Research Article Detection of Structural Changes in Tachogram …downloads.hindawi.com/journals/cmmm/2013/373401.pdf · 2019-07-31 · Research Article Detection of Structural Changes

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2013 Article ID 373401 11 pageshttpdxdoiorg1011552013373401

Research ArticleDetection of Structural Changes in Tachogram Series forthe Diagnosis of Atrial Fibrillation Events

Francesca Ieva Anna Maria Paganoni and Paolo Zanini

Dipartimento di Matematica Modellistica e Calcolo Scientifico (MOX) Politecnico di MilanoVia Bonardi 9 20133 Milano Italy

Correspondence should be addressed to Anna Maria Paganoni annapaganonipolimiit

Received 25 October 2012 Accepted 25 March 2013

Academic Editor Linamara Rizzo Battistella

Copyright copy 2013 Francesca Ieva et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Atrial Fibrillation (AF) is the most common cardiac arrhythmia It naturally tends to become a chronic condition and chronicAtrial Fibrillation leads to an increase in the risk of death The study of the electrocardiographic signal and in particular of thetachogram series is a usual and effective way to investigate the presence of Atrial Fibrillation and to detect when a single eventstarts and endsThis work presents a new statistical method to deal with the identification of Atrial Fibrillation events based on theorder identification of the ARIMAmodels used for describing the RR time series that characterize the different phases of AF (pre-during and post-AF) A simulation study is carried out in order to assess the performance of the proposed method Moreover anapplication to real data concerning patients affected by Atrial Fibrillation is presented and discussed Since the proposed methodlooks at structural changes of ARIMA models fitted on the RR time series for the AF event with respect to the pre- and post-AFphases it is able to identify starting and ending points of an AF event even when AF follows or comes before irregular heartbeattime slots

1 Introduction

During the last 20 years there has been a widespread interestin the study of variations in the beat-to-beat timing of theheart known as Heart Rate Variability (HRV) [1 2] Thisis due to several different reasons HRV has been reportedas strong predictor of cardiovascular mortality and it is oneof most popular parameter to assess the autonomic tone(see [3] and the references therein for a detailed discussion)Moreover it represents a noninvasive way to assess post-surgical risks (see eg [4]) or to investigate and tune goldstandard practices [5] Nevertheless as highlighted in [6]the potential for HRV to be used widely in clinical practiceremains to be established When the sinus rhythm is normalthe tachogram series (ie the series of RR intervals seeFigure 1(a)) presents spontaneous beat-to-beat oscillationsrelated to the autonomic nervous system regulatory action[7] On the other hand during arrhythmias the spontaneousRR variability is perturbed and the spectral pattern changesaccording to the generating mechanisms of arrhythmia (see[8 9]) Atrial Fibrillation (AF) is the most common cardiac

arrhythmia and involves the two upper chambers (atria) ofthe heart [10] During AF the normal electrical impulsesgenerated by sinoatrial node are overwhelmed by disor-ganized electrical impulses that originate in the atria andpulmonary veins leading to conduction of irregular impulsesto the ventricles that generate the heartbeat The result isan irregular heartbeat (see Figure 1(b)) which may occur inepisodes lasting from minutes to weeks or it could occur allthe time for years The natural tendency of AF is to become achronic condition and chronic AF leads to an increase in therisk of death

Themain device used in order to investigate the heartbeatis the Electrocardiogram (ECG) [11] This diagnostic toolmeasures and records the electrical activity of the heart indetailsThe interpretation of these details allows for diagnosisof a wide range of heart diseases and AF among othersA stylized shape of an ECG is depicted in Figure 2 Ingeneral atrial contraction shows up as the Pwave ventricularcontraction is identified as a series of three waves Q Rand S known as the QRS complex The third wave in anECG is the T wave It reflects the electrical activity produced

2 Computational and Mathematical Methods in Medicine

0 1000 2000 3000 4000

RR intervals during normal sinus rhythm

Beat number

0

1000

2500

RR in

terv

al (m

s)

(a)

0 1000 2000 3000 4000

0

1000

2500RR intervals during Atrial Fibrillation

Beat number

RR in

terv

al (m

s)

(b)

Figure 1 Typical series of RR intervals during normal sinus rhythm (a) and during Atrial Fibrillation (b)

