Separation of the fetal heart signal in a synchronous network consisting of maternal and fetal hearts

Document Type : Article

Authors

Department of Biomedical Engineering, Amirkabir University of Technology, Tehran 15875-4413, Iran

Abstract

This paper studies the heart's oscillation model to separate fetal and maternal ECGs from abdominal recordings. To this aim, two phases are designed. A Modified version of the Duffing-Van der Pol oscillator is considered a computational heart model in the modeling phase. To evaluate the interaction effects of the maternal and fetal heart and the differences and features of the fetal heart structure, the fetal heart model is Modified based on the maternal heart model. A non-identical network is employed as an interactive network of the mother and the fetus's heart. Then the degree of the network synchronization is measured with the help of a pattern synchronization index of the non-identical network. An attempt is made to separate the fetal signal from the mother's in abdominal signals in the separation phase. Two problem-solving approaches are explained; the step-by-step mode that calculates the signal at any given moment and the construction of general equations. These approaches end up calculating the variables, which stand for maternal and fetal signal. That makes it possible to achieve the separation of maternal and fetal ECGs.

Keywords


References:
1. Warnes, C.A., Liberthson, R., Danielson, G.K., et al. "Task force 1: the changing profile of congenital heart disease in adult life", J. Am. Coll. Cardiol., 37(5), pp. 1170-1175 (2001).
2. Neilson, J.P. "Fetal electrocardiogram (ECG) for fetal monitoring during labour", Cochrane Database Syst. Rev., 2015(12), CD000116 (2015).
3. Westgate, J., Harris, M., Curnow, J.S., et al. "Plymouth randomized trial of cardiotocogram only versus ST waveform plus cardiotocogram for intrapartum monitoring in 2400 cases", Am. J. Obstet. Gynecol., 169(5), pp. 1151-1160 (1993).
4. Newbold, S., Wheeler, T., and Clewlow, F. "Comparison of the T/QRS ratio of the fetal electrocardiogram and the fetal heart rate during labour and the relation of these variables to condition at delivery", BJOG, 98(2), pp. 173-178 (1991).
5. Jaros, R., Martinek, R., and Kahankova, R. "Nonadaptive methods for fetal ECG signal processing: A review and appraisal", Sensors, 18(11), 3648 (2018).
6. Sameni, R. and Clifford, G.D. "A review of fetal ECG signal processing; issues and promising directions", Open Pacing Electrophysiol. Ther. J., 3, pp. 4-20 (2010).
7. Alnuaimi, S.A., Jimaa, S., and Khandoker, A.H. "Fetal cardiac doppler signal processing techniques: challenges and future research directions", Front. Bioeng. Biotechnol., 5, p. 82 (2017).
8. Martinek, R., Kahankova, R., Jezewski, J., et al.  Comparative effectiveness of ICA and PCA in extraction of fetal ECG from abdominal signals: Toward non-invasive fetal monitoring", Front. Physiol., 9, p. 648 (2018).
9. Clifford, G.D., Silva, I., Behar, J., et al. "Non-invasive fetal ECG analysis", Physiol. Meas., 35(8), p. 1521 (2014).
10. Behar, J., Oster, J., and Clifford, G.D. "Non-invasive FECG extraction from a set of abdominal sensors", In 2013 Computing in Cardiology Conference (CinC 2013) (No. ISBN 9781479908851), pp. 297-300, Institute of Electrical and Electronics Engineers (IEEE),Curran Associates, Inc (2013).
11. Li, S., Hou, Z., and Li, Q. "A new algorithm for extracting fetal ECG signal using singular value decomposition method", In Acoustics, Speech, and Signal Processing, ICASSP-92., 1992 IEEE International Conference on, pp. 585-588 (1992).
12. Queyam, A.B., Pahuja, S.K., and Singh, D. "Noninvasive feto-maternal well-being monitoring: A review of methods", J. Eng. Sci. Technol. Rev., 10(1), pp. 177-190 (2017).
13. Zarzoso, V., Millet-Roig, J., and Nandi, A. "Fetal ECG extraction from maternal skin electrodes using blind source separation and adaptive noise cancellation techniques", in Computers in Cardiology 2000, 2000, pp. 431-434.
