Time Series Analysis using Embedding Dimension on Heart Rate Variability

Heart Rate Variability (HRV) is the measurement sequence with one or more visible variables of an underlying dynamic system, whose state changes with time. In practice, it is difficult to know what variables determine the actual dynamic system. In this research, Embedding Dimension (ED) is used to find out the nature of the underlying dynamical system. False Nearest Neighbour (FNN) method of estimating ED has been adapted for analysing and predicting variables responsible for HRV time series. It shows that the ED can provide the evidence of dynamic variables which contribute to the HRV time series. Also, the embedding of the HRV time series into a four-dimensional space produced the smallest number of FNN. This result strongly suggests that the Autonomic Nervous System that drives the heart is a two features dynamic system: sympathetic and parasympathetic nervous system.Peer reviewedFinal Published versio

Assessing Variability of EEG and ECG/HRV Time Series Signals Using a Variety of Non-Linear Methods

Time series signals, such as Electroencephalogram (EEG) and Electrocardiogram (ECG) represent the complex dynamic behaviours of biological systems. The analysis of these signals using variety of nonlinear methods is essential for understanding variability within EEG and ECG, which potentially could help unveiling hidden patterns related to underlying physiological mechanisms. EEG is a time varying signal, and electrodes for recording EEG at different positions on the scalp give different time varying signals. There might be correlation between these signals. It is important to know the correlation between EEG signals because it might tell whether or not brain activities from different areas are related. EEG and ECG might be related to each other because both of them are generated from one co-ordinately working body. Investigating this relationship is of interest because it may reveal information about the correlation between EEG and ECG signals. This thesis is about assessing variability of time series data, EEG and ECG, using variety of nonlinear measures. Although other research has looked into the correlation between EEGs using a limited number of electrodes and a limited number of combinations of electrode pairs, no research has investigated the correlation between EEG signals and distance between electrodes. Furthermore, no one has compared the correlation performance for participants with and without medical conditions. In my research, I have filled up these gaps by using a full range of electrodes and all possible combinations of electrode pairs analysed in Time Domain (TD). Cross-Correlation method is calculated on the processed EEG signals for different number unique electrode pairs from each datasets. In order to obtain the distance in centimetres (cm) between electrodes, a measuring tape was used. For most of our participants the head circumference range was 54-58cm, for which a medium-sized I have discovered that the correlation between EEG signals measured through electrodes is linearly dependent on the physical distance (straight-line) distance between them for datasets without medical condition, but not for datasets with medical conditions. Some research has investigated correlation between EEG and Heart Rate Variability (HRV) within limited brain areas and demonstrated the existence of correlation between EEG and HRV. But no research has indicated whether or not the correlation changes with brain area. Although Wavelet Transformations (WT) have been performed on time series data including EEG and HRV signals to extract certain features respectively by other research, so far correlation between WT signals of EEG and HRV has not been analysed. My research covers these gaps by conducting a thorough investigation of all electrodes on the human scalp in Frequency Domain (FD) as well as TD. For the reason of different sample rates of EEG and HRV, two different approaches (named as Method 1 and Method 2) are utilised to segment EEG signals and to calculate Pearson’s Correlation Coefficient for each of the EEG frequencies with each of the HRV frequencies in FD. I have demonstrated that EEG at the front area of the brain has a stronger correlation with HRV than that at the other area in a frequency domain. These findings are independent of both participants and brain hemispheres. Sample Entropy (SE) is used to predict complexity of time series data. Recent research has proposed new calculation methods for SE, aiming to improve the accuracy. To my knowledge, no one has attempted to reduce the computational time of SE calculation. I have developed a new calculation method for time series complexity which could improve computational time significantly in the context of calculating a correlation between EEG and HRV. The results have a parsimonious outcome of SE calculation by exploiting a new method of SE implementation. In addition, it is found that the electrical activity in the frontal lobe of the brain appears to be correlated with the HRV in a time domain. Time series analysis method has been utilised to study complex systems that appear ubiquitous in nature, but limited to certain dynamic systems (e.g. analysing variables affecting stock values). In this thesis, I have also investigated the nature of the dynamic system of HRV. I have disclosed that Embedding Dimension could unveil two variables that determined HRV

