Effect of AP morphology on BVR.

<p><b>A.</b> Overlay of 30 APs (top panel) and Poincaré plot of corresponding APDs (bottom panel) for the control myocyte, without alterations in ion currents, simulated with deterministic I_CaL, I_K1, I_Kur, and I_To and stochastic gating of the remaining 9 currents. APs with the shortest and longest duration are shown in black, others in grey. Average APD and STV are indicated below the APs. <b>B.</b> Similar to panel A for a triangular AP morphology obtained by reducing I_K1 and I_To (by 70% and 60%, respectively) and increasing I_Kur (by 275%). <b>C.</b> Similar to panels A and B for a square AP morphology obtained by increasing I_K1 and I_Kur (by 20% each) and decreasing I_CaL and I_To (by 75% and 20%), respectively.</p

Mechanisms underlying increased BVR under LQT1 conditions with SR Ca²⁺ overload.

<p><b>A.</b> STV vs. APD relationship under control (open symbols) or LQT1 conditions (filled symbols) in individual canine ventricular myocytes (left panel). Right panel shows the parameters of the non-linear fit of the STV vs. APD relationship under control or LQT1 conditions (solid and dashed lines in left panel, respectively), or under LQT2 conditions (from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003202#pcbi-1003202-g008" target="_blank"><b>Figure 8</b></a>). <b>B.</b> Consecutive APDs (top panel) and Ca²⁺-transient amplitudes (middle panel) during simulated application of 1.0 µmol/L isoproterenol (ISO) at a 500-ms CL in the deterministic model. Membrane potential and intracellular [Ca²⁺] for the beats indicated by the black vertical boxes are shown in the bottom panel. APD (in ms) is indicated below each beat and a Poincaré plot is shown on the right. Simulations were performed with 100% I_Ks inhibition to simulate LQT1 conditions and with 10% inhibition of I_NaK, resulting in increased [Na⁺]_i and reduced Ca²⁺ extrusion via I_NaCa, to promote Ca²⁺-handling abnormalities. <b>C.</b> Similar to panel B for the stochastic model with a single domain. <b>D.</b> Similar to panel B for the stochastic model divided into four identical domains connected via Ca²⁺-diffusion terms with time constant τ = 20 ms.</p

Contribution of channel density of stochastic ion currents to BVR and its rate dependence.

<p><b>A.</b> STV magnitude induced by stochastic channel gating of individual currents in an otherwise deterministic model or stochastic channel gating of all 13 currents/fluxes combined (right-most bars) at CL of 500 ms, 1000 ms, or 2000 ms. Top panel shows 5-fold reduction in channel density (with 5-fold increase in single-channel conductance), middle panel shows channel density based on estimates from experimental data (Section 2.5 in the Supplemental Information), and bottom panel shows 5-fold increase in channel density with reduced single-channel conductance. <b>B.</b> Rate dependence of average APD (left), STV (middle) and LTV (right) in experiments (symbols) and model (lines) with stochastic gating of all 13 targets combined at 100% channel density.</p

Role of APD in the observed increase in BVR under simulated LQT2 conditions.

<p><b>A.</b> Overlay of 30 consecutive APs in the model using control conditions, simulated LQT2, simulated LQT2 with deterministic I_Kr, or simulated LQT2 with reduced APD due to injection of a deterministic stimulus current. Shortest and longest APs are shown in black, intermediate APs in grey. APD, STV, and Poincaré plots are shown below each overlay. <b>B.</b> STV vs. APD relationship under control conditions (left panel) or LQT2 conditions (right panel) in individual canine ventricular myocytes (filled symbols) or individual model cells (open symbols; based on whole-cell conductances drawn from a Gaussian distribution, as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003202#pcbi-1003202-g003" target="_blank"><b>Figure 3A</b></a>). Data were fit with a monoexponential function (lines). <b>C.</b> Parameters of the monoexponential fits of panel B under control and LQT2 conditions in experiments (grey bars) and model (white bars). The model shows a quantitatively similar STV vs. APD relationship as experiments, and this relationship is not different between control and LQT2 conditions.</p

Role of APD and stochastic gating in BVR reverse rate dependence.

