Heart Rate Variability Analysis Using ApproximateEntropy and Detrended Fluctuation for Monitoring

Heart ConditionAinul Anam Shahjamal Khan∗, Umme Mumtahina† and Nusrat Yeasmin‡

∗Department of Electrical & Electronic EngineeringChittagong University of Engineering & Technology

Chittagong-4349, BangladeshEmail: khanshahjamal@yahoo.com

†Chittagong University of Engineering & TechnologyEmail: mumtahina58eee@gmail.com

‡Chittagong University of Engineering & TechnologyEmail: yeasminnusrat@gmail.com

Abstract—Variation in time between two successive heart beatsoccurring due to internal and external stimulation causes HeartRate Variability (HRV). HRV is a tool for indirect investigation ofboth cardiac and autonomic system function in both healthy anddiseased condition. It has been speculated that HRV analysisby nonlinear method might bring potentially useful prognosisinformation into light which will be helpful for assessment ofcardiac condition. In this study, HRV from two types of data sets(normal sinus rhythm and sinus arrhythmia) are analyzed whichare stored in MIT-BIH (Massachusetts Institute of Technology –Beth Israel hospital) database, an extended collection of recordedphysiological signals. Then two nonlinear methods, approximateentropy (ApEn) and detrended fluctuation analysis (DFA), havebeen applied to analyze HRV of both Arrhythmia patients andpeople having normal sinus rhythm. It has been clearly shownthat nonlinear parameters obtained from these two methodsreflect the opposite heart condition of the two types of subjectsunder study, healthy and diseased, by HRV measures. Thus,value of the nonlinear parameters found in this work can beused as standard when treating suspected patients for diagnosisof Arrhythmia. Also, by measuring these nonlinear parametervalues, heart condition can be understood.

I. INTRODUCTION

Thoughts, emotional reactions, changes in environmentalcondition — all these internal and external stimulations im-mediately change heart rate. Heart beat comes slightly early,or late. This phenomenon is termed as “Heart Rate Variability”(HRV). Therefore, HRV is a physiological condition where thetime interval between heart beats varies.

Autonomic Nervous System (ANS) is the part of nervoussystem that non-voluntarily controls all organs and systemsof the body and maintains the body under stable conditions(homeostasis). ANS consists of two subsystems: SympatheticNervous System (SNS) and Parasympathetic Nervous System(PNS). SNS helps to prepare the body for action. Whena person is under challenging situations, SNS produces socalled “flight or fight” response. PNS, on the other hand,is more active under unchallenging situations, such as restand digestion. It tends to work in opposite direction of SNS,bringing the body towards a rest state. SNS activation increasesheart rate and breathing rate, but PNS decreases it. Constantinteraction of these two systems is reflected in HRV. Therefore,HRV can be used to estimate the activity and activation level

of both systems.Indirect investigation of both cardiac and autonomic system

function in both healthy and diseased condition is possibleby means of HRV analysis. HRV provides various featuresfor distinguishing heart rate under healthy and life threateningcondition.

There are three main approaches in HRV analysis —1) time domain analysis of HRV for standard deviation of

normal to normal intervals (SDNN)2) frequency domain analysis for Power Spectral Density

(PSD)3) nonlinear methodPhysiological signals often vary in a complex and irregular

manner. Analysis of linear statistics such as mean values, vari-ability measures, and spectra of such signals generally does notaddress directly their complexity and thus may miss potentiallyuseful information. Since the underlying mechanisms involvedin the control of heart rate are mainly nonlinear, the applicationof nonlinear techniques seems appropriate [1]. It has beenconjectured that HRV analysis by nonlinear method might shedlight on unexplored horizons for assessment of sudden death.The parameters that have been used to measure nonlinearproperties of HRV include: 1/f slope [2], approximate entropy(ApEn) [3] and detrended fluctuation analysis [4].

In this study, two nonlinear methods, approximate entropy(ApEn) and detrended fluctuation analysis (DFA), have beenapplied to analyze HRV of both Arrhythmia patients andpeople having normal sinus rhythm. It is evidently shown thatthe contrary heart condition of the two types of subjects understudy, healthy and diseased, is reflected by nonlinear parametervalue. The results obtained from this study can thus help indiagnosis of Arrhythmia in probable patients.