Non-linear dynamical analysis of biosignals

Biosignals are physiological signals that are recorded from various parts of the body. Some of the major biosignals are electromyograms (EMG), electroencephalograms (EEG) and electrocardiograms (ECG). These signals are of great clinical and diagnostic importance, and are analysed to understand their behaviour and to extract maximum information from them. However, they tend to be random and unpredictable in nature (non-linear). Conventional linear methods of analysis are insufficient. Hence, analysis using non-linear and dynamical system theory, chaos theory and fractal dimensions, is proving to be very beneficial. In this project, ECG signals are of interest. Changes in the normal rhythm of a human heart may result in different cardiac arrhythmias, which may be fatal or cause irreparable damage to the heart when sustained over long periods of time. Hence the ability to identify arrhythmias from ECG recordings is of importance for clinical diagnosis and treatment and also for understanding the electrophysiological mechanism of arrhythmias. To achieve this aim, algorithms were developed with the help of MATLAB® software. The classical logic of correlation was used in the development of algorithms to place signals into the various categories of cardiac arrhythmias. A sample set of 35 known ECG signals were obtained from the Physionet website for testing purposes. Later, 5 unknown ECG signals were used to determine the efficiency of the algorithms. A peak detection algorithm was written to detect the QRS complex. This complex is the most prominent waveform within an ECG signal and its shape, duration and time of occurrence provides valuable information about the current state of the heart. The peak detection algorithm gave excellent results with very good accuracy for all the downloaded ECG signals, and was developed using classical linear techniques. Later, a peak detection algorithm using the discrete wavelet transform (DWT) was implemented. This code was developed using nonlinear techniques and was amenable for implementation. Also, the time required for execution was reduced, making this code ideal for real-time processing. Finally, algorithms were developed to calculate the Kolmogorov complexity and Lyapunov exponent, which are nonlinear descriptors and enable the randomness and chaotic nature of ECG signals to be estimated. These measures of randomness and chaotic nature enable us to apply correct interrogative methods to the signal to extract maximum information. The codes developed gave fair results. It was possible to differentiate between normal ECGs and ECGs with ventricular fibrillation. The results show that the Kolmogorov complexity measure increases with an increase in pathology, approximately 12.90 for normal ECGs and increasing to 13.87 to 14.39 for ECGs with ventricular fibrillation and ventricular tachycardia. Similar results were obtained for Lyapunov exponent measures with a notable difference between normal ECG (0 – 0.0095) and ECG with ventricular fibrillation (0.1114 – 0.1799). However, it was difficult to differentiate between different types of arrhythmias.Biosignals are physiological signals that are recorded from various parts of the body. Some of the major biosignals are electromyograms (EMG), electroencephalograms (EEG) and electrocardiograms (ECG). These signals are of great clinical and diagnostic importance, and are analysed to understand their behaviour and to extract maximum information from them. However, they tend to be random and unpredictable in nature (non-linear). Conventional linear methods of analysis are insufficient. Hence, analysis using non-linear and dynamical system theory, chaos theory and fractal dimensions, is proving to be very beneficial. In this project, ECG signals are of interest. Changes in the normal rhythm of a human heart may result in different cardiac arrhythmias, which may be fatal or cause irreparable damage to the heart when sustained over long periods of time. Hence the ability to identify arrhythmias from ECG recordings is of importance for clinical diagnosis and treatment and also for understanding the electrophysiological mechanism of arrhythmias. To achieve this aim, algorithms were developed with the help of MATLAB® software. The classical logic of correlation was used in the development of algorithms to place signals into the various categories of cardiac arrhythmias. A sample set of 35 known ECG signals were obtained from the Physionet website for testing purposes. Later, 5 unknown ECG signals were used to determine the efficiency of the algorithms. A peak detection algorithm was written to detect the QRS complex. This complex is the most prominent waveform within an ECG signal and its shape, duration and time of occurrence provides valuable information about the current state of the heart. The peak detection algorithm gave excellent results with very good accuracy for all the downloaded ECG signals, and was developed using classical linear techniques. Later, a peak detection algorithm using the discrete wavelet transform (DWT) was implemented. This code was developed using nonlinear techniques and was amenable for implementation. Also, the time required for execution was reduced, making this code ideal for real-time processing. Finally, algorithms were developed to calculate the Kolmogorov complexity and Lyapunov exponent, which are nonlinear descriptors and enable the randomness and chaotic nature of ECG signals to be estimated. These measures of randomness and chaotic nature enable us to apply correct interrogative methods to the signal to extract maximum information. The codes developed gave fair results. It was possible to differentiate between normal ECGs and ECGs with ventricular fibrillation. The results show that the Kolmogorov complexity measure increases with an increase in pathology, approximately 12.90 for normal ECGs and increasing to 13.87 to 14.39 for ECGs with ventricular fibrillation and ventricular tachycardia. Similar results were obtained for Lyapunov exponent measures with a notable difference between normal ECG (0 – 0.0095) and ECG with ventricular fibrillation (0.1114 – 0.1799). However, it was difficult to differentiate between different types of arrhythmias

Review and classification of variability analysis techniques with clinical applications

