and presented 2.5 times as many cell-to-cell appositions per unit length. If the decrease in conduction velocity results entirely from this increased number of cell-to-cell boundaries per unit length, the mean activation delay introduced by each boundary can be estimated to be 70 microseconds. Using this novel experimental system, we could also demonstrate the electrical coupling of fibroblasts and endotheloid cells to myocytes in culture.