Permutation Lempel-Ziv Complexity Research Articles

Dorsal and median raphe neuronal firing dynamics characterized by nonlinear measures.

The dorsal (DRN) and median (MRN) raphe are important nuclei involved in similar functions, including mood and sleep, but playing distinct roles. These nuclei have a different composition of neuronal types and set of neuronal connections, which among other factors, determine their neuronal dynamics. Most works characterize the neuronal dynamics using classic measures, such as using the average spiking frequency (FR), the coefficient of variation (CV), and action potential duration (APD). In the current study, to refine the characterization of neuronal firing profiles, we examined the neurons within the raphe nuclei. Through the utilization of nonlinear measures, our objective was to discern the redundancy and complementarity of these measures, particularly in comparison with classic methods. To do this, we analyzed the neuronal basal firing profile in both nuclei of urethane-anesthetized rats using the Shannon entropy (Bins Entropy) of the inter-spike intervals, permutation entropy of ordinal patterns (OP Entropy), and Permutation Lempel-Ziv Complexity (PLZC). Firstly, we found that classic (i.e., FR, CV, and APD) and nonlinear measures fail to distinguish between the dynamics of DRN and MRN neurons, except for the OP Entropy. We also found strong relationships between measures, including the CV with FR, CV with Bins entropy, and FR with PLZC, which imply redundant information. However, APD and OP Entropy have either a weak or no relationship with the rest of the measures tested, suggesting that they provide complementary information to the characterization of the neuronal firing profiles. Secondly, we studied how these measures are affected by the oscillatory properties of the firing patterns, including rhythmicity, bursting patterns, and clock-like behavior. We found that all measures are sensitive to rhythmicity, except for the OP Entropy. Overall, our work highlights OP Entropy as a powerful and useful quantity for the characterization of neuronal discharge patterns.

Major depressive disorder recognition by quantifying EEG signal complexity using proposed APLZC and AWPLZC

BackgroundSeeking objective quantitative indicators is important for accurately recognizing major depressive disorder (MDD). Lempel-Ziv complexity (LZC), employed to characterize neurological disorders, faces limitations in tracking dynamic changes in EEG signals due to defects in the coarse-graining process, hindering its precision for MDD objective quantitative indicators. MethodsThis work proposed Adaptive Permutation Lempel-Ziv Complexity (APLZC) and Adaptive Weighted Permutation Lempel-Ziv Complexity (AWPLZC) algorithms by refining the coarse-graining process and introducing weight factors to effectively improve the precision of LZC in characterizing EEGs and further distinguish MDD patients better. APLZC incorporated the ordinal pattern, while False Nearest Neighbor and Mutual Information algorithms were introduced to determine and adjust key parameters adaptively. Furthermore, we proposed AWPLZC by assigning different weights to each pattern based on APLZC. Thirty MDD patients and 30 healthy controls (HCs) were recruited and their 64-channel resting EEG signals were collected. The complexities of gamma oscillations were then separately computed using LZC, APLZC, and AWPLZC algorithms. Subsequently, a multi-channel adaptive K-nearest neighbor model was constructed for identifying MDD patients and HCs. ResultsLZC, APLZC, and AWPLZC algorithms achieved accuracy rates of 78.29 %, 90.32 %, and 95.13 %, respectively. Sensitivities reached 67.96 %, 85.04 %, and 98.86 %, while specificities were 88.62 %, 95.35 %, and 89.92 %, respectively. Notably, AWPLZC achieved the best performance in accuracy and sensitivity, with a specificity limitation. LimitationThe sample size is relatively small. ConclusionAPLZC and AWPLZC algorithms, particularly AWPLZC, demonstrate superior effectiveness in differentiating MDD patients from HCs compared with LZC. These findings hold significant clinical implications for MDD diagnosis.

