Nonlinear Complexity Measures Research Articles

Characterization of antiseizure medications effects on the EEG neurodynamic by fractal dimension.

An important challenge in epilepsy is to define biomarkers of response to treatment. Many electroencephalography (EEG) methods and indices have been developed mainly using linear methods, e.g., spectral power and individual alpha frequency peak (IAF). However, brain activity is complex and non-linear, hence there is a need to explore EEG neurodynamics using nonlinear approaches. Here, we use the Fractal Dimension (FD), a measure of whole brain signal complexity, to measure the response to anti-seizure therapy in patients with Focal Epilepsy (FE) and compare it with linear methods. Twenty-five drug-responder (DR) patients with focal epilepsy were studied before (t1, named DR-t1) and after (t2, named DR-t2) the introduction of the anti-seizure medications (ASMs). DR-t1 and DR-t2 EEG results were compared against 40 age-matched healthy controls (HC). EEG data were investigated from two different angles: frequency domain-spectral properties in δ, θ, α, β, and γ bands and the IAF peak, and time-domain-FD as a signature of the nonlinear complexity of the EEG signals. Those features were compared among the three groups. The δ power differed between DR patients pre and post-ASM and HC (DR-t1 vs. HC, p < 0.01 and DR-t2 vs. HC, p < 0.01). The θ power differed between DR-t1 and DR-t2 (p = 0.015) and between DR-t1 and HC (p = 0.01). The α power, similar to the δ, differed between DR patients pre and post-ASM and HC (DR-t1 vs. HC, p < 0.01 and DR-t2 vs. HC, p < 0.01). The IAF value was lower for DR-t1 than DR-t2 (p = 0.048) and HC (p = 0.042). The FD value was lower in DR-t1 than in DR-t2 (p = 0.015) and HC (p = 0.011). Finally, Bayes Factor analysis showed that FD was 195 times more likely to separate DR-t1 from DR-t2 than IAF and 231 times than θ. FD measured in baseline EEG signals is a non-linear brain measure of complexity more sensitive than EEG power or IAF in detecting a response to ASMs. This likely reflects the non-oscillatory nature of neural activity, which FD better describes. Our work suggests that FD is a promising measure to monitor the response to ASMs in FE.

Recurrence quantification analysis of postural sway in patients with persistent postural perceptual dizziness.

Persistent postural perceptual dizziness (PPPD) is a common cause of chronic dizziness and imbalance. Emerging evidence suggests that changes in quantitative measures of postural control may help identify individuals with PPPD, however, traditional linear metrics of sway have yielded inconsistent results. Methodologies to examine the temporal structure of sway, including recurrent quantification analysis (RQA), have identified unique changes in dynamic structure of postural control in other patient populations. This study aimed to determine if adults with PPPD exhibit changes in the dynamic structure of sway and whether this change is modulated on the basis of available sensory cues. Twelve adults diagnosed with PPPD and twelve age-matched controls, completed a standard battery of quiet stance balance tasks that involved the manipulation of visual and/or proprioceptive feedback. For each group, the regularity and complexity of the CoP signal was assessed using RQA and the magnitude and variability of the CoP signal was quantified using traditional linear measures. An overall effect of participant group (i.e., healthy controls vs. PPPD) was seen for non-linear measures of temporal complexity quantified using RQA. Changes in determinism (i.e., regularity) were also modulated on the basis of availability of sensory cues in patients with PPPD. No between-group difference was identified for linear measures assessing amount and variability of sway. Participants with PPPD on average exhibited sway that was similar in magnitude to, but significantly more repeatable and less complex than, healthy controls. These data show that non-linear measures provide unique information regarding the effect of PPPD on postural control, and as a result, may serve as potential rehabilitation outcome measures.

