Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes

Figures

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  Figure 1. Distribution of MSE calculated between the target and simulated APs modified by randomizing the sfx of nine ionic currents in coordinates of MSE-sfx. All MSE data points were plotted on the logarithmic ordinate against the linear sfx. A total of 5,141,382 points were calculated in cell model No. 86 over the range of 1/10 to approximately 10 times the default sfx. Since the configuration of Vm records were largely unrealistic at sfx > 3, MSE points were omitted over sfx > 3.0. To demonstrate the sharp decrease in MSE, the data points were densely populated near the default sfx.

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  Figure 2. Manual fitting of variable AP configurations in 12 different hiPSC-CMs. Each panel shows the experimental record (red) superimposed by the model output (black) of the baseline model adjusted by the conventional manual fitting. The experimental cell number is presented at the top of each pair of AP records, The extra fluctuations are obvious during the AP plateau in Cells 78, 08, and 01, and during SDD in Cells 15 and 74. The length of abscissa is markedly different to illustrate the interval between two successive peaks of AP.

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  Figure 3. Successful optimization in Cell 86. (A-1) Target AP (Vm,t, red) and AP generated by randomized initial sfxs (Vm,orp, black). (A-2) Vm,t (red) and Vm,orp (black) generated after 50 cycles of adjusting BP. (A-3) Vm: Vm,t (red) and Vm,orp (black) generated by the final sfxs. Im: corresponding time courses of each current for the finalized AP shown in (A-3) Vm. (B-1) Changes in sfxs vs. log(MSE) during a successful optimization process of PS. (B-2) log(MSE) of all BP points during the search process in PS. The initial values of sfxs are plotted by corresponding colors at the top of each sfx-log(MSE) graph.

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  Figure 4. Convergence of sfx in the orp test for Cell86. The ordinate is the log(MSE) and the abscissa is the normalized amplitude of sfx. x denotes Kr, CaL, Na, ha, K1, and bNSC. Black points were obtained in the progress of optimization, and red points are the final points in 829 runs of PS optimization.

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  Figure 5. Distribution of sfx in the top 20 sets of sfxs obtained from the multi-run orp test in Cell86 in Fig. 2. Data points of normalized sfx in each set are depicted in different colors. (A) Plot of the amplitudes of each sfx (indicated on the abscissa). (B) Three-dimensional plot of the three parameters of sfha, sfK1, and sfbNSC. (C) A different solid angle view of the three-dimensional plot showing a linear correlation; see text for the plot in (D).

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  Figure 6. The complementary relations among sfK1, sfha and sfbNSC. (A) and (B) results of the multi-run orp test. A; the perfect convergence of sfK1 when sfha and sfbNSC were fixed. (B1) improved convergence of sfha and (B2) sfbNSC when sfK1 was fixed. In these two orp tests, sfx of other currents showed quite comparable convergence as in Fig. 4A. (C) the correlation between sfha and sfbNSC.

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  Figure 7. PC1 ~ 6 to describe distribution of the 6 sfxs. PC analysis was performed on the data population of the top 200 runs of the orp test as in Fig. 4, which showed good optimization results (Cell 86). Each magnitude of 6 PCs was normalized to give a unit magnitude. Note each PC is composed of multiple components of ionic current, which are indicated in the Index with corresponding colors.