The EEG complexity, information integration and brain network changes in minimally conscious state patients during general anesthesia

Objective. General anesthesia (GA) can induce reversible loss of consciousness. Nonetheless, the electroencephalography (EEG) characteristics of patients with minimally consciousness state (MCS) during GA are seldom observed. Approach. We recorded EEG data from nine MCS patients during GA. We used the permutation Lempel–Ziv complexity (PLZC), permutation fluctuation complexity (PFC) to quantify the type I and II complexities. Additionally, we used permutation cross mutual information (PCMI) and PCMI-based brain network to investigate functional connectivity and brain networks in sensor and source spaces. Main results. Compared to the preoperative resting state, during the maintenance of surgical anesthesia state, PLZC decreased (p < 0.001), PFC increased (p < 0.001) and PCMI decreased (p < 0.001) in sensor space. The results for these metrics in source space are consistent with sensor space. Additionally, node network indicators nodal clustering coefficient (NCC) (p < 0.001) and nodal efficiency (NE) (p < 0.001) decreased in these two spaces. Global network indicators normalized average path length () (p < 0.01) and modularity (Q) (p < 0.05) only decreased in sensor space, while the normalized average clustering coefficient () and small-world index () did not change significantly. Moreover, the dominance of hub nodes is reduced in frontal regions in these two spaces. After recovery of consciousness, PFC decreased in the two spaces, while PLZC, PCMI increased. NCC, NE, and frontal region hub node dominance increased only in the sensor space. These indicators did not return to preoperative levels. In contrast, global network indicators and Q were not significantly different from the preoperative resting state in sensor space. Significance. GA alters the complexity of the EEG, decreases information integration, and is accompanied by a reconfiguration of brain networks in MCS patients. The PLZC, PFC, PCMI and PCMI-based brain network metrics can effectively differentiate the state of consciousness of MCS patients during GA.

Application of brain functional connectivity and nonlinear dynamic analysis in brain function assessment for infants with controlled infantile spasm

To investigate the role of brain functional connectivity and nonlinear dynamic analysis in brain function assessment for infants with controlled infantile spasm (IS). A retrospective analysis was performed on 14 children with controlled IS (IS group) who were admitted to the Department of Neurology, Anhui Provincial Children's Hospital, from January 2019 to January 2023. Twelve healthy children, matched for sex and age, were enrolled as the control group. Electroencephalogram (EEG) data were analyzed for both groups to compare the features of brain network, and nonlinear dynamic indicators were calculated, including approximate entropy, sample entropy, permutation entropy, and permutation Lempel-Ziv complexity. Brain functional connectivity showed that compared with the control group, the IS group had an increase in the strength of functional connectivity, and there was a significant difference between the two groups in the connection strength between the Fp2 and F8 channels (P<0.05). The network stability analysis showed that the IS group had a significantly higher network stability than the control group at different time windows (P<0.05). The nonlinear dynamic analysis showed that compared with the control group, the IS group had a significantly lower sample entropy of Fz electrode (P<0.05). Abnormalities in brain network and sample entropy may be observed in some children with controlled IS, and it is suggested that quantitative EEG analysis parameters can serve as neurological biomarkers for evaluating brain function in children with IS.

Comparative Study on Feature Extraction of Marine Background Noise Based on Nonlinear Dynamic Features.

Marine background noise (MBN) is the background noise of the marine environment, which can be used to invert the parameters of the marine environment. However, due to the complexity of the marine environment, it is difficult to extract the features of the MBN. In this paper, we study the feature extraction method of MBN based on nonlinear dynamics features, where the nonlinear dynamical features include two main categories: entropy and Lempel-Ziv complexity (LZC). We have performed single feature and multiple feature comparative experiments on feature extraction based on entropy and LZC, respectively: for entropy-based feature extraction experiments, we compared feature extraction methods based on dispersion entropy (DE), permutation entropy (PE), fuzzy entropy (FE), and sample entropy (SE); for LZC-based feature extraction experiments, we compared feature extraction methods based on LZC, dispersion LZC (DLZC) and permutation LZC (PLZC), and dispersion entropy-based LZC (DELZC). The simulation experiments prove that all kinds of nonlinear dynamics features can effectively detect the change of time series complexity, and the actual experimental results show that regardless of the entropy-based feature extraction method or LZC-based feature extraction method, they both present better feature extraction performance for MBN.

