Structural Health Monitoring (SHM) Study of Polymer Matrix Composite (PMC) Materials Using Nonlinear Vibration Methods Based on Embedded Piezoelectric Transducers

Nowadays, nonlinear vibration methods are increasingly used for the detection of damage mechanisms in polymer matrix composite (PMC) materials, which are anisotropic and heterogeneous. The originality of this study was the use of two nonlinear vibration methods to detect different types of damage within PMC through an in situ embedded polyvinylidene fluoride (PVDF) piezoelectric sensor. The two used methods are nonlinear resonance (NLR) and single frequency excitation (SFE). They were first tested on damage introduced during the manufacturing of the smart PMC plates, and second, on the damage that occurred after the manufacturing. The results show that both techniques are interesting, and probably a combination of them will be the best choice for SHM purposes. During the experimentation, an accelerometer was used, in order to validate the effectiveness of the integrated PVDF sensor.

Autonomic nervous system assessment using heart rate variability

The role of the autonomic nervous system in the onset of supraventricular and ventricular arrhythmias is well established. It can be analysed by the spontaneous behaviour of the heart rate with ambulatory ECG recordings, through heart rate variability measurements. Input of heart rate variability parameters into artificial intelligence models to make predictions regarding the detection or forecast of rhythm disorders is becoming routine and neuromodulation techniques are now increasingly used for their treatment. All this warrants a reappraisal of the use of heart rate variability for autonomic nervous system assessment.Measurements performed over long periods such as 24H-variance, total power, deceleration capacity, and turbulence are suitable for estimating the individual basal autonomic status. Spectral measurements performed over short periods provide information on the dynamics of systems that disrupt this basal balance and may be part of the triggers of arrhythmias, as well as premature atrial or ventricular beats. All heart rate variability measurements essentially reflect the modulations of the parasympathetic nervous system which are superimposed on the impulses of the adrenergic system. Although heart rate variability parameters have been shown to be useful for risk stratification in patients with myocardial infarction and patients with heart failure, they are not part of the criteria for prophylactic implantation of an intracardiac defibrillator, because of their high variability and the improved treatment of myocardial infarction. Graphical methods such as Poincaré plots allow quick screening of atrial fibrillation and are set to play an important role in the e-cardiology networks. Although mathematical and computational techniques allow manipulation of the ECG signal to extract information and permit their use in predictive models for individual cardiac risk stratification, their explicability remains difficult and making inferences about the activity of the ANS from these models must remain cautious.

Association of heartbeat complexity with survival in advanced non-small cell lung cancer patients

Background

Previous studies have shown that the predictive value of traditional linear (time domain and frequency domain) heart rate variability (HRV) for the survival of patients with advanced non-small cell lung cancer (NSCLC) is controversial. Nonlinear methods, based on the concept of complexity, have been used to evaluate HRV, providing a new means to reveal the physiological and pathological changes in HRV. This study aimed to assess the association between heartbeat complexity and overall survival in patients with advanced NSCLC.

Methods

This study included 78 patients with advanced NSCLC (mean age: 62.0 ± 9.3 years). A 5-min resting electrocardiogram of advanced NSCLC patients was collected to analyze the following HRV parameters: time domain indicators, i.e., standard deviation of the normal-normal intervals (SDNN) and root mean square of successive interval differences (RMSSD); frequency domain indicators, i.e., total power (TP), low frequency power (LF), high frequency power (HF), and the ratio of LF to HF (LF/HF); nonlinear HRV indicators characterizing heartbeat complexity, i.e., approximate entropy (ApEn), sample entropy (SampEn), and recurrence quantification analysis (RQA) indexes: mean diagonal line length (Lmean), maximal diagonal line length (Lmax), recurrence rate (REC), determinism (DET), and shannon entropy (ShanEn).

Results

Univariate analysis revealed that the linear frequency domain parameter HF and nonlinear RQA parameters Lmax, REC, and DET were significantly correlated with the survival of advanced NSCLC patients (all p < 0.05). After adjusting for confounders in the multivariate analysis, HF, REC, and DET were found to be independent prognostic factors for the survival of patients with advanced NSCLC (all p < 0.05).

