A graphical method for understanding the relationship between spontaneous SAN activity and restitution.

<p>Simulated spontaneous APs are shown in <i>top</i> of each panel with schematic representation of corresponding restitution curve in <i>bottom</i>. The identity line may be superimposed on the restitution curve to create a return map for tracking CL dynamics in response to a perturbation (<i>arrows</i> demonstrate iterative response to perturbation from fixed point, defined as intersection of return map with identity line). (<b>A</b>) Regular periodic activity (control model) occurs when restitution slope is shallow (slope >−1). Perturbation from steady-state results in eventual return to stable fixed point. (<b>B</b>) 2:2 periodic behavior (APs correspond to control model with bias current  = 0.0274 mA/mF) results from a monophasic curve with a slope equal to the critical value of −1 (in this example, CL stably alternates between 306 ms and 283 ms). (<b>C</b>) Higher dimensional periodic activity (e.g. 4:4) and skipped beats may result from a multiphasic curve with regions of steep slope (<−1) (APs correspond to [Na⁺]_o = 63 mM), (<b>D</b>) irregular activity with long skipped beat runs may occur in instances where the CL restitution curve experiences an abrupt transition from a shallow region (slope<−1) to a very steep region (slope>>−1) (APs are shown for [Na⁺]_o = 100 mM, bias current  = 0.0077 µA/µF). Schematic curves and corresponding return map trajectory are shown as spontaneous activity progresses from time point <i>a</i> (onset of activity) to <i>b</i> (just before termination). In this case, dynamic changes in [Na⁺]_i may produce intermittent long skipped beat runs by shifting the curve and altering its slope.</p

Ionic mechanism for irregular SAN activity with long pauses.

<p>(<b>A</b>) Simulated spontaneous APs and (<b>B</b>) [Na⁺]_i from a single SAN cell subjected to low [Na⁺]_o (100 mM) and constant, low amplitude (0.0077 µA/µF) bias current stimulation. During AP firing, [Na⁺]_i rises until a threshold is reached (∼6.98 mM) at which point spontaneous activation terminates and [Na⁺]_i slowly falls until a second threshold is reached (∼5.91 mM) and the pattern repeats. Clamping [Na⁺]_i to the termination threshold (<i>red line</i> in <b>A</b> and <b>B</b>, clamp applied at time point labeled <i>b</i>) results in complete termination of activity, while clamping to the recovery threshold (<i>gray line</i>) eliminates the skipped beat runs resulting in regular periodic activity. (<b>C</b>) The CL restitution curve was determined for the model with low [Na⁺]_o and bias current stimulation just after onset of regular periodic activity (<i>black line</i>, determined at time point labeled <i>a</i> in panels <b>A</b> and <b>B</b>) or prior to onset of skipped beat run (red line, determined at point marked <i>b</i>). [Na⁺]_i was then reset to the low threshold value and restitution was determined again at the same time point (<i>gray line</i>). The restitution curve from the control model (normal [Na⁺]_o, no bias current) is shown for reference (<i>black line</i>). Dashed line denotes a slope of −1. [Na⁺]_i alters the slope of the restitution curve with much steeper slope at higher [Na⁺]_i.</p

Termination modes of spontaneous activity in a mathematical model of the mouse sinoatrial node cell.

<p>(<b>A</b>) Irregular activation and periodic skipped beat runs are apparent prior to termination as [Na⁺]_o is decreased stepwise from 70 mM to 58 mM. (<b>B</b>) In contrast, a gradual decline in regular activity occurs as <i>g_Kr</i> is decreased from 0.37 to 0.31 times its control value. (<b>C-E</b>) Representative spontaneous action potentials under (<b>C</b>) control conditions, and during stepwise decrease in (<b>D</b>) [Na⁺]_o and (<b>E</b>) <i>g_Kr</i> (corresponding time periods marked by <i>red bars</i> in panels <b>A</b> and <b>B</b>).</p

Termination of spontaneous activity in the one-dimensional fiber model.

<p>(<b>A</b>) [Na⁺]_o or (<b>B</b>) <i>g_Kr</i> was decreased in a stepwise fashion under normal coupling conditions (<i>black</i>) and with uniform gap junction uncoupling (twofold increase in gap junction resistance, <i>gray</i>) to reduce electrotonic loading of sinoatrial node cells. Termination of spontaneous activity occurs earlier in the fiber than in the single cell as [Na⁺]_o decreases, preceded by irregular activation and long runs (up to 20 sec) of skipped beats. Furthermore, uniform gap junctional uncoupling (<i>gray</i>) delays termination. In contrast, termination is delayed in the fiber relative to the single as <i>g_Kr</i> is decreased (gradual decline) and uncoupling accelerates termination.</p

Effect of bias current on cycle length dynamics.

