Nonlinear Dynamics

, Volume 96, Issue 4, pp 2327–2340 | Cite as

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

  • Yanbing Jia
  • Huaguang GuEmail author
Original Paper


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.


Sample entropy Nonlinear dynamics Dynamic functional connectivity Brain functional networks Schizophrenia 


Compliance with ethical standard

Conflict of interest

The authors declare that they have no conflict of interest.


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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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