Analysis of patterns of variation of time-series, termed variability analysis, represents a rapidly evolving discipline with increasing applications in different fields of science. In medicine and in particular critical care, efforts have focussed on evaluating the clinical utility of variability. However, the growth and complexity of techniques applicable to this field have made interpretation and understanding of variability more challenging. Our objective is to provide an updated review of variability analysis techniques suitable for clinical applications. We review more than 70 variability techniques, providing for each technique a brief description of the underlying theory and assumptions, together with a summary of clinical applications. We propose a revised classification for the domains of variability techniques, which include statistical, geometric, energetic, informational, and invariant. We discuss the process of calculation, often necessitating a mathematical transform of the time-series. Our aims are to summarize a broad literature, promote a shared vocabulary that would improve the exchange of ideas, and the analyses of the results between different studies. We conclude with challenges for the evolving science of variability analysis

ComEDA: A new tool for stress assessment based on electrodermal activity

Non-specific sympathetic arousal responses to different stressful elicitations can be easily recognized from the analysis of physiological signals. However, neural patterns of sympathetic arousal during physical and mental fatigue are clearly not unitary. In the context of physiological monitoring through wearable and non-invasive devices, electrodermal activity (EDA) is the most effective and widely used marker of sympathetic activation. This study presents ComEDA, a novel approach for the characterization of complex dynamics of EDA. ComEDA overcomes the methodological limitations related to the application of nonlinear analysis to EDA dynamics, is not parameter-sensitive and is suitable for the analysis of ultra-short time series. We validated the proposed algorithm using synthetic series of white noise and 1/f noise, varying the number of samples from 50 to 5000. By applying our approach, we were able to discriminate a statistically significant increase of complexity in the 1/f noise with respect to white noise, obtaining p-values in the range [4.35 × 10−6, 0.03] after the Mann–Whitney test. Then, we tested ComEDA on both EDA signal and its tonic and phasic components, acquired from healthy subjects during four experimental protocols: two inducing a sympathetic activation through physical efforts and two based on mentally stressful tasks. Results are encouraging and promising, outperforming state of the art metrics such as the Sample Entropy. ComEDA shows good performance not only in discriminating between stressful tasks and resting state (p-value < 0.01 after the Wilcoxon non-parametric statistical test applied to EDA signals of all the four datasets), but also in differentiating different trends of complexity of EDA dynamics when induced by physical and mental stressors. These findings suggest future applications to automatically detect and selectively identify threats due to overwhelming stress impacting both physical and mental health or in the field of telemedicine to monitor autonomic diseases correlated to atypical sympathetic activation. The Matlab code implementing the ComEDA algorithm is available online

Design, Evaluation, and Application of Heart Rate Variability Analysis Software (HRVAS)

The analysis of heart rate variability (HRV) has become an increasingly popular and important tool for studying many disease pathologies in the past twenty years. HRV analyses are methods used to non-invasively quantify variability within heart rate. Purposes of this study were to design, evaluate, and apply an easy to use and open-source HRV analysis software package (HRVAS). HRVAS implements four major categories of HRV techniques: statistical and time-domain analysis, frequency-domain analysis, nonlinear analysis, and time-frequency analysis. Software evaluations were accomplished by performing HRV analysis on simulated and public congestive heart failure (CHF) data. Application of HRVAS included studying the effects of hyperaldosteronism on HRV in rats. Simulation and CHF results demonstrated that HRVAS was a dependable HRV analysis tool. Results from the rat hyperaldosteronism model showed that 5 of 26 HRV measures were statistically significant (p\u3c0.05). HRVAS provides a useful tool for HRV analysis to researchers

Statistical Models for Detecting Existence of Obstructive Sleep Apnea, Predicting Its Severity, and Forecasting Future Episodes

This dissertation presents three statistical models based on data mining and nonlinear time-series analysis techniques as an alternative method for the diagnosis and treatment of obstructive sleep apnea disease (OSA). From a diagnosis perspective, our method reduces the time and cost associated with the conventional method by first screening a non-OSA subject from the population, then individually determining the OSA�s severity by utilizing the data from a single-lead electrocardiogram (ECG) device that is worn overnight at the subject�s location. Our OSA forecasting model can be used to activate an OSA therapy device such as a continuous positive airway pressure (CPAP) machine or a hypoglossal nerve stimulator (HNS) as needed or before an OSA episode so that the latter can be averted in real time.In particular, our contributions are: 1) Detect the existence of OSA in an individual based on the pattern of biological physiology and simple clinical data with a low false negative rate and reasonable accuracy (FNR: 5.3%, Accuracy: 84.47%). People with some degree of probability of having OSA will be confirmed by the next model. 2) Determine the OSA severity by classifying the OSA episode (event) from one-lead ECG data collected overnight (accuracy: 92.26% with 10,052 equally sampled events from 24 subjects). The advantage of our model is that the variations (i.e., different body build, age, gender, activity, health conditions, and race) have very little effect on the prediction because the neighboring patterns in the reconstructed phase spaces have very little or no correlation to those variations. This benefit can be seen from our model�s performance compared to two other models that exist in the literature. 3) Forecast an incoming OSA episode in real time using the one-lead ECG data (accuracy: 92%, 88%, and 87% for 1, 5, and 10 minutes ahead). This forecasting model with any appropriate OSA episode prevention device (i.e., HNS, and just-in-time CPAP) will allow for an effective OSA treatment method for CPAP nonadherence OSA sufferers. 4) Develop a wearable device that can collect the biological data via a single-lead ECG as a home sleep test (HST) device.Industrial Engineering & Managemen

