This document provides a synopsis on chaos analysis of heart rate variability. It discusses how heart rate is non-stationary and nonlinear, and that chaos analysis can provide insights not seen with traditional time and frequency domain analysis. It describes several nonlinear parameters used in chaos analysis, including Lyapunov exponents, fractal dimension, Poincare plots, entropy measures, and detrended fluctuation analysis. The parameters help quantify chaos, complexity, self-similarity, and scaling behaviors that may be present in heart rate variability signals.
Review: Nonlinear Techniques for Analysis of Heart Rate VariabilityIJRES Journal
Heart rate variability (HRV) is a measure of the balance between sympathetic mediators of heart
rate that is the effect of epinephrine and norepinephrine released from sympathetic nerve fibres acting on the
sino-atrial and atrio-ventricular nodes which increase the rate of cardiac contraction and facilitate conduction at
the atrio-ventricular node and parasympathetic mediators of heart rate that is the influence of acetylcholine
released by the parasympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes leading to a
decrease in the heart rate and a slowing of conduction at the atrio-ventricular node. Sympathetic mediators
appear to exert their influence over longer time periods and are reflected in the low frequency power(LFP) of
the HRV spectrum (between 0.04Hz and 0.15 Hz).Vagal mediators exert their influence more quickly on the
heart and principally affect the high frequency power (HFP) of the HRV spectrum (between 0.15Hz and 0.4
Hz). Thus at any point in time the LFP:HFP ratio is a proxy for the sympatho- vagal balance. Thus HRV is a
valuable tool to investigate the sympathetic and parasympathetic function of the autonomic nervous system.
Study of HRV enhance our understanding of physiological phenomenon, the actions of medications and disease
mechanisms but large scale prospective studies are needed to determine the sensitivity, specificity and predictive
values of heart rate variability regarding death or morbidity in cardiac and non-cardiac patients. This paper
presents the linear and nonlinear to analysis the HRV.
Heart rate variability (HRV) is the physiological phenomenon of variation in the time interval between heartbeats. It is measured by the variation in the beat-to-beat interval.
Other terms used include: "cycle length variability", "RR variability" (where R is a point corresponding to the peak of the QRS complex of the ECG wave; and RR is the interval between successive Rs), and "heart period variability".
See also Heart rate turbulence, Sinus rhythm.
Methods used to detect beats include: ECG, blood pressure, ballistocardiograms,[1][2] and the pulse wave signal derived from a photoplethysmograph (PPG). ECG is considered superior because it provides a clear waveform, which makes it easier to exclude heartbeats not originating in the sinoatrial node. The term "NN" is used in place of RR to emphasize the fact that the processed beats are "normal" beats.
Heart Rate Variability (HRV) plays an important role for reporting several cardiological and noncardiological
diseases. Also, the HRV has a prognostic value and is therefore quite important in modelling
the cardiac risk. The nature of the HRV is chaotic, stochastic and it remains highly controversial. Because
the HRV has utmost importance, it needs a sensitive tool to analyze the variability. In previous work,
Rosenstein and Wolf had used the Lyapunov exponent as a quantitative measure for HRV detection
sensitivity. However, the two methods diverge in determining the HRV sensitivity. This paper introduces a
modification to both the Rosenstein and Wolf methods to overcome their drawbacks. The introduced
Mazhar-Eslam algorithm increases the sensitivity to HRV detection with better accuracy.
Review: Linear Techniques for Analysis of Heart Rate Variabilityinventionjournals
Heart rate variability (HRV) is a measure of the balance between sympathetic mediators of heart rate that is the effect of epinephrine and norepinephrine released from sympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes which increase the rate of cardiac contraction and facilitate conduction at the atrio-ventricular node and parasympathetic mediators of heart rate that is the influence of acetylcholine released by the parasympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes leading to a decrease in the heart rate and a slowing of conduction at the atrio-ventricular node. Sympathetic mediators appear to exert their influence over longer time periods and are reflected in the low frequency power(LFP) of the HRV spectrum (between 0.04Hz and 0.15 Hz).Vagal mediators exert their influence more quickly on the heart and principally affect the high frequency power (HFP) of the HRV spectrum (between 0.15Hz and 0.4 Hz). Thus at any point in time the LFP:HFP ratio is a proxy for the sympatho- vagal balance. Thus HRV is a valuable tool to investigate the sympathetic and parasympathetic function of the autonomic nervous system. Study of HRV enhance our understanding of physiological phenomenon, the actions of medications and disease mechanisms but large scale prospective studies are needed to determine the sensitivity, specificity and predictive values of heart rate variability regarding death or morbidity in cardiac and noncardiac patients. This paper presents the linear techniques to analysis the HRV
Review: Nonlinear Techniques for Analysis of Heart Rate VariabilityIJRES Journal
Heart rate variability (HRV) is a measure of the balance between sympathetic mediators of heart
rate that is the effect of epinephrine and norepinephrine released from sympathetic nerve fibres acting on the
sino-atrial and atrio-ventricular nodes which increase the rate of cardiac contraction and facilitate conduction at
the atrio-ventricular node and parasympathetic mediators of heart rate that is the influence of acetylcholine
released by the parasympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes leading to a
decrease in the heart rate and a slowing of conduction at the atrio-ventricular node. Sympathetic mediators
appear to exert their influence over longer time periods and are reflected in the low frequency power(LFP) of
the HRV spectrum (between 0.04Hz and 0.15 Hz).Vagal mediators exert their influence more quickly on the
heart and principally affect the high frequency power (HFP) of the HRV spectrum (between 0.15Hz and 0.4
Hz). Thus at any point in time the LFP:HFP ratio is a proxy for the sympatho- vagal balance. Thus HRV is a
valuable tool to investigate the sympathetic and parasympathetic function of the autonomic nervous system.