14. Zhou, X., Engler, P., and Coblentz, M.G. "Adaptive filter application in fetal electrocardiography", in Computer-Based Medical Systems, 1992. Proceedings., Fifth Annual IEEE Symposium on, pp. 656-662 (1992). 
15. Kam, A. and Cohen, A. "Detection of fetal ECG with IIR adaptive filtering and genetic algorithms", in Acoustics, Speech, and Signal Processing, Proceedings., IEEE International Conference on, pp. 2335-2338 (1999).
16. Horner, S., Holls, W., and Crilly, P.B. "Non-invasive fetal electrocardiograph enhancement", in Computers in Cardiology Proceedings of, 1992, pp. 163-166 (1992).
17. Kanjilal, P.P., Palit, S., and Saha, G. "Fetal ECG extraction from single-channel maternal ECG using singular value decomposition", IEEE. Trans. Biomed. Eng., 44(1), pp. 51-59 (1997).
18. Vigneron, V., Paraschiv-Ionescu, A., Azancot, A., et al. "Fetal electrocardiogram extraction based on nonstationary ICA and wavelet denoising", in Signal Processing and Its Applications, 2003. Proceedings. Seventh International Symposium on, pp. 69-72 (2003).
19. Lee, J., Park, K., and Lee, K. "Temporally constrained ICA-based foetal ECG separation", Electron. Lett., 41(21), pp. 1158-1160 (2005).
20. Gao, P., Chang, E.-C., and Wyse, L. "Blind separation of fetal ECG from single mixture using SVD and ICA", in Information, Communications and Signal Processing, 2003 and Fourth Pacific Rim Conference on Multimedia. Proceedings of the 2003 Joint Conference of the Fourth International Conference on, pp. 1418-1422 (2003).
21. Bell, A.J. and Sejnowski, T.J. "The 'independent components' of natural scenes are edge filters", Vis. Res., 37(23), pp. 3327-3338 (1997).
22. Datian, Y. and Xuemei, O. "Application of wavelet analysis in detection of fetal ECG", in Engineering in Medicine and Biology Society, 1996. Bridging Disciplines for Biomedicine. Proceedings of the 18th Annual International Conference of the IEEE, pp. 1043-1044(1996). 
23. Khamene, A. and Negahdaripour, S. "A new method for the extraction of fetal ECG from the composite abdominal signal", IEEE. Trans. Biomed. Eng., 47(4), pp. 507-516 (2000).
24. Vaidya, R.R. and Chaitra, N. "Comparison of Adaptive filters in extraction of Fetal ECG", in 2020 International Conference on Smart Electronics and Communication (ICOSEC), pp. 1066-1070 (2020).
25. Kahankova, R., Martinek, R., and Bilik, P. "Fetal ECG extraction from abdominal ECG using RLS based adaptive algorithms", in 2017 18th International Carpathian Control Conference (ICCC), pp. 337-342 (2017).
26. Nasiri, M. "Fetal electrocardiogram signal extraction by ANFIS trained with PSO method", Int. J. Electr. Comput. Eng., 2(2), p. 247 (2012).
27. Uddin, Z., Orakzai, F., and Qamar, A. "Order and phase ambiguities correction in the ICA based separation of speech signals", Int. J. Speech Technol., 23(2), pp. 459-469 (2020).
28. Jimenez-Gonzalez, A. and Castaneda-Villa, N. "Blind extraction of fetal and maternal components from the abdominal electrocardiogram: An ICA implementation for low-dimensional recordings", Biomed. Signal Process. Control., 58, 101836 (2020).
29. Baldazzi, G., Sulas, E., Brungiu, E., et al. "Waveletbased post-processing methods for the enhancement of non-invasive fetal ECG", in 2019 Computing in Cardiology (CinC), pp. 1-4 (2019).
30. Vijila, C.K.S., Kanagasabapathy, P., Johnson, S., et al. "Interference cancellation in FECG using artificial intelligence techniques", in Intelligent Sensing and Information Processing, ICISIP 2006. Fourth International Conference on, pp. 174-177 (2006).
31. Ungureanu, M., Bergmans, J.W., Mischi, M., et al."Improved  method for fetal heart rate monitoring", in Engineering in Medicine and Biology Society, 2005.IEEE-EMBS 2005. 27th Annual International Conference of the, pp. 5916-5919 (2006).
