In the field of neuroscience, it is very important to evaluate the causal coupling characteristics between bioelectrical signals accurately and effectively. Transfer entropy is commonly used to analyze complex data, especially the causal relationship between data with non-linear, multidimensional characteristics. However, traditional transfer entropy needs to estimate the probability density function of the variable, which is computationally complex and unstable. In this paper, a new and effective method for entropy transfer is proposed, by means of applying R-vine copula function estimation. The effectiveness of R-vine copula transfer entropy is first verified on several simulations, and then applied to intermuscular coupling analysis to explore the characteristics of the intermuscular coupling network of muscles in non-fatigue and fatigue conditions. The experiment results show that as the muscle group enters the fatigue state, the community structure can be adjusted and the muscle nodes participating in the exercise are fully activated, enabling the two-way interaction between different communities. Finally, it comes to the conclusion that the proposed method can make accurate inferences about complex causal coupling. Moreover, the characteristics of the intermuscular coupling network in both non-fatigue and fatigue states can provide a new theoretical perspective for the diagnosis of neuromuscular fatigue and sports rehabilitation, which has good application value.
Citation: Shaojun Zhu, Jinhui Zhao, Yating Wu, Qingshan She. Intermuscular coupling network analysis of upper limbs based on R-vine copula transfer entropy[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9437-9456. doi: 10.3934/mbe.2022439
In the field of neuroscience, it is very important to evaluate the causal coupling characteristics between bioelectrical signals accurately and effectively. Transfer entropy is commonly used to analyze complex data, especially the causal relationship between data with non-linear, multidimensional characteristics. However, traditional transfer entropy needs to estimate the probability density function of the variable, which is computationally complex and unstable. In this paper, a new and effective method for entropy transfer is proposed, by means of applying R-vine copula function estimation. The effectiveness of R-vine copula transfer entropy is first verified on several simulations, and then applied to intermuscular coupling analysis to explore the characteristics of the intermuscular coupling network of muscles in non-fatigue and fatigue conditions. The experiment results show that as the muscle group enters the fatigue state, the community structure can be adjusted and the muscle nodes participating in the exercise are fully activated, enabling the two-way interaction between different communities. Finally, it comes to the conclusion that the proposed method can make accurate inferences about complex causal coupling. Moreover, the characteristics of the intermuscular coupling network in both non-fatigue and fatigue states can provide a new theoretical perspective for the diagnosis of neuromuscular fatigue and sports rehabilitation, which has good application value.
| [1] |
M. Bourguignon, V. Jousmaki, S. S. Dalai, K. Jerbi, X. D. Tiège, Coupling between human brain activity and body movements: Insights from non-invasive electromagnetic recordings, Neuroimage, 203 (2019), 116177. https://doi.org/10.1016/j.neuroimage.2019.116177 doi: 10.1016/j.neuroimage.2019.116177
|
| [2] |
Q. She, H. Zheng, T. Tan, B. Zhang, Y. Fan, Z. Luo, Time-frequency-domain copula-based Granger causality and application to corticomuscular coupling in stroke, Int. J. Human. Robot., 16 (2019), 1950018. https://doi.org/10.1142/S021984361950018X doi: 10.1142/S021984361950018X
|
| [3] |