Study of HRV enhance our understanding of physiological phenomenon, the actions of medications and disease
mechanisms but large scale prospective studies are needed to determine the sensitivity, specificity and predictive
values of heart rate variability regarding death or morbidity in cardiac and non-cardiac patients. This paper
presents the linear and nonlinear to analysis the HRV.
Heart rate variability (HRV) is the physiological phenomenon of variation in the time interval between heartbeats. It is measured by the variation in the beat-to-beat interval.
Other terms used include: "cycle length variability", "RR variability" (where R is a point corresponding to the peak of the QRS complex of the ECG wave; and RR is the interval between successive Rs), and "heart period variability".
See also Heart rate turbulence, Sinus rhythm.
Methods used to detect beats include: ECG, blood pressure, ballistocardiograms,[1][2] and the pulse wave signal derived from a photoplethysmograph (PPG). ECG is considered superior because it provides a clear waveform, which makes it easier to exclude heartbeats not originating in the sinoatrial node. The term "NN" is used in place of RR to emphasize the fact that the processed beats are "normal" beats.
Heart Rate Variability (HRV) plays an important role for reporting several cardiological and noncardiological
diseases. Also, the HRV has a prognostic value and is therefore quite important in modelling
the cardiac risk. The nature of the HRV is chaotic, stochastic and it remains highly controversial. Because
the HRV has utmost importance, it needs a sensitive tool to analyze the variability. In previous work,
Rosenstein and Wolf had used the Lyapunov exponent as a quantitative measure for HRV detection
sensitivity. However, the two methods diverge in determining the HRV sensitivity. This paper introduces a
modification to both the Rosenstein and Wolf methods to overcome their drawbacks. The introduced
Mazhar-Eslam algorithm increases the sensitivity to HRV detection with better accuracy.
Review: Linear Techniques for Analysis of Heart Rate Variabilityinventionjournals
Heart rate variability (HRV) is a measure of the balance between sympathetic mediators of heart rate that is the effect of epinephrine and norepinephrine released from sympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes which increase the rate of cardiac contraction and facilitate conduction at the atrio-ventricular node and parasympathetic mediators of heart rate that is the influence of acetylcholine released by the parasympathetic nerve fibres acting on the sino-atrial and atrio-ventricular nodes leading to a decrease in the heart rate and a slowing of conduction at the atrio-ventricular node. Sympathetic mediators appear to exert their influence over longer time periods and are reflected in the low frequency power(LFP) of the HRV spectrum (between 0.04Hz and 0.15 Hz).Vagal mediators exert their influence more quickly on the heart and principally affect the high frequency power (HFP) of the HRV spectrum (between 0.15Hz and 0.4 Hz). Thus at any point in time the LFP:HFP ratio is a proxy for the sympatho- vagal balance. Thus HRV is a valuable tool to investigate the sympathetic and parasympathetic function of the autonomic nervous system. Study of HRV enhance our understanding of physiological phenomenon, the actions of medications and disease mechanisms but large scale prospective studies are needed to determine the sensitivity, specificity and predictive values of heart rate variability regarding death or morbidity in cardiac and noncardiac patients. This paper presents the linear techniques to analysis the HRV
The paper describes a system for analyzing of heart auscultation so every person can get information about their own heart condition. The auscultation means the sound created by any organ due to turbulent blood flow. The murmurs are heart abnormal sounds. The murmur can be detected and analyzed by using Digital Signal Processing (DSP) stethoscope but looking cost aspect a system should have maximum accuracy level. The noise in audio files (.wave) is degraded by using Finite Impulse Response (FIR) filtering. The designed system calculates Root Mean Square (RMS) value and Low Energy Rate (LER) for sound signals directly taken from internet by using MATLAB platform. From the calculation, system classifies the signal either normal or murmur signals. Results are consulted with a physician. If signals are normal then Root Mean Square value is less than 0.3 (RMS<0.3)>0.8).
Denoising of ECG -- A discrete time approach using DWTIJERA Editor
This paper is about denoising of ECG signal using DWT transform. In this paper, ECG signals are denoised using DWT transform.Ecg signals are taken and noise at different frequencies are generated which are superimposed on this original ecg signal.High frequency noise is of 4000 hertz and power line interference is of 50 hertz.Decomposition of noisy signal is achieved through wavelet packet .wavelet packets are reconstructed and appropriate wavelet packets are combined to obtain a signal, very similar to original ecg signal.This technique results in the minimization of mean square error in the filtered signals.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
The paper describes a system for analyzing of heart auscultation so every person can get information about their own heart condition. The auscultation means the sound created by any organ due to turbulent blood flow. The murmurs are heart abnormal sounds. The murmur can be detected and analyzed by using Digital Signal Processing (DSP) stethoscope but looking cost aspect a system should have maximum accuracy level. The noise in audio files (.wave) is degraded by using Finite Impulse Response (FIR) filtering. The designed system calculates Root Mean Square (RMS) value and Low Energy Rate (LER) for sound signals directly taken from internet by using MATLAB platform. From the calculation, system classifies the signal either normal or murmur signals. Results are consulted with a physician. If signals are normal then Root Mean Square value is less than 0.3 (RMS<0.3)>0.8).