EEG complexity correlates with residual consciousness level of disorders of consciousness

Background and objectiveElectroencephalography (EEG) and neuroimaging measurements have been highly encouraged to be applied in clinics of disorders of consciousness (DOC) to improve consciousness detection. We tested the relationships between neural complexity measured on EEG and residual consciousness levels in DOC patients.MethodsResting-state EEG was recorded from twenty-five patients with DOC. Lempel–Ziv complexity (LZC) and permutation Lempel–Ziv complexity (PLZC) were measured on the EEG, and their relationships were analyzed with the consciousness levels of the patients.ResultsPLZC and LZC values significantly distinguished patients with a minimally conscious state (MCS), vegetative state/unresponsive wakefulness syndrome (VS/UWS), and healthy controls. PLZC was significantly correlated with the Coma Recovery Scale-Revised (CRS-R) scores of DOC patients in the global brain, particularly in electrodes locating in the anterior and posterior brain regions. Patients with higher CRS-R scores showed higher PLZC values. The significant difference in PLZC values between MCS and VS/UWS was mainly located in the bilateral frontal and right hemisphere regions.ConclusionNeural complexity measured on EEG correlates with residual consciousness levels of DOC patients. PLZC showed higher sensitivity than LZC in the classification of consciousness levels.

Permutation Lempel-Ziv 복잡성 척도를 적용한 근 피로도 추정

A new approach for quantifying muscle fatigue is presented by analyzing the deterministic complexity in the surface electromyogram(SEMG) using Permutation Lempel-Ziv(PLZ) complexity measure. The PLZ complexity measure provide a metric for the number of distinct deterministic patterns in signals by combining permutation patterns and Lempel-Ziv complexity analysis. For muscle fatigue experiment by using PLZ complexity measure, surface EMG signals from eleven subjects were recorded in biceps brachii muscle with constant isometric 20, 50, and 80%MVC contractions. The PLZ complexity measure is evaluated with the performance of muscle fatigue estimation for the SEMG signals compared to the performance of previous reported LZ complexity measure. This PLZ complexity measure has advantages that is computationally easy to compute and does not require any assumptions about the stationarity of the SEMG signal.

Multi-scale permutation Lempel-Ziv complexity and its application in feature extraction for Ship-radiated noise

Permutation Lempel-Ziv complexity (PLZC) is a recently proposed method for analyzing signal complexity. However, PLZC only characterizes the signal complexity from single scale and has certain limitations. In order to overcome these shortcomings and improve the performance of feature extraction for underwater acoustic signal, this paper introduced coarse graining operation, proposed the multi-scale permutation Lempel-Ziv complexity (MPLZC), and proposed an automatic hybrid multi-feature extraction method for ship-radiated noise signal (S-S) based on multi-scale Lempel-Ziv complexity (MLZC), multi-scale permutation entropy (MPE) and MPLZC. The results of simulation and realistic experiments show that MPLZC can better reflect the change of signal complexity in detecting the dynamic change of signals, and more effectively distinguish white noise, pink noise and blue noise than MPE and MLZC; compared with the three feature extraction methods based on MLZC, MPE and MPLZC respectively, the proposed method has the highest recognition rates of six S-Ss under the same number of features, and the recognition rate reaches 100% when the number of features is 5; the introduction of MPLZC significantly improves the performance for ship-radiated noise signal of the automatic hybrid multi-feature extraction method. It is indicated that the proposed method, as a new underwater acoustic technology, is valid in other underwater acoustic signals.