The complexity analysis of cerebral oxygen saturation during pneumoperitoneum and Trendelenburg position: a retrospective cohort study

BackgroundThe human brain is a highly complex and nonlinear system, nonlinear complexity measures such as approximate entropy (ApEn) and sample entropy (SampEn) can better reveal characteristics of brain dynamics. However, no studies report complexity of perioperative physiological signals to reveal how brain complexity associates with age, varies along with the development of surgery and postoperative neurological complications.AimThis study examined the complexity of intraoperative regional cerebral oxygen saturation (rSO2), aiming to reveal brain dynamics during surgery.MethodsThis retrospective cohort study enrolled patients who scheduled for robot-assisted urological surgery. Intraoperative rSO2 was continuously monitored throughout the surgery. Postoperative delirium (POD) was diagnosed by the Confusion Assessment Method. ApEn and SampEn were used to characterize the complexity of rSO2. Pearson correlation coefficients were used to measure the correlation between complexity of rSO2 and age. The association between complexity of rSO2 and POD was examined using T tests.ResultsA total of 68 patients (mean [SD] age, 63.0 (12.0) years; 47 (69.1%) males) were include in this analysis. There was a significant reverse relationship between the complexity of rSO2 and age (The correlation coefficients range between − 0.32 and − 0.28, all p < 0.05). Patients ≥ 75 years showed significantly lower complexity of rSO2 than the other two groups. Older age remained an independent factor influencing complexity of rSO2 after adjusting for a number of covariates. Six patients (8.8%) developed POD, and POD patients had lower complexity of rSO2 compared with non-POD patients.ConclusionsThe complexity of rSO2 may serve as a new candidate marker of aging and POD prediction.

Differences in Performance of ASD and ADHD Subjects Facing Cognitive Loads in an Innovative Reasoning Experiment

We aim to investigate whether EEG dynamics differ in adults with ASD (Autism Spectrum Disorders) and ADHD (attention-deficit/hyperactivity disorder) compared with healthy subjects during the performance of an innovative cognitive task, Aristotle’s valid and invalid syllogisms, and how these differences correlate with brain regions and behavioral data for each subject. We recorded EEGs from 14 scalp electrodes (channels) in 21 adults with ADHD, 21 with ASD, and 21 healthy, normal subjects. The subjects were exposed in a set of innovative cognitive tasks (inducing varying cognitive loads), Aristotle’s two types of syllogism mentioned above. A set of 39 questions were given to participants related to valid–invalid syllogisms as well as a separate set of questionnaires, in order to collect a number of demographic and behavioral data, with the aim of detecting shared information with values of a feature extracted from EEG, the multiscale entropy (MSE), in the 14 channels (‘brain regions’). MSE, a nonlinear information-theoretic measure of complexity, was computed to extract a feature that quantifies the complexity of the EEG. Behavior-Partial Least Squares Correlation, PLSC, is the method to detect the correlation between two sets of data, brain, and behavioral measures. -PLSC, a variant of PLSC, was applied to build a functional connectivity of the brain regions involved in the reasoning tasks. Graph-theoretic measures were used to quantify the complexity of the functional networks. Based on the results of the analysis described in this work, a mixed 14 × 2 × 3 ANOVA showed significant main effects of group factor and brain region* syllogism factor, as well as a significant brain region* group interaction. There are significant differences between the means of MSE (complexity) values at the 14 channels of the members of the ‘pathological’ groups of participants, i.e., between ASD and ADHD, while the difference in means of MSE between both ASD and ADHD and that of the control group is not significant. In conclusion, the valid–invalid type of syllogism generates significantly different complexity values, MSE, between ASD and ADHD. The complexity of activated brain regions of ASD participants increased significantly when switching from a valid to an invalid syllogism, indicating the need for more resources to ‘face’ the task escalating difficulty in ASD subjects. This increase is not so evident in both ADHD and control. Statistically significant differences were found also in the behavioral response of ASD and ADHD, compared with those of control subjects, based on the principal brain and behavior saliences extracted by PLSC. Specifically, two behavioral measures, the emotional state and the degree of confidence of participants in answering questions in Aristotle’s valid–invalid syllogisms, and one demographic variable, age, statistically and significantly discriminate the three groups’ ASD. The seed-PLC generated functional connectivity networks for ASD, ADHD, and control, were ‘projected’ on the regions of the Default Mode Network (DMN), the ‘reference’ connectivity, of which the structural changes were found significant in distinguishing the three groups. The contribution of this work lies in the examination of the relationship between brain activity and behavioral responses of healthy and ‘pathological’ participants in the case of cognitive reasoning of the type of Aristotle’s valid and invalid syllogisms, using PLSC, a machine learning approach combined with MSE, a nonlinear method of extracting a feature based on EEGs that captures a broad spectrum of EEGs linear and nonlinear characteristics. The results seem promising in adopting this type of reasoning, in the future, after further enhancements and experimental tests, as a supplementary instrument towards examining the differences in brain activity and behavioral responses of ASD and ADHD patients. The application of the combination of these two methods, after further elaboration and testing as new and complementary to the existing ones, may be considered as a tool of analysis in helping detecting more effectively such types of disorders.