Denoising of ECG -- A discrete time approach using DWTIJERA Editor
This paper is about denoising of ECG signal using DWT transform. In this paper, ECG signals are denoised using DWT transform.Ecg signals are taken and noise at different frequencies are generated which are superimposed on this original ecg signal.High frequency noise is of 4000 hertz and power line interference is of 50 hertz.Decomposition of noisy signal is achieved through wavelet packet .wavelet packets are reconstructed and appropriate wavelet packets are combined to obtain a signal, very similar to original ecg signal.This technique results in the minimization of mean square error in the filtered signals.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Ever wondered if what you do on a daily basis is important? This gentle presentation for managers and Board members will discuss how everything you do has some effect on someone or something, and how your decisions matter to more people than you are aware.
Chaos theory is a mathematical field of study which states that non-linear dynamical systems
that are seemingly random are actually deterministic from much simpler equations. The
phenomenon of Chaos theory was introduced to the modern world by Edward Lorenz in 1972
with conceptualization of ‘Butterfly Effect’. As chaos theory was developed by inputs of
various mathematicians and scientists, it found applications in a large number of scientific
fields.
The purpose of the project is the interpretation of chaos theory which is not as familiar as
other theories. Everything in the universe is in some way or the other under control of Chaos
or product of Chaos. Every motion, behavior or tendency can be explained by Chaos Theory.
The prime objective of it is the illustration of Chaos Theory and Chaotic behavior.
This project includes origin, history, fields of application, real life application and limitations
of Chaos Theory. It explores understanding complexity and dynamics of Chaos.
The fundamentals in this slide presentation are important in understanding the concept of planning, the various types of plans, and the strategic management process
A STUDY ON IMPACT OF ALCOHOL AMONG YOUNG INDIAN POPULATION USING HRV ANALYSISijcseit
Heart Rate Variability (HRV) is the measure of time difference between two successive heart beats and its
variation occurring due to internal and external stimulation causes. HRV is a non-invasive tool for indirect
investigation of both cardiac and autonomic system function in both healthy and diseased condition. It has
been speculated that HRV analysis by nonlinear method might bring potentially useful prognosis
information into light which will be helpful for assessment of cardiac condition. In this study, HRV from
two types of data sets are analyzed which are collected from different subjects in the age group of 18 to 22.
Then parameters of linear methods and three nonlinear methods, approximate entropy (ApEn), detrended
fluctuation analysis (DFA) and Poincare plot have been applied to analyze HRV among 158 subjects of
which 79 are control study and 79 are alcoholics. It has been clearly shown that the linear and nonlinear
parameters obtained from these two methods reflect the opposite heart condition of the two types of data
under study among alcoholics non-alcoholic’s by HRV measures. Poincare plot clearly distinguishes
between the alcoholics by analysing the location of points in the ellipse of the Poincare plot. In alcoholics
the points of the Poincare plot will be concentrated at the centre of the ellipse and in nonalchoholics the
points will be much concentrated along the periphery of the ellipse. The Approximate Entropy value will be
lesser than one in alcoholics and in nonalcoholics the entropy shows values greater than one. The
increased LF/HF value in alcoholics denotes the increase in sympathetic nervous system activities and
decrease of the parasympathetic activity which will be lesser in alcoholics subjects.
Heart Rate Variability (HRV) is the measure of time difference between two successive heart beats and its
variation occurring due to internal and external stimulation causes. HRV is a non-invasive tool for indirect
investigation of both cardiac and autonomic system function in both healthy and diseased condition. It has
been speculated that HRV analysis by nonlinear method might bring potentially useful prognosis
information into light which will be helpful for assessment of cardiac condition. In this study, HRV from
two types of data sets are analyzed which are collected from different subjects in the age group of 18 to 22.
Then parameters of linear methods and three nonlinear methods, approximate entropy (ApEn), detrended
fluctuation analysis (DFA) and Poincare plot have been applied to analyze HRV among 158 subjects of
which 79 are control study and 79 are alcoholics. It has been clearly shown that the linear and nonlinear
parameters obtained from these two methods reflect the opposite heart condition of the two types of data
under study among alcoholics non-alcoholic’s by HRV measures. Poincare plot clearly distinguishes
between the alcoholics by analysing the location of points in the ellipse of the Poincare plot. In alcoholics
the points of the Poincare plot will be concentrated at the centre of the ellipse and in nonalchoholics the
points will be much concentrated along the periphery of the ellipse. The Approximate Entropy value will be
lesser than one in alcoholics and in nonalcoholics the entropy shows values greater than one. The
increased LF/HF value in alcoholics denotes the increase in sympathetic nervous system activities and
decrease of the parasympathetic activity which will be lesser in alcoholics subjects.
HEART RATE VARIABILITY ANALYSIS FOR ABNORMALITY DETECTION USING TIME FREQUENC...cscpconf
Heart rate variability (HRV) is derived from the time duration between consecutive heart beats. The HRV is to reflect the heart’s ability to adapt to changing circumstances by detecting and quickly responding to unpredictable stimuli to cardiac system. Depressed HRV is a powerful predictor of mortality and of arrhythmic complications in patients after diseases like acute
Myocardial Infarction. The degree of variability in the HR provides information about the nervous system control on the HR and the heart’s ability to respond .Spectral analysis of HRV is a frequency domain approach to assess the cardiac condition. In this paper one such method for analyzing HRV signals known as smoothed pseudo Wigner Ville distribution (SPWVD) is
applied, The sub-band decomposition technique used in SPWVD, based on Instantaneous Autocorrelation (IACR) of the signal provides time-frequency representation for very lowfrequency (VLF), low-frequency (LF) and high-frequency (HF) regions identified in HRV spectrum. Results suggest that SPWVD analysis provides useful information for the assessment of dynamic changes and patterns of HRV during cardiac abnormalities.
