Modeling specific action potentials in the human atria based on a minimal single-cell model

Figures

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  Fig 1. Overview. Schematic illustration of the optimized adjustment of the BOCF model by a parameter converter that determines the set of parameter values (τfi, τsi, and τso1) giving a best match with the amplitude and duration of a specific action potential.

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  Fig 2. Illustration of an action potential. The amplitude APA and four AP durations at 90%, 50%, 40% and 20% of the total amplitude are also indicated. These five values are used to determine three characteristic time scales of the BOCF model (see text).

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  Fig 3. Amplitude as function of model parameters. (a) Amplitude APA as a function of τsi for four different pairs of fixed values τfi and τso1 (in ms). (b) Dependence of the amplitude APA on time τso1 for τsi = 10.7 ms and four different values of τfi. (c) Time τfi as a function of APA for τsi = 10.7 ms and τso1 = 73.7 ms.

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  Fig 4. APDn as functions of model parameters. (a) APDn as a function of τfi for a pair of fixed values τsi = 10.7 ms and τso1 = 73.675 ms. (b)-(e) Dependence of the APDn on τsi and τso1 for fixed τfi = 0.0835 ms. The meshes of points (black bullets) indicate the simulation results, and the surfaces refer to the fits of the meshes, according to Eq (5). All quantities are given in ms. Plots (f)-(i) show contour plots of the APD surfaces in (b)-(e), respectively.

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  Fig 5. Restitution curves of the BOCF model for APD90, APD50, APD40 and APD20, with the remodelled parameter set. The activation frequency of the external stiumulus was varied between 1 Hz and 10 Hz in steps of 1 Hz. The red dashed line indicates the BCL corresponding to f = 3 Hz, which we used to illustrate the mapping from APA and APD to the three time scales (see Figs 3 and 4, and Table 1). The AP were taken after 104 ms, beyond the time needed for achieving the stationary state.

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  Fig 6. Comparison between CRN model and BOCF model. Five surrogate AP generated with the CRN model (solid lines) for different gNa and gCa in comparison with the corresponding AP modeled with the BOCF model (dashed lines). The reference values are the ones corresponding to the remodeling case, namely γCa = 0.0433 nS/pF and γNa = 7.8 nS/pF.

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  Fig 7. Deviation ΔA (a,b), ΔAPA (c,d) and ΔAPD (e,f) as a function of gCa/γCa for fixed gNa = γNa = 7.8 nS/pF (a,c,e) and as a function of gNa/γNa for fixed gCa = γCa = 0.0433 nS/pF (b,d,f). The assignment of the symbols in plot (f) is the same as in plot (e). The dashed line in each plot indicates deviations of 10%.

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  Fig 8. Dependence of the coefficients (a) C0, (b) C1, and (c) C2 in Eq (4) on the activation frequency f; (d) the R2 values of the corresponding fits.

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  Fig 9. Dependence of the coefficients cmk(n) in Eq (5) on the activation frequency f, where the symbol assignment refers to the different APDn as given in the inset of the last graph, which shows the R2 values of the corresponding fits [Eq (5)].

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  Fig 10. Two illustrative examples of the optimization procedure for fitting AP, taken from sets of measured AP at the University of Dresden.