Interindividual Signatures of fMRI Temporal Fluctuations.

The complexity and variability of human brain activity, such as quantified from Functional Magnetic Resonance Imaging (fMRI) time series, have been widely studied as potential markers of healthy and pathological states. However, the extent to which fMRI temporal features exhibit stable markers of inter-individual differences in brain function across healthy young adults is currently an open question. In this study, we draw upon two widely used time-series measures-a nonlinear complexity measure (sample entropy; SampEn) and a spectral measure of low-frequency content (fALFF)-to capture dynamic properties of resting-state fMRI in a large sample of young adults from the Human Connectome Project. We observe that these two measures are closely related, and that both generate reproducible patterns across brain regions over four different fMRI runs, with intra-class correlations of up to 0.8. Moreover, we find that both metrics can uniquely differentiate subjects with high identification rates (ca. 89%). Canonical correlation analysis revealed a significant relationship between multivariate brain temporal features and behavioral measures. Overall, these findings suggest that regional profiles of fMRI temporal characteristics may provide stable markers of individual differences, and motivate future studies to further probe relationships between fMRI time series metrics and behavior.

Vascular health and diffusion properties of normal appearing white matter in midlife

In this study, we perform a region of interest diffusion tensor imaging and advanced diffusion complexity analysis of normal appearing white matter to determine the impact of vascular health on these diffusivity metrics in midlife adults. 77 participants (26 black, 35 female) at year 30 visit in the Coronary Artery Risk Development in Young Adults longitudinal study were scanned with an advanced diffusion-weighted imaging and fluid-attenuated inversion recovery protocol. Fractional anisotropy and non-linear diffusion complexity measures were estimated. Cumulative measures across 30 years (9 study visits) of systolic blood pressure, body mass index, glucose, smoking and cholesterol were calculated as the area under the curve from baseline up to year 30 examination. Partial correlation analyses assessed the association between cumulative vascular health measures and normal appearing white matter diffusion metrics in these participants. Midlife normal appearing white matter diffusion properties were significantly associated (P < 0.05) with cumulative exposure to vascular risk factors from young adulthood over the 30-year time period. Higher cumulative systolic blood pressure exposure was associated with increased complexity and decreased fractional anisotropy. Higher cumulative body mass index exposure was associated with decreased fractional anisotropy. Additionally, in the normal appearing white matter of black participants (P < 0.05), who exhibited a higher cumulative vascular risk exposure, fractional anisotropy was lower and complexity was higher in comparison to normal appearing white matter in white participants. Higher burden of vascular risk factor exposure from young adulthood to midlife is associated with changes in the diffusion properties of normal appearing white matter in midlife. These changes which may reflect axonal disruption, increased inflammation and/or increased glial proliferation, were primarily observed in both anterior and posterior normal appearing white matter regions of the corpus callosum. These results suggest that microstructural changes in normal appearing white matter are sensitive to vascular health during young adulthood and are possibly therapeutic targets in interventions focused on preserving white matter health across life.

Changes in nonlinear dynamic complexity measures of blood pressure during anesthesia for cardiac surgeries using cardio pulmonary bypass.

Nonlinear complexity measures computed from beat-to-beat arterial BP dynamics have shown associations with standard cardiac surgical risk indices. They reflect the physiological adaptability of a system and has been proposed as dynamical biomarkers of overall health status. We sought to determine the impact of anesthetic induction and cardiopulmonary bypass (CPB) upon the complexity measures computed from perioperative BP time series. In this prospective, observational study, 300 adult patients undergoing cardiac surgery were included. Perioperative period was divided as: (1) Preoperative (PreOp); (2) ORIS-induction to sternotomy; (3) ORSB- sternotomy to CPB; (4) ORposB-post CPB and within 30min before leaving OR and (5) postoperative phase (PostOp)-initial 30min in the cardiac surgical intensive care unit. BP waveforms for systolic (SAP), diastolic (DAP), mean arterial pressure (MAP) and pulse pressure (PP) were recorded, and their corresponding complexity index (MSE∑) was calculated. Significant decrease in MSE∑ from Preop to PostOp phases was observed for all BP time series. Maximum fall was seen during post anesthetic induction (ORIS) phase. Mild recovery during the subsequent phases was observed but they never reached the baseline values. In an exploratory analysis, preoperative MSE∑ showed a significant correlation with postoperative length of ICU stay. Blood pressure complexity varies at different time points and is not fixed for a given individual. Preoperative BP Complexity decreased significantly following anesthetic induction and did not recover to baseline until 30min after surgery. Prevention of this significant fall may offer restoration of MSE∑ throughout surgery. Furthermore, preoperative BP complexity needs to be explored as a predictor of major postoperative adverse events by itself or in addition with the current risk indices.

