A noise-robust Koopman spectral analysis of an intermittent dynamics method for complex systems: a case study in pathophysiological processes of obstructive sleep apnea

References

• Abarbanel, H. D., Brown, R., Sidorowich, J. J., & Tsimring, L. S. (1993). The analysis of observed chaotic data in physical systems. Reviews of Modern Physics, 65(4), 1331–1392. https://doi.org/10.1103/RevModPhys.65.1331
   Web of Science ®Google Scholar
• Atri, R., & Mohebbi, M. (2015). Obstructive sleep apnea detection using spectrum and bispectrum analysis of single-lead ECG signal. Physiological Measurement, 36(9), 1963–1980. https://doi.org/10.1088/0967-3334/36/9/1963
   PubMedGoogle Scholar
• Bessaih, H., Hausenblas, E., & Razafimandimby, P. A. (2015). Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type. Nonlinear Differential Equations and Applications NoDEA, 22(6), 1661–1697. https://doi.org/10.1007/s00030-015-0339-9
   Web of Science ®Google Scholar
• Brunton, S. L., Brunton, B. W., Proctor, J. L., Kaiser, E., & Kutz, J. N. (2017). Chaos as an intermittently forced linear system. Nature Communications, 8(1), 1–9. https://doi.org/10.1038/s41467-017-00030-8
   PubMedGoogle Scholar
• Brunton, S. L., Brunton, B. W., Proctor, J. L., & Kutz, J. N. (2016a). Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control. PLoS One, 11(2), e0150171.
   PubMed Web of Science ®Google Scholar
• Brunton, S. L., & Kutz, J. N. (2019). Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press.
   Google Scholar
• Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016b). Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15), 3932–3937. https://doi.org/10.1073/pnas.1517384113
   PubMed Web of Science ®Google Scholar
• Byun, S., Kim, A. Y., Jang, E. H., Kim, S., Choi, K. W., Yu, H. Y., & Jeon, H. J. (2019). Detection of major depressive disorder from linear and nonlinear heart rate variability features during mental task protocol. Computers in Biology and Medicine, 112, 103381.
   PubMed Web of Science ®Google Scholar
• Champion, K. P., Brunton, S. L., & Kutz, J. N. (2019). Discovery of nonlinear multiscale systems: Sampling strategies and embeddings. SIAM Journal on Applied Dynamical Systems, 18(1), 312–333. https://doi.org/10.1137/18M1188227
   Web of Science ®Google Scholar
• Chang, Y.-M., Huang, Y.-T., Chen, I.-L., Yang, C.-L., Leu, S.-C., Su, H.-L., Kao, J.-L., Tsai, S.-C., Jhen, R.-N., & Shiao, C.-C. (2020). Heart rate variability as an independent predictor for 8-year mortality among chronic hemodialysis patients. Scientific Reports, 10(1), 1–9. https://doi.org/10.1038/s41598-020-57792-3
   PubMedGoogle Scholar
• Contoyiannis, Y., Diakonos, F., & Malakis, A. (2002). Intermittent dynamics of critical fluctuations. Physical Review Letters, 89(3), 035701.
   PubMed Web of Science ®Google Scholar
• Donnelly, L. F., Shott, S. R., LaRose, C. R., Chini, B. A., & Amin, R. S. (2004). Causes of persistent obstructive sleep apnea despite previous tonsillectomy and adenoidectomy in children with down syndrome as depicted on static and dynamic cine MRI. AJR. American Journal of Roentgenology, 183(1), 175–181.
   PubMed Web of Science ®Google Scholar
• Donoho, D. L., & Gavish, M. (2013). The optimal hard threshold for singular values is 4/√ 3 (Vol. 4). Citeseer.
   Google Scholar
• Giannakis, D. (2019). Data-driven spectral decomposition and forecasting of ergodic dynamical systems. Applied and Computational Harmonic Analysis, 47(2), 338–396. https://doi.org/10.1016/j.acha.2017.09.001
   Web of Science ®Google Scholar
• Giannakis, D., & Majda, A. J. (2012). Nonlinear Laplacian spectral analysis for time series with intermittency and low-frequency variability. Proceedings of the National Academy of Sciences, 109(7), 2222–2227. https://doi.org/10.1073/pnas.1118984109
   PubMed Web of Science ®Google Scholar
• Grebogi, C., Ott, E., Romeiras, F., & Yorke, J. A. (1987). Critical exponents for crisis-induced intermittency. Physical Review A, 36(11), 5365–5380. https://doi.org/10.1103/PhysRevA.36.5365
   Web of Science ®Google Scholar
• Guckenheimer, J., & Holmes, P. (2013). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (Vol. 42). Springer Science & Business Media.