P-R

P-R

QRSinterval

interval

interval

Q-T interval

S-T

S-T

segmentseg-ment

5mm

5mm

05mV

02 s

1mm 004 s 1mm 01mV

25mms 10mmmV

R

P

Q

S

T

U

Figure 2 Stylized shape of a physiological single beat recorded on ECG graph paper Main relevant points segments and waves arehighlighted

when the ventricles recharge for the next contraction namedrepolarization (see [12] for more details on ECG)

Concerning the ECG detection of AF events character-istic findings are the absence of P waves with unorganizedelectrical activity in their place and irregular RR intervals dueto irregular conduction of impulses to the ventricles Whilethe analysis of P wave is quite complicate the study of RRintervals is simpler Hence it could be an effective way toinvestigate the presence of AF and to detect when a singleevent starts and ends Several examples exist in the literature(see [13ndash16]) which are focused on the peculiar variance ofRR intervals during the AF process and this variance is muchgreater than the one during the physiological heartbeat

Anyway in many situations an AF event does not followa physiological time slot but comes after other types ofarrythmia At the same time in many cases the irregu-lar heartbeat does not disappear when the event finishesAccording to these problems it may be possible to look atan irregular heartbeat even when the AF event itself has notalready started or has already finished So a method basedon detection of changes in the variance of the process canlead to inaccurate results and can fail as described previouslyHence methods which are not based on the analysis of theprocess variance are needed in order to identify suitablequantities to characterize the different phases say ldquopre- AFrdquoldquoAFrdquo and ldquopost- AFrdquo To this aim efforts are usually focused

Computational and Mathematical Methods in Medicine 3

on changepoint detection of the spectrum or of the meanof a time series (see [17ndash20] among others) In these casesthe tachogram is considered as a time series (see [21 22])the order of the model is fixed that is orders 119901 119889 and 119902 ofthe autoregressive (AR) integrated (I) and moving average(MA) component respectively are previously establishedand the focus is on the evolution of the estimated modelparameters

In this work we assume that the tachogram during anAF event is characterized by a specific process Hence wepropose a different approach we describe the phases of AF bymeans of ARIMAmodels characterized by different orders 119901119889 and 119902 The main issue becomes then to point out properstatistical methods for detecting changes in the order of themodel To achieve this goal we firstly carry out a simulationstudy to test the new statistical method we propose then weanalyze data of 8 patients affected by AF In particular wehave for each patient the tachogram from two hours beforeto two hours after an event of AF Although there are a lotof readings about the change point detection of time seriesthere is a lack of literature if the approachwe justmentioned isconsidered

The paper is organized as follows In Section 2 weintroduce some elements of time series processes theoryrelated to ARIMAmodels used for modeling the RR intervalstime series We present the statistical method developedfor identifying the AF event (Section 23) based on theanalysis of multiple test 119875-values with an improvement ofthe Bonferroni correction and we test it in a simulationsetting (Section 24) in order to assess the performance of theproposed method Then in Section 3 we present the resultsobtained applying our method to real data (tachograms ofpatients affected by AF) Section 4 contains discussion andconclusions

All the simulations and the analyses of real data have beencarried out using R statistical software [23]

2 Materials and Methods

In this section we introduce ARIMA models [24] as a toolfor modeling the RR time series dynamic Then we presentthe statistical techniques developed for identifying onset andend of AF events Moreover a simulation study is carried outto test the performance of the new method we propose andresults of simulations are discussed

21 Autoregressive Integrated Moving Average (ARIMA) Mod-els Many empirical time series have no constant mean Evenso they exhibit a sort of homogeneity in the sense that a suit-able affine transformation could have constant mean Modelswhich describe such homogeneous nonstationary behaviorcan be obtained by supposing some suitable differences ofthe process to be stationary Referring to the frameworkand theory treated in [24] we focus on the properties ofthe important class of models for which the 119889th difference(nabla119889119911119905 = 119911119905 minus 119911119905minus119889) is a stationary ARMA process Then let usconsider the model

120601 (119861) nabla119889119911119905 = 120579 (119861) 119886119905 (1)

where 119861 is the backward shift operator

120601 (119861) = 1 minus

119901

sum

119895=1

120601119895119861119895 120579 (119861) = 1 minus

119902

sum

ℎ=1

120579ℎ119861ℎ (2)

with 120601119895 119895 = 1 119901 and 120579ℎ ℎ = 1 119902 suitable parametersto be estimated Generally these estimates are performedthrough ML methods [24] Process (1) is an Autoregres-sive Integrated Moving Average (ARIMA) process If theautoregressive operator 120601(119861) in (1) is of order 119901 and themoving average operator 120579(119861) is of order 119902 then (1) is anARIMA(119901 119889 119902) process

