Electrical Pacing of Cardiac Tissue Including Potassium Inward Rectification

Accuracy of electromagnetic models to estimate cardiomyocyte membrane polarization

External electric fields (E) induce a spatially heterogeneous variation in the membrane potential (ΔV_m) of cardiomyocytes that, if sufficiently large, results in an action potential and contraction. Insights into the phenomenon of ΔV_m induction by E have been classically gained with electromagnetic models due to the lack of adequate experimental approaches. However, it is not clear yet how reliable these models are. To assess the accuracy of commonly used models, a reference 3D numerical model for cardiomyocytes (NMReal) was developed, consisting of the cell membrane shell reconstructed from rendered confocal microscopy images of freshly isolated ventricular myocytes. NMReal was used to estimate the E-induced maximum ΔV_m values (ΔV_max), which were compared with estimates from seven other electromagnetic models. Accurate ΔV_max estimates (average error < 2%) were obtained with a less complex 3D model (NM3D) based on the extruded 2D image of the cell longitudinal section. Acceptable ΔV_max estimates (average error < 5%) were obtained with the prolate spheroid analytical model (PSAM) when the angle of E incidence and the cell major axis was < 30°. In this case, PSAM, a much simpler model requiring only the measurement of the longitudinal and transversal cell dimensions, can be a suitable alternative for ΔV_max calculation. Graphical abstract (A) Confocal images of the cell were used to reconstruct the realistic geometry of cardiomyocytes (NMReal). (B) NMReal was used to estimate the maximum variation in the transmembrane potential (ΔV_max) induced by an external electric field (E) applied at different angles with respect to the cell major axis. Plus (anode) and minus (cathode) signs indicate electrode position (E direction is from minus to plus). (C) Relative error (vs. NMReal) of ΔV_max estimation with simplified electromagnetic models, presented in descending order of accuracy (left-to-right, top-to-bottom). NM2D: 2D numerical model based on the longitudinal cell image; NM3D: numerical model based on the z extrusion of NM2D; EAM, PSAM, and CAM: ellipsoidal, prolate spheroidal, and cylindrical analytical models, respectively; PNM and CNM: parallelepipedal and cylindrical numerical models, respectively.

Cardiac strength-interval curves calculated using a bidomain tissue with a parsimonious ionic current

The strength-interval curve plays a major role in understanding how cardiac tissue responds to an electrical stimulus. This complex behavior has been studied previously using the bidomain formulation incorporating the Beeler-Reuter and Luo-Rudy dynamic ionic current models. The complexity of these models renders the interpretation and extrapolation of simulation results problematic. Here we utilize a recently developed parsimonious ionic current model with only two currents—a sodium current that activates rapidly upon depolarization I_Na and a time-independent inwardly rectifying repolarization current I_K—which reproduces many experimentally measured action potential waveforms. Bidomain tissue simulations with this ionic current model reproduce the distinctive dip in the anodal (but not cathodal) strength-interval curve. Studying model variants elucidates the necessary and sufficient physiological conditions to predict the polarity dependent dip: a voltage and time dependent I_Na, a nonlinear rectifying repolarization current, and bidomain tissue with unequal anisotropy ratios.