Continuous biological signals, like blood pressure recordings, exhibit non-linear and non-stationary properties which must be considered when analyzing them. Heart rate variability analyses have identified several frequency components and their autonomic origin. There is need for more knowledge on the time-changing properties of these frequencies. The power spectrum, continuous wavelet transform and Hilbert-Huang transform are applied on a continuous blood pressure signal to investigate how the different methods compare to each other. The Hilbert-Huang transform shows high ability to analyzing such data, and can, by identifying instantaneous frequency shifts, provide new insights into the nature of these kinds of data.
... Features that are incorporated in biological signals, such as nonlinearity and nonstationarity, are challenging when analyzing them. We have earlier addressed the challenge by applying Fourier-based analyses to such signals, suggesting the data-driven Hilbert-Huang Transform as a better approach (Knai, Kulia, Molinas, & Skjaervold, 2017). However, the Hilbert-Huang transform is hampered by being computationally challenging and requiring thorough validation. ...
The circulatory system is oscillatory in its nature. Oscillatory components linked to physiological processes and underlying regulatory mechanisms are identifiable in circulatory signals. Autonomic regulation is essential for the system's ability to deal with external exposure, and the integrity of oscillations may be considered a hallmark of a healthy system. Loss of complexity is seen as a consequence of several diseases and aging. Heart rate variability is known to decrease after cardiac surgery and remain reduced for up to 6 months. Oscillatory components of circulatory signals are linked to the system's overall complexity. We therefore hypothesize that the frequency distributions of circulatory signals show loss of oscillatory components after cardiac surgery and that the observed changes persist. We investigated the development of the circulatory frequency distributions of eight patients undergoing cardiac surgery by extracting three time series from conventional blood pressure and electrocardiography recordings: systolic blood pressure, heart rate, and amplitude of the electrocardiogram's R-wave. Four 30-min selections, representing key events of the perioperative course, were analyzed with the continuous wavelet transform, and average wavelet power spectra illustrated the circulatory frequency distributions. We identified oscillatory components in all patients and variables. Contrary to our hypothesis, they were randomly distributed through frequencies, patients, and situations, thus, not representing any reduction in the overall complexity. One patient showed loss of a 25-s oscillation after surgery. We present a case where noise is misclassified as an oscillation, raising questions about the robustness of such analyses.
Aim of the project: David against Goliath: Could Small Data from single-channel or low-density EEG compete in the Big Data contest with high density EEG on equal footing or could David and Goliath join forces? Yes, they can and FlexEEG will show how. FlexEEG proposes a new concept of dry single-channel EEG with enriched information extraction that will materialize into a sensor-embedded data-driven approach to the real-time localization of brain activity.
Level of impact and excellence: While a laboratory setting and research-grade electroencephalogram (EEG) equipment will ensure a controlled environment and high-quality multiple-channel EEG recording, there are situations and populations for which this is not suitable. FlexEEG aims at validating a new concept of single-channel or low-density EEG system that while being portable and relying on dry-sensor technology, will produce recordings of comparable quality to a research-grade EEG system but will surpass the capabilities and scope of conventional lab-based EEG equipment: In short, a single more intelligent EEG sensor could defeat high-density EEG. Conventional EEG is challenged by high cost, immobility of equipment and the use of inconvenient conductive gels. Ease of use and quality of information extraction are much awaited in a new EEG concept that produces recording of comparable quality to a research-grade system but that puts EEG within the reach of everyone. FlexEEG will bring that. This project will exploit methods of inverse problems, data-driven non-linear and non-stationary signal analysis 1,2,3 combined with dry-sensor technology to develop a pioneering system that will enable a single, properly localized EEG channel, to provide research-grade information comparable to and surpassing the capabilities of high density-channel EEG. Through this, the range of applications of EEG signals will be expanded from clinical diagnosis and research to healthcare, to better understanding of cognitive processes, to learning and education, and to today hidden/unknown properties behind ordinary human activity and ailments (e.g. walking, sleeping, complex cognitive activity, chronic pain, insomnia).
This will be made possible by the implementation of adaptive non-linear and non-stationary data analysis tools in combination with inverse modelling to solve the brain-mapping problem.
Heart rate variability (HRV), the change in the time intervals between adjacent heartbeats, is an emergent property of interdependent regulatory systems that operate on different time scales to adapt to challenges and achieve optimal performance. This article briefly reviews neural regulation of the heart, and its basic anatomy, the cardiac cycle, and the sinoatrial and atrioventricular pacemakers. The cardiovascular regulation center in the medulla integrates sensory information and input from higher brain centers, and afferent cardiovascular system inputs to adjust heart rate and blood pressure via sympathetic and parasympathetic efferent pathways. This article reviews sympathetic and parasympathetic influences on the heart, and examines the interpretation of HRV and the association between reduced HRV, risk of disease and mortality, and the loss of regulatory capacity. This article also discusses the intrinsic cardiac nervous system and the heart-brain connection, through which afferent information can influence activity in the subcortical and frontocortical areas, and motor cortex. It also considers new perspectives on the putative underlying physiological mechanisms and properties of the ultra-low-frequency (ULF), very-low-frequency (VLF), low-frequency (LF), and high-frequency (HF) bands. Additionally, it reviews the most common time and frequency domain measurements as well as standardized data collection protocols. In its final section, this article integrates Porges’ polyvagal theory, Thayer and colleagues’ neurovisceral integration model, Lehrer, Vaschillo, and Vaschillo’s resonance frequency model, and the Institute of HeartMath’s coherence model. The authors conclude that a coherent heart is not a metronome because its rhythms are characterized by both complexity and stability over longer time scales. Future research should expand understanding of how the heart and its intrinsic nervous system influence the brain.
