Survival versus collapse: Abrupt drop of excitability kills the traveling pulse, while gradual change results in adaptation

Excitable media show changes in their basic characteristics that reflect temporal changes in the environment. In the photosensitive Belousov-Zhabotinsky (BZ) reaction, excitability is decreased by illumination. We found that a traveling pulse failed to propagate when a certain level of light intensity was switched on abruptly, but the pulse continued propagating when the light intensity reached the same level gradually. We investigated the mechanism of adaptation of pulse propagation to the change in light intensity using two mathematical models, the Oregonator model (a specific model for the photosensitive BZ reaction), and the FitzHugh-Nagumo model (a generic model for excitable media). The appearance of a characteristic such as adaptation is shown to be a general feature for a traveling pulse in excitable media. © 2007 The American Physical Society

Conditions for Waveblock Due to Anisotropy in a Model of Human Ventricular Tissue.

Waveblock formation is the main cause of reentry. We have performed a comprehensive numerical modeling study of block formation due to anisotropy in Ten Tusscher and Panfilov (2006) ionic model for human ventricular tissue. We have examined the border between different areas of myocardial fiber alignment and have shown that blockage can occur for a wave traveling from a transverse fiber area to a longitudinal one. Such blockage occurs for reasonable values of the anisotropy ratio (AR): from 2.4 to 6.2 with respect to propagation velocities. This critical AR decreases by the suppression of INa and ICa, slightly decreases by the suppression of IKr and IKs, and substantially increases by the suppression of IK1. Hyperkalemia affects the block formation in a complex, biphasic way. We provide examples of reentry formation due to the studied effects and have concluded that the suppression of IK1 should be the most effective way to prevent waveblock at the areas of abrupt change in anisotropy

Formation of transient reentry (ectopic beats) at the border between areas with orthogonal fiber orientation.

<p>Two stimuli were applied 6 mm from the border with a delay of 500 ms. The AR is 2.0 and [<i>K</i>⁺]<i>o</i> is 10 mM. Size of the tissue: 6.4 cm x 3.2 cm.</p

The dependencies of the critical period of stimulation on the AR for normal cardiomyocytes (red line) and with various potassium currents suppressed.

<p>Inhibition of (a)—<i>I</i>_<i>Kr</i> and (b)—<i>I</i>_<i>Ks</i>. The vertical asymptotes to these plots correspond to the critical AR for a single travelling pulse.</p

Reentry formation at the border between areas with orthogonal fiber orientation, stabilized at the isotropic area.

<p>Two point stimuli were applied 6 mm from the border with a delay of 500 ms. The AR is 2.0 and [<i>K</i>⁺]<i>o</i> is 10 mM. Fiber alignment is shown in the left figure. Size of the tissue: 6.4 cm x 3.2 cm.</p

Schematic representation of the computational setup in 2D.

<p>The tissue is divided into two parts with an orthogonal fiber orientation. The boundary is shown by the yellow dashed line. In the left part, the fibers (represented by thin lines) are parallel to the boundary, and in the right part, the fibers are orthogonal to the boundary. Two propagating waves are schematically shown as greyscale images. When stimulation was applied to the left border, wave propagation was observed to be translationally symmetric along the y axis and could be studied in 1D simulations.</p

The dependencies of the critical period of stimulation on the AR for normal cardiomyocytes (red line) and with the inward rectifier potassium current <i>I</i>_<i>K</i>1 suppressed.

<p>The dependencies of the critical period of stimulation on the AR for normal cardiomyocytes (red line) and with the inward rectifier potassium current <i>I</i>_<i>K</i>1 suppressed.</p

Drift of the reentry.

<p>The same simulation as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0141832#pone.0141832.g008" target="_blank">Fig 8</a>. Size of the tissue: 25.6 cm x 3.2 cm.</p

The dependencies of the critical period of stimulation on the AR for normal cardiomyocytes (blue line), with the addition of various channel blockers.

<p>Inhibition of (a)—<i>I</i>_<i>Na</i>, (b)—<i>I</i>_<i>Ca</i>.</p

Conditions for waveblock formation in hyperkalemia.

<p>a) The dependence of the critical period of stimulation on the AR for various potassium concentrations outside of the cell [<i>K</i>⁺]_<i>o</i>. The blue line shows the critical period of stimulation under normal conditions ([<i>K</i>⁺]_<i>o</i> = 5.4 mM). b) The dependence of the critical AR on potassium concentration outside of the cell [<i>K</i>⁺]_<i>o</i> for various stimulation frequencies.</p