Conclusion

There was an independent association between heartbeat complexity and survival in advanced NSCLC patients. The nonlinear analysis method based on RQA may provide valuable additional information for the prognostic stratification of patients with advanced NSCLC and may supplement the traditional time domain and frequency domain analysis methods.

Linear and Non-linear Quantification of the Respiratory Sinus Arrhythmia Using Support Vector Machines

Respiratory sinus arrhythmia (RSA) is a form of cardiorespiratory coupling. It is observed as changes in the heart rate in synchrony with the respiration. RSA has been hypothesized to be due to a combination of linear and nonlinear effects. The quantification of the latter, in turn, has been suggested as a biomarker to improve the assessment of several conditions and diseases. In this study, a framework to quantify RSA using support vector machines is presented. The methods are based on multivariate autoregressive models, in which the present samples of the heart rate variability are predicted as combinations of past samples of the respiration. The selection and tuning of a kernel in these models allows to solve the regression problem taking into account only the linear components, or both the linear and the nonlinear ones. The methods are tested in simulated data as well as in a dataset of polysomnographic studies taken from 110 obstructive sleep apnea patients. In the simulation, the methods were able to capture the nonlinear components when a weak cardiorespiratory coupling occurs. When the coupling increases, the nonlinear part of the coupling is not detected and the interaction is found to be of linear nature. The trends observed in the application in real data show that, in the studied dataset, the proposed methods captured a more prominent linear interaction than the nonlinear one.

Convergent Validation of Methods for the Identification of Psychotherapeutic Phase Transitions in Time Series of Empirical and Model Systems

Aim

In many cases, the dynamics of psychotherapeutic change processes is characterized by sudden and critical transitions. In theoretical terms, these transitions may be “phase transitions” of self-organizing nonlinear systems. Meanwhile, a variety of methods is available to identify phase transitions even in short time series. However, it is still an open question if different methods for timeseries analysis reveal convergent results indicating the moments of critical transitions and related precursors.

Methods and Procedures

Seven concepts which are commonly used in nonlinear time series analysis were investigated in terms of their ability to identify changes in psychological time series: Recurrence Plots, Change Point Analysis, Dynamic Complexity, Permutation Entropy, Time Frequency Distributions, Instantaneous Frequency, and Synchronization Pattern Analysis, i.e., the dynamic inter-correlation of the system’s variables. Phase transitions were simulated by shifting control parameters in the Hénon map dynamics, in a simulation model of psychotherapy processes (one by an external shift of the control parameter and one created by a simulated control parameter shift), and three sets of empirical time series generated by daily self-ratings of patients during the treatment.

Results

The applied methods showed converging results indicating the moments of dynamic transitions within an acceptable tolerance. The convergence of change points was confirmed statistically by a comparison to random surrogates. In the three simulated dynamics with known phase transitions, these could be identified, and in the empirical cases, the methods converged indicating one and the same transition (possibly the phase transitions of the cases). Moreover, changes that did not manifest in a shift of mean or variance could be detected.

Conclusion

Changes can occur in many different ways in the psychotherapeutic process. For instance, there can be very slow and small transitions or very high and sudden ones. The results show the validity and stability of different measures indicating pattern transitions and/or early warning signals of those transitions. This has profound implications for real-time monitoring in psychotherapy, especially in cases where a transition is not obvious to the eye. Reliably identifying points of change is mandatory also for research on precursors, which in turn can help improving treatment.

Nonlinear Methods Most Applied to Heart-Rate Time Series: A Review

The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincaré plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.