Multiresolution analysis on nonlinear complexity measurement of EEG signal for epileptic discharge monitoring

Various epileptic discharge detection studies have been conducted however, not many clinically significant outcomes have been achieved in developing reliable algorithm using nonlinear measurement techniques. Study has reported that some of the linear measurement techniques performances better than nonlinear technique in detecting the epileptic discharge in terms of accuracy, sensitivity and specificity. The reliability issue has been addressed in nonlinear techniques, by introducing Multiresolution analysis (MRA). MRA with approximate entropy are the most common combination used to detect epileptic discharge, leaving other nonlinear complexity measures are yet to be explored with MRA. Previously, we have study the performance of Approximate Entropy (ApEn) and Lempel Ziv (LZ) using MRA. In this paper, we have expanded the scope by studying performance of MRA with other complexity measurement including Hurst exponent (HE), Kolmogorov complexity (KC), Shannon Entropy (SE) and Sample Entropy (SampEn). Groups of normal with interictal (Set A and B), normal with ictal (Set A and C) and interictal with ictal (Set B and C) were used to evaluate the performance. For the result, MRA managed to enhance the accuracy of ApEn (AB: 74% to 89%, AC: 98% to 100%, BC:88% to 94%) and SE (AB: 69% to 98%, AC: 100% to 100%, BC:96% to 97%) in detecting epileptic discharge the best while deteriorating LZ (AB: 49% to 83%, AC: 91% to 86%, BC:89% to 88%) and HE (AB: 65% to 70%, AC: 89% to 78%, BC:80% to 54%) performance. Computation time tends to increase with the implementation of MRA.

Deep brain stimulation enhances movement complexity during gait in individuals with Parkinson’s disease

Deep brain stimulation (DBS) is associated with substantial improvements in motor symptoms of PD. Emerging evidence has suggested that nonlinear measures of complexity may provide greater insight into the efficacy of anti-PD treatments. This study investigated sample entropy and complexity index values in individuals with PD when DBS was OFF compared to ON. Five individuals with PD using DBS performed a four-minute treadmill walking task while 3D kinematics were collected over two periods of 30 s. Participants were tested in the DBS-ON and DBS-OFF conditions. Sample entropy (SE) and complexity index (CI) values were calculated for ankle, knee and hip joint angles. Paired samples t-tests were used to compare mean SE and CI values between the DBS-OFF and DBS-ON conditions, respectively. No differences in SE or CI were observed between the DBS-ON and DBS-OFF conditions at the ankle. At the knee, the DBS-ON was associated with greater SE and CI values than the DBS-OFF condition. At the hip, DBS-ON was associated with greater SE and CI values than the DBS-OFF condition. DBS enhances complexity of movement at the hip and knee joints while complexity at the ankle joint is not significantly altered. Greater complexity of knee and hip joint motion may represent increased adaptability and a greater number of available strategies to complete the gait task.

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.

Diminished autonomic neurocardiac function in patients with generalized anxiety disorder.

BackgroundGeneralized anxiety disorder (GAD) is a chronic and highly prevalent disorder that is characterized by a number of autonomic nervous system symptoms. The purpose of this study was to investigate the linear and nonlinear complexity measures of heart rate variability (HRV), measuring autonomic regulation, and to evaluate the relationship between HRV parameters and the severity of anxiety, in medication-free patients with GAD.MethodsAssessments of linear and nonlinear complexity measures of HRV were performed in 42 medication-free patients with GAD and 50 healthy control subjects. In addition, the severity of anxiety symptoms was assessed using the State-Trait Anxiety Inventory and Beck Anxiety Inventory. The values of the HRV measures of the groups were compared, and the correlations between the HRV measures and the severity of anxiety symptoms were assessed.ResultsThe GAD group showed significantly lower standard deviation of RR intervals and the square root of the mean squared differences of successive normal sinus intervals values compared to the control group (P<0.01). The approximate entropy value, which is a nonlinear complexity indicator, was also significantly lower in the patient group than in the control group (P<0.01). In correlation analysis, there were no significant correlations between HRV parameters and the severity of anxiety symptoms.ConclusionThe present study indicates that GAD is significantly associated with reduced HRV, suggesting that autonomic neurocardiac integrity is substantially impaired in patients with GAD. Future prospective studies are required to investigate the effects of pharmacological or non-pharmacological treatment on neuroautonomic modulation in patients with GAD.

