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Identifying nonlinear dynamics of brain functional networks of patients with schizophrenia by sample entropy

  • Yanbing Jia
  • Huaguang GuEmail author
Original Paper
  • 35 Downloads

Abstract

Different regions in the human brain functionally connect with each other forming a brain functional network, and the time evolution of functional connectivity between different brain regions exhibits complex nonlinear dynamics. This study intends to characterize the nonlinear properties of dynamic functional connectivity and to explore how schizophrenia influences such nonlinear properties. The dynamic functional connectivity is constructed by analyzing resting-state functional magnetic resonance imaging data, and its nonlinear properties are characterized by sample entropy (SampEn), with larger SampEn values corresponding to more complexity. To identify the influence of schizophrenia on SampEn, the difference in SampEn between patients with schizophrenia and healthy controls is analyzed at different levels of the brain. It is shown that the patients exhibit significantly higher SampEn at different levels of the brain, and such phenomenon is mainly caused by a significantly higher SampEn in the visual cortex of the patients. Furthermore, it is also shown that SampEn of the visual cortex is significantly and positively correlated with the illness duration or the symptom severity scores. Because the visual cortex is implicated in the visual information processing, these results can shed light on abnormal visual functions of patients with schizophrenia, and also are consistent with the notion that the nonlinearity underlies the irregularity in psychotic symptoms of schizophrenia. This study extends the application of nonlinear dynamics in brain sciences and suggests that nonlinear properties are effective biomarkers in characterizing the brain functional networks of patients with brain diseases.

Keywords

Sample entropy Nonlinear dynamics Dynamic functional connectivity Brain functional networks Schizophrenia 