A M ODIFIED M ETHOD F OR P REDICTIVITY OF H EART R ATE V ARIABILITYcsandit
Heart Rate Variability (HRV) plays an important rol
e for reporting several cardiological and
non-cardiological diseases. Also, the HRV has a pro
gnostic value and is therefore quite
important in modelling the cardiac risk. The nature
of the HRV is chaotic, stochastic and it
remains highly controversial. Because the HRV has u
tmost importance, it needs a sensitive tool
to analyze the variability. In previous work, Rosen
stein and Wolf had used the Lyapunov
exponent as a quantitative measure for HRV detectio
n sensitivity. However, the two methods
diverge in determining the HRV sensitivity. This pa
per introduces a modification to both the
Rosenstein and Wolf methods to overcome their drawb
acks. The introduced Mazhar-Eslam
algorithm increases the sensitivity to HRV detectio
n with better accuracy.
Effect of Body Posture on Heart Rate Variability Analysis of ECG Signal.pdfIJEACS
An assessment of cardiac function derived from the
ECG signal is known as heart charge variability (HRV). The
evaluation of HRV provides ways for analyzing entry into the
heart rhythm non-invasively, which can be used to guide
treatment. For the prevailing study, records of ten members in
two one-of-a-kind frame postures have been taken. Sets of
records have been received in sleeping and sitting positions. In
addition, The R-peak produced from the ECG is employed in the
evaluation of the RR interval. It is also applied for the evaluation
of HRV. In the context of coronary heart rate (HR), HRV is
linked to tachycardia (HR > 100 bpm) and bradycardia (HR 60
bpm). Linear HRV characteristics with unique time-domain and
frequency-domain indices are interpreted into two distinct
postures. As a result, it is possible to conclude that the RR
interval increases for the supine position during all two poses, as
sitting appears to be a more comfortable situation than the
alternative one. Also, as the frequency-area evaluation result
proposes, the LF/HF ratio is better in the supine position, i.e.,
better sympathetic has an effect. Consequently, supine has a
higher resting circumstance than that sitting. A non-linear
Poincare plot has also been incorporated for accessing variability.
Heart Rate Variability (HRV) analysis is the
ability to assess overall cardiac health and the state of the
autonomic nervous system (ANS), responsible for regulating
cardiac activity. ST-change due to ischemia and their HRV
analysis have not been well discussed in the previous works.
The proposed simple and time efficient TBC algorithm has
been tested in four sets of standard databases with selected
patient’s data having ischemic conditions (i.e.MIT-BIH
Normal-Sinus Rhythm Database (NSRDB), European ST-T
Database (EDB), MIT-BIH ST Change Database (STDB) &
Long-Term ST Database (LTSTDB))for the detection of R-peak
& HRV analysis. The pre-processing is done by MAF and DWT
to remove the baseline drift and noise induced in the ECG
signal. The mean/average of HR is calculated for each set of
databases and in case of EDB it is of 57 BPM (subjected to
bradycardia). The Probability with normal distribution is
analyzed by comparing the NSRDB data with the ischemic data sets. The performance of this algorithm is found to be 98.5%.
A novel reliable method assess hrv forijbesjournal
In a simple words, the heart rate variability (HRV) refers to the divergence in heart complex wave (beat- to-beat) intervals. It is a reliable repercussion of many, psychological, physiological, also environmental factors modulating therhythm of the heart. Seriously, the HRV act as a powerful tool for observation the interaction between the sympathetic and parasympathetic nervous systems. However, it has a frequency that is great for supervision, surveillance, and following up the cases. Finally, the generating structure of heart complex wave signal is not simply linear, but also it involves the nonlinear contributions. Those two contributions are totally correlated.
HRV is stochastic and chaotic (stochaotic) signal. It has utmost importance in heart diseases diagnosis, and it needs a sensitive tool to analyze its variability. In early works, Rosenstein and Wolf had used the Lyapunov exponent (LE) as a quantitative measure for HRV detection sensitivity, but the Rosenstein and Wolf methods diverge in determining the main features of HRV sensitivity, while Mazhar-Eslam introduced a modification algorithm to overcome the Rosenstein and Wolf drawbacks.