Dispersion entropy-based Lempel-Ziv complexity: A new metric for signal analysis

Lempel-Ziv complexity (LZC) is one of the most important metrics for detecting dynamic changes in non-linear signals, but due to its dependence on binary conversion, LZC tends to lose some of the effective information of the time series, while the noise immunity is not guaranteed and cannot be applied to the detection of real-world signals. To address these limitations, we have developed a dispersion entropy-based LZC (DELZC) based on the normal cumulative distribution function (NCDF) and dispersion permutation patterns. In DELZC, the time series are first processed by NCDF to increase the number of classes and thus reduce the loss of information, and in addition, the dispersive entropy (DE) in terms of the ordinal number of the permutation pattern is considered to replace the binary conversion of LZC, thus improving the ability to capture the dynamic changes in the time series. In signal analysis using a set of time series, several easy-to-understand concepts are used to demonstrate the superiority of DELZC over other three LZC metrics in detecting the dynamic variability of the signals, namely LZC, dispersion LZC (DLZC) and permutation LZC (PLZC). The synthetic signal experiments demonstrate the superiority of DELZC in detecting the dynamic changes of time series and characterizing the complexity of signal, and also have lower noise sensitivity. Moreover, DELZC has the best performance in diagnosing four states of rolling bearing fault signals and classifying five types of ship radiation noise signals, with higher recognition rates than LZC, PLZC and DLZC.

Cortical complexity and connectivity during isoflurane-induced general anesthesia: a rat study

Objective. The investigation of neurophysiologic mechanisms of anesthetic drug-induced loss of consciousness (LOC) by using the entropy, complexity, and information integration theories at the mesoscopic level has been a hot topic in recent years. However, systematic research is still lacking. Approach. We analyzed electrocorticography (ECoG) data recorded from nine rats during isoflurane-induced unconsciousness. To characterize the complexity and connectivity changes, we investigated ECoG power, symbolic dynamic-based entropy (i.e. permutation entropy (PE)), complexity (i.e. permutation Lempel-Ziv complexity (PLZC)), information integration (i.e. permutation cross mutual information (PCMI)), and PCMI-based cortical brain networks in the frontal, parietal, and occipital cortical regions. Main results. Firstly, LOC was accompanied by a raised power in the ECoG beta (12–30 Hz) but a decreased power in the high gamma (55–95 Hz) frequency band in all three brain regions. Secondly, PE and PLZC showed similar change trends in the lower frequency band (0.1–45 Hz), declining after LOC (p < 0.05) and increasing after recovery of consciousness (p < 0.001). Thirdly, intra-frontal and inter-frontal-parietal PCMI declined after LOC, in both lower (0.1–45 Hz) and higher frequency bands (55–95 Hz) (p < 0.001). Finally, the local network parameters of the nodal clustering coefficient and nodal efficiency in the frontal region decreased after LOC, in both the lower and higher frequency bands (p < 0.05). Moreover, global network parameters of the normalized average clustering coefficient and small world index increased slightly after LOC in the lower frequency band. However, this increase was not statistically significant. Significance. The PE, PLZC, PCMI and PCMI-based brain networks are effective metrics for qualifying the effects of isoflurane.

Multiscale Permutation Lempel-Ziv Complexity Measure for Biomedical Signal Analysis: Interpretation and Application to Focal EEG Signals.

This paper analyses the complexity of electroencephalogram (EEG) signals in different temporal scales for the analysis and classification of focal and non-focal EEG signals. Futures from an original multiscale permutation Lempel–Ziv complexity measure (MPLZC) were obtained. MPLZC measure combines a multiscale structure, ordinal analysis, and permutation Lempel–Ziv complexity for quantifying the dynamic changes of an electroencephalogram (EEG). We also show the dependency of MPLZC on several straight-forward signal processing concepts, which appear in biomedical EEG activity via a set of synthetic signals. The main material of the study consists of EEG signals, which were obtained from the Bern-Barcelona EEG database. The signals were divided into two groups: focal EEG signals (n = 100) and non-focal EEG signals (n = 100); statistical analysis was performed by means of non-parametric Mann–Whitney test. The mean value of MPLZC results in the non-focal group are significantly higher than those in the focal group for scales above 1 (p < 0.05). The result indicates that the non-focal EEG signals are more complex. MPLZC feature sets are used for the least squares support vector machine (LS-SVM) classifier to classify into the focal and non-focal EEG signals. Our experimental results confirmed the usefulness of the MPLZC method for distinguishing focal and non-focal EEG signals with a classification accuracy of 86%.

