Permutation relative entropy is proposed to quantify time irreversibilityin our nonlinear dynamics analysis of electroencephalogram (EEG). Ordinal patterns in multi-dimension phase space of time series are symbolized, and the probabilistic divergences of all symmetric ordinal pairs are measured by relative entropy as time irreversibility. Analyzing multi-channel EEG from 18 healthy volunteers and 18 epileptic patients (all in their seize-free intervals), the derived relative entropy of symmetrical ordinal patterns shows advantages to other time irreversible parameters and significantly distinguish two kinds of brain electric signals (the epileptic have lower temporal asymmetries than the healthy) . Test results prove that it is effective to quantity time irreversibility by measuring probabilistic divergence of symmetrical ordinal patternsand validate our hypothesis that epilepsy has lasting impacts on brain' nonlinear dynamics, leading to a decline in brain signals directional asymmetry or time irreversibility, and the losing temporal asymmetries stemming from our findings may contribute to the preclinical diagnosis of epilepsy .
To simplify the quantification of time irreversibility, we employ order patterns instead of the raw multi-dimension vectors in time series, and considering the existence of forbidden permutation, we propose a subtraction-based parameter, Ys, to measure the probabilistic differences between symmetric permutations for time irreversibility. Two chaotic models, the logistic and Henon systems, and reversible Gaussian process and their surrogate data are used to validate the time-irreversible measure, and time irreversibility of epileptic EEGs from Nanjing General Hospital is detected by the parameter . Test results prove that it is promising to quantify time irreversibility by measuring the subtraction-based probabilistic differences between symmetric order patterns, and our findings highlight the manifestation of nonlinearity of whether healthy or diseased EEGs and suggest that the epilepsy leads to a decline in the nonlinearity of brain electrical activities during seize-free intervals .
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Permutation relative entropy is proposed to quantify time irreversibilityin our nonlinear dynamics analysis of electroencephalogram (EEG). Ordinal patterns in
To simplify the quantification of time irreversibility, we employ order patterns instead of the raw
R
phase space of
vectors in time series, and considering the existence of forbidden permutation, we propose a subtraction-based parameter, Ys, to measure the probabilistic differences between symmetric permutations for
D
series are symbolized, and the probabilistic divergences of all symmetric ordinal pairs are measured by relative entropy as time
R
Analyzing multi-channel EEG from 18 healthy volunteers and 18 epileptic patients (all in their seize-free intervals), the derived relative entropy of symmetrical ordinal patterns shows advantages to other time irreversible parameters and significantly distinguish two kinds of brain electric signals (the epileptic have lower temporal asymmetries than the healthy)
Two chaotic models, the logistic and Henon systems, and reversible Gaussian process and their surrogate data are used to validate the time-irreversible measure, and time irreversibility of epileptic EEGs from Nanjing General Hospital is detected by the parameter
R
effective to quantity
promising to quantify
R
probabilistic divergence of symmetrical ordinal patternsand validate our hypothesis that epilepsy has lasting impacts on brain' nonlinear dynamics, leading
the subtraction-based probabilistic differences between symmetric order patterns, and our findings highlight the manifestation of nonlinearity of whether healthy or diseased EEGs and suggest that the epilepsy leads
R
brain signals directional asymmetry or time irreversibility, and the losing temporal asymmetries stemming from our findings may contribute to the preclinical diagnosis of epilepsy
the nonlinearity of brain electrical activities during seize-free intervals