The paper is organized as follows. In section II, someprevious works related to HRV and nonlinear method arereviewed for ease of understanding. In section III, steps ofour work is described. Section IV describes the process ofdata collection from MIT-BIH database. In section V, heartrate data is analyzed by two nonlinear methods, approximateentropy and detrended fluctuation analysis method. Section VIshows the result found from two nonlinear methods. The finalsection includes important conclusions drawn from this work.

978-1-4799-0400-6/13/$31.00 ©2013 IEEE

II. HRV ANALYSIS IN NONLINEAR METHODS

Research in HRV analysis started in 1966 when a variationin the beat-to-beat intervals between heartbeats was noticed.Initially all recording devices were averaging heart rate datastream trying to get rid of any rapid HR (Heart Rate) fluc-tuations. A great number of papers appeared in connectionwith HRV related cardiological issues [2], [5], [6], [7], whichreiterate the significance of HRV in assessing the cardiachealth.

Recently, new dynamic methods of HRV quantification havebeen used to uncover nonlinear fluctuations in heart rate thatare not otherwise apparent. Fell et al. [8] and RadhakrishnaRao et al. [9] have tried the nonlinear analysis of ECG andHRV signals, respectively. In 1996, a special task force wasformed between the US and European physiological associa-tions to outline current finds on HRV and set specific standardson using HRV in medical science and future practice. Sincethen a steady stream of new information and value continuesto come out of HRV research.

The work in reference [10] has focused to review themethods most widely used and tested in various clinicalsettings.

The work in reference [11] has compared the performanceof spectral analysis and detrended fluctuation analysis todiscriminate sleep stages and sleep apnea.

The work in reference [12] has applied ApEn to thecharacterization of three patterns of fetal heart rate (FHR):calm sleep (A), calm vigilance (C), pathological flat-sinusoidal(FS) condition. It has been conclude that ApEn can perfectlydiscriminate the pathological FS pattern from the normal Aand C patterns and is far better for FHR pattern discriminationthan classic time-domain variability indexes used in clinicalpractice.

III. METHODOLOGY

In this work, Heart Rate Variability (HRV) has been studiedfrom MIT-BIH (Massachusets Institute and Technology – BethIsrael Hospital) database of people having arrhythmia and peo-ple having normal sinus rhythm. These HRV data have beenanalyzed by approximate entropy and detrended fluctuationanalysis method. It is seen that these two analysis methodscan significantly differentiate between the two opposite typesof data. The steps of our work is shown in Fig. 1.

Fig. 1. Methodology of the work

IV. HEART RATE DATA COLLECTION FROM MIT-BIHDATABASE

MIT-BIH Database is the result of joint effort of Boston’sBeth Israel Hospital (now the Beth Israel Deaconess MedicalCenter) and MIT on arrhythmia analysis and related subjects.MIT-BIH Database is an extended collection of recordedphysiological signal.

The MIT-BIH Arrhythmia Database contains 48 half-hourexcerpts of two-channel ambulatory ECG recordings, obtainedfrom 47 subjects studied by the BIH Arrhythmia Laboratorybetween 1975 and 1979. The recordings were digitized at360 samples per second per channel with 11-bit resolutionover a 10 mV range. In MIT-BIH Arrhythmia Database, eachrecorded data consists of three files, named .hea, .dat and .atrsuch as 100.hea, 100.atr, 100.dat etc.

In MIT-BIH Normal Sinus Rythm Database, each recordeddata consists of 5 files, named .hea (header file), .hea- (headerfile), .dat (digitized signal(s)), .atr (reference annotations), and.xws (WAVEScript); such as 16265.atr, 16265.dat, 16265.hea,16265.hea-, 16265.xws etc. For Instantaneous Heart Rate(IHR) measurement from MIT-BIH Database, following stepsare followed:

Fig. 2. Block diagram of finding Instantaneous Heart Rate from MIT-BIHdatabase.

Output of each step of finding IHR from MIT-BIH databaseare shown in Fig. 3.