The entropy of RR intervals is associated to gestational age in full-term newborns with adequate weight for gestational age

Introduction: The variability of successive RR intervals has been pointed out as an indicator of systemic homeostasis. The entropy of successive RR intervals is associated with a greater adaptive capacity, which is essential after childbirth, characterized by a change from an intrauterine environment that constantly adapts to the fetal demands, to an extrauterine environment that requires constant biological adaptations by the neonate.Objectives: To analyze the association between gestational age (GA) and the entropy of RR intervals in term infants with adequate birth weight in the first hours of extrauterine life.Methods: In a cross-sectional study design maternal, labor and neonatal characteristics were collected from the obstetric records. Successive RR intervals were recorded from neonates up to 72 hours (i.e. 3 days) of birth.Subjects: Fifty term infants, healthy and with adequate birth weight. Outcome measures: the variability of RR intervals was analyzed obtaining the entropy of 1000 successive RR intervals. Pearson's correlation was used to evaluate the association between GA and the entropy of successive RR intervals, while linear regression was used to obtain the coefficient of determination (r²) as well as a prediction model. The adequacy of the prediction model was evaluated using the Komolgorov-Smirnov test to evaluate the residuals distribution.Results: There was a positive and significant association between the studied variables (r = 0.437; p = .002). The coefficient of determination allowed us to infer that approximately 19.3% of the RR interval entropy from the studied sample can be explained by the GA (r² = 0.193; p = .002). The analysis of the residuals distribution confirmed that the regression model obtained here was adequate.Conclusion: Our results indicate that, even within a normal range of GA (≥37 a < 42 weeks) and birth weight, a longer intrauterine life allows a greater entropy of successive RR intervals, indicating a greater maturation of biological systems and adaptive capacity.

Using nonlinear methods to quantify changes in infant limb movements and vocalizations

The pairing of dynamical systems theory and complexity science brings novel concepts and methods to the study of infant motor development. Accordingly, this longitudinal case study presents a new approach to characterizing the dynamics of infant limb and vocalization behaviors. A single infant's vocalizations and limb movements were recorded from 51-days to 305-days of age. On each recording day, accelerometers were placed on all four of the infant's limbs and an audio recorder was worn on the child's chest. Using nonlinear time series analysis methods, such as recurrence quantification analysis and Allan factor, we quantified changes in the stability and multiscale properties of the infant's behaviors across age as well as how these dynamics relate across modalities and effectors. We observed that particular changes in these dynamics preceded or coincided with the onset of various developmental milestones. For example, the largest changes in vocalization dynamics preceded the onset of canonical babbling. The results show that nonlinear analyses can help to understand the functional co-development of different aspects of infant behavior.

Entropy and convexity for nonlinear partial differential equations

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

Influence of atropine on fractal and complexity measures of heart rate variability

BACKGROUND

Measurement of short-term fractal-like correlation properties of heart rate dynamics has been shown to be a useful prognostic indicator of adverse events in cardiac patients. Complexity measurements of heart rate variability (HRV) have already provided important information in many cardiac conditions. However, data on the physiological background of these newer nonlinear measures of HRV are limited.

METHODS

Nine healthy subjects (aged from 22 to 35 years, 6 males, 3 females) had an electrocardiographic (ECG) recording during controlled breathing in supine position. HRV was analyzed for 5 min periods before and after intravenous injection of 0.6 mg of atropine using conventional HRV measures and newer nonlinear HRV measures including the short-term scaling exponent (alpha(1)) and approximate entropy (ApEn).

RESULTS

The short-term scaling exponent alpha(1) increased significantly after atropine injection (1.01 +/- 0.23 vs 1.43 +/- 0.19, P = 0.001). There was no significant difference between ApEn values before and after atropine injection (0.87 +/- 0.17 vs 0.70 +/- 0.31, respectively, P = 0.27). At baseline before atropine administration, alpha(1) had a significant negative correlation with SDNN, RMSSD, and HF (r = -0.70, -0.76, -0.67, respectively, P < 0.05 for all), and a significant positive correlation with heart rate (r = 0.76, P < 0.05). After atropine injection, alpha(1) did not have significant correlation with any of the HRV parameters or heart rate. There were no significant correlations between ApEn and any of the HRV measures or heart rate either before or after atropine administration.

CONCLUSIONS

Vagal tone has an important influence on the values of the short-term scaling exponent alpha(1). However, vagal modulation is not a major determinant of the values of ApEn.