<p><b>A.</b> Magnitude of channel gating stochastics (assessed by Std(I_m) for 50 beats) over time for CL of 350–4000 ms using the fully stochastic model under control conditions. <b>B.</b> Rate dependence of total magnitude of I_m fluctuations (given by area under Std(I_m) curve). <b>C.</b> STV rate dependence in the fully stochastic model during fixed-CL pacing (solid line) or fixed-DI pacing (dash-dotted line), or in the deterministic model during fixed-CL pacing with a CL-independent stochastic term (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003202#s2" target="_blank">Results</a>, section “BVR rate dependence”) added to I_m (dashed line). CL-independent stochastic behavior results in a blunted STV rate dependence. <b>D.</b> STV vs. APD relationship at CLs of 500 ms (dark grey symbols), 1000 ms (white symbols), or 2000 ms (light grey symbols). APD was varied through injection of a deterministic stimulus current between −0.1 and 0.1 pA/pF for the duration of the AP.</p

Datasheet1_The circle of reentry: Characteristics of trigger-substrate interaction leading to sudden cardiac arrest.docx

Sudden cardiac death is often caused by ventricular arrhythmias driven by reentry. Comprehensive characterization of the potential triggers and substrate in survivors of sudden cardiac arrest has provided insights into the trigger-substrate interaction leading to reentry. Previously, a “Triangle of Arrhythmogenesis”, reflecting interactions between substrate, trigger and modulating factors, has been proposed to reason about arrhythmia initiation. Here, we expand upon this concept by separating the trigger and substrate characteristics in their spatial and temporal components. This yields four key elements that are required for the initiation of reentry: local dispersion of excitability (e.g., the presence of steep repolarization time gradients), a critical relative size of the region of excitability and the region of inexcitability (e.g., a sufficiently large region with early repolarization), a trigger that originates at a time when some tissue is excitable and other tissue is inexcitable (e.g., an early premature complex), and which occurs from an excitable region (e.g., from a region with early repolarization). We discuss how these findings yield a new mechanistic framework for reasoning about reentry initiation, the “Circle of Reentry.” In a patient case of unexplained ventricular fibrillation, we then illustrate how a comprehensive clinical investigation of these trigger-substrate characteristics may help to understand the associated arrhythmia mechanism. We will also discuss how this reentry initiation concept may help to identify patients at risk, and how similar reasoning may apply to other reentrant arrhythmias.</p

Contribution of currents to BVR determined via linear regression of 200 unique virtual myocytes.

<p><b>A.</b> Relative changes in the maximal conductance (G_x) of the 13 currents/fluxes (lanes correspond to the column pairs in panel B) for 100 (out of 200) trials (left panel) and corresponding changes in outputs (APD, STV and LTV) during steady-state pacing at CL = 1000 ms (right panel). Middle panel shows the coefficients that indicate the contribution of each current to every output measure as determined via linear regression. <b>B.</b> Bar plot of the magnitude of the coefficients from panel A regarding their impact on APD (white bars) or STV (shaded bars). I_Kr and I_Na have a large impact on both APD and BVR, consistent with the results from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003202#pcbi-1003202-g002" target="_blank"><b>Figure 2</b></a>. In addition, I_NaK also strongly affects STV. LTV showed similar pattern as STV and is not shown for clarity.</p

BVR in simulated LQT syndrome types 1–3 in the absence or presence of βARS.

<p><b>A.</b> Overlay of 30 consecutive APs in the absence (−βARS) or presence (+βARS) of β-adrenergic receptor stimulation under control conditions (top-left panel) or simulated LQT1 (top-right panel), LQT2 (bottom-left panel), or LQT3 (bottom-right panel) at 1000-ms CL. Shortest and longest APs are shown in black, intermediate APs in grey. A Poincaré plot of the 30 APDs is shown below. <b>B.</b> Quantification of BVR in LQT1-3 at CL of 500, 1000, or 2000 ms in the absence or presence of βARS. HMR indicates simulation of the I_Ks blocker HMR1556 (simulated LQT1), Dof simulation of the I_Kr blocking drug dofetilide (LQT2) and ATXII indicates simulations with enhanced persistent I_Na (LQT3). βARS reduces BVR significantly in LQT2 and LQT3, but not in LQT1, consistent with experimental results <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003202#pcbi.1003202-Johnson1" target="_blank">[8]</a>.</p