V. METHODS ANALYZED

A. Detrended Fluctuation Analysis

For measuring long range correlation in noisy, non-stationary time series, Detrended Fluctuation Analysis (DFA)method is used. In this method, investigation of scaling be-havior of heart beat fluctuation is done for correlation mea-surement. Detrended Fluctuation Analysis (DFA) method canbe used as diagnosis tool for patient with cardiac disease [13].In DFA, the scaling exponent α (Hurst exponent) indicatesthe power law correlation in signal fluctuation. If the value ofscaling component α is 1 or around 1, then it represents thehealthy condition.

In order to calculate the scaling exponents with DFA,a given series x(i) of length N is firstly integrated. Theintegrated values of time series is given by

y(k) =k∑i=1

x(i)− x (1)

(a) (b)

(c) (d)

(e) (f)

(g) (h)

(i) (j)

Fig. 3. ECG signal (a) Input 105.dat (b) After cancelation of dc drift (c)After passing through LPF (d) After passing through HPF (e) After derivative(f) After squaring (g) After averaging (h) After integration (i) Detected QRS(j) Comparison between input and result signal

where

x =1

N

N∑i=1

x(i) (2)

This integration step maps a time series to a self-similar pro-cess. The next goal is now to measure the vertical characteristicscale for the integrated time series, and this is achieved bydividing the integrated time series into boxes of equal length.For each one of these boxes, a least squares linear fitting ofthe data (called the local trend on that box) is performed [14].The value of the y coordinate of this fitted straight line is

Fig. 4. The integrated time series.

denoted by yn(k). Next, we detrend the integrated time seriesy(k) by subtracting the local trend, yn(k), in each box. Theroot-mean-square fluctuation of this integrated and detrendedtime series is calculated by

F (n) =

√√√√ 1

N

N∑k=1

(y(k)− yn(k))2 (3)

where F (n) represents the average fluctuation as a functionof the box size, n. A linear relationship on a double log graphbetween F (n) vs. n indicates the presence of scaling in theseries and establishes the relationship between F (n) and n asF (n) ∝ nα. Typically, F (n) will increase with box size [15].

Hence, the scaling exponent α represents the scaling of thefluctuations and can be approximated as the slope of the linerelating log(F (n)) and log(n).

B. Approximate Entropy Method

Approximate Entropy (ApEn) method is a mathematicalformula which is the measure of lack of regularity in physio-logical time series. It has been used to characterize the irreg-ularity of various pathological signal such as fetal heart rate[12]. It was proposed by Steve Pincus and described in manyworks [16]. ApEn detects the changes in underlying episodicbehavior not reflected in peak occurrences or amplitudes [16].

Approximate Entropy (ApEn) can be efficiently evaluatedeven over relatively short time series, making it particularlysuitable for the analysis of physiological signals. ApEn isrelated to the probability that segments of m data sampleswhich are similar i.e., closer to each other than a given distancer, remain similar when the segment length increases to m+1[3].

The importance of ApEn lies in the fact that it is a measureof the disorder in the HR signal. It has higher value in the caseof normal heart. Hence, the ApEn will have smaller valuefor cardiac abnormal cases, indicating smaller variability (highregularity) in beat to beat.

In calculation of ApEn, two parameters, m and r, mustbe fixed during computation of ApEn. Embedding dimensionm = 2 and threshold r between 10% to 25% of standarddeviation of data set was recommended in many articles andnow r = 0.2 is used in almost all HRV studies. The article[12] discusses about the right choice of threshold r and discussthe relation between ApEn and r.

Computation of ApEn is done in following steps• Input parameter m is the value of size of vectors for

comparison in selected segment of RR intervals.• It creates N−m+1 vectors of m components from input

data:Rm(i) = RR(i), RR(i+ 1), . . . , RR(i+m)

The vector Rm(i) represents the sequence of m consec-utive RRI values starting at the beat i.

• Two vectors Rm(i) and Rm(j) are similar if the absolutedifferences between each couple of corresponding scalarcomponents are less then distance r ∗ SDNN .

• The second input parameter r, mentioned above, desig-nates the threshold for comparison differences betweenRm vectors. This parameter is usually chosen from valuesbetween 0.1 and 0.25 (the recommended range in manyarticles).

• If nmi is the number of N −m+1 vectors Rm(j) whichare similar to Rm(i), then

cmi (r) =nmi (r)

N −m+ 1(4)

where cmi (r) is the probability to find a sequence of mbeats similar to the sequence represented by Rm(i).