Notes

Compliance with ethical standard

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Elbert, T., Ray, W.J., Kowalik, Z.J., Skinner, J.E., Graf, K.E., Birbaumer, N.: Chaos and physiology: deterministic chaos in excitable cell assemblies. Physiol. Rev. 74, 1–47 (1994)CrossRefGoogle Scholar
  2. 2.
    Gu, H.G., Pan, B.B., Chen, G.R., Duan, L.X.: Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models. Nonlinear Dyn. 78, 391–407 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Li, Y.Y., Gu, H.G.: The distinct stochastic and deterministic dynamics between period-adding and period-doubling bifurcations of neural bursting patterns. Nonlinear Dyn. 87, 2541–2562 (2017)CrossRefGoogle Scholar
  4. 4.
    Shilnikov, A.: Complete dynamical analysis of a neuron model. Nonlinear Dyn. 68, 305–328 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    van Vreeswijk, C., Sompolinsky, H.: Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724–1726 (1996)CrossRefGoogle Scholar
  6. 6.
    Buzsaki, G., Draguhn, A.: Neuronal oscillations in cortical networks. Science 304, 1926–1929 (2004)CrossRefGoogle Scholar
  7. 7.
    Ma, J., Hu, B.L., Wang, C.N., Jin, W.Y.: Simulating the formation of spiral wave in the neuronal system. Nonlinear Dyn. 73, 73–83 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ma, J., Tang, J.: A review for dynamics in neuron and neuronal network. Nonlinear Dyn. 89, 1569–1578 (2017)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Wang, G.P., Jin, W.Y., Wang, A.: Synchronous firing patterns and transitions in small-world neuronal network. Nonlinear Dyn. 81, 1453–1458 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wang, X.J.: Neurophysiological and computational principles of cortical rhythms in cognition. Physiol. Rev. 90, 1195–1268 (2010)CrossRefGoogle Scholar
  11. 11.
    Fernandez, A., Lopez-Ibor, M.I., Turrero, A., Santos, J.M., Moron, M.D., Hornero, R., Gomez, C., Mendez, M.A., Ortiz, T., Lopez-Ibor, J.J.: Lempel-Ziv complexity in schizophrenia: a MEG study. Clin. Neurophysiol. 122, 2227–2235 (2011)CrossRefGoogle Scholar
  12. 12.
    Liu, C.Y., Krishnan, A.P., Yan, L.R., Smith, R.X., Kilroy, E., Alger, J.R., Ringman, J.M., Wang, D.J.J.: Complexity and synchronicity of resting state blood oxygenation level-dependent (BOLD) functional MRI in normal aging and cognitive decline. J. Magn. Reson. Imaging 38, 36–45 (2013)CrossRefGoogle Scholar
  13. 13.
    Maksimenko, V.A., Pavlov, A., Runnova, A.E., Nedaivozov, V., Grubov, V., Koronovslii, A., Pchelintseva, S.V., Pitsik, E., Pisarchik, A.N., Hramov, A.E.: Nonlinear analysis of brain activity, associated with motor action and motor imaginary in untrained subjects. Nonlinear Dyn. 91, 2803–2817 (2018)CrossRefGoogle Scholar
  14. 14.
    Wang, Z., Li, Y., Childress, A.R., Detre, J.A.: Brain entropy mapping using fMRI. Plos One 9, e89948 (2014)CrossRefGoogle Scholar
  15. 15.
    Sokunbi, M.O.: Sample entropy reveals high discriminative power between young and elderly adults in short fMRI data sets. Front. Neuroinform. 8, 69 (2014)CrossRefGoogle Scholar
  16. 16.
    Sokunbi, M.O., Gradin, V.B., Waiter, G.D., Cameron, G.G., Ahearn, T.S., Murray, A.D., Steele, D.J., Staff, R.T.: Nonlinear complexity analysis of brain fMRI signals in schizophrenia. Plos One 9, e95146 (2014)CrossRefGoogle Scholar
  17. 17.
    Yan, J.Q., Wang, Y.H., Ouyang, G.X., Yu, T., Li, Y.J., Sik, A., Li, X.L.: Analysis of electrocorticogram in epilepsy patients in terms of criticality. Nonlinear Dyn. 83, 1909–1917 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yang, A.C., Huang, C.C., Yeh, H.L., Liu, M.E., Hong, C.J., Tu, P.C., Chen, J.F., Huang, N.E., Peng, C.K., Lin, C.P., Tsai, S.J.: Complexity of spontaneous BOLD activity in default mode network is correlated with cognitive function in normal male elderly: a multiscale entropy analysis. Neurobiol. Aging 34, 428–438 (2013)CrossRefGoogle Scholar
  19. 19.
    Yeh, C.H., Shi, W.B.: Generalized multiscale Lempel-Ziv complexity of cyclic alternating pattern during sleep. Nonlinear Dyn. 93, 1899–1910 (2018)CrossRefGoogle Scholar
  20. 20.
    Deco, G., Jirsa, V.K.: Ongoing cortical activity at rest: criticality, multistability, and ghost attractors. J. Neurosci. 32, 3366–3375 (2012)CrossRefGoogle Scholar
  21. 21.
    Biswal, B., Yetkin, F.Z., Haughton, V.M., Hyde, J.S.: Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn. Reson. Med. 34, 537–541 (1995)CrossRefGoogle Scholar
