Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study

Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses

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

<div><p>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>I</i>_<i>Na</i> and a time-independent inwardly rectifying repolarization current <i>I</i>_<i>K</i>—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>I</i>_<i>Na</i>, a nonlinear rectifying repolarization current, and bidomain tissue with unequal anisotropy ratios.</p></div

Transmembrane potential for normal and elevated potassium.

<p><i>V_m</i> vs time at <i>x</i> = 0.35 cm and <i>y</i> = 0.1 cm for different <i>E_K</i> values (-83 mV normal red, and -69 mV elevated potassium blue).</p

SI curves for different nonlinearities but similar action potential durations.

<p><i>k_r</i> = 21.28 mV and <i>g_K</i> = 0.3 mS cm^-2 red, <i>k_r</i> = 40 mV and <i>g_K</i> = 0.06 mS cm^-2 purple, and <i>k_r</i> = ∞ and <i>g_K</i> = 0.016 mS cm^-2 black. The parameters were chosen so the action potential duration is approximately the same in each case. CM = cathode make (open circles), CB = cathode break (filled circles), AM = anode make (open squares), and AB = anode break (filled squares).</p

Parameters in the model.

<p>Parameters in the model.</p

Comparison of SI curves for different <i>E_K</i> values.

<p> Normal (<i>E_K</i> = -83 mV red) and elevated (<i>E_K</i> = -69 mV blue) extracellular potassium concentration. CM = cathode make (open circles), CB = cathode break (filled circles), AM = anode make (open squares), and AB = anode break (filled squares).</p

Anode make excitation.

<p>The transmembrane potential is shown as a function of <i>x</i> (horizontal, parallel to the fibers) and <i>y</i> (vertical, perpendicular to the fibers). The black rectangle is the electrode and the number in each frame is the time in ms. S₁-S₂ interval = 158 ms, S₂ stimulus = 640 mA/cm. These frames are taken from the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0171144#pone.0171144.s003" target="_blank">S3 Movie</a> (see supplementary files).</p

Failed anodal excitation for the linear case.

<p><i>k</i>_<i>r</i> = ∞ and <i>g</i>_<i>K</i> = 0.016 mS cm^-2 (linear). The transmembrane potential is shown as a function of <i>x</i> (horizontal, parallel to the fibers) and <i>y</i> (vertical, perpendicular to the fibers). The black rectangle is the electrode and the number in each frame is the time in ms. S₁-S₂ interval = 130 ms, S₂ stimulus = 750 mA/cm. These frames are taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0171144#pone.0171144.s007" target="_blank">S7 Movie</a> (see supplementary files).</p

The cathodal and anodal strength-interval curves for the parsimonious ionic model.

<p>Cathodal (blue) and anodal (red), with <i>k_r</i> = 21.28 mV, <i>g_K</i> = 0.3 mS cm^-2, and <i>E_K</i> = -83 mV. The simulations included as movies in the supplementary information are indicated by black open ovals.</p