   Google Scholar
• Hossen, A. (2019). A new simple efficient classification technique for severity of sleep apnea with mathematical model and interpretation. Technology and Health Care, 27(4), 389–406. https://doi.org/10.3233/THC-181541
   PubMed Web of Science ®Google Scholar
• Hramov, A. E., Koronovskii, A. A., & Kurovskaya, M. K. (2014). Intermittent behavior near the synchronization threshold in system with fluctuating control parameter. EPL (Europhysics Letters), 105(5), 50003. https://doi.org/10.1209/0295-5075/105/50003
   Google Scholar
• Huynh, P. K., Setty, A., Phan, H., & Le, T. Q. (2021). Probabilistic domain-knowledge modeling of disorder pathogenesis for dynamics forecasting of acute onset. Artificial Intelligence in Medicine, 115, 102056.
   PubMed Web of Science ®Google Scholar
• Juang, J.-N., & Pappa, R. S. (1985). An eigensystem realization algorithm for modal parameter identification and model reduction. Journal of Guidance, Control, and Dynamics, 8(5), 620–627. https://doi.org/10.2514/3.20031
   Web of Science ®Google Scholar
• Kantz, H., & Schreiber, T. (2004). Nonlinear time series analysis (Vol. 7). Cambridge University Press.
   Google Scholar
• Koopman, B. O. (1931). Hamiltonian systems and transformation in Hilbert space. Proceedings of the National Academy of Sciences of the United States of America, 17(5), 315–318. https://doi.org/10.1073/pnas.17.5.315
   PubMedGoogle Scholar
• Kunisaki, K. M., Greer, N., Khalil, W., Koffel, E., Koeller, E., MacDonald, R., & Wilt, T. J. (2018). Provider types and outcomes in obstructive sleep apnea case finding and treatment: A systematic review. Annals of Internal Medicine, 168(3), 195–202.
   PubMed Web of Science ®Google Scholar
• Le, T. Q., & Bukkapatnam, S. T. (2016). Nonlinear dynamics forecasting of obstructive sleep apnea onsets. PLoS One, 11(11), e0164406.
   PubMed Web of Science ®Google Scholar
• Le, T. Q., Cheng, C., Sangasoongsong, A., Wongdhamma, W., & Bukkapatnam, S. T. (2013). Wireless wearable multisensory suite and real-time prediction of obstructive sleep apnea episodes. IEEE Journal of Translational Engineering in Health and Medicine, 1, 2700109.
   PubMedGoogle Scholar
• Lilly, J. M. (2017). Element analysis: A wavelet-based method for analysing time-localized events in noisy time series. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 473(2200), 20160776. https://doi.org/10.1098/rspa.2016.0776
   PubMed Web of Science ®Google Scholar
• Majda, A. J., & Harlim, J. (2013). Physics constrained nonlinear regression models for time series. Nonlinearity, 26(1), 201–217. https://doi.org/10.1088/0951-7715/26/1/201
   Web of Science ®Google Scholar
• Majda, A. J., & Lee, Y. (2014). Conceptual dynamical models for turbulence. Proceedings of the National Academy of Sciences, 111(18), 6548–6553. https://doi.org/10.1073/pnas.1404914111
   PubMed Web of Science ®Google Scholar
• Mendez, M. O., Bianchi, A. M., Matteucci, M., Cerutti, S., & Penzel, T. (2009). Sleep apnea screening by autoregressive models from a single ECG lead. IEEE Transactions on Bio-Medical Engineering, 56(12), 2838–2850.
   PubMed Web of Science ®Google Scholar
• Mezić, I. (2005). Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynamics, 41(1–3), 309–325. https://doi.org/10.1007/s11071-005-2824-x
   Web of Science ®Google Scholar
• Nussbaumer, H. J. (1981). "The fast Fourier transform": Fast Fourier Transform and Convolution Algorithms. Springer.
