Neural network emulation of the human ventricular cardiomyocyte action potential for more efficient computations in pharmacological studies
- Department of Mathematics and Scientific Computing, University of Graz, Austria
- NAWI Graz, University of Graz, Austria
- Gottfried Schatz Research Center for Cell Signaling, Metabolism and Aging - Division of Medical Physics and Biophysics, Medical University of Graz, Austria
- BioTechMed-Graz, Austria
- Department of Pharmacology and Pharmacotherapy, University of Szeged, Hungary
- HUN-REN-TKI, Research Group of Pharmacology, Hungary
- Centre for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham, United Kingdom
- Division of Imaging Sciences & Biomedical Engineering, King’s College London, United Kingdom
Figures
Figure 1
Methodology of this study including the emulator development and the evaluation.
The simulator is visualized by a schematic human ventricular cardiomyocyte that includes all currents considered for the emulator training. Inputs of the emulator (see Figure 3) are the …
Figure 2
Processed APs used for training and validation (left and center).
Additionally we show the excluded APs on the right (see text for description of the exclusion criteria).
Figure 3
Conceptual architecture of the neural network emulator.
The maximum conductances are encoded into depolarization parameters di and a latent space representation that uniquely defines the time series functional . The time is normalized and encoded …
Figure 4
Comparison of an averaged raw and an averaged filtered experimental AP.
One dofetilide control AP is shown as example.
Figure 5
Analysis of solution accuracy of the forward problem on synthetic data including normal APs (drug data of data set #2).
Left: histogram of RMSEs for the APs, right: APs with the largest RMSEs. The RMSE is given above each subplot.
Figure 6
Analysis of solution accuracy of the forward problem on synthetic data including normal APs (drug data of data set #2) with respect to AP biomarkers.
Histograms of mismatches for each biomarker are shown and the RMSE is given in the upper left corner. The number in the right upper corner denotes the number of outliers of the 10,000 samples which …
Figure 7
Analysis of solution accuracy of the forward problem on synthetic data including abnormal APs exhibiting EADs (subset of data set #3).
Left: histogram of RMSEs for the APs, right: APs with the largest RMSEs. Of the 171 emulated APs, 124 exhibit the expected EADs (based on the criterion outlined in Appendix 1). The RMSE is given …
Figure 8
Analysis of solution accuracy of the inverse problem on synthetic data (data set #2).
Left: boxplot of errors between normalized estimated and ground truth control maximum conductances, middle: boxplot of errors between normalized estimated and ground truth drugged maximum …
Figure 9
Analysis of fit quality of the inverse problem on experimental data.
Comparison of the fitted APs (solid lines) and the experimental APs (dashed lines) at control (red) and after drug administration (blue) for all drugs.
Figure 10
Analysis of solution accuracy of the inverse problem using experimental data.
The histograms compare the estimated pharmacological parameters (dashed vertical lines) from data of multiple preparations with the CiPA distributions (blue; see Inverse problem). The black dash …
Appendix 2—figure 1
Global sensitivity analysis of the ToR-ORd simulator.
Sobol’ sensitivity indices are shown for each maximum conductance relative to each AP biomarker. Left: first-order (S1), right: total-effect (ST) Sobol’ sensitivity coefficient.
Appendix 3—figure 1
Emulated APs based on the pharmacological parameters of data set #3.
See also Forward problem and Figure 7. From left to right and top to bottom, the plot shows the true positive, false negative, false positive and true negative samples. The number next to the title …
Appendix 3—figure 2
Same as Figure 1, but showing the simulated APs.
Tables
Table 1
AP biomarkers and their experimental ranges used to generate the population of synthetic cardiomyocytes.
These were adopted from Passini et al., 2017. Experimental data were collected at 37°C in small right ventricular trabeculae and papillary tissue preparations obtained from healthy human hearts …
| AP biomarker | Unit | Min | Max |
|---|---|---|---|
| mV | -95 | -80 | |
| mVms-1 | 100 | 1000 | |
| mV | 10 | 55 | |
| ms | 85 | 320 | |
| ms | 110 | 350 | |
| ms | 180 | 440 | |
| ms | 50 | 150 |
Table 2
Pharmacological parameter samples (synthetic drugs) with scaling factors for Gkr and Pca to generate the drug data of data set #3.
| ID | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Gkr | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 | 0.10 | 0.11 | 0.12 | 0.13 | 0.14 |
| Pca | 1.20 | 1.22 | 1.24 | 1.26 | 1.28 | 1.30 | 1.32 | 1.34 | 1.36 | 1.38 |
Table 3
Summary of the data used in this study, along with their usage and the number of valid samples.
Note that each AP is counted individually, also in cases of control/drug pairs.
| ID | Description | Usage | Origin | Samples |
|---|---|---|---|---|
| #1 | Training/validation data | Training and validating the emulator, choosing the best architecture (Architecture) | Simulation | 39,884 |
| #2 | Synthetic drug data, normal APs | Testing forward and inverse performance for normal APs (‘Forward problem’ and ‘Inverse problem based on synthetic data’) | Simulation | 104 |
| #3 | Synthetic drug data, including EAD APs | Testing forward performance of abnormal (EAD) APs (‘Forward problem’) | Simulation | 950 |
| #4 | Experimental cardiomyocytes | Testing and comparing the inverse performance with data published by the CiPA initiative (Li et al., 2017; Chang et al., 2017; ’Inverse problem based on experimental data’) | Orvos, 2019 | 26 |
Table 4
Average RMSE over control and drugged APs measured in all preparations per drug.
All values in mV.
| Drug | RMSE control | RMSE drug |
|---|---|---|
| Cisapride | 1.53 | 2 |
| Dofetilide | 2.05 | 1.73 |
| Sotalol | 1.4 | 2.51 |
| Terfenadine | 1.22 | 1.08 |
| Verapamil | 1.93 | 2.21 |
Table 5
Pharmacological parameters related to maximum conductances that were considered successfullyor unsuccessfully estimated across all preparations and drugs.
For each channel, the drugs are stated forwhich respective data from the CiPA initiative were available. C, D, S, T, V, A mark cisapride, dofetilide, sotalol,terfenadine, verapamil, all drugs …
| Gna | GNaL | Gto | GKr | GKs | GK | PCa | Total | |
|---|---|---|---|---|---|---|---|---|
| Successful | 6 | 6 | 8 | 3 | 9 | 0 | 5 | 37 |
| Unsuccessful | 3 | 1 | 5 | 10 | 0 | 10 | 8 | 37 |
| Ratio | 0.67 | 0.86 | 0.62 | 0.23 | 1 | 0 | 0.38 | 0.5 |
Author response table 1
Summary of the data used in this study, along with their usage and the number of valid samples.
Note that each AP is counted individually, also in cases of control/drug pairs.
| ID | Description | Usage | Origin | Samples |
|---|---|---|---|---|
| #1 | Training/validation data | Training and validating the emulator, choosing the best architecture (Section ‘Architecture’) | Simulation | 39,884 |
| #2 | Synthetic drug data, normal APs | Testing forward and inverse performance for normal APs (Sections ‘Forward problem’ and ‘Inverse problem based on synthetic data’) | Simulation | 104 |
| #3 | Synthetic drug data, including EAD APs | Testing forward performance of abnormal (EAD) APs (‘Forward problem’) | Simulation | 950 |
| #4 | Experimental cardiomyocytes | Testing and comparing the inverse performance with data published by the CiPA initiative (Li et al.. 2017, Chang et al., 2017; Section ‘Inverse problem based onexperimental data’) | Orvos et al., 2019 | 26 |
