The importance of mechanical conditions in the testing of excitation abnormalities in a population of electro-mechanical models of human ventricular cardiomyocytes

Figures

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  FIGURE 1. Convergence of the HM algorithm. (A) The number of permissive parameter sets from the current parametric space after calibration of emulators at each wave of the HM algorithm. (B) The ratio of permissive emulators in the current wave with respect to the previous one. (C) The acceptance rate is the proportion of calculated models (simulators) that meet the calibration criteria (Table 1) in each wave. The X-axis is the wave number. In the seventh wave, additional points are generated (see the description of the HM procedure in the “Methods” section).

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  FIGURE 2. Model re-calibration using mechanical tests. Action potentials (upper panels), Ca 2+ transients (middle panels) and active force generated by models (bottom panels) from the initial population re-calibrated step-by-step using mechanical tests: the calibration using the force biomarkers (A); the calibration during preload tests when models were rejected due to excitation abnormalities that occurred at reduced initial cell lengths (B); the calibration when models were rejected due to abnormalities in the ‘length - force’ and ‘force - velocity’ dependencies (C). The colored lines in panels A–C indicate the rejected models in the respective calibration step. The gray lines indicate models meeting calibration criteria at a current re-calibration step. The blue lines show the final population of accepted models (D). The black line indicates the reference TP + M model. The dashed line on the right panel represents one of the accepted models. Force is normalized to the peak isometric force (FT peak ) of the reference TP + M model.

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  FIGURE 3. Preload tests. Examples of an accepted (A) and rejected (B) model under re-calibration of the models using variation in the initial length during isometric contractions. The rejected model produces excitation abnormalities at reduced preloads. The figure shows action potential (AP, upper panels), Ca 2+ transients ( [Ca2+]i , middle panels) and active force (Force, bottom panels) generated by the virtual cardiomyocyte during steady-state isometric twitches at different initial lengths.

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  FIGURE 4. ‘Length – force’ (L-F) relationship test. The L-F curves were obtained during re-calibration by preload tests of the population that consisted of models that had no excitation abnormalities. The L-F diagram shows the dependence between the initial cell length and the isometric peak force developed. The curves derived from experimental data on human cardiac preparations are shown by the blue line (Vahl et al., 1997) and the green line (Holubarsch et al., 1998). The L-F dependence for the reference TP + M model is shown by the solid black line. The models rejected after the preload tests are shown in red lines. The X-axis indicates the initial length of the virtual cell, normalized to L max (the length at which the cell develops maximum isometric force). The Y-axis represents the isometric peak force at the corresponding length, normalized to the value of the isometric peak force at an initial length of 0.93L max, which is different for each model of the population.

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  FIGURE 5. Afterload tests. Panels (A, B) show examples of an accepted (A) and a rejected (B) model during afterload tests. The panels show action potentials (AP), Ca 2+ transients ([Ca2+]i) , force and length (normalized to initial length) during isotonic contractions at different afterloads (0.25, 0.5 and 0.75 of F max, where F max is the isometric peak active force). (C) ‘Force - velocity’ (F–V) relationships in the models calibrated during the afterload tests. The black line shows the F-V relationship for the reference TP + M model. The F-V curve for the accepted model in panel A is indicated by the black dashed line. The F-V curves for all models rejected in the afterload tests are shown by red lines, with the dashed line corresponding to the model shown in panel (B). The X-axis indicates the afterload, normalized to the respective F max. The Y-axis indicates the velocity of shortening of cardiomyocytes during afterloaded isotonic twitches.

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  FIGURE 6. Distribution of input parameters and output biomarkers in the electro-mechanically calibrated models. (A) Scaling factors of input parameters in accepted models from the final population, shown as boxplot diagrams. The middle marker of the boxes shows the median, the box boundaries are the 25th and 75th percentiles, and the whiskers extend to the most extreme data points. (B) Boxplots (upper) and histograms (lower) of the distribution of biomarker values of action potential, Ca 2+ transient and isometric force in the population of accepted electro-mechanical models. The dotted vertical lines indicate the minimum and maximum values of the biomarkers derived from experimental data (Table 1), and the dashed vertical lines indicate the experimental mean values of the AP biomarkers (Table 1). The Y-axis indicates the number of models, and the X-axis the biomarker value. RMP is the resting membrane potential; APD xx is the duration of AP at the XX% level of repolarization; Tri 9040 - triangularity of AP, defined as the difference between APD 90 and APD 40; CT min, CT max are diastolic and systolic values of the concentration of free Ca 2+ in the cytosol; CaTTP is the time to reach the…

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  FIGURE 7. Correlation between scaling factors for parameters P NaK and g CaL in the final population of accepted models. Dots indicate values in individual models, histograms show the marginal distribution of the corresponding parameters, and the blue line shows a linear regression line with the equation P NaK = 0.59 ⋅ g CaL + 0.46. Pearson’s correlation coefficient r = 0.733, p < 0.001.

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  FIGURE 8. Difference in the distributions of the scaling factor for the maximum rate of the SR SERCA pump (V maxup ) between the accepted models (blue) and the models rejected from the electrophysiologically calibrated population using mechanical testing (red). Boxplots (top) and histograms (bottom) show the V maxup scaling factor distribution in the population of accepted (blue) and rejected (red) models. Each histogram was normalized so that the column area be equal to 1. The vertical dotted line marks the threshold for V maxup , above which anomalies in the cell models are predicted in mechanical tests (see Results for details).

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  FIGURE 9. Drug effects in the population of accepted models. (A) Action potential and isometric force of a model sample from the final population under different concentrations of Verapamil and Dofetilide. The model that has no anomalies under drug exposure has been selected. The concentrations are coded in shades of blue, from dark blue, corresponding to baseline (zero concentration), to light blue, corresponding to 100 times the maximum effective free therapeutic concentration (EFTPCmax). The arrows indicate the direction of the changes in action potential duration with increasing drug concentration. Force is normalized to the peak isometric force (FT peak ) of the reference TP + M model. (B) Action potential, Ca 2+ transient and isometric force of a model sample under different concentrations of Dofetilide. The model showing repolarization abnormalities was selected. Concentrations are coded in shades of red, from dark red, corresponding to baseline (zero concentration), to light red, corresponding to 100xEFTPCmax. At high concentrations, the model shows repolarization abnormalities in the form of additional peaks in the repolarization phase of AP and additional Ca 2+ peaks. (C) Boxplot…

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  FIGURE 10. Abnormal events under Dofetilide and Verapamil. Heatmap shows a number of models with repolarization abnormalities (top line) and failed contraction (bottom line) in the final population of 674 models during contractions at different initial cell lengths from 0.93 to 0.80L max with increasing drug concentration. The vertical axis plots the concentration of the compound (from 1 to 100xEFTPCmax), and the horizontal axis plots the initial cell length.