32. Yang, Y. and Guo, C. "Blind extraction for noisy fetal electrocardiogram by using Gaussian m oments", in Fourth International Conference on Natural Computation,pp. 44-47 (2008). 
33. Zhang, Z.-L. and Yi, Z. "Variable step-size extraction algorithm for extracting fetal electrocardiogram", in Neural Networks and Brain, 2005. ICNN&B'05. International Conference on, pp. 434-437 (2005).
34. Egan, F. "Computational models: A modest role for content", Stud. Hist. Philos. Sci. A, 41(3), pp. 253-259 (2010).
35. An, G., Mi, Q., Dutta-Moscato, J., et al. "Agentbased models in translational systems biology", Wiley Interdiscip. Rev. Syst. Biol. Med., 1(2), pp. 159-171 (2009).
36. Barlas, Y. "Formal aspects of model validity and validation in system dynamics", Syst. Dyn. Rev., 12(3), pp. 183-210 (1996).
37. Kresh, J.Y., Izrailtyan, I., and Wechsler, A.S. "The heart as a complex adaptive system", in Unifying Themes in Complex Systems, Ed: CRC Press, pp. 289- 304 (2018).
38. Lim, G.B. "Evolutionary adaptations of human hearts", Nat. Rev. Cardiol., 16(12), pp. 700-700 (2019).
39. Bonabeau, E. "Agent-based modeling: Methods and techniques for simulating human systems", Proceedings of the National Academy of Sciences, 99(suppl 3), pp. 7280-7287 (2002).
40. Jovanovic, V.T. and Kazerounian, K. "Using chaos to obtain global solutions in computational kinematics", Transactions-American Society of Mechanical Engineers Journal of Mechanical Design, 120(2), pp. 299- 304 (1998).
41. Eskov, V., Eskov, V., Vochmina, J., et al. "The evolution of the chaotic dynamics of collective modes as a method for the behavioral description of living systems", Mosc. Univ. Phys. Bull., 71(2), pp. 143-154 (2016).
42. Bazeia, D., Pereira, M., Brito, A., et al. "A novel procedure for the identification of chaos in complex biological systems", Sci. Rep., 7(1), pp. 1-9 (2017).
43. Harrar, K. and Hamami, L. "The box counting method for evaluate the fractal Dimension in radiographic images", in 6th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing, Egypt, p. 385 (2007).
44. Mishra, A.K. and Raghav, S. "Local fractal dimension based ECG arrhythmia classification", Biomed. Signal Process. Control., 5(2), pp. 114-123 (2010).
45. Sharma, V. "Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier", Open Cardiovasc. Med. J., 3, p. 110 (2009).
46. Wagner, C.D. and Persson, P.B. "Chaos in the cardiovascular  system: an update", Cardiovasc. Res., 40(2), pp. 257-264 (1998).
47. Chialvo, D.R., Michaels, D.C., and Jalife, J. "Supernormal flexcitability as a mechanism of chaotic dynamics of activation in cardiac Purkinje fibers", Circ. Res., 66(2), pp. 525-545 (1990).
48. Qu, Z., Hu, G., Garfinkel, A., et al. "Nonlinear and stochastic dynamics in the heart", Phys. Rep., 543(2), pp. 61-162 (2014).
49. Van Der Pol, B. and Van Der Mark, J. "LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart", Lond. Edinb. Dubl. Phil. Mag. J. Sci., 6(38), pp. 763-775 (1928).
50. Grudzinski, K. and Z_ ebrowski, J.J. "Modeling cardiac pacemakers with relaxation oscillators", Physica A, 336(1-2), pp. 153-162 (2004).
51. Zduniak, B., Bodnar, M., and Forys, U. "A modified van der Pol equation with delay in a description of the heart action", Int. J. Appl. Math. Comput. Sci., 24(4), pp. 853-863 (2014).
52. Raja, M.A.Z., Shah, F.H., and Syam, M.I. "Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model", Neural. Comput. Appl., 30(12), pp. 3651-3675 (2018).
53. dos Santos, A.M., Lopes, S.R., and Viana, R.R.L. "Rhythm synchronization and chaotic modulation of coupled Van der Pol oscillators in a model for the heartbeat", Physica A, 338(3-4), pp. 335-355 (2004).
54. Pereira, T.L., de Paula, A.S., Cheffer, A., et al. "Bifurcation from normal functioning to pathologies in a cardiac model using a three modified coupled van der pol Oscillator", in Proceedings of the XVIII International Symposium on Dynamic Problems of Mechanics (DINAME 2019), Brazil (2019).