Complexity behaviors of volatility dynamics for stochastic Potts financial model

To investigate the price fluctuation mechanism of stock markets, this research aims to develop a novel stochastic financial model based on Potts dynamics and compound Poisson process. The new model considers two aspects: information interaction among traders and the uncertain events outside the system. Then, three different volatility statistics (return series \(r_t\), absolute return series \(|r_t|\) and volatility duration average intensity \(V_t\)) are introduced to explore the volatility and complexity properties of the proposed model. The descriptive statistical methods, such as basic statistical properties and distribution analysis, are studied to validate the practicable of the proposed stochastic financial model. The permutation Lempel-Ziv complexity of moving average series is referred to different volatility sequences to evaluate the complexity of the simulative data from proposed model and the real data from stock market. Moreover, the complexity analysis of fractional sample entropy and multiscale fractional sample entropy is improved to illustrate the complexity of volatility behaviors in different scales. Compared with the real stock data, the empirical results demonstrate that the new model could reproduce the fluctuation and volatility behaviors of real stock markets to some extent.

Contrasting stochasticity with chaos in a permutation Lempel–Ziv complexity — Shannon entropy plane

This paper aims at introducing the Lempel–Ziv permutation complexity vs. permutation entropy plane (EC-plane) as a tool to analyze time series with diverse dynamical nature. These two quantities use the Bandt and Pompe representation to quantify a continuous-state time series. The main strength of this approach lies in the fact that this plane combines two different perspectives to study a signal, one being purely statistic (the permutation entropy) and the other being algorithmic (the Lempel–Ziv complexity). The results allow us to conclude that the EC-plane constitutes an appropriate framework for: (i) characterizing non-linear chaotic maps, (ii) distinguishing deterministic from stochastic processes and (iii) to discriminate between fractional Brownian motion, fractional Gaussian noise and K-noise.

Constructing a Consciousness Meter Based on the Combination of Non-Linear Measurements and Genetic Algorithm-Based Support Vector Machine.

Constructing a framework to evaluate consciousness is an important issue in neuroscience research and clinical practice. However, there is still no systematic framework for quantifying altered consciousness along the dimensions of both level and content. This study builds a framework to differentiate the following states: coma, general anesthesia, minimally conscious state (MCS), and normal wakefulness. This study analyzed electroencephalography (EEG) recorded from frontal channels in patients with disorders of consciousness (either coma or MCS), patients under general anesthesia, and healthy participants in normal waking consciousness (NWC). Four non-linear methods-permutation entropy (PE), sample entropy (SampEn), permutation Lempel-Ziv complexity (PLZC), and detrended fluctuation analysis (DFA)-as well as relative power (RP), extracted features from the EEG recordings. A genetic algorithm-based support vector machine (GA-SVM) classified the states of consciousness based on the extracted features. A multivariable linear regression model then built EEG indices for level and content of consciousness. The PE differentiated all four states of consciousness (p<0.001). Altered contents of consciousness for NWC, MCS, coma, and general anesthesia were best differentiated by the SampEn, and PLZC. In contrast, the levels of consciousness for these four states were best differentiated by RP of Gamma and PE. A multi-dimensional index, combined with the GA-SVM, showed that the integration of PE, PLZC, SampEn, and DFA had the highest classification accuracy (92.3%). The GA-SVM was better than random forest and neural networks at differentiating these four states. The 'coordinate value' in the dimensions of level and content were constructed by the multivariable linear regression model and the non-linear measures PE, PLZC, SampEn, and DFA. Multi-dimensional measurements, especially the PE, SampEn, PLZC, and DFA, when combined with GA-SVM, are promising methods for constructing a framework to quantify consciousness.

Sex Differences in the Complexity of Healthy Older Adults' Magnetoencephalograms.