P. Grosse, M. J. Cassidy, P. Brown, EEG-EMG, MEG-EMG and EMG-EMG frequency analysis: physiological principles and clinical applications, Clin. Neurophysiol., 113 (2002), 1523-1531. https://doi.org/10.1016/S1388-2457(02)00223-7 doi: 10.1016/S1388-2457(02)00223-7
|
| [4] |
X. Chen, P. Xie, Y. Zhang, Y. Chen, S. Cheng, L. Zhang, Abnormal functional corticomuscular coupling after stroke, Neuroimage-Clinical, 19 (2018), 147-159. https://doi.org/10.1016/j.nicl.2018.04.004 doi: 10.1016/j.nicl.2018.04.004
|
| [5] |
C. M. Laine, F. J. Valero-Cuevas, Parkinson's disease exhibits amplified intermuscular coherence during dynamic voluntary action, Front. Neurol., 11 (2020), 204. https://doi.org/10.3389/fneur.2020.00204 doi: 10.3389/fneur.2020.00204
|
| [6] |
E. Colamarino, V. D. Seta, M. Masciullo, F. Cincotti, D. Mattia, F. Pichiorri, et al., Corticomuscular and intermuscular coupling in simple hand movements to enable a hybrid brain-computer interface, Int. J. Neural Syst., 31 (2021), 2150052. https://doi.org/10.1142/s0129065721500520 doi: 10.1142/s0129065721500520
|
| [7] |
V. Medved, S. Medved, I. Kovač, Critical appraisal of surface electromyography (sEMG) as a taught subject and clinical tool in medicine and kinesiology, Front. Neurol., 11 (2020), 1-17. https://doi.org/10.3389/fneur.2020.560363 doi: 10.3389/fneur.2020.560363
|
| [8] |
C. J. Houtman, D. F. Stegeman, J. P. V. Dijk, M. J. Zwarts, Changes in muscle fiber conduction velocity indicate recruitment of distinct motor unit populations, J. Appl. Physiol., 95 (2003), 1045-1054. https://doi.org/10.1152/japplphysiol.00665.2002 doi: 10.1152/japplphysiol.00665.2002
|
| [9] |
J. Murillo-Escobar, Y. E. Jaramillo-Munera, D. A. Orrego-Metaute, E. Delgado-Trejos, D. Cuesta-Frau, Muscle fatigue analysis during dynamic contractions based on biomechanical features and permutation entropy, Math. Biosci. Eng., 17 (2020), 2592-2615. https://doi.org/10.3934/mbe.2020142 doi: 10.3934/mbe.2020142
|
| [10] |
S. E. Jero, K. D. Bharathi, P. A. Karthick, S. Ramakrishnan, Muscle fatigue analysis in isometric contractions using geometric features of surface electromyography signals, Biomed. Signal. Process., 68 (2021), 1-11. https://doi.org/10.1016/j.bspc.2021.102603 doi: 10.1016/j.bspc.2021.102603
|
| [11] |
Q. Gao, J. Liu, Z. Ju, X. Zhang, Dual-hand detection for human-robot interaction by a parallel network based on hand detection and body pose estimation, IEEE Trans. Ind. Electron., 66 (2019), 9663-9672. https://doi.org/10.1109/TIE.2019.2898624 doi: 10.1109/TIE.2019.2898624
|
| [12] |
Q. Gao, J. Liu, Z. Ju, Robust real-time hand detection and localization for space human robot interaction based on deep learning, Neurocomputing, 390 (2020), 198-206. https://doi.org/10.1016/j.neucom.2019.02.066 doi: 10.1016/j.neucom.2019.02.066
|
| [13] |
Y. Sun, C. Xu, G. Li, F. Wan, J. Kong, D. Jiang, et al., Intelligent human computer interaction based on non redundant EMG signal, Alex. Eng. J., 59 (2020), 1149-1157. https://doi.org/10.1016/j.aej.2020.01.015 doi: 10.1016/j.aej.2020.01.015
|
| [14] |
Z. Yang, D. Jiang, Y. Sun, B. Tao, X. Tong, G. Jiang, et al., Dynamic gesture recognition using surface EMG signals based on multi-stream residual network, Front. Bioeng. Biotechnol., 9 (2021), 779353. https://doi.org/10.3389/fbioe.2021.779353 doi: 10.3389/fbioe.2021.779353
|
| [15] |
J. Qi, G. Jiang, G. Li, Y. Sun, B. Tao, Surface EMG hand gesture recognition system based on PCA and GRNN, Neural. Comput. Appl., 32 (2020), 6343-6351. https://doi.org/10.1007/s00521-019-04142-8 doi: 10.1007/s00521-019-04142-8
|
| [16] |
Y. Cheng, G. Li, M. Yu, D. Jiang, J. Yun, Y. Liu, et al., Gesture recognition based on surface electromyography-feature image, Concurr. Comput. Pract. Exp., 33 (2021), e6051. https://doi.org/10.1002/cpe.6051 doi: 10.1002/cpe.6051
|
| [17] |