55. Gois, S.R. and Savi, M.A. "An analysis of heart rhythm dynamics using a three-coupled oscillator model", Chaos Solitons Fractals, 41(5), pp. 2553-2565 (2009).
56. Boccaletti, S., Hwang, D.-U., Chavez, M., et al. "Synchronization in dynamical networks: Evolution along commutative graphs", Phys. Rev. E, 74(1), 016102 (2006).
57. Hindes, J. and Schwartz, I.B. "Rare slips in fluctuating synchronized oscillator networks", Chaos, 28(7), 071106 (2018).
58. Pikovsky, A. and Rosenblum, M. "Dynamics of globally coupled oscillators: Progress and perspectives", Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(9), 097616 (2015).
59. Zhang, Y., Nishikawa, T., and Motter, A.E. "Asymmetry-induced synchronization in oscillator networks", Phys. Rev. E, 95(6), 062215 (2017).
60. Zhang, L., Motter, A.E., and Nishikawa, T. "Incoherence-mediated remote synchronization", Phys. Rev. Lett., 118(17), 174102 (2017).
61. Chen, T., Peng, S., and Zhang, Z. "Finite-time synchronization of Markovian jumping complex networks with non-identical nodes and impulsive effects", Entropy, 21(8), p. 779 (2019).
62. Panahi, S. and Jafari, S. "New synchronization index of non-identical networks", Discrete Contin. Dyn. Syst. Ser. S, 14(4), p. 1359 (2021).
63. Silvestri, F., Acciarito, S., and Khanal, G.M. "Relationship between mathematical parameters of modified Van der Pol Oscillator model and ECG morphological features", Int. J. Adv. Sci. Eng. Inf. Technol., 9(2), pp. 601-608 (2019). 
64. Rajagopal, K., Li, C., Nazarimehr, F., et al. "Chaotic dynamics of modified wien bridge oscillator with fractional order memristor", Radioengineering, 28(1), pp. 165-174 (2019).
65. Kim, Y.J., Park, C.S., and Kim, K.W. "Chaos time series model for nonlinear multi-step ahead prediction", in Proceedings of BS2015:14th Conference of International Building Performance Simulation Association, Hyderabad, India (2015).
66. Fathima, T. and Jothiprakash, V. "Behavioural analysis of a time series-A chaotic approach", Sadhana, 39(3), pp. 659-676 (2014).
67. Hajiloo, R., Salarieh, H., and Alasty, A. "Chaos control in delayed phase space constructed by the Takens embedding theory", Commun. Nonlinear. Sci. Numer. Simul., 54, pp. 453-465 (2018).
68. Xu, P. "Differential phase space reconstructed for chaotic time series", Appl. Math. Model., 33(2), pp. 999-1013 (2009).
69. Pikovsky, A., Rosenblum, M., and Kurths, J.  Synchronization: a universal concept in nonlinear sciences", 12: Cambridge University Press (2003).
70. Avila, G.R., Kurths, J., Guisset, J.-L., et al. "How do small differences in nonidentical pulse-coupled oscillators induce great changes in their synchronous behavior?", Eur. Phys. J. : Spec. Top., 223(13), pp. 2759-2773 (2014).
71. Xiang, J. and Chen, G. "On the V-stability of complex dynamical networks", Automatica, 43(6), pp. 1049- 1057 (2007).
72. Hill, D.J. and Zhao, J. "Global synchronization of complex dynamical networks with non-identical nodes", in 2008 47th IEEE Conference on Decision and Control, pp. 817-822 (2008).
73. Zhao, J., Hill, D.J., and Liu, T. "Passivity-based output synchronization of dynamical networks with non-identical nodes", in 49th IEEE Conference on Decision and Control (CDC), pp. 7351-7356 (2010).
74. Zhang, Y. and Motter, A.E. "Identical synchronization of nonidentical oscillators: when only birds of different feathers  flock together", Nonlinearity, 31(1) (2017).
75. Rosenblum, M.G., Pikovsky, A.S., and Kurths, J. "Phase synchronization of chaotic oscillators", Phys. Rev. Lett., 76(11), 1804 (1996).
76. Wen, D., Zhou, Y., and Li, X. "A critical review: coupling and synchronization analysis methods of EEG signal with mild cognitive impairment", Front. Aging Neurosci., 7, p. 54 (2015).
77. Zandi-Mehran, N., Jafari, S., and Golpayegani, S.M.R.H. "Signal separation in an aggregation of chaotic signals", Chaos Solitons Fractals, 138, 109851 (2020).