The analysis of resting-state brain activity recording in magnetoencephalograms (MEGs) with new algorithms of symbolic dynamics analysis could help obtain a deeper insight into the functioning of the brain and identify potential differences between males and females. Permutation Lempel-Ziv complexity (PLZC), a recently introduced non-linear signal processing algorithm based on symbolic dynamics, was used to evaluate the complexity of MEG signals in source space. PLZC was estimated in a broad band of frequencies (2–45 Hz), as well as in narrow bands (i.e., theta (4–8 Hz), alpha (8–12 Hz), low beta (12–20 Hz), high beta (20–30 Hz), and gamma (30–45 Hz)) in a sample of 98 healthy elderly subjects (49 males, 49 female) aged 65–80 (average age of 72.71 ± 4.22 for males and 72.67 ± 4.21 for females). PLZC was significantly higher for females than males in the high beta band at posterior brain regions including the precuneus, and the parietal and occipital cortices. Further statistical analyses showed that higher complexity values over highly overlapping regions than the ones mentioned above were associated with larger hippocampal volumes only in females. These results suggest that sex differences in healthy aging can be identified from the analysis of magnetoencephalograms with novel signal processing methods.

Effects of Ageing and Sex on Complexity in the Human Sleep EEG: A Comparison of Three Symbolic Dynamic Analysis Methods

Symbolic dynamic analysis (SDA) methods have been applied to biomedical signals and have been proven efficient in characterising differences in the electroencephalogram (EEG) in various conditions (e.g., epilepsy, Alzheimer’s, and Parkinson’s diseases). In this study, we investigated the use of SDA on EEGs recorded during sleep. Lempel-Ziv complexity (LZC), permutation entropy (PE), and permutation Lempel-Ziv complexity (PLZC), as well as power spectral analysis based on the fast Fourier transform (FFT), were applied to 8-h sleep EEG recordings in healthy men (n=31) and women (n=29), aged 20-74 years. The results of the SDA methods and FFT analysis were compared and the effects of age and sex were investigated. Surrogate data were used to determine whether the findings with SDA methods truly reflected changes in nonlinear dynamics of the EEG and not merely changes in the power spectrum. The surrogate data analysis showed that LZC merely reflected spectral changes in EEG activity, whereas PE and PLZC reflected genuine changes in the nonlinear dynamics of the EEG. All three SDA techniques distinguished the vigilance states (i.e., wakefulness, REM sleep, NREM sleep, and its sub-stages: stage 1, stage 2, and slow wave sleep). Complexity of the sleep EEG increased with ageing. Sex on the other hand did not affect the complexity values assessed with any of these three SDA methods, even though FFT detected sex differences. This study shows that SDA provides additional insights into the dynamics of sleep EEG and how it is affected by ageing.

Complexity Changes in Brain Activity in Healthy Ageing: A Permutation Lempel-Ziv Complexity Study of Magnetoencephalograms.

Maturation and ageing, which can be characterised by the dynamic changes in brain morphology, can have an impact on the physiology of the brain. As such, it is possible that these changes can have an impact on the magnetic activity of the brain recorded using magnetoencephalography. In this study changes in the resting state brain (magnetic) activity due to healthy ageing were investigated by estimating the complexity of magnetoencephalogram (MEG) signals. The main aim of this study was to identify if the complexity of background MEG signals changed significantly across the human lifespan for both males and females. A sample of 177 healthy participants (79 males and 98 females aged between 21 and 80 and grouped into 3 categories i.e., early-, mid- and late-adulthood) was used in this investigation. This investigation also extended to evaluating if complexity values remained relatively stable during the 5 min recording. Complexity was estimated using permutation Lempel-Ziv complexity, a recently introduced complexity metric, with a motif length of 5 and a lag of 1. Effects of age and gender were investigated in the MEG channels over 5 brain regions, i.e., anterior, central, left lateral, posterior, and, right lateral, with highest complexity values observed in the signals recorded by the channels over the anterior and central regions of the brain. Results showed that while changes due to age had a significant effect on the complexity of the MEG signals recorded over 5 brain regions, gender did not have a significant effect on complexity values in all age groups investigated. Moreover, although some changes in complexity were observed between the different minutes of recording, due to the small magnitude of the changes it was concluded that practical significance might outweigh statistical significance in this instance. The results from this study can contribute to form a fingerprint of the characteristics of healthy ageing in MEGs that could be useful when investigating changes to the resting state activity due to pathology.

