Exercise-induced QT/R-R-interval hysteresis as a predictor of myocardial ischemia

Abstract: Objectives: Exercise-induced QT/RR hysteresis exists when, for a given R-R interval, the QT interval duration is shorter during recovery after exercise than during exercise. We sought to assess the association between QT/RR hysteresis and imaging evidence of myocardial ischemia. Background: Because ischemia induces cellular disturbances known to decrease membrane action potential duration, we hypothesized a correlation between QT/RR and myocardial ischemia

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Larger stimulation current (<i>i</i>₀ = 800<i>μ</i>A/cm²) is used for a shorter time (<i>T</i>₀ = 50Δ<i>t</i>) in the middle of the cable.

<p>The modified stimulation protocol produces qualitatively similar results to those shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0122401#pone.0122401.g007" target="_blank">Fig. 7</a></p

Map in (<i>V</i>₀, <i>α</i>) space of resonant frequencies using typical parameters for Morris Lecar model.

<p>Regions colored in white correspond to points where no stable limit cycles exist in the absence of a stimulation current.</p

Vulnerable window in the modified Morris Lecar model depicted in phase space.

<p>The system’s limit-cycle trajectory for <i>α</i> = 1, <i>V</i>₀ = 6.2mV is shown (thin black line) with the vulnerable region indicated by a thick red line for varying values of <i>V</i>₀ with <i>α</i> = 1. Within the vulnerable window, a short stimulation takes the system from its stable limit cycle to a stable equilibrium point in phase space. The size of the vulnerable window increases as (<i>V</i>₀, <i>α</i>) approaches the Hopf bifurcation point.</p

Typical values for the Morris-Lecar model, Equations (7)–(8).

<p>Typical values for the Morris-Lecar model, Equations (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0122401#pone.0122401.e007" target="_blank">7</a>)–(<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0122401#pone.0122401.e008" target="_blank">8</a>).</p

Complex spatiotemporal pattern generated with increased stimulation time near the crossover between quiescent and synchronized steady-states.

<p>A fourth-order, five-point stencil was used for evaluation of the spatial derivative. Compare to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0122401#pone.0122401.g011" target="_blank">Fig. 11</a>.</p

Vulnerable window of the one-dimensional cable shown in phase space.

<p>The system’s limit-cycle trajectory for <i>α</i> = 1, <i>V</i>₀ = 6.4mV is shown (thin black line) with the vulnerable region indicated by a thick red line. Localized stimulations applied within this window result in a long-time quiescent state for the entire system. Regions of instability are shown in dashed blue line. For all other points (thin black line), localized stimulations only give rise to transient effects, and the entire cable eventually returns to synchronized oscillations.</p

Time series and phase space diagrams for modified Morris-Lecar model.

<p>Upper left: Single neuron (<i>α</i> = 0.7, <i>V</i>₀ = 6.2mV) firing once after stimulus is applied at <i>t</i> = 0ms and approaching a stable equilibrium. Upper right: Single neuron (<i>α</i> = 1 and <i>V</i>₀ = 6.2mV) entering a stable limit cycle after initial stimulus. Phase space trajectories for each case are shown in the panel below the corresponding time-series plot.</p

Long-time steady states for cables of varying lengths.

<p>Fixing all parameters except cable length generically yields a region of vulnerability in extended cables. For small (left) and large (right) cables, an initial stimulation sufficient to quiesce a single cell causes a transient quiescent region which results in full synchronization. For a range of cable lengths (center) the stimulation results in the entire cable approaching an equilibrium state.</p