Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (Gx) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of Gx estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of Gxs of the baseline model. Gxs of 4–6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5–15% and used as an initial parameter set for the gradient-based automatic Gxs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE–Gx relationship during optimization revealed progressive convergence of the randomized population of Gxs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing Gxs over a range of 0.1–10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

Premature cardiac myocytes derived from human-induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), most probably because of different expression patterns of membrane ionic currents. We aim to develop a method of determining expression patterns of functional channels in terms of the whole-cell ionic conductances (Gx) using individual spontaneous AP configurations. However, it has been suggested that apparently identical AP configurations were obtained by different sets of ionic currents in a mathematical model of cardiac membrane excitation. If so, the inverse problem of Gx estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP record by the conventional manual adjustment of Gxs of the baseline model. Then, Gxs of 4 ~ 6 major ionic currents of the 'cell-specific models' were randomized within a range of ±5 ~ 15% and were used as initial parameter sets for the gradient-based automatic Gxs recovery by decreasing the mean square error (MSE) between the target and model output. When plotted all data points of MSE - Gx relation during the optimization, we found that the randomized population of Gxs progressively converged to the original value of the cell-specific model with decreasing MSE. To confirm the absence of any other local minimum in the global search space, we mapped the MSE by randomizing Gxs over a range of 0.1 ~ 10 times the control. No additional local minimum of MSE was obvious in the whole parameter space besides the global minimum of MSE at the default model parameter.

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Premature cardiac myocytes derived from human-induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), most probably because of different expression patterns of membrane ionic currents. We aim to develop a method of determining expression patterns of functional channels in terms of the whole-cell ionic conductances (Gx) using individual AP configurations. However, it has been suggested that apparently identical AP configurations were obtained by different sets of ionic currents in a mathematical model of cardiac membrane excitation. If so, the inverse problem of Gx estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output on each experimental AP record by the conventional manual adjustment of Gx of the baseline model. Then, Gxs of 4 ~6 major ionic currents of the 'cell-specific model' were randomized within a range of ±5 ~15% and were used as an initial parameter set for the gradient-based automatic Gx recovery by decreasing the mean square error (MSE) between the target and model output. When plotted all data points of MSE - Gx relation during the optimization, we found that the randomized population of Gxs progressively converged to the original value of the cell-specific model with decreasing MSE. To confirm the absence of any other local minimum in the global search space, we mapped the MSE by randomizing Gxs over a range of 0.1 ~ 10 times the control. No additional local minimum of MSE was obvious in the whole parameter space except the global minimum of MSE at the default model parameter.