Investigating the effects of visual biofeedback therapy on recovery of postural balance in stroke patients using a complexity measure

Background and purpose: Postural balance deficit is one of the common post-stroke disabilities. Providing visual biofeedback while balance activities are performed is a way to improve postural balance disorders following stroke. But among the research publications, there is incoherency about the positive effects of visual biofeedback therapy. The purpose of this study was to investigate the effects of using visual biofeedback as an adjunct to physical therapy exercises on recovery of postural balance of stroke patients. Materials and methods: A total of 31 hemiplegic stroke patients were recruited in this study and randomly assigned into case and control groups. Both groups received conventional physical therapy interventions and balance training exercises. During balance training, the case group received visual biofeedback, whereas the control group did not receive visual information. Balance performance of stroke patients were examined quantitatively using the EquiTest testing system. Center of pressure data were collected before starting, during, and after completion of the rehabilitation program and a nonlinear complexity measure, approximate entropy (ApEn), calculated and used for the analysis. Results: No significant between-group differences were detected after completion of the program. Noticeable increase was found in ApEn values of both groups along anterior–posterior direction, whereas no statistically significant improvement was found along mediolateral direction after rehabilitation. Conclusion: Both rehabilitation routines created advances in the postural control system of stroke patients. Visual biofeedback balance training did not produce extra advantage for balance ability of participants who received this treatment program in comparison with those who were treated without visual biofeedback.

We should be using nonlinear indices when relating heart-rate dynamics to cognition and mood.

Both heart rate (HR) and brain functioning involve the integrated output of a multitude of regulatory mechanisms, that are not quantified adequately by linear approximations such as means and standard deviations. It was therefore considered whether non-linear measures of HR complexity are more strongly associated with cognition and mood. Whilst resting, the inter-beat (R-R) time series of twenty-one males and twenty-four females were measured for five minutes. The data were summarised using time, frequency and nonlinear complexity measures. Attention, memory, reaction times, mood and cortisol levels were assessed. Nonlinear HR indices captured additional information, enabling a greater percentage of the variance in behaviour to be explained. On occasions non-linear indices were related to aspects for behaviour, for example focused attention and cortisol production, when time or frequency indices were not. These effects were sexually dimorphic with HR complexity being more strongly associated with the behaviour of females. It was concluded that nonlinear rather than linear methods of summarizing the HR times series offers a novel way of relating brain functioning and behaviour. It should be considered whether non-linear measures of HR complexity can be used as a biomarker of the integrated functioning of the brain.

Day to Day Stability of Heart Rate Variability

Heart rate variability (HRV) is widely utilized as an indicator of autonomic outflow in a broad range of contexts despite continued debate of the reliability of HRV metrics. PURPOSE: The purpose of this study was to examine the stability of heart rate variability (HRV) and complexity [ApEn (approximate entropy) & SampEn (sample entropy)] in healthy, young adults. METHODS: As part of a larger study, 14 participants [Age=25.4±5.3yrs, BMI=23.2±1.98, WC=74.9±7.85 cm, 36% male, 64% Caucasian], completed assessments of HRV during an orthostatic challenge [Condition=5 min each for supine, seated & standing]. Sessions were completed 1-4 days apart and participants abstained from food, caffeine and alcohol for 12 hrs and from physical activity for 24 hrs prior to each session. All participants were non-smokers and voided immediately prior to HRV measures. HRV data was collected with the BioPac MP150 and was assessed using Kubios v2.1. ICC and RMANOVA were performed using SPSSv22. RESULTS: RMANOVA revealed that HR, RR, RMSSD, pNN50, HFpower and SDNN were significantly altered by condition (p values =0.000-0.007), but not by day. HFpeak (p=0.024) and LFpeak (p=0.038) were altered by day, but not condition. Only LF/HF had a significant main effect for day (p=0.05) and condition (p=0.007). ICC for time domain variables were consistently in the good (α=.7-.9) to excellent (α>.9) range for supine and standing, but only mean HR and RR reached this range for seated. Conversely, frequency domain variables generally had lower ICCs (α<.7). ApEn averaged 0.86±0.03 on day 1 and 0.82±0.04 on day 2. ApEn was not altered by condition (p=0.21) or day (p=0.14) and ICC values were .87, .7 and .89 for supine, seated and standing, respectively. ICC values for SampEn were .74, .91 and .91 for supine, seated and standing. CONCLUSION: Similar to previous studies, frequency domain variables had lower ICC values than time domain or complexity measures. Frequency domain measures showed greater variability to orthostatic challenge and seated measures had lower ICC values than either standing or supine measures. Both nonlinear complexity measures resulted in good to excellent ICCs, but SampEn has more data length independence and may be a better complexity measure for short recordings of HRV.