The present work introduces a novel reliable method to analyze the linear and nonlinear behaviour of heart complex wave variability, and to assess the use of the HRV as a versatile tool for heart disease diagnosis. This paper introduces a declaration for the concept of the LE parameters to be used for HRV diagnosis and proposes a modified algorithm for a more sensitive parameters computation
Analyzing Employee’s Heart rate using Nonlinear Cellular Automata modelIOSR Journals
Non-linear Cellular Automata model is a simulation tool which can be used to diagnosis the intensity of the disease. This paper aims to study the Heart rate behavior between normal respiratory patients and healthy controls/unhealthy controls. We also discuss about Heart Rate Variability (HRV) of employee’s through non-linear Cellular Automata model. Cellular Automata model gives us striking results for further studies
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
this presentation overviews about heart rate variability and its uses as a biofeedback mechanism in varying the heart rate and thus releaving stress and other applications of it
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
MEDITATION: ITS TREMENDOUS IMPACT ON HEART RATE VARIABILITYcscpconf
The heart is connected through the nervous system directly to major organs and is able to sense
their need. The heart also responds to adrenaline in the blood flowing through it. With these
inputs the heart is able to adjust its rate to accommodate the needs of the whole body. By its
heartbeat, it is able to broadcast a common signal to every cell. One measure of heart health is
Heart Rate Variability (HRV). HRV is defined in terms of how different the lengths of time
between each heart beat is. The greater the difference in times between heart beats, the
healthier is the heart thought to be. Individuals may be able to learn to increase their own HRV
and become healthier by a daily meditation practice. This paper uses Heart Variability as the
base signal for studying the impact of meditation on it. The paper brings out the difference
between pre and post meditation conditions in terms qualitative measure of Power Spectral
Density (PSD) variations using Smoothed Pseudo Wigner Ville (SPWVD) distribution method.The simulations highlight the meditation effects overtime period in PSDs
1. SYNOPSIS
ON
CHAOS ANALYSIS OF HEART RATE VARIABILITY
Submitted by
Name of Project Members Roll No
MONODIP SINGHA ROY 11900310004
SHAIBAL CHAKRABORTY 11900310005
SUKRIT GHORUI 11900310023
BIKASH RASAILY 11900310047
Under the guidance of
MR. SUBHOJIT SARKER
ASSISTANT PROFESSOR
ECE DEPARTMENT
DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING
SILIGURI INSTITUTE OF TECHNOLOGY
PO: SUKNA, SILIGURI, PIN: 734 009, WEST BENGAL
2013-2014
2. Chaos Analysis of Heart Rate Variability
Abstract:
This paper presents a classification method based on chaotic analysis of heart rate
variability. Heart rate variability (HRV) is a reliable reflection of the many physiological
factors modulating the normal rhythm of the heart. Heart rate (HR) is a non stationary
signal, has been conventionally analyzed with time & frequency domain methods, which
measure the overall magnitude of R-R interval. It has been proposed that the normal
heartbeat is associated with complex nonlinear dynamics and chaos This paper uses
non-linear parameters for analyzing of chaos in heart rate variability, the parameters
used are: Lyapunov exponent, Fractal dimension(FD), Poincarẻ plot, Entropy
(Approximate entropy(ApEn), Sample entropy(SampEn), Multiscale entropy(MSEn)),
Detrended fluctuation analysis(DFA). Lyapunov exponent is a chaotic analysis which
measures the rate at which the trajectories separate from one another. Fractal
dimension (FD) that refers to a non-integer or fractional dimension originates from
fractal geometry. Poincaré plot is a visual tool in which each RR interval is plotted as a
function of previous RR
Interval. ApEn, a non-linear complexity index, to quantify the randomness of
physiological time-series. SampEn, measuring complexity and regularity of clinical and
experimental time-series data and compared it with ApEn. The DFA method, used to
quantify the scaling behavior of a time series was previously described and used to
quantify the fractal-like scaling properties of R-R interval data.
INTRODUCTION
eart Rate Variability (HRV) refers to changes in the interval or distance between one
beat of the heart and the next. These variations are produced by the influence of
the sympathetic and Para-sympathetic branches of the Autonomic Nervous System
(ANS) on the sino-atrial (SA) node.
Fig. : R-R Interval Variation
Analysis of HRV by non-linear dynamics can significantly improve the identification
Cardiac disease. The rationale in the emergence of non-linear measures of HRV is that
the heart is not a periodic oscillator under normal physiological conditions and
complicated feedback control of the heart may give rise to non-linear dynamics that are
not well reflected by conventional measures of HRV. The software Kubios is used
H
3. for analyzing Heart Rate Variability. Kubios HRV is an advanced tool for
studying the variability of heart rate intervals, due to its wide variety of
different analysis options and the easy to use interface. The software is
mainly designed for the analysis of normal human HRV, but it is also
usable for animal researches.
CHAOS:
What exactly is chaos?
The name "chaos theory" comes from the fact that the systems that the
theory describes are apparently disordered, but chaos theory is really about finding the
underlying order in apparently random data.
In general, a chaotic system is a deterministic system with
random fluctuations. It has a bounded steady-state behavior that is quasi-periodic and
not at equilibrium. Its spectrum exhibits the character of a continuous and broadband
signal. These attributes are characteristic of electrocardiographic signals and suggest the
use of chaotic theory for analysis of their variation in time.
Chaos theory studies the behavior of dynamical systems that are highly sensitive to
initial condition, an effect which is popularly referred to as “BUTTERFLY EFFECT”,
because the flapping of the wings of butterfly represents a small change in initial
condition of the system, which causes a chain of events leading to large scale
phenomenon. But if the butterfly not flapped the wings, the trajectories of the system
have been vastly different.
Chaos In Heart Rate Variability:
Many people confuse Heart Rate with Heart Rate Variability. The human heart is a bio-
electrical pump beating at an ever changing rate: it is not like a clock that beats at a
Steady, unchanging rate. This variability in heart rate is an adaptive quality in a healthy
body.
Heart Rate Variability (HRV):
The human heart is a bio-electrical pump beating an ever changing rate. By variability
we mean changes in the interval or distance between one heart and the next. The inter
beat interval (IBI) is the time between the R- wave and the next in millisecond. The IBI is
highly variable within any given time period. IBI or HRV have relevance for physical,
emotional and mental function. HRV has been analyzed with time & frequency domain
methods, which measure the overall magnitude of R-R interval fluctuation around its
mean value or the magnitude of fluctuation in some predetermined frequencies.
There are two primary fluctuations for HRV:
1. Respiratory Arrhythmia- This HRV is associated with respiratory & faithfully
tracks the respiratory rate across range of frequencies.
2. Low Frequency oscillation- This HRV is associated with Mayer waves (Traube-
Hering-Mayer waves) of blood pressure & is usually at a frequency of 0.1Hz or a
10 sec period.
4. Typesof Heart Rate are:
1. Neurogenic Heart Rate.
2. Mynogenic Heart Rate.
Autonomic influences of Heart Rate:
Cardiac automatically intrinsic to various pacemaker tissues.
Heart rate & rhythm are largely under control of the autonomic nervous
system.