<p>(<b>A</b>) Bias current threshold to induce irregular activity in control, <i>I_Kr</i> block (<i>g_Kr</i> = 0.35*control), or low [Na⁺]_o (100 mM). (<b>B</b>) CL restitution curves and (<b>C</b>) maximal slope for control, <i>I_Kr</i> block, and low [Na⁺]_o at baseline and during bias current injection.</p

The cycle length restitution curve.

<p>(<b>A–B</b>) Simulated spontaneous action potentials during a protocol to determine the cycle length restitution curve. A 10-ms stimulus is applied with varying amplitude at the maximum diastolic potential to accelerate or delay the subsequent spontaneous action potential. Time between 2^nd and 1^st APs following perturbation (CL₂) is then plotted as a function of time between 1^st perturbed and steady-state APs (CL₁). (<b>C</b>) CL restitution curves for control (<i>black</i>), low [Na⁺]_o (<i>red</i>) and <i>I_Kr</i> block (<i>gray</i>). Note that low [Na⁺]_o results in a curve with an abrupt transition from a relatively flat region to a very steep region (maximal slope >>−1 indicated by <i>arrow</i>; <i>dashed line</i> has slope of −1 for reference).</p

Video_6_Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study.MP4

<p>Computational studies using mathematical models of the sinoatrial node (SAN) cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, cardiac arrhythmias, and potential therapies. While the impact of ion channel dynamics on SAN pacemaking has been studied, the governing dynamics responsible for regulating spatial and temporal control of SAN synchrony remain elusive. Here, we attempt to develop methods to explore cohesion in a network of coupled spontaneously active SAN cells. We present the updated version of a previously published graphical user interface LongQt: a cross-platform, threaded application for advanced cardiac electrophysiology studies that does not require advanced programming skills. We incorporated additional features to the existing LongQt platform that allows users to (1) specify heterogeneous gap junction conductivity across a multicellular grid, and (2) set heterogeneous ion channel conductance across a multicellular grid. We developed two methods of characterizing the synchrony of SAN tissue based on alignment of activation in time and similarity of voltage peaks among clusters of functionally related cells. In pairs and two-dimensional grids of coupled cells, we observed a range of conductivities (0.00014–0.00033 1/Ω-cm) in which the tissue was more susceptible to developing asynchronous spontaneous pro-arrhythmic behavior (e.g., spiral wave formation). We performed parameter sensitivity analysis to determine the relative impact of ion channel conductances on cycle length (CL), diastolic and peak voltage, and synchrony measurements in isolated and coupled cell pairs. We also defined measurements of evaluating synchrony based on peak AP voltage and the rate of wave propagation. Cell-to-cell coupling had a non-linear effect on the relationship between ion channel conductances, AP properties, and synchrony measurements. Our simulations demonstrate that conductivity plays an important role in regulating synchronous firing of heterogeneous SAN tissue, and demonstrate how to evaluate the role of coupling and ion channel conductance in pairs and grids of SAN cells. We anticipate that the approach outlined here will facilitate identification of key cell- and tissue-level factors responsible for cardiac disease.</p

Video_5_Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study.MP4

<p>Computational studies using mathematical models of the sinoatrial node (SAN) cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, cardiac arrhythmias, and potential therapies. While the impact of ion channel dynamics on SAN pacemaking has been studied, the governing dynamics responsible for regulating spatial and temporal control of SAN synchrony remain elusive. Here, we attempt to develop methods to explore cohesion in a network of coupled spontaneously active SAN cells. We present the updated version of a previously published graphical user interface LongQt: a cross-platform, threaded application for advanced cardiac electrophysiology studies that does not require advanced programming skills. We incorporated additional features to the existing LongQt platform that allows users to (1) specify heterogeneous gap junction conductivity across a multicellular grid, and (2) set heterogeneous ion channel conductance across a multicellular grid. We developed two methods of characterizing the synchrony of SAN tissue based on alignment of activation in time and similarity of voltage peaks among clusters of functionally related cells. In pairs and two-dimensional grids of coupled cells, we observed a range of conductivities (0.00014–0.00033 1/Ω-cm) in which the tissue was more susceptible to developing asynchronous spontaneous pro-arrhythmic behavior (e.g., spiral wave formation). We performed parameter sensitivity analysis to determine the relative impact of ion channel conductances on cycle length (CL), diastolic and peak voltage, and synchrony measurements in isolated and coupled cell pairs. We also defined measurements of evaluating synchrony based on peak AP voltage and the rate of wave propagation. Cell-to-cell coupling had a non-linear effect on the relationship between ion channel conductances, AP properties, and synchrony measurements. Our simulations demonstrate that conductivity plays an important role in regulating synchronous firing of heterogeneous SAN tissue, and demonstrate how to evaluate the role of coupling and ion channel conductance in pairs and grids of SAN cells. We anticipate that the approach outlined here will facilitate identification of key cell- and tissue-level factors responsible for cardiac disease.</p