22 Model Diagnostic Checking Suppose to fit model (1)obtaining ML estimates (120601 120579) for the parameters of interestWe will refer to the quantities

119886119905 = 120579minus1(119861) 120601 (119861) nabla

119889119911119905 (3)

as the residuals As the number of observations increases119886119905 becomes closer to the white noise 119886119905 Now suppose 119901119889 and 119902 were chosen correctly and that we knew the trueparameter values120601 and 120579Then the estimated autocorrelation119903119896(119886) of the process 119886 would be distributed approximatelynormally with zero mean (see [25]) Now in practice theparameters 119901 119889 and 119902 are unknown and only the estimates(120601 120579) are available for calculating 119886 Then autocorrelation119903119896(119886) of 119886 can yield valuable evidence concerning the lackof fit An interesting way to analyze the goodness of fit ofthe model is then to consider the 119903119896(119886) taken as a whole Letus suppose that we have the first 119870 autocorrelations 119903119896(119886)(119896 = 1 2 119870) from any ARIMA(119901 119889 119902) process Thenit is possible to show (see [26]) that if the fitted model isappropriate the statistic

119876 = 119899 (119899 + 2)

119870

sum

119896=1

1199032

119896(119886)

(119899 minus 119896)(4)

is approximately distributed as 1205942(119870 minus 119901 minus 119902) where 119899 = 119899 minus119889 with 119899 equal to the number of observations Therefore anapproximate test of the hypothesis of model adequacymay beperformed The statistic 119876 is called Ljung-Box statistic

23 A Method to Detect Structural Changes in Time SeriesWe now consider a phenomenon that evolves according toan ARIMA process We wish to analyse a time series and todetect when such a phenomenon starts andor ends If thisspecific phenomenon is characterized by a higher (or lower)variability with respect to the current situation then there is ahuge number of methods effective in detecting these changesin variability Examples are control charts (see [27]) andmethods based on graphical analysis among others (see [15])However there are a lot of situations in which a phenomenonis not characterized by amodification of the variability but bysome changes in the process that generates the observationsIn these cases methods such those mentioned earlier areuseless and other methodologies have to be considered Forexample in the literature there is a huge quantity of methods


that deal with structural changes in time series concerningchanges of the mean or of the parameters values of theARIMA model (see [19 20] and the references therein)Nevertheless we may be interested in dealing with a differentsituation For example wemay consider a problemwhere thepresence or the absence of a phenomenon is characterized notin a change of the parameters values of the model but in amodification of the process itself We wish to present here amethod for dealing with this kind of situations

As we mentioned before our main goal is to identify thebeginning and the end of a specific phenomenon modeledby an ARIMA process This means firstly to identify themodel parameters of the phenomenon under study that isthe values of 119889 119901 and 119902 As we have previously presentedin the case of a stationary model the autocorrelation andpartial autocorrelation function will quickly approach zeroKnowing that the estimated autocorrelation function tendsto follow the behavior of the theoretical autocorrelationfunction failure of this estimated function approaching zerorapidly might logically suggest that we should treat theunderlying stochastic process as nonstationary in 119911119905 butpossibly as stationary in nabla119889119911119905 Once identifying one or morepossible values for 119889 we move to the choice of 119901 and 119902This may be done considering the specific behaviors of theautocorrelation and partial autocorrelation functions andcorresponding cut-off lags (see [24] for the details)

To identify the starting and ending times of the phe-nomenon of interest we propose the following procedureConsider the first119873 observations (with119873much smaller thenthe number 119899 of observations) and fit the identified modelon this subsample Then the 119875-value of the Ljung-Box test(choosing a value for 119870) is recorded These operations haveto be repeated over the sub-sample from the second to the119873+ 1th observation Once reaching the last observation theprocedure ends producing a ldquotime seriesrdquo of 119875-values whichmay be used to detect the beginning and the end of thephenomenon of interest

The purpose is to test the null hypothesis that thephenomenon is present against the alternative hypothesis thatthe phenomenon is absentThismay be formalised as follows

