Table 1.
Ion current changes in PeAF condition.
Table 2.
Courtemanche et al. model parameters used for the sensitivity analysis.
Fig 1.
Parameter sensitivity analysis.
(A) Simulation of AP by randomly varying model parameters (B) Prediction of APD by linear regression model with 94.8% correlation. Parameter sensitivities of model parameters on APD in control (C) and PeAF (D). Parameter group in the upper part were selected for ionic currents remodeled and the lower part not-remodeled in PeAF. Each value in the bar graph represents how change in a parameter influences on APD change. For example, GK1, the maximum conductance of IK1, showed the largest negative sensitivity in control. This implies that IK1 up-regulation will decrease APD.
Fig 2.
Effects of elevated INaCa on APD in control and PeAF.
INaCa(max) was set to two times (+100%) (blue) the base value (black) for simulations. Superimposed action potentials (A), INaCa (B), and Ca2+ transients (C). Integrals of the forward and reverse mode INaCa in control and PeAF (D). We integrated the current INaCa from the time at which INaCa = 0 (denoted by a and b in 2B) to the time of AP repolarization, where INaCa has the minimum values (denoted by c and d in 2B).
Fig 3.
Simulation results of rate-dependent APD changes in six different conditions.
APs were drawn in the steady-state condition at the pacing rates of 2 Hz (A) and 1 Hz (B). (C) The relationships between APD and BCL were drawn at the control condition (a), ICaL decreased by 50% (b), 70% (c), IK1 increased by 100% (d), the PeAF condition with ICaL decreased by 50% (e), and the PeAF condition (f) with ICaL decreased by 70%.
Fig 4.
Quantifying the contribution of individual currents to rate-dependent APD adaptation.
AP shapes changed during the transition between 0.5 Hz to 2 Hz in control (A) and the PeAF condition (PeAF1) (B). Evaluation of ionic current contribution during the transition from 2 Hz to 0.5 Hz in control (C) and PeAF (PeAF1) (D), where ΔQ is the total charge difference between 0.5 Hz and 2 Hz pacing rates. Negative value of ΔQ with ICaL implies that more inward currents increased and contributed to the prolongation of APD from 2 Hz to 0.5 Hz. In other words, more depolarizing current decreased to lead to APD reduction during the transition from 0.5 Hz to 2 Hz.
Fig 5.
Emerging pattern formation of spiral waves in six different conditions.
(A) control, (B) 50% reduction of ICaL, (C) 70% reduction of ICaL, (D) 100% increase of IK1, (E) PeAF condition with 50% reduction of ICaL (PeAF1). (F) PeAF condition with 70% reduction of ICaL (PeAF2). APs at the right and bottom corner (denoted by a red solid circle) were plotted to monitor the electrical activity of single cell. Phase singularity point maps (in the last column) were drawn to keep track of spiral cores. (G) Phase singularities in six different conditions. control (0.53 s-1cm-2), 50% reduction of ICaL (1.87 s-1cm-2), 70% reduction of ICaL (0.43 s-1cm-2), 100% increase of IK1 (0.57 s-1cm-2), PeAF1, PeAF condition with 50% reduction of ICaL (1.95 s-1cm-2), PeAF2, PeAF condition with 70% reduction of ICaL (0.4322 s-1cm-2).
Fig 6.
APD restitution curves and maximum slopes in a one-dimensional cable model.
(A) The relation of the steady-state APDs (APD90) at varying basic cycle lengths (BCLs) were represented by the diastolic intervals (DI) for the one-dimensional cable model with 128 nodes (Δx = 0.025 cm). BCLs were progressively decreased by the steps of 600, 500, 400, 350, 320, 310, and 300 ms and further decreased by step of 5-ms until APD alternans or 2:1 block occurred. At each BCL, 40 stimuli were applied at one end in the cable model and used to calculate the steady-state APD in the middle of the cable. (B) The maximal slopes of APD restitution curves at six conditions are compared.