Measurement of Heart Rate Variability:
Heart rate variability is the difference between the highest heart rate and the lowest
heart rate within each cardiac cycle measured in beats per minute. The index is called
“HR max – HR min”. A second index of HRV is widely used in medical research is the
Standard Deviation (SD) of “N-N interval”. The N-N interval is the normalized beat to
beat interval.
Heart Rate Variability Artifact:
Errors in the location of the instantaneous heart beat will result in errors in the
calculation of the HRV. HRV is highly sensitive to artifact & errors are as low as even 2%
of the data will result in unwanted biases in HRV calculation.
Chaos In HRV:
The nature of Heart Rate Variability (HRV) is not fully understood yet.
Recently many studies have indicated that HRV is chaotic. However most of these
studies used return maps or correlation dimension estimates to reach this conclusion. But
none of these methods discriminate chaos from fractal signal.
By variability we mean changes in the interval or distance between one beat of the
heart and the next. The interbeat interval (IBI) is the time between one R-wave (or heart
beat) and the next, in milliseconds. The IBI is highly variable within any given time
period. So, we can say that there is chaos in Herat Rate Variability (HRV).
Chaotic Analysis Of Heart Rate Variability:
The beat-to-beat variability of heart rate (HRV) arises in both
healthy persons and patients with organic heart diseases. Analysis of HRV from recorded
Ambulatory electrocardiograms (ECG) can help identify patients who are at high risk of
sudden cardiac death. Although a great deal of work has been devoted to the analysis of
HRV, a reliable method of evaluation has not emerged. These methods can be classified
into four major categories: statistical analysis, spectral analysis, and model analysis and
chaotic analysis. In general, a chaotic system is a deterministic system with random
fluctuations. It has a bounded steady-state behavior that is quasi-periodic and not at
equilibrium. Its spectrum exhibits the character of a continuous and broadband signal.
These attributes are characteristic of electrocardiographic signals and suggest the use of
chaotic theory for analysis of their variation in time.
5. There are six types of non-linear parameters that are used for the chaos analysis of
heart rate variability, they are:
1. Lyapunov Exponent.
2. Entropy (Approximate Entropy, Sample Entropy, Multiscale Entropy).
3. Poincare Plot.
4. Fractal Dimension.
5. Correlation Dimension.
6. Detrended Fluctuation Analysis.
Lyapunov Exponent:
The method of Lyapunov characteristic exponents serves as a useful tool to
quantify chaos. Specifically, Lyapunov exponents measure the rates of convergence or
divergence of nearby trajectories .Negative Lyapunov exponents indicates convergence,
while positive Lyapunov exponents demonstrate divergence and chaos. The magnitude
of the Lyapunov exponent is an indicator of the time scale on which chaotic behavior
respectively.
Physically, the Lyapunov exponent is a measure of how rapidly nearby trajectories
converges or diverges.
To determine Lyapunov exponent, two nearby points x0 and x0+ Δ x0 will generate
orbits of its own and separation Δx0 will be function of time Δ x0(x0, t) . For chaotic data
the mean exponential rate of divergence of two initially close orbits is characterized by:
𝜆 = lim
𝑡→∝
1
𝑡
𝑙𝑛
│∆𝑥( 𝑋0, 𝑡)│
│𝛥𝑋0│
Maximum positive λ is chosen as it quantifies sensitivity of the system to initial
conditions and gives a measure of predictability.
Approximate Entropy (ApEn):
The ApEn is a measure of system complexity, which quantifies the
unpredictability of fluctuations in a time series such as heart rate time series. The
method examines the time series for similar epochs (period marked by distinctive
Character). The more frequent and more similar epoch lead to lower value of ApEn.
Informally, given N points, the family of statistics ApEn (m, r, N) is approximately equal
to the negative average natural logarithm of the conditional probability that two
sequences that are similar for m points remain similar within a tolerance r, at the next
point. If ‘N’ is length of time series and ‘m’ is length of sequence to be compared and ‘r’
is tolerance for accepting matches. It is convenient to set tolerance = r*SD. The standard
deviation (SD) of data has been set at SD =1.
Define vector u (j) for time series of N data points:
u ( j) :1 ≤ j ≤ N (9)
This series forms N − m +1 number of xm (i) vectors where, xm (i):1 ≤ i ≤ N − m +1 and
xm (i) has data length of m points defined as [u (i + k): 0 ≤ k ≤ m −1 ] from
u (i) tou(i + m −1) . If Bi is number of vectors xm ( j) within ‘r’ of xm (i) , ( xm (i) –
template and xm ( j) -template match) and Ai is number of vectors xm+1 ( j) within ‘r’ of
xm+1 (i) .
6. Then Cm (r) i - probability that xm ( j) is within ‘r’ of xm (i) Cm (r), i = ( Bi )/( N − m +1)
The average of the natural logarithm of Cm (r), the average of the natural logarithm of
Ci
m (r) is,
∅ 𝑚 ( 𝑟) =
1
(𝑁−𝑚+1)
∑ ln[𝑐𝑖
𝑚( 𝑟)]𝑁−𝑚+1
𝑖=1
The ApEn for fixed parameters of n, m & r is:-
ApEn (m, r, N) = Φm(r-Φm+1(r))
After algebraic manipulation:
𝐴𝑝𝐸𝑛( 𝑚, 𝑟, 𝑁) = (
1
𝑁−𝑚+1
)∑ ln[ 𝑐𝑖
𝑚( 𝑟)]−
1
(𝑁−𝑚)
𝑁−𝑚+1
𝑖=1 ∑ ln[𝑐𝑖
𝑚+1
(𝑟)𝑁−𝑚
𝑖=1 ]
[When N is large]
𝐴𝑝𝐸𝑛( 𝑚, 𝑟, 𝑁) ≅ (
1
𝑁−𝑚
)∑ [− ln(
𝐴𝑖
𝐵𝑖
)]𝑁−𝑚
𝑖=1
Approximate entropy is used for chaos analysis for low dimensional signals of heart; the
analysis is performed by transforming data to a phase space in which there are ‘N’
dimensional space, where ‘N’ is the number of dynamical variable.