• cm(r), defined as the mean of all cmi (r), quantifies theprevalence of similar strings of m beats.

• ApEn(r,m) is calculated as,

ApEn(r,m) = lncmi (r)

cm+1i (r)

(5)

• A high degree of regularity means that sequences whichare similar for m points are likely to be similar also forthe next m+ 1 point, while this is unlikely to occur forirregular time series. Thus low values of ApEn reflectshigh regularity, which means disease.

C. Relative advantage of Detrended Fluctuation Analysis andApproximate Entropy Method

For measuring long range correlation in noisy, non-stationary time series, Detrended Fluctuation Analysis (DFA)method is used. For the analysis of physiological signals evenover relatively short time series, Approximate Entropy (ApEn)is particularly suitable.

VI. RESULTS

A. Summary of Detrended Fluctuation AnalysisFrom Table I, we can see that the scaling exponent α for

people having normal sinus rhythm (such as: data no 16420,16539, 16773 and so on), is around one and for people havingArrhythmia (such as: 103, 104, 104 and so on) is away fromone. Power law correlation in signal fluctuation and oppositeheart condition of the two types of subjects under study,healthy and diseased, is reflected clearly from the scalingexponent α value.

So, by Detrended Fluctuation technique, we can easilydifferentiate between normal sinus rhythm and Arrhythmia.

TABLE IDETRENDED FLUCTUATION ANALYSIS: VALUE OF SCALING EXPONENT α

FOR 2 DATA SETS (ARRHYTHMIA AND NORMAL SINUS RHYTHM) OFMIT-BIH DATABASE

Data sets forpeople havingnormal sinusrhythm

Scaling ex-ponent α

Data sets forpeople havingArrhythmia

Scaling ex-ponent α

16265 0.9257 103 2.028716420 1.2232 104 2.442716539 0.8677 105 2.093516773 0.9026 106 1.592217453 0.9269 111 1.549918177 1.2985 118 1.879518184 0.9015 119 1.959819088 0.9360 201 2.091419140 1.1445 203 1.9923

B. Summary of ApEn Method

TABLE IIApEn ANALYSIS: VALUE OF ApEn FOR 2 DATA SETS (ARRHYTHMIA AND

NORMAL SINUS RHYTHM) OF MIT-BIH DATABASE

Data Sets forPeople HavingNormal SinusRhythm

Value ofApEn

Data Sets forPeople HavingArrhythmias

Value ofApEn

16265 1.8715 103 0.836516420 1.6576 104 0.506416539 1.4813 105 0.950716773 1.7471 106 0.312417453 1.9251 111 0.805218177 1.7215 118 0.652818184 1.7518 119 0.747619088 1.8073 201 0.132719140 1.8392 203 0.0054

From Table II, it is seen that people having normal sinusrhythm (such as: data 16420, 16539, 16773 and so on), havehigher ApEn value and people having Arrhythmia (such as:data 103, 104, 104 and so on) have lower ApEn, thus clearlydistinguishing the two groups. Disorder in the Heart rate signaland opposite heart condition of the two types of subjects understudy, healthy and diseased, is reflected clearly from ApEnvalue.

So, by Approximate Entropy Method, we can easily differ-entiate between normal sinus rhythm and Arrhythmia.

VII. CONCLUSIONS AND FUTURE PERSPECTIVES

As cardiovascular regulation mechanism is a nonlinearprocess, nonlinear methods, like Detrended Fluctuation Anal-ysis and Approximate Entropy Method, may provide morepowerful prognostic information than the traditional HR vari-ability indexes. In this work, a comparative study is doneon different techniques to distinguish HRV of normal sinusrhythm and sinus arrhythmia data from MIT-BIH database.It has been demonstrated that both of these two nonlinearmethods can successfully differentiate between two types ofdata and reflect the opposite heart condition of the two typesof subjects under study, healthy and diseased. Thus, value ofthe nonlinear parameters found in this work can be used asstandard in diagnosis of arrhythmia in probable patients. Also,by measuring these nonlinear parameter values, a qualitativeidea of heart condition can be obtained. In future, this workcan be extended to distinguish heart rate data for people in

various opposite heart conditions, for example, in differentmental stress levels.

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