R. Ma, L. Zhang, G. Li, D. Jiang, S. Xu, D. Chen, Grasping force prediction based on sEMG signals, Alex. Eng. J., 59 (2020), 1135-1147. https://doi.org/10.1016/j.aej.2020.01.007 doi: 10.1016/j.aej.2020.01.007
|
| [18] |
O. Sporns, Graph theory methods: Applications in brain networks, Dialogues Clin. Neurosci., 20 (2018), 111-120. https://doi.org/10.31887/dcns.2018.20.2/osporns doi: 10.31887/dcns.2018.20.2/osporns
|
| [19] |
J. N. Kerkman, D. Andreas, L. L. Gollo, B. Michael, T. W. Boonstra, Network structure of the human musculoskeletal system shapes neural interactions on multiple timescales, Sci. Adv., 4 (2018), 0497. https://doi.org/10.1126/sciadv.aat0497 doi: 10.1126/sciadv.aat0497
|
| [20] |
T. W. Boonstra, L. Faes, J. N. Kerkman, D. Marinazzo, Information decomposition of multichannel EMG to map functional interactions in the distributed motor system, Neuroimage, 202 (2019), 116093. https://doi.org/10.1016/j.neuroimage.2019.116093 doi: 10.1016/j.neuroimage.2019.116093
|
| [21] |
L. Barnett, A. K. Seth, The MVGC multivariate Granger causality toolbox: A new approach to Granger-causal inference, J. Neurosci. Methods, 223 (2014), 50-68. https://doi.org/10.1016/j.jneumeth.2013.10.018 doi: 10.1016/j.jneumeth.2013.10.018
|
| [22] | P. A. Stokes, P. L. Purdon, A study of problems encountered in Granger causality analysis from a neuroscience perspective, in Proceedings of the National Academy of Sciences, 114 (2017), 7063-7072. https://doi.org/10.1073/pnas.1704663114 |
| [23] |
T. Schreiber, Measuring information transfer, Phys. Rev. Lett., 85 (2000), 461-464. https://doi.org/10.1103/physrevlett.85.461 doi: 10.1103/physrevlett.85.461
|
| [24] |
R. Marschinski, H. Kantz, Analysing the information flow between financial time series, Eur. Phys. J. B., 30 (2002), 275-281. http://dx.doi.org/10.1140/epjb/e2002-00379-2 doi: 10.1140/epjb/e2002-00379-2
|
| [25] |
H. Kiwata, Analysis of dynamic Ising model by a variational approximate method: Estimation of transfer entropy, Phys. Rev. E., 101 (2020), 042102. https://doi.org/10.1103/PhysRevE.101.042102 doi: 10.1103/PhysRevE.101.042102
|
| [26] | A. Sklar, Random variables, joint distributions, and copulas, Kybernetica, 9 (1973), 449-460. |
| [27] |
S. R. Kasa, S. Bhattacharya, V. Rajan, Gaussian mixture copulas for high-dimensional clustering and dependency-based subtyping, Bioinformatics, 36 (2020), 621-628. https://doi.org/10.1093/bioinformatics/btz599 doi: 10.1093/bioinformatics/btz599
|
| [28] |
T. M. Erhardt, C. Czado, U. Schepsmeier, R-vine models for spatial time series with an application to daily mean temperature, Biometrics, 71 (2015), 323-332. http://dx.doi.org/10.1111/biom.12279 doi: 10.1111/biom.12279
|
| [29] |
M. Hu, H. Liang, A copula approach to assessing Granger causality, Neuroimage, 100 (2014), 125-134. https://doi.org/10.1016/j.neuroimage.2014.06.013 doi: 10.1016/j.neuroimage.2014.06.013
|
| [30] |
F. Sun, W. Zhang, N. Wang, W. Zhang, A copula entropy approach to dependence measurement for multiple degradation processes, Entropy, 21 (2019), 724. https://doi.org/10.3390/e21080724 doi: 10.3390/e21080724
|
| [31] |
U. Schepsmeier, A goodness-of-fit test for regular vine copula models, Econ. Rev., 38 (2019), 25-46. http://dx.doi.org/10.1080/07474938.2016.1222231 doi: 10.1080/07474938.2016.1222231
|
| [32] |
J. Dissmann, E. C. Brechmann, C. Czado, D. Kurowicka, Selecting and estimating regular vine copula and application to financial returns, Comput. Stat. Data Anal., 59 (2013), 52-69. http://dx.doi.org/10.1016/j.csda.2012.08.010 doi: 10.1016/j.csda.2012.08.010
|
| [33] | J. Ma, Discovering association with copula entropy, preprint, arXiv: 1907.12268, 2019. https://arXiv.org/abs/1907.12268 |
| [34] |
T. Bedford, R. M. Cooke, Probability density decomposition for conditionally dependent random variables modeled by vines, Ann. Math. Artif. Intell., 32 (2001), 245-268. http://dx.doi.org/10.1023/A:1016725902970 doi: 10.1023/A:1016725902970
|
