Benchmark de Emuladores para Simulação Cardíaca, Quantificação de Incerteza e Análise de Sensibilidade
Resumo
Este trabalho apresenta um benchmark de três famílias de emuladores — expansões de caos polinomial, processos gaussianos e redes neurais — aplicados a quatro problemas representativos de modelagem cardíaca envolvendo mecânica ventricular e eletrofisiologia celular. Os emuladores são treinados para aproximar o mapeamento entre parâmetros de entrada e quantidades de interesse (QoIs), caracterizando um problema de regressão. Os modelos são avaliados em termos de precisão preditiva, custo computacional e fidelidade na reprodução de análises de quantificação de incerteza e sensibilidade global. Os resultados mostram que os emuladores alcançam erros relativos tipicamente inferiores a 2% e proporcionam acelerações de até 109 em relação aos modelos originais. Além disso, evidenciam diferenças qualitativas no desempenho das diferentes famílias conforme a complexidade do problema.
Referências
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Barros, B. G. D., Oliveira, R. S., Meira, W., Lobosco, M., and Santos, R. W. D. (2012). Simulations of complex and microscopic models of cardiac electrophysiology powered by multi-gpu platforms. Computational and Mathematical Methods in Medicine, 2012.
Bhagirath, P., Strocchi, M., Bishop, M., Boyle, P., and Plank, G. (2023). From bits to bedside: entering the age of digital twins in cardiac electrophysiology. Europace, 26(12):euae295.
Campos, J., Guedes, R., Werneck, Y., Barra, L., dos Santos, R., and Rocha, B. (2023). Polynomial chaos expansion surrogate modeling of passive cardiac mechanics using the holzapfel–ogden constitutive model. Journal of Computational Science, 71:102039.
Cluitmans, M. J. M., Plank, G., and Heijman, J. (2024). Digital twins for cardiac electrophysiology: state of the art and future challenges. Herzschrittmachertherapie & Elektrophysiologie, 35(2):118–123.
Feinberg, J. and Pinkus, A. (2018). Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science, 11:46–57.
FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1(6):445–466.
Gardner, J. R., Pleiss, G., Bindel, D., Weinberger, K. Q., and Wilson, A. G. (2018). Gpytorch: Blackbox matrix-matrix gaussian process inference with gpu acceleration. Advances in Neural Information Processing Systems (NeurIPS), 31.
Gherman, I. M., Abdallah, Z. S., Pang, W., Gorochowski, T. E., Grierson, C. S., and Marucci, L. (2023). Bridging the gap between mechanistic biological models and machine learning surrogates.
Jaffery, O. A., Melki, L., Slabaugh, G., Good, W. W., and Roney, C. H. (2024). A review of personalised cardiac computational modelling using electroanatomical mapping data. Arrhythmia & Electrophysiology Review, 13:e08. Open Access article, PMCID PMC11131150, PMID 38807744.
Kingma, D. P. and Ba, J. (2015). Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR).
Kudela, J., Škřivánková, I., Zahradník, P., et al. (2022). Recent advances and applications of surrogate models for finite element method-based computations: a literature review. Soft Computing, 27:1–27. Large survey ( 180 papers) covering GP, PCE, NN and hybrid approaches; discusses trends, gaps and practical recommendations.
Lawson, B. A. J., Oliveira, R. S., Berg, L. A., Silva, P. A. A., Burrage, K., and dos Santos, R. W. (2020). Variability in electrophysiological properties and conducting obstacles controls re-entry risk in heterogeneous ischaemic tissue. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 378(2173):20190341.
Liu, Z., Zhan, L., Pan, R., et al. (2020). Surrogate modelling based on resampled polynomial chaos expansion (rpce): methodology and applications. Expert Systems with Applications, 153:113409. Improves robustness of PCE selection procedures; useful when comparing practical PCE pipelines to ML surrogates.
McKay, M. D., Beckman, R. J., and Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239–245.
Niederer, S. A., Lumens, J., and Trayanova, N. A. (2019). Computational models in cardiology.
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S. (2019). Pytorch: An imperative style, high-performance deep learning library. Advances in Neural Information Processing Systems (NeurIPS), 32.