ApEn represents the chaos as the complex degree of a data sequence and
its value is proportional to the complex degree. Usually, the value of approximate
entropy is a non negative number. More complex the sequence is, larger the value of
the approximate entropy is. Approximate entropy has a strong ability to characterize the
complexity of the signals, such as the chaotic signals and the random signals. The
amount of the data required to calculate the approximate entropy is small, so it is
suitable for analyzing short time data. Besides, approximate entropy has a strong
anti-noise capability.
Sample Entropy (SampEn):
Sample Entropy is the negative logarithm of the conditional
probability that a point which repeats itself with a tolerance of ε in an m dimensional
phase space will repeat itself in an m+1 dimensional phase space. Self-matches are not
included in calculating the probability, described a reduction in SampEn of neonatal HR
prior to the clinical diagnosis of sepsis and sepsis-like illness. The SampEn was found to
be significantly reduced before the onset of atrial fibrillation.
Mathematical Representation :
𝑆𝑎𝑚𝑝𝐸𝑛( 𝑚, ∈) = −log(
𝐶( 𝑚+1,∈)
𝐶( 𝑚,∈)
)
Limitations of SampEn:
Stationary is required; higher pattern length requires an increased number of
data points; evaluates regularity on one scale only; outliers (missed beats, artifacts) may
affect the entropy values.
7. Multiscale Entropy:
Multiscale entropy is a new method for measuring the complexity of a
finite length time series. This computation tool can be applied both to the physical and
physiological data sets, and can be used with a variety of measures of entropy, the heart
period changes on a beat to beat basis & its variations occurs over a large set pf
temporal scale. Due to such multiscale behavior HRV cannot be completely
characterized on a single time scale & cardiac interbeat time series have a complex
temporal structure with multiscale correlation under healthy conditions. Although ApEn
& SampEn for measuring the complexity of physiological time series have been widely
used & proved to be useful in discriminating b/w health & disease states, but due to
multiple scale mechanism of HR some result may lead to misleading conclusion.
Multiscale Entropy is used for the chaos analysis with the help of
white noise, fractal Brownian noise & the 1/f noise. It is seen that the entropy measure
for the deterministic chaotic time series increase on small scale & the gradually
decrease indicating the reduction of complexity on the large scales. This trend of the
variation of the SampEn with scale is entirely different from the white-fractal Brownian-
1/f noises. Moreover the variations of SampEn for all chaotic data sets showed a similar
behavior. This established the fact that the MSE analysis of chaos can be used to detect
the determinism in a time series.
Poincarẻ Plot:
A Poincare plot named after Henri Poincare, is used to quantify self-similarity in
process, usually periodic function.Poincaré plot is a visual tool in which each RR interval
is plotted as a function of previous RR interval.Poincaré plot provides summary
information as well as detailed beat-to-beat information on the behavior of heart. The
problem regarding Poincaré plot use has been lack of obvious quantitative measures
that characterize the salient features of Poincaré plots. To quantitatively characterize
the plot, a number of techniques like converting the two-dimensional plot into various
one-dimensional views; the fitting of an ellipse to the plot shape; and measuring the
correlation coefficient of the plot have been suggested The width of the plot (sd2)
corresponds to the level of short term HRV while the length of the plot(sd1)
corresponds to level of long term HRV.The advantage of Poincare plot is their ability to
identify beat-to-beat cycle and patterns in data that are difficult to identify with spectral
analysis.
The Poincare Plot is a graphical representation of the correlation between
successive RR intervals, i.e. plot of RRj+1 as a function of RRj as described in Fig. 4.
The shape of the plot is the essential feature. A common approach to parameterize the
shape is to fit an ellipse to the plot as shown in Fig . The ellipse is oriented according to
the line-of-identity (RRj = RRj+1). The standard deviation of the point’s perpendicular to
the line-of identity denoted by SD1 describes short-term variability which is mainly
caused by RSA. The standard deviation along the line-of-identity denoted by SD2, on the
other hand, describes long-term variabilitySD1 related to the fast beat-to-beat variability
in the data, while SD2describes the longer-term variability of R–R. The ratio SD1/SD2
may also be computed to describe the relationship between these components.
8. Fig: Poincare Plot with its descriptors SD1 & SD2
Fractal dimension:
A fractal dimension is a ratio providing a statical index of complexity
comparing how detail in a pattern changes with the scale at which it is measured. It is
an index for characterizing fractal patterns or sets by quantifying their complexity as a
ratio of change in the detail tocharatrize a broad spectrum objects ranging from the
abstract to practical phenomena, including turbulence, human physiology.
Chaos theory has evolved into the study of the fractal behavior of physical
systems that at first seem entirely random but in fact are not entirely so. A fractal is a
set of points that when looked at smaller scales, resembles the whole set. The concept
of fractal dimension (FD) that refers to a non-integer or fractional dimension originates
from fractal geometry. The FD emerges to provide a measure of how much space an
object occupies between Euclidean dimensions. The FD of a waveform represents a
powerful tool for transient detection. The fractal dimension computes the number of
degrees of freedom of the data in local areas of attractors using q neighbours of
representative point (hence its name local intrinsic dimension) then performs an
average of all these LID on the whole attractor to obtain the estimate. It is relatively
immune to noise, by opposition to the correlation dimension estimation , and since it
requires a large embedding dimension, it frees the user from its parameters are very
difficult to tune ,which redirects its application to chaos detection only.