Characterisation of the Effects of Sleep Deprivation on the Electroencephalogram Using Permutation Lempel–Ziv Complexity, a Non-Linear Analysis Tool

Specific patterns of brain activity during sleep and waking are recorded in the electroencephalogram (EEG). Time-frequency analysis methods have been widely used to analyse the EEG and identified characteristic oscillations for each vigilance state (VS), i.e., wakefulness, rapid-eye movement (REM) and non-rapid-eye movement (NREM) sleep. However, other aspects such as change of patterns associated with brain dynamics may not be captured unless a non-linear-based analysis method is used. In this pilot study, Permutation Lempel–Ziv complexity (PLZC), a novel symbolic dynamics analysis method, was used to characterise the changes in the EEG in sleep and wakefulness during baseline and recovery from sleep deprivation (SD). The results obtained with PLZC were contrasted with a related non-linear method, Lempel–Ziv complexity (LZC). Both measure the emergence of new patterns. However, LZC is dependent on the absolute amplitude of the EEG, while PLZC is only dependent on the relative amplitude due to symbolisation procedure and thus, more resistant to noise. We showed that PLZC discriminates activated brain states associated with wakefulness and REM sleep, which both displayed higher complexity, compared to NREM sleep. Additionally, significantly lower PLZC values were measured in NREM sleep during the recovery period following SD compared to baseline, suggesting a reduced emergence of new activity patterns in the EEG. These findings were validated using PLZC on surrogate data. By contrast, LZC was merely reflecting changes in the spectral composition of the EEG. Overall, this study implies that PLZC is a robust non-linear complexity measure, which is not dependent on amplitude variations in the signal, and which may be useful to further assess EEG alterations induced by environmental or pharmacological manipulations.

Measures of entropy and complexity in altered states of consciousness.

Quantification of complexity in neurophysiological signals has been studied using different methods, especially those from information or dynamical system theory. These studies have revealed a dependence on different states of consciousness, and in particular that wakefulness is characterized by a greater complexity of brain signals, perhaps due to the necessity for the brain to handle varied sensorimotor information. Thus, these frameworks are very useful in attempts to quantify cognitive states. We set out to analyze different types of signals obtained from scalp electroencephalography (EEG), intracranial EEG and magnetoencephalography recording in subjects during different states of consciousness: resting wakefulness, different sleep stages and epileptic seizures. The signals were analyzed using a statistical (permutation entropy) and a deterministic (permutation Lempel-Ziv complexity) analytical method. The results are presented in complexity versus entropy graphs, showing that the values of entropy and complexity of the signals tend to be greatest when the subjects are in fully alert states, falling in states with loss of awareness or consciousness. These findings were robust for all three types of recordings. We propose that the investigation of the structure of cognition using the frameworks of complexity will reveal mechanistic aspects of brain dynamics associated not only with altered states of consciousness but also with normal and pathological conditions.

Complexity-Entropy Maps as a Tool for the Characterization of the Clinical Electrophysiological Evolution of Patients under Pharmacological Treatment with Psychotropic Drugs

In the clinical electrophysiological practice, reading and comparing electroencephalographic (EEG) recordings are sometimes insufficient and take too much time. Tools coming from the information theory or nonlinear systems theory such as entropy and complexity have been presented as an alternative to address this problem. In this work, we introduce a novel method—the permutation Lempel–Ziv Complexity vs. Permutation Entropy map. We apply this method to the EEGs of two patients with specific diagnosed pathologies during respective follow up processes of pharmacological changes in order to detect alterations that are not evident with the usual inspection method. The method allows for comparing between different states of the patients’ treatment, with a healthy control group, given global information about the signal, supplementing the traditional method of visual inspection of EEG.