  22. 22.
    Eguiluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V.: Scale-free brain functional networks. Phys. Rev. Lett. 94, 018102 (2005)CrossRefGoogle Scholar
  23. 23.
    Fox, M.D., Raichle, M.E.: Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nat. Rev. Neurosci. 8, 700–711 (2007)CrossRefGoogle Scholar
  24. 24.
    Sheffield, J.M., Barch, D.M.: Cognition and resting-state functional connectivity in schizophrenia. Neurosci. Biobehav. R. 61, 108–120 (2016)CrossRefGoogle Scholar
  25. 25.
    Hull, J.V., Dokovna, L.B., Jacokes, Z.J., Torgerson, C.M., Irimia, A., Van Horn, J.D.: Resting-state functional connectivity in autism spectrum disorders: a review. Front. Psychiatry 7, 205 (2016)CrossRefGoogle Scholar
  26. 26.
    Mulders, P.C., van Eijndhoven, P.F., Schene, A.H., Beckmann, C.F., Tendolkar, I.: Resting-state functional connectivity in major depressive disorder: a review. Neurosci. Biobehav. R. 56, 330–344 (2015)CrossRefGoogle Scholar
  27. 27.
    Wang, R., Wang, L., Yang, Y., Li, J.J., Wu, Y., Lin, P.: Random matrix theory for analyzing the brain functional network in attention deficit hyperactivity disorder. Phys. Rev. E 94, 052411 (2016)CrossRefGoogle Scholar
  28. 28.
    Friston, K.J., Frith, C.D., Liddle, P.F., Frackowiak, R.S.: Functional connectivity: the principal-component analysis of large (PET) data sets. J. Cerebr. Blood F. Met. 13, 5–14 (1993)CrossRefGoogle Scholar
  29. 29.
    Bullmore, E., Sporns, O.: The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349 (2012)CrossRefGoogle Scholar
  30. 30.
    Cheng, W., Rolls, E.T., Gu, H.G., Zhang, J., Feng, J.F.: Autism: reduced connectivity between cortical areas involved in face expression, theory of mind, and the sense of self. Brain 138, 1382–1393 (2015)CrossRefGoogle Scholar
  31. 31.
    Takahashi, T.: Complexity of spontaneous brain activity in mental disorders. Prog. Neuro-Psychoph. 45, 258–266 (2013)CrossRefGoogle Scholar
  32. 32.
    Cabral, J., Fernandes, H.M., Van Hartevelt, T.J., James, A.C., Kringelbach, M.L., Deco, G.: Structural connectivity in schizophrenia and its impact on the dynamics of spontaneous functional networks. Chaos 23, 046111 (2013)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Cheng, W., Palaniyappan, L., Li, M., Kendrick, K.M., Zhang, J., Luo, Q., Liu, Z., Yu, R., Deng, W., Wang, Q., Ma, X., Guo, W., Francis, S., Liddle, P., Mayer, A.R., Schumann, G., Li, T., Feng, J.: Voxel-based, brain-wide association study of aberrant functional connectivity in schizophrenia implicates thalamocortical circuitry. NPJ. Schizophrenia 1, 15016 (2015)CrossRefGoogle Scholar
  34. 34.
    Lynall, M.E., Bassett, D.S., Kerwin, R., McKenna, P.J., Kitzbichler, M., Muller, U., Bullmore, E.: Functional connectivity and brain networks in schizophrenia. J. Neurosci. 30, 9477–9487 (2010)CrossRefGoogle Scholar
  35. 35.
    Manoliu, A., Riedl, V., Zherdin, A., Muhlau, M., Schwerthoffer, D., Scherr, M., Peters, H., Zimmer, C., Forstl, H., Bauml, J., Wohlschlager, A.M., Sorg, C.: Aberrant dependence of default mode/central executive network interactions on anterior insular salience network activity in schizophrenia. Schizophrenia Bull. 40, 428–437 (2014)CrossRefGoogle Scholar
  36. 36.
    Whitfield-Gabrieli, S., Thermenos, H.W., Milanovic, S., Tsuang, M.T., Faraone, S.V., McCarley, R.W., Shenton, M.E., Green, A.I., Nieto-Castanon, A., LaViolette, P., Wojcik, J., Gabrieli, J.D., Seidman, L.J.: Hyperactivity and hyperconnectivity of the default network in schizophrenia and in first-degree relatives of persons with schizophrenia. P. Natl. Acad. Sci. USA 106, 1279–1284 (2009)CrossRefGoogle Scholar
  37. 37.
    Allen, E.A., Damaraju, E., Plis, S.M., Erhardt, E.B., Eichele, T., Calhoun, V.D.: Tracking whole-brain connectivity dynamics in the resting state. Cereb. Cortex 24, 663–676 (2014)CrossRefGoogle Scholar
  38. 38.
    Chang, C., Glover, G.H.: Time-frequency dynamics of resting-state brain connectivity measured with fMRI. NeuroImage 50, 81–98 (2010)CrossRefGoogle Scholar
  39. 39.
    Hutchison, R.M., Womelsdorf, T., Gati, J.S., Everling, S., Menon, R.S.: Resting-state networks show dynamic functional connectivity in awake humans and anesthetized macaques. Hum. Brain Mapp. 34, 2154–2177 (2013)CrossRefGoogle Scholar
  40. 40.
    Kaiser, R.H., Whitfield-Gabrieli, S., Dillon, D.G., Goer, F., Beltzer, M., Minkel, J., Smoski, M., Dichter, G., Pizzagalli, D.A.: Dynamic resting-state functional connectivity in major depression. Neuropsychopharmacol. 41, 1822–1830 (2016)CrossRefGoogle Scholar