Resting-state EEG delta power is associated with psychological pain in adults with a history of depression

Psychological pain is a prominent symptom of clinical depression. We asked if frontal alpha asymmetry, frontal EEG power, and frontal fractal dimension asymmetry predicted psychological pain in adults with a history of depression.Resting-state frontal EEG (F3/F4) was recorded while participants (N=35) sat upright with their eyes closed.Frontal delta power predicted psychological pain while controlling for depressive symptoms, with participants who exhibited less power experiencing greater psychological pain. Frontal fractal dimension asymmetry, a nonlinear measure of complexity, also predicted psychological pain, such that greater left than right complexity was associated with greater psychological pain. Frontal alpha asymmetry did not contribute unique variance to any regression model of psychological pain.As resting-state delta power is associated with the brain's default mode network, results suggest that the default mode network was less activated during high psychological pain. Findings are consistent with a state of arousal associated with psychological pain.

Nonlinear analysis of electroencephalogram in frontotemporal lobar degeneration

Frontotemporal lobar degeneration (FTLD) is a form of dementia characterized by a profound alteration in personality and social behavior and is associated with atrophy in the frontal and temporal brain regions. Despite recent advances, diagnosis of FTLD remains challenging. In the last decade, different studies have combined EEG analysis with mathematical models and theories that consider EEG signals as the result of nonlinear chaotic activity. The aim of the present study was to determine whether new nonlinear dynamic analysis can provide useful information on brain activity in FTLD patients. 19-lead EEG was recorded in patients with clinical diagnosis of FTLD and in healthy controls under two different conditions: closed eyes and open eyes. A nonlinear measure of complexity, correlation dimension (D2), was calculated. Our results show an increase in D2 in healthy individuals when the eyes are open, in keeping with an increase in information processing. Conversely, in FTLD patients, no increase in D2 occurred in the open eyes condition, and D2 was significantly lower than that observed in controls. Our results suggest that the dynamic processes underlying the EEG are less chaotic and complex in FTLD patients compared with normal individuals, thus providing important information on both brain functioning and possible clinical diagnostic applications.

Effects of Clozapine on Heart Rate Dynamics and Their Relationship With Therapeutic Response in Treatment-Resistant Schizophrenia

Previous studies have suggested the utility of nonlinear complexity measures of heart rate variability (HRV) in evaluating the regulatory capacity of the neuroautonomic system. The purpose of the present study was to investigate the effects of clozapine on the nonlinear complexity measures of HRV in patients with treatment-resistant schizophrenia to find novel electrophysiological markers that indicate response to clozapine treatment. Forty patients with treatment-resistant schizophrenia were evaluated during 8 weeks of clozapine monotherapy. For nonlinear complexity measures of HRV, the approximate entropy (ApEn) and sample entropy (SampEn) values were obtained. The response rate to clozapine was 37.5%. The results of multivariate analysis of covariance revealed that the ApEn and the SampEn values of HRV at week 8 were significantly higher in the responders than in the nonresponders. Repeated-measures analysis of covariance showed a significant group by time interaction effect in the ApEn and SampEn indices. The responder group showed an increasing pattern of change in these complexity measures after administration of clozapine, whereas the nonresponder group showed a decreasing pattern of change. These results suggest that the nonlinear dynamic complexity measures of HRV, which indicate the irregularity and complexity of the biosystem, may be useful in evaluating the therapeutic changes of neuroautonomic function in schizophrenia. The response to clozapine treatment is expected to be more favorable when the plasticity of the neuroautonomic system reflected in the nonlinear complexity measures is high.