Rodero, C., Baptiste, T. M. G., Barrows, R. K., Keramati, H., Sillett, C. P., Strocchi, M., Lamata, P., and Niederer, S. A. (2023). A systematic review of cardiac in-silico clinical trials. Progress in Biomedical Engineering, 5(3):032004. Published by IOP Publishing Ltd.
Saltelli, A., Chan, K., and Scott, E. M. (2008). Sensitivity Analysis. John Wiley & Sons, Chichester, UK.
Shahzadi, G., Ahmad, W., Nawab, K., et al. (2021). Deep neural network and polynomial chaos expansion based surrogate models for computationally intensive environmental models. Water, 13(13):1830. Empirical comparison of deep NN and PCE surrogates for environmental model emulation; highlights data requirements and generalization trade-offs.
Sobol’, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates. Mathematics and Computers in Simulation, 55(1-3):271–280.
Sundnes, J., Lines, G. T., Cai, X., Nielsen, B. F., Mardal, K. A., and Tveito, A. (2006). Computing the Electrical Activity in the Heart. Springer.
Ten Tusscher, K. H. W. J., Noble, D., Noble, P. J., and Panfilov, A. V. (2004). A model for human ventricular tissue. American Journal of Physiology-Heart and Circulatory Physiology, 286(4):H1573–H1589. PMID: 14656705.
Trayanova, N. A., Lyon, A., Shade, J., and Heijman, J. (2024). Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation. Physiological Reviews, 104(3):1265–1333. Epub 2023 Dec 28.
Tsokanas, N., Simpson, T., Pastorino, R., Chatzi, E., and Stojadinović, B. (2022). Model order reduction for real-time hybrid simulation: Comparing polynomial chaos expansion and neural network methods. Mechanics and Machine Theory, 166:104178. Direct comparative study of PCE and feedforward neural networks for real-time model-reduction in hybrid simulation.
Waight, M. C., Prakosa, A., Li, A. C., Bunce, N., Marciniak, A., Trayanova, N. A., and Saba, M. M. (2025). Heart digital twins predict features of invasive reentrant circuits and ablation lesions in scar-dependent ventricular tachycardia. Circulation: Arrhythmia and Electrophysiology, 18. 18: (2025), forthcoming.
Barros, B. G. D., Oliveira, R. S., Meira, W., Lobosco, M., and Santos, R. W. D. (2012). Simulations of complex and microscopic models of cardiac electrophysiology powered by multi-gpu platforms. Computational and Mathematical Methods in Medicine, 2012.
Bhagirath, P., Strocchi, M., Bishop, M., Boyle, P., and Plank, G. (2023). From bits to bedside: entering the age of digital twins in cardiac electrophysiology. Europace, 26(12):euae295.
Campos, J., Guedes, R., Werneck, Y., Barra, L., dos Santos, R., and Rocha, B. (2023). Polynomial chaos expansion surrogate modeling of passive cardiac mechanics using the holzapfel–ogden constitutive model. Journal of Computational Science, 71:102039.
Cluitmans, M. J. M., Plank, G., and Heijman, J. (2024). Digital twins for cardiac electrophysiology: state of the art and future challenges. Herzschrittmachertherapie & Elektrophysiologie, 35(2):118–123.
Feinberg, J. and Pinkus, A. (2018). Chaospy: An open source tool for designing methods of uncertainty quantification. Journal of Computational Science, 11:46–57.
FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1(6):445–466.
Gardner, J. R., Pleiss, G., Bindel, D., Weinberger, K. Q., and Wilson, A. G. (2018). Gpytorch: Blackbox matrix-matrix gaussian process inference with gpu acceleration. Advances in Neural Information Processing Systems (NeurIPS), 31.
Gherman, I. M., Abdallah, Z. S., Pang, W., Gorochowski, T. E., Grierson, C. S., and Marucci, L. (2023). Bridging the gap between mechanistic biological models and machine learning surrogates.
Jaffery, O. A., Melki, L., Slabaugh, G., Good, W. W., and Roney, C. H. (2024). A review of personalised cardiac computational modelling using electroanatomical mapping data. Arrhythmia & Electrophysiology Review, 13:e08. Open Access article, PMCID PMC11131150, PMID 38807744.
Kingma, D. P. and Ba, J. (2015). Adam: A method for stochastic optimization. In International Conference on Learning Representations (ICLR).