Mathematical representation
𝐷𝑜 = lim
𝑒→0
logN(𝑒)
𝑙𝑜𝑔1/𝑒
Correlation dimension:-
The correlation dimension is a measure of dimensionality of the space occupied
by a set of random point. It describes the dimensionality of the process in relation to its
geometrical reconstruction in phase space. It is one of the most widely used measures
of fractal dimension and is usefull indicator for various chaotic analysis of HRV.
For an R-R interval series having N data points, the phase space plot is
constructed with heart rate [n] on the x-axis and heart rate. The idea of correlation
dimension is to construct a probability function c(n) such that two arbitrary points on
the orbit . The CD can be calculated using distance between each pair of points .
We could then define the correlation dimension as
CD = lim
𝑟→0
log(c( 𝑟))
log(𝑟)
9. It is another tool for detecting chaotic motion is the fractal (Hussdroff) dimension. The
correlation dimension measures spatial correlation between the points in a
reconstructed multi dimensional space, depending on the value of ED. According to the
theory chaos and the characteristic behavior of systems the relationship between the
steady behavior of system and its dimension can be summarized as
Steady state systems Dimensions
Equilibrium point 0
1- periodic 1
K-periodic K
Chaotic Non-integer
If the dimension is a non- integer then system is chaotic. The Correlation dimension
value will be high for the chaotic data and it decreases as the variation of R-R signal
becomes less or rhythmic.
DeterndedFluctuation Analysis:
In the DFA method, the variation of each point in a time series from its mean
value is treated as a step in a random walk. These variations are partially integrated to
obtain the random walk time series. It permits detection of intrinsic self-similarity in a
seemingly non stationary time series and avoids spurious detection of apparent self-
similarity which may be due to artifact extrinsic trends. DFA provides quantitative
method for determining the degree to which a time series is random at the one extreme
and correlated at the other. DFA ranges in values from 0.5(random) to 1.5(correlated),
which normal values of just over 1.
The detrended fluctuation analysis (DFA) is a chaotic measure that can be used to
quantify the fractal scaling properties of HR signals of short interval. Therefore, we apply
DFA to the analysis of RR interval time-series data, which calculates the root mean
square fluctuation of integrated and detrended time series, permits the detection of
intrinsic self similarity, embedded in a time series, and also avoids the spurious
detection of apparent self-similarity. DFA is scaling analysis technique proposed, to
detect long-range correlations in the time-series having non-stationeries. DFA was
developed specifically to distinguish between intrinsic fluctuations generated by the
complex systems and those caused by the external or environmental stimuli. Another
principal advantage of DFA is that it is able to detect long-range correlation in time-
series having non-stationarities. DFA was found to carry additional information about
smoothness of time series that was not provided by the traditional time and frequency
HRV measures.
We can take it as
𝐹( 𝑙) = [
1
𝐿
∑ (𝑦𝑖 − 𝑖𝑎 − 𝑏)2
]1/2𝐿
𝑗=1
So that, xt is a bounded time series.
Where Xt is called cumulative sum, where Xt is divided into time windows .Yi of length L
sample and a,b are slope and intercept parameter respectively. And L is window size.
10. Work Done:
Detail study about Chaos Analysis, Heart Rate variability and
Non-linear Parameters.
Analyzed application of chaos analysis in HRV.
Having the detailed concept of non-linear parameters of
Heart Rate Variability Studied application of non- linear
parameter in chaos analysis.
Work To Be Done:
Analysis of non-linear parameters using Kubios software.
Using software we have to calculate the non-linear
parameters of hrv from database.
Compare the theoretical result from the obtained result from
analysis of database.
Conclusion:
Heart rate variability has considerable potential to assess the role
of autonomic nervous system fluctuations in normal healthy individuals
and in patients with various cardiovascular and non-cardiovascular
disorders.
Till now we have concluded that it is possible to perform chaos
analysis of heart rate variability using non-linear parameters.
References:
1. http://en.wikipedia.org/w/index.php?title=Heart_rate_variability&oldid=556325
566
2. Multiscale Analysis of Complex Time Series: Integration oj.
Chaos and Random Fractal Theory, and Beyond by Jianbo Gao, Yinhe Cao,
Wenwen Tung and Jing Hu.
3. Www.IEEExplore.com
4. 2nd International Conference on Biomedical Engineering & Assistive
Technologies, by Dr Butta Singh and Dr Dilbag Singh.
5. On Establishment of Power Law Slope (PLS) as an Effective Tool in Non-Linear
Analysis of Heart Rate Variability , by Subhojit Sarker, Dr. Ankur Ganguly and D.N.
Tibarewala.
11. 6. Chaos, Complexity, and Entropy, by Michel Beranger.
7. Complexity quantification of dense array EEG using Sample Entropy, by Pravitha
8. Recent Trends in Nonlinear Methods of HRV Analysis: A Review by Ramesh K.
Sunkaria
9. On the Presence of Deterministic Chaos in HRV Signals by I RadojiCiC, D Mandie,
D Vulie
10. Linear and non-linear analyses of heart rate variability: a mini review by Pascale
Mansier ,Jean Clairambault ,Nathalie Charlotte, Claire Medigue ,Christophe
Vermeiren ,Gilles LePape , Fraqois Car& , Athanassia Gounaropoulou,
Bernard Swynghedauw.