Video_3_Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study.MP4

<p>Computational studies using mathematical models of the sinoatrial node (SAN) cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, cardiac arrhythmias, and potential therapies. While the impact of ion channel dynamics on SAN pacemaking has been studied, the governing dynamics responsible for regulating spatial and temporal control of SAN synchrony remain elusive. Here, we attempt to develop methods to explore cohesion in a network of coupled spontaneously active SAN cells. We present the updated version of a previously published graphical user interface LongQt: a cross-platform, threaded application for advanced cardiac electrophysiology studies that does not require advanced programming skills. We incorporated additional features to the existing LongQt platform that allows users to (1) specify heterogeneous gap junction conductivity across a multicellular grid, and (2) set heterogeneous ion channel conductance across a multicellular grid. We developed two methods of characterizing the synchrony of SAN tissue based on alignment of activation in time and similarity of voltage peaks among clusters of functionally related cells. In pairs and two-dimensional grids of coupled cells, we observed a range of conductivities (0.00014–0.00033 1/Ω-cm) in which the tissue was more susceptible to developing asynchronous spontaneous pro-arrhythmic behavior (e.g., spiral wave formation). We performed parameter sensitivity analysis to determine the relative impact of ion channel conductances on cycle length (CL), diastolic and peak voltage, and synchrony measurements in isolated and coupled cell pairs. We also defined measurements of evaluating synchrony based on peak AP voltage and the rate of wave propagation. Cell-to-cell coupling had a non-linear effect on the relationship between ion channel conductances, AP properties, and synchrony measurements. Our simulations demonstrate that conductivity plays an important role in regulating synchronous firing of heterogeneous SAN tissue, and demonstrate how to evaluate the role of coupling and ion channel conductance in pairs and grids of SAN cells. We anticipate that the approach outlined here will facilitate identification of key cell- and tissue-level factors responsible for cardiac disease.</p

Video_1_Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study.MP4

<p>Computational studies using mathematical models of the sinoatrial node (SAN) cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, cardiac arrhythmias, and potential therapies. While the impact of ion channel dynamics on SAN pacemaking has been studied, the governing dynamics responsible for regulating spatial and temporal control of SAN synchrony remain elusive. Here, we attempt to develop methods to explore cohesion in a network of coupled spontaneously active SAN cells. We present the updated version of a previously published graphical user interface LongQt: a cross-platform, threaded application for advanced cardiac electrophysiology studies that does not require advanced programming skills. We incorporated additional features to the existing LongQt platform that allows users to (1) specify heterogeneous gap junction conductivity across a multicellular grid, and (2) set heterogeneous ion channel conductance across a multicellular grid. We developed two methods of characterizing the synchrony of SAN tissue based on alignment of activation in time and similarity of voltage peaks among clusters of functionally related cells. In pairs and two-dimensional grids of coupled cells, we observed a range of conductivities (0.00014–0.00033 1/Ω-cm) in which the tissue was more susceptible to developing asynchronous spontaneous pro-arrhythmic behavior (e.g., spiral wave formation). We performed parameter sensitivity analysis to determine the relative impact of ion channel conductances on cycle length (CL), diastolic and peak voltage, and synchrony measurements in isolated and coupled cell pairs. We also defined measurements of evaluating synchrony based on peak AP voltage and the rate of wave propagation. Cell-to-cell coupling had a non-linear effect on the relationship between ion channel conductances, AP properties, and synchrony measurements. Our simulations demonstrate that conductivity plays an important role in regulating synchronous firing of heterogeneous SAN tissue, and demonstrate how to evaluate the role of coupling and ion channel conductance in pairs and grids of SAN cells. We anticipate that the approach outlined here will facilitate identification of key cell- and tissue-level factors responsible for cardiac disease.</p