| [35] |
J. N. Kerkman, A. Bekius, T. W. Boonstra, A. Daffertshofer, N. Dominic, Muscle synergies and coherence networks reflect different modes of coordination during walking, Front. Physiol., 11 (2020), 751. https://doi.org/10.3389/fphys.2020.00751 doi: 10.3389/fphys.2020.00751
|
| [36] |
S. Wang, J. Zheng, B. Zheng, X. Jiang, Phase-based grasp classification for prosthetic hand control using sEMG, Biosensors, 12 (2022), 57. https://doi.org/10.3390/bios12020057 doi: 10.3390/bios12020057
|
| [37] |
D. Chmielewska, G. Sobota, P. Dolibog, P. Dolibog, A. Opala-Berdzik, Reliability of pelvic floor muscle surface electromyography (sEMG) recordings during synchronous whole body vibration, Plos One, 16 (2021), e0251265. https://doi.org/10.1371/journal.pone.0251265 doi: 10.1371/journal.pone.0251265
|
| [38] |
C. Wang, M. Cai, Z. Hao, S. Nie, C. Liu, H. Du, et al., Stretchable, multifunctional epidermal sensor patch for surface electromyography and strain measurements, Adv. Intell. Syst., 3 (2021), 2100031. http://dx.doi.org/10.1002/aisy.202100031 doi: 10.1002/aisy.202100031
|
| [39] |
J. D. Cavalcanti, G. A. F. Fregonezi, A. J. Sarmento, T. Bezerra, L. P. Gualdi, F. Pennati, et al., Electrical activity and fatigue of respiratory and locomotor muscles in obstructive respiratory diseases during field walking test, Plos One, 17 (2022), e0266365. https://doi.org/10.1371/journal.pone.0266365 doi: 10.1371/journal.pone.0266365
|
| [40] |
J. G. Augustson, J. Minker, An analysis of some graph theoretical cluster techniques, J. ACM., 17 (1970), 571-588. https://doi.org/10.1145/321607.321608 doi: 10.1145/321607.321608
|
| [41] |
M. Windzio, The "social brain" reciprocity, and social network segregation along ethnic boundaries, Hum. Nat., 31 (2020), 443-461. https://doi.org/10.1007/s12110-020-09382-5 doi: 10.1007/s12110-020-09382-5
|
| [42] |
J. Ushiyama, M. Katsu, Y. Masakado, A. Kimura, M. Liu, J. Ushiba, Muscle fatigue-induced enhancement of corticomuscular coherence following sustained submaximal isometric contraction of the tibialis anterior muscle, J. Appl. Physiol., 110 (2011), 1233-1240. https://doi.org/10.1152/japplphysiol.01194.2010 doi: 10.1152/japplphysiol.01194.2010
|
| [43] |
T. W. Boonstra, A. Danna-Dos-Santos, H. B. Xie, M. Roerdink, J. F. Stins, M. Breakspear, Muscle networks: Connectivity analysis of EMG activity during postural control, Sci. Rep., 5 (2015), 1-14. https://doi.org/10.1038/srep17830 doi: 10.1038/srep17830
|
| [44] |
A. Zhang, J. Fang, W. Hu, V. D. Calhoun, Y. Wang, A latent Gaussian copula model for mixed data analysis in brain imaging genetics, IEEE/ACM Trans. Comput. Biol. Bioinform., 18 (2021), 1350-1360. https://doi.org/10.1109/TCBB.2019.2950904 doi: 10.1109/TCBB.2019.2950904
|
| [45] |
M. T. Amin, F. Khan, S. Ahmed, S. Imtiaz, Risk-based fault detection and diagnosis for nonlinear and non-Gaussian process systems using R-vine copula, Process Saf. Environ. Prot., 150 (2021), 123-136. https://doi.org/10.1016/j.psep.2021.04.010 doi: 10.1016/j.psep.2021.04.010
|
| [46] |
K. M. Steele, M. C. Tresch, E. J. Perreault, The number and choice of muscles impact the results of muscle synergy analyses, Front. Comput. Neurosci., 7 (2013), 105. http://dx.doi.org/10.3389/fncom.2013.00105 doi: 10.3389/fncom.2013.00105
|
| [47] |
C. Li, G. Li, G. Jiang, D. Chen, H. Liu, Surface EMG data aggregation processing for intelligent prosthetic action recognition, Neural Comput. Appl., 32 (2020), 16795-16806. https://doi.org/10.1007/s00521-018-3909-z doi: 10.1007/s00521-018-3909-z
|
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Shaojun Zhu, Jinhui Zhao, Yating Wu, Qingshan She. Intermuscular coupling network analysis of upper limbs based on R-vine copula transfer entropy[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9437-9456. doi: 10.3934/mbe.2022439
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