A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the `empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit well-behaved Hilbert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hilbert transform, the 'instrinic mode functions' yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum. In this method, the main conceptual innovations are the introduction of `intrinsic mode functions' based on local properties of the signal, which make the instantaneous frequency meaningful; and th
Characteristic patterns of variation over time, namely rhythms, represent a defining feature of complex systems, one that is synonymous with life. Despite the intrinsic dynamic, interdependent and nonlinear relationships of their parts, complex biological systems exhibit robust systemic stability. Applied to critical care, it is the systemic properties of the host response to a physiological insult that manifest as health or illness and determine outcome in our patients. Variability analysis provides a novel technology with which to evaluate the overall properties of a complex system. This review highlights the means by which we scientifically measure variation, including analyses of overall variation (time domain analysis, frequency distribution, spectral power), frequency contribution (spectral analysis), scale invariant (fractal) behaviour (detrended fluctuation and power law analysis) and regularity (approximate and multiscale entropy). Each technique is presented with a definition, interpretation, clinical application, advantages, limitations and summary of its calculation. The ubiquitous association between altered variability and illness is highlighted, followed by an analysis of how variability analysis may significantly improve prognostication of severity of illness and guide therapeutic intervention in critically ill patients.
The concept of instantaneous frequency (IF), its definitions, and
the correspondence between the various mathematical models formulated
for representation of IF are discussed. The extent to which the IF
corresponds to the intuitive expectation of reality is also considered.
A historical review of the successive attempts to define the IF is
presented. The relationships between the IF and the group-delay,
analytic signal, and bandwidth-time (BT) product are explored, as well
as the relationship with time-frequency distributions. The notions of
monocomponent and multicomponent signals and instantaneous bandwidth are
discussed. It is shown that these notions are well described in the
context of the theory presented
In 1999 three prominent scientists suggested in a paper printed in this journal that the definitions of the instantaneous amplitude, phase and frequency of an analytic signal are ambiguous. However, a detailed analysis using the notion of instantaneous complex frequency and Mikusiński's theory of distributions shows that the above definitions are unique. Several aspects of this problem are discussed. The approach using moments defined using the Wigner distribution confirms the above-mentioned uniqueness.
This paper introduces a modified technique based on Hilbert-Huang transform (HHT) to improve the spectrum estimates of heart rate variability (HRV). In order to make the beat-to-beat (RR) interval be a function of time and produce an evenly sampled time series, we first adopt a preprocessing method to interpolate and resample the original RR interval. Then, the HHT, which is based on the empirical mode decomposition (EMD) approach to decompose the HRV signal into several monocomponent signals that become analytic signals by means of Hilbert transform, is proposed to extract the features of preprocessed time series and to characterize the dynamic behaviors of parasympathetic and sympathetic nervous system of heart. At last, the frequency behaviors of the Hilbert spectrum and Hilbert marginal spectrum (HMS) are studied to estimate the spectral traits of HRV signals. In this paper, two kinds of experiment data are used to compare our method with the conventional power spectral density (PSD) estimation. The analysis results of the simulated HRV series show that interpolation and resampling are basic requirements for HRV data processing, and HMS is superior to PSD estimation. On the other hand, in order to further prove the superiority of our approach, real HRV signals are collected from seven young health subjects under the condition that autonomic nervous system (ANS) is blocked by certain acute selective blocking drugs: atropine and metoprolol. The high-frequency power/total power ratio and low-frequency power/high-frequency power ratio indicate that compared with the Fourier spectrum based on principal dynamic mode, our method is more sensitive and effective to identify the low-frequency and high-frequency bands of HRV.
The elucidation of biological systems will be one of great keys to scientific advance. However, it is difficult to analyze such biological systems because of their non-linear and non-stationary characteristics. This paper reviews newly developed methods for analysing such non-linear and non-stationary characteristics.
To analyze signals measured from human blood flow in the time-frequency domain, we used the wavelet transform which gives good time resolution for high-frequency components and good frequency resolution for low-frequency components. Five characteristic frequency peaks, corresponding to five almost periodic rhythmic activities, were found on the time scale of minutes. These oscillations were characterized by time and spatial invariant measures. The potential of this approach in studying the blood-flow dynamics was illustrated by revealing differences between the groups of control subjects and athletes.