Symbolic Dynamics Analysis: a new methodology for foetal heart rate variability analysis

Cardiotocography (CTG) is a widespread foetal diagnostic methods. However, it lacks of objectivity and reproducibility since its dependence on observer's expertise. To overcome these limitations, more objective methods for CTG interpretation have been proposed. In particular, many developed techniques aim to assess the foetal heart rate variability (FHRV). Among them, some methodologies from nonlinear systems theory have been applied to the study of FHRV. All the techniques have proved to be helpful in specific cases. Nevertheless, none of them is more reliable than the others. Therefore, an in-depth study is necessary. The aim of this work is to deepen the FHRV analysis through the Symbolic Dynamics Analysis (SDA), a nonlinear technique already successfully employed for HRV analysis. Thanks to its simplicity of interpretation, it could be a useful tool for clinicians. We performed a literature study involving about 200 references on HRV and FHRV analysis; approximately 100 works were focused on non-linear techniques. Then, in order to compare linear and non-linear methods, we carried out a multiparametric study. 580 antepartum recordings of healthy fetuses were examined. Signals were processed using an updated software for CTG analysis and a new developed software for generating simulated CTG traces. Finally, statistical tests and regression analyses were carried out for estimating relationships among extracted indexes and other clinical information. Results confirm that none of the employed techniques is more reliable than the others. Moreover, in agreement with the literature, each analysis should take into account two relevant parameters, the foetal status and the week of gestation. Regarding the SDA, results show its promising capabilities in FHRV analysis. It allows recognizing foetal status, gestation week and global variability of FHR signals, even better than other methods. Nevertheless, further studies, which should involve even pathological cases, are necessary to establish its reliability.La Cardiotocografia (CTG) è una diffusa tecnica di diagnostica fetale. Nonostante ciò, la sua interpretazione soffre di forte variabilità intra- e inter- osservatore. Per superare tali limiti, sono stati proposti più oggettivi metodi di analisi. Particolare attenzione è stata rivolta alla variabilità della frequenza cardiaca fetale (FHRV). Nel presente lavoro abbiamo suddiviso le tecniche di analisi della FHRV in tradizionali, o lineari, e meno convenzionali, o non-lineari. Tutte si sono rivelate efficaci in casi specifici ma nessuna si è dimostrata più utile delle altre. Pertanto, abbiamo ritenuto necessario effettuare un’indagine più dettagliata. In particolare, scopo della tesi è stato approfondire una specifica metodologia non-lineare, la Symbolic Dynamics Analysis (SDA), data la sua notevole semplicità di interpretazione che la renderebbe un potenziale strumento di ausilio all’attività clinica. Sono stati esaminati all’incirca 200 riferimenti bibliografici sull’analisi di HRV e FHRV; di questi, circa 100 articoli specificamente incentrati sulle tecniche non-lineari. E’ stata condotta un’analisi multiparametrica su 580 tracciati CTG di feti sani per confrontare le metodologie adottate. Sono stati realizzati due software, uno per l’analisi dei segnali CTG reali e l’altro per la generazione di tracciati CTG simulati. Infine, sono state effettuate analisi statistiche e di regressione per esaminare le correlazioni tra indici calcolati e parametri di interesse clinico. I risultati dimostrano che nessuno degli indici calcolati risulta più vantaggioso rispetto agli altri. Inoltre, in accordo con la letteratura, lo stato del feto e le settimane di gestazione sono parametri di riferimento da tenere sempre in considerazione per ogni analisi effettuata. Riguardo la SDA, essa risulta utile all’analisi della FHRV, permettendo di distinguere – meglio o al pari di altre tecniche – lo stato del feto, la settimana di gestazione e la variabilità complessiva del segnale. Tuttavia, sono necessari ulteriori studi, che includano anche casi di feti patologici, per confermare queste evidenze