   Google Scholar
• Park, C., Worth, R. M., & Rubchinsky, L. L. (2010). Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson’s disease. Journal of Neurophysiology, 103(5), 2707–2716.
   PubMed Web of Science ®Google Scholar
• Pecchia, L., Castaldo, R., Montesinos, L., & Melillo, P. (2018). Are ultra-short heart rate variability features good surrogates of short-term ones? State-of-the-art review and recommendations. Healthcare Technology Letters, 5(3), 94–100.
   PubMed Web of Science ®Google Scholar
• Penzel, T., Moody, G. B., Mark, R. G., Goldberger, A. L., & Peter, J. H. (2000). The apnea-ECG database. Paper Presented at the Computers in Cardiology 2000, 27(Cat. 00CH37163).
   Google Scholar
• Rozenbaum, E. B., Ganeshan, S., & Galitski, V. (2017). Lyapunov exponent and out-of-time-ordered correlator’s growth rate in a chaotic system. Physical Review Letters, 118(8), 086801. https://doi.org/10.1103/PhysRevLett.118.086801
   PubMed Web of Science ®Google Scholar
• Shelhamer, M. (2007). Nonlinear dynamics in physiology: A state-space approach. World Scientific.
   Google Scholar
• Sugihara, G., May, R., Ye, H., Hsieh, C.-h., Deyle, E., Fogarty, M., & Munch, S. (2012). Detecting causality in complex ecosystems. Science (New York, N.Y.), 338(6106), 496–500.
   PubMed Web of Science ®Google Scholar
• Takens, F. (1981). Detecting strange attractors in turbulence. In Dynamical systems and turbulence, Warwick 1980 (pp. 366–381). Springer.
   Google Scholar
• Tu, J. H. (2013). Dynamic mode decomposition: Theory and applications. Princeton University.
   Google Scholar
• Urtnasan, E., Park, J.-U., Joo, E.-Y., & Lee, K.-J. (2018). Automated detection of obstructive sleep apnea events from a single-lead electrocardiogram using a convolutional neural network. Journal of Medical Systems, 42(6), 1–8. https://doi.org/10.1007/s10916-018-0963-0
   Web of Science ®Google Scholar
• Vautard, R., Yiou, P., & Ghil, M. (1992). Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D: Nonlinear Phenomena, 58(1-4), 95–126.
   Google Scholar
• Vollmer, M. (2019). HRVTool–an open-source matlab toolbox for analyzing heart rate variability. Paper Presented at the 2019 Computing in Cardiology (CinC).
   Google Scholar
• Wang, S.-Y., Aziz, T. Z., Stein, J. F., & Liu, X. (2005). Time–frequency analysis of transient neuromuscular events: Dynamic changes in activity of the subthalamic nucleus and forearm muscles related to the intermittent resting tremor. Journal of Neuroscience Methods, 145(1–2), 151–158. https://doi.org/10.1016/j.jneumeth.2004.12.009
   PubMed Web of Science ®Google Scholar
• Williams, M. O., Kevrekidis, I. G., & Rowley, C. W. (2015). A data–driven approximation of the Koopman operator: Extending dynamic mode decomposition. Journal of Nonlinear Science, 25(6), 1307–1346. https://doi.org/10.1007/s00332-015-9258-5
   Web of Science ®Google Scholar
• Wu, X., Zheng, Y., Chu, C.-H., & He, Z. (2020). Extracting deep features from short ECG signals for early atrial fibrillation detection. Artificial Intelligence in Medicine, 109, 101896.
   PubMed Web of Science ®Google Scholar
• Ye, H., Beamish, R. J., Glaser, S. M., Grant, S. C. H., Hsieh, C.-H., Richards, L. J., Schnute, J. T., & Sugihara, G. (2015). Equation-free mechanistic ecosystem forecasting using empirical dynamic modeling. Proceedings of the National Academy of Sciences of the United States of America, 112(13), E1569–E1576. https://doi.org/10.1073/pnas.1417063112
   PubMed Web of Science ®Google Scholar
• Zaslavsky, G. M., & Zaslavskij, G. M. (2005). Hamiltonian chaos and fractional dynamics. Oxford University Press on Demand.
   Google Scholar