  41. 41.
    Marusak, H.A., Calhoun, V.D., Brown, S., Crespo, L.M., Sala-Hamrick, K., Gotlib, I.H., Thomason, M.E.: Dynamic functional connectivity of neurocognitive networks in children. Hum. Brain Mapp. 38, 97–108 (2017)CrossRefGoogle Scholar
  42. 42.
    Rashid, B., Damaraju, E., Pearlson, G.D., Calhoun, V.D.: Dynamic connectivity states estimated from resting fMRI identify differences among schizophrenia, bipolar disorder, and healthy control subjects. Front. Hum. Neurosci. 8, 897 (2014)CrossRefGoogle Scholar
  43. 43.
    Wang, R., Zhang, Z.Z., Ma, J., Yang, Y., Lin, P., Wu, Y.: Spectral properties of the temporal evolution of brain network structure. Chaos 25, 123112 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Zhang, J., Cheng, W., Liu, Z., Zhang, K., Lei, X., Yao, Y., Becker, B., Liu, Y., Kendrick, K.M., Lu, G., Feng, J.: Neural, electrophysiological and anatomical basis of brain-network variability and its characteristic changes in mental disorders. Brain 139, 2307–2321 (2016)CrossRefGoogle Scholar
  45. 45.
    Jia, Y., Gu, H., Luo, Q.: Sample entropy reveals an age-related reduction in the complexity of dynamic brain. Sci. Rep. 7, 7990 (2017)CrossRefGoogle Scholar
  46. 46.
    http://www.fil.ion.ucl.ac.uk/spm. Accessed 20 Apr 2018
  47. 47.
    Yan, C.G., Zang, Y.F.: DPARSF: a MATLAB toolbox for pipeline data analysis of resting-state fMRI. Front. Syst. Neurosci. 4, 13 (2010)Google Scholar
  48. 48.
    Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., Mazoyer, B., Joliot, M.: Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage 15, 273–289 (2002)CrossRefGoogle Scholar
  49. 49.
    Shirer, W.R., Ryali, S., Rykhlevskaia, E., Menon, V., Greicius, M.D.: Decoding subject-driven cognitive states with whole-brain connectivity patterns. Cereb. Cortex 22, 158–165 (2012)CrossRefGoogle Scholar
  50. 50.
    Li, X., Zhu, D., Jiang, X., Jin, C., Zhang, X., Guo, L., Zhang, J., Hu, X., Li, L., Liu, T.: Dynamic functional connectomics signatures for characterization and differentiation of PTSD patients. Hum. Brain Mapp. 35, 1761–1778 (2014)CrossRefGoogle Scholar
  51. 51.
    Richman, J.S., Moorman, J.R.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol Heart. C. 278, H2039–H2049 (2000)CrossRefGoogle Scholar
  52. 52.
    Pincus, S.M.: Assessing serial irregularity and its implications for health. Ann. NY. Acad. Sci. 954, 245–267 (2001)CrossRefGoogle Scholar
  53. 53.
    Pincus, S.M., Goldberger, A.L.: Physiological time—series analysis—what does regularity quantify. Am. J. Physiol. 266, H1643–H1656 (1994)Google Scholar
  54. 54.
    Guo, S., Kendrick, K.M., Yu, R., Wang, H.L., Feng, J.: Key functional circuitry altered in schizophrenia involves parietal regions associated with sense of self. Hum. Brain Mapp. 35, 123–139 (2014)CrossRefGoogle Scholar
  55. 55.
    Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate—a practical and powerful approach to multiple testing. J. Roy. Stat. Soc. B. 57, 289–300 (1995)MathSciNetzbMATHGoogle Scholar
  56. 56.
    Breakspear, M.: The nonlinear theory of schizophrenia. Aust. NZ. J. Psychiat. 40, 20–35 (2006)CrossRefGoogle Scholar
  57. 57.
    Hoptman, M.J., Zuo, X.N., D’Angelo, D., Mauro, C.J., Butler, P.D., Milham, M.P., Javitt, D.C.: Decreased interhemispheric coordination in schizophrenia: a resting state fMRI study. Schizophr. Res. 141, 1–7 (2012)CrossRefGoogle Scholar
  58. 58.
    Kyriakopoulos, M., Dima, D., Roiser, J.P., Corrigall, R., Barker, G.J., Frangou, S.: Abnormal functional activation and connectivity in the working memory network in early-onset schizophrenia. J. Am. Acad. Child Psy. 51, 911–920 (2012)CrossRefGoogle Scholar
  59. 59.
    White, T., Schmidt, M., Kim, D.I., Calhoun, V.D.: Disrupted functional brain connectivity during verbal working memory in children and adolescents with schizophrenia. Cereb. Cortex 21, 510–518 (2011)CrossRefGoogle Scholar
  60. 60.
    Zhuo, C., Zhu, J., Qin, W., Qu, H., Ma, X., Tian, H., Xu, Q., Yu, C.: Functional connectivity density alterations in schizophrenia. Front. Behav. Neurosci. 8, 404 (2014)CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsHenan University of Science and TechnologyLuoyangChina
  2. 2.School of Aerospace Engineering and Applied MechanicsTongji UniversityShanghaiChina

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