Altered heart rate dynamics associated with antipsychotic-induced subjective restlessness in patients with schizophrenia

BackgroundAntipsychotic-induced subjective inner restlessness is one of the common and distressing adverse effects associated with antipsychotics; however, its underlying neurobiological basis is not well understood. We examined the relationship between antipsychotic-induced subjective inner restlessness and autonomic neurocardiac function.MethodsTwenty-two schizophrenia patients with antipsychotic-induced subjective restlessness, 28 schizophrenia patients without antipsychotic-induced subjective restlessness, and 28 matched healthy control subjects were evaluated. Assessments of the linear and nonlinear complexity measures of heart rate dynamics were performed. Multivariate analysis of variance and correlation analysis were conducted.ResultsThe mean interbeat (RR) interval value was significantly higher in control subjects than in patients with and without antipsychotic-induced subjective restlessness (P < 0.05). The low frequency/high frequency ratio was significantly higher in patients with antipsychotic-induced subjective restlessness than in control subjects and in patients without antipsychotic-induced subjective restlessness (P < 0.05), while the approximate entropy value was significantly lower in patients with antipsychotic-induced subjective restlessness than in control subjects and in patients without antipsychotic-induced subjective restlessness (P < 0.05). Correlation analyses controlling for psychotic symptom severity showed that the degree of antipsychotic-induced restlessness had a significant negative correlation with the value of approximate entropy (P < 0.05).ConclusionThe results indicate that antipsychotic-induced subjective restlessness is associated with altered heart rate dynamics parameters, particularly the nonlinear complexity measure, suggesting that it might adversely affect autonomic neurocardiac integrity. Further prospective research is necessary to elucidate the precise interrelationships and causality.

Nonlinear analysis of electroencephalogram at rest and during cognitive tasks in patients with schizophrenia

In spite of the large number of studies on schizophrenia, a full understanding of its core pathology still eludes us. The application of the nonlinear theory of electroencephalography (EEG) analysis provides an interesting tool to differentiate between physiologic conditions (e.g., resting state and mathematical task) and normal and pathologic brain activities. The aim of the present study was to investigate nonlinear EEG activity in patients with schizophrenia. We recorded 19-lead EEGs in patients with stable schizophrenia and healthy controls under 4 different conditions: eyes closed, eyes open, forward counting and backward counting. A nonlinear measure of complexity was calculated by means of correlation dimension (D2). We included 17 patients and 17 controls in our analysis. Comparing the 2 populations, we observed greater D2 values in the patient group. In controls, increased D2 values were observed during active states (eyes open and the 2 cognitive tasks) compared with baseline conditions. This increase of brain complexity, which can be interpreted as an increase of information processing and integration, was not preserved in the patient population. Patients with schizophrenia were taking antipsychotic medications, so the presence of medication effects cannot be excluded. Our results suggest that patients with schizophrenia present changes in brain activity compared with healthy controls, and this pathologic alteration can be successfully studied with nonlinear EEG analysis.

Modified permutation-entropy analysis of heartbeat dynamics

Heart rate variability (HRV) contains important information about the modulation of the cardiovascular system. Various methods of nonlinear dynamics (e.g., estimating Lyapunov exponents) and complexity measures (e.g., correlation dimension or entropies) have been applied to HRV analysis. Permutation entropy, which was proposed recently, has been widely used in many fields due to its conceptual and computational simplicity. It maps a time series onto a symbolic sequence of permutation ranks. The original permutation entropy assumes the time series under study has a continuous distribution, thus equal values are rare and can be ignored by ranking them according to their order of emergence, or broken by adding small random perturbations to ensure every symbol in a sequence is different. However, when the observed time series is digitized with lower resolution leading to a greater number of equal values, or the equalities represent certain characteristic sequential patterns of the system, it may not be rational to simply ignore or break them. In the present paper, a modified permutation entropy is proposed that, by mapping the equal value onto the same symbol (rank), allows for a more accurate characterization of system states. The application of the modified permutation entropy to the analysis of HRV is investigated using clinically collected data. Results show that modified permutation entropy can greatly improve the ability to distinguish the HRV signals under different physiological and pathological conditions. It can characterize the complexity of HRV more effectively than the original permutation entropy.