Kudela, J., Škřivánková, I., Zahradník, P., et al. (2022). Recent advances and applications of surrogate models for finite element method-based computations: a literature review. Soft Computing, 27:1–27. Large survey ( 180 papers) covering GP, PCE, NN and hybrid approaches; discusses trends, gaps and practical recommendations.
Lawson, B. A. J., Oliveira, R. S., Berg, L. A., Silva, P. A. A., Burrage, K., and dos Santos, R. W. (2020). Variability in electrophysiological properties and conducting obstacles controls re-entry risk in heterogeneous ischaemic tissue. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 378(2173):20190341.
Liu, Z., Zhan, L., Pan, R., et al. (2020). Surrogate modelling based on resampled polynomial chaos expansion (rpce): methodology and applications. Expert Systems with Applications, 153:113409. Improves robustness of PCE selection procedures; useful when comparing practical PCE pipelines to ML surrogates.
McKay, M. D., Beckman, R. J., and Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239–245.
Niederer, S. A., Lumens, J., and Trayanova, N. A. (2019). Computational models in cardiology.
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S. (2019). Pytorch: An imperative style, high-performance deep learning library. Advances in Neural Information Processing Systems (NeurIPS), 32.
Rodero, C., Baptiste, T. M. G., Barrows, R. K., Keramati, H., Sillett, C. P., Strocchi, M., Lamata, P., and Niederer, S. A. (2023). A systematic review of cardiac in-silico clinical trials. Progress in Biomedical Engineering, 5(3):032004. Published by IOP Publishing Ltd.
Saltelli, A., Chan, K., and Scott, E. M. (2008). Sensitivity Analysis. John Wiley & Sons, Chichester, UK.
Shahzadi, G., Ahmad, W., Nawab, K., et al. (2021). Deep neural network and polynomial chaos expansion based surrogate models for computationally intensive environmental models. Water, 13(13):1830. Empirical comparison of deep NN and PCE surrogates for environmental model emulation; highlights data requirements and generalization trade-offs.
Sobol’, I. M. (2001). Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates. Mathematics and Computers in Simulation, 55(1-3):271–280.
Sundnes, J., Lines, G. T., Cai, X., Nielsen, B. F., Mardal, K. A., and Tveito, A. (2006). Computing the Electrical Activity in the Heart. Springer.
Ten Tusscher, K. H. W. J., Noble, D., Noble, P. J., and Panfilov, A. V. (2004). A model for human ventricular tissue. American Journal of Physiology-Heart and Circulatory Physiology, 286(4):H1573–H1589. PMID: 14656705.
Trayanova, N. A., Lyon, A., Shade, J., and Heijman, J. (2024). Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation. Physiological Reviews, 104(3):1265–1333. Epub 2023 Dec 28.
Tsokanas, N., Simpson, T., Pastorino, R., Chatzi, E., and Stojadinović, B. (2022). Model order reduction for real-time hybrid simulation: Comparing polynomial chaos expansion and neural network methods. Mechanics and Machine Theory, 166:104178. Direct comparative study of PCE and feedforward neural networks for real-time model-reduction in hybrid simulation.
Waight, M. C., Prakosa, A., Li, A. C., Bunce, N., Marciniak, A., Trayanova, N. A., and Saba, M. M. (2025). Heart digital twins predict features of invasive reentrant circuits and ablation lesions in scar-dependent ventricular tachycardia. Circulation: Arrhythmia and Electrophysiology, 18. 18: (2025), forthcoming.
Publicado
01/06/2026
Como Citar
WERNECK, Yan B.; OLIVEIRA, Lucas T.; ROCHA, Bernardo M.; OLIVEIRA, Rafael; CAMPOS, Joventino O.; SANTOS, Rodrigo W. dos.
Benchmark de Emuladores para Simulação Cardíaca, Quantificação de Incerteza e Análise de Sensibilidade. In: SIMPÓSIO BRASILEIRO DE COMPUTAÇÃO APLICADA À SAÚDE (SBCAS), 26. , 2026, Ouro Preto/MG.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 1098-1109.
ISSN 2763-8952.
DOI: https://doi.org/10.5753/sbcas.2026.21636.
