Global Sensitivity Analysis and Uncertainty Quantification for Simulated Atrial Electrocardiograms
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Atrial Model
2.2. Global Sensitivity Analysis, Uncertainty Quantification and Sobol Indices
2.3. Polynomial Chaos Expansion
2.4. Data Description
3. Results
3.1. Convergence of the Surrogate Model
3.1.1. Error Estimation
3.1.2. Normalization of the Surrogate Error
3.1.3. Surrogate Error Convergence
3.1.4. Convergence with Polynomial Order
3.1.5. Convergence with Sample Size
3.2. Sensitivity Analysis
3.2.1. Sobol Indices along the Signal
3.2.2. Time-Integrated Sobol Indices and Dataset Interpretation
3.3. Uncertainty Quantification
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
PCE | Polynomial Chaos Expansion |
SA | Sensitivity Analysis |
UQ | Uncertainty Quantification |
ECG | Electrocardiogram |
SI | Sobol index |
DS | dataset |
GTD | ground truth data |
Appendix A. Mean Signals
Appendix B. Usage, Limitations and Further Directions
References
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Model Parameter | Small Variation | Large Variation |
---|---|---|
CV (bulk tissue) | ||
CV (interatrial connections) | ||
translation X | [−10 mm, 10 mm] | [−20 mm, 20 mm] |
translation Y | [−10 mm, 10 mm] | [−20 mm, 20 mm] |
translation Z | [−10 mm, 10 mm] | [−20 mm, 20 mm] |
angle X | [, ] | [, ] |
angle Y | [, ] | [, ] |
angle Z | [, ] | [, ] |
I | II | III | aVL | aVR | aVF | V1 | V2 | V3 | V4 | V5 | V6 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |
0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | |
0.106 | 0.136 | 0.003 | 0.177 | 0.032 | 0.038 | 0.162 | 0.176 | 0.165 | 0.119 | 0.157 | 0.146 | |
0.092 | 0.119 | 0.001 | 0.155 | 0.027 | 0.032 | 0.250 | 0.283 | 0.321 | 0.340 | 0.252 | 0.049 | |
0.346 | 0.039 | 0.167 | 0.236 | 0.294 | 0.037 | 0.103 | 0.139 | 0.075 | 0.024 | 0.015 | 0.034 | |
0.032 | 0.154 | 0.090 | 0.082 | 0.045 | 0.144 | 0.110 | 0.124 | 0.185 | 0.189 | 0.172 | 0.154 | |
0.202 | 0.378 | 0.710 | 0.062 | 0.497 | 0.713 | 0.006 | 0.016 | 0.020 | 0.031 | 0.064 | 0.318 | |
0.176 | 0.138 | 0.016 | 0.231 | 0.079 | 0.024 | 0.127 | 0.102 | 0.171 | 0.249 | 0.286 | 0.236 | |
0.954 | 0.963 | 0.988 | 0.943 | 0.974 | 0.986 | 0.758 | 0.840 | 0.937 | 0.952 | 0.946 | 0.938 |
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Winkler, B.; Nagel, C.; Farchmin, N.; Heidenreich, S.; Loewe, A.; Dössel, O.; Bär, M. Global Sensitivity Analysis and Uncertainty Quantification for Simulated Atrial Electrocardiograms. Metrology 2023, 3, 1-28. https://doi.org/10.3390/metrology3010001
Winkler B, Nagel C, Farchmin N, Heidenreich S, Loewe A, Dössel O, Bär M. Global Sensitivity Analysis and Uncertainty Quantification for Simulated Atrial Electrocardiograms. Metrology. 2023; 3(1):1-28. https://doi.org/10.3390/metrology3010001
Chicago/Turabian StyleWinkler, Benjamin, Claudia Nagel, Nando Farchmin, Sebastian Heidenreich, Axel Loewe, Olaf Dössel, and Markus Bär. 2023. "Global Sensitivity Analysis and Uncertainty Quantification for Simulated Atrial Electrocardiograms" Metrology 3, no. 1: 1-28. https://doi.org/10.3390/metrology3010001