1198670 119901 = 119901 and 119889 = 119889 and 119902 = 119902 versus

1198671 119901 = 119901 or 119889 = 119889 or 119902 = 119902

(5)

where 119901 119889 and 119902 are the parameters indicating the order ofthe ARIMA process related to the phenomenon under studyIn order to build the critical region for the test (5) the first119875-values say119872 can be considered and the rejection regioncan be constructed through a multiple test procedure wherethe adjustment for multiplicity is based on the correctionproposed by Simes So doing the approximate level of the testis equal to 120572 (see [28] for the detailed work) The decisionalcriterion is the following After the 119872 119875-values have beenordered from the minimum (say 119901(1)) to the maximum (say119901(119872)) the null hypothesis is rejected if for at least one 119895 from1 to119872 the following inequality is satisfied

119901(119895) le119895120572

119872 (6)

It can be proved that this procedure provides an approximatelevel equal to 120572 Furthermore the test results are less conser-vative than a test implemented using a classical Bonferronicorrection especially in this situation where single tests arehighly correlated

The method to detect start andor end of a specificphenomenon follows these steps

(1) implement the test in (5)-(6) over the first119872119875-valuesand at the119873 +119872 minus 1th observation the output is setto 0 if there is statistical evidence to reject the nullhypothesis while it is set at 1 otherwise

(2) repeat step (1) after a shift of one observation until thelast one is reached

Once the procedure ends an output of 01015840

s and 11015840

s isavailable Also 1 indicates the presence of the phenomenon0 the absence Starting and end points can be then detectedthrough this last 01 time series

24 Simulation Study In order to validate the proposedmethod different situations have been tested and analysedThe main goals are the following

(i) to point out settings where our method performs atbest

(ii) to assess the robustness of the method varying 120572 and119873

(iii) to make a sensitivity analysis over the parameter119870 ofthe Ljung-Box statistics

The method presented in this paper is a technique todetect modification in the process underlying the observedphenomenon We chose an ARIMA (0 1 1) as ReferenceProcess (RP) considering a sequence of 7000 realizationsfrom a process say 119875pre then 40000 realizations from thereference model and finally 7000 realizations from anotherdifferent process say 119875post For all the simulations the valueof 119872 was fixed equal to 100 In this particular case test (5)becomes

1198670 119901 = 0 and 119889 = 1 and 119902 = 1 versus1198671 119901 = 0 or 119889 = 1 or 119902 = 1

(7)

We tested it in different situations in the first second andthird simulations 119875pre and 119875post are very different fromRP whereas in the fourth one they are quite similar Inparticular we set 119875pre equiv 119875post and we considered an ARIMA(4 1 2) ARIMA (5 1 3) ARIMA (2 2 0) and ARIMA (1 1 1)respectively

The parameters values for these simulations have beenchosen randomly under the constraint that the models wereadmissible Their values are reported in Table 1 Figures 3(a)3(b) and 3(c) obtained fixing 119870 = 5 119873 = 600 and 120572 =

001 show that our method works very well in the first 3settings where the correspondence among the real startingand end points (red lines) and the 01 sequence is visible Inthe fourth simulation instead themethod is less able to catchthe phenomenon under study as it is shown in Figure 3(d)


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations

(a) Output of the method before and after the phenomenon understudy the process is an ARIMA (412)

Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations

(b) Output of the method before and after the phenomenon understudy the process is an ARIMA (513)

Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations

(c) Output of the method before and after the phenomenon understudy the process is an ARIMA (220)

Stat

us0

0

02

04

06

08

1

10000 20000 30000 40000 50000Observations

(d) Output of the method before and after the phenomenon understudy the process is an ARIMA (111)

Figure 3 Analysis of the output of themethod changing the process underlying the observations before and after the phenomenon Red linesrepresent the start and the end of the phenomenon

Table 1 Parameters values used in the simulations The first fourmodels refer to 119875pre and 119875post while the fifth model refers to RP

ARIMA 1206011 1206012 1206013 1206014 1206015 1205791 1205792 1205793

(412) 052 035 minus004 011 minus007 012 (513) minus066 minus03 024 001 014 minus008 minus019 minus029(220) minus008 minus025 (111) minus015 012 (011) 03

Table 2 Empirical type-I error probability varying 119873 and thenominal value 120572

119873 = 400 119873 = 600 119873 = 800

120572 = 001 0004547 0005300 0004969120572 = 005 0025889 0028244 0027377120572 = 01 0051221 0055458 0058005

In the following we focus on the case related toFigure 3(b) where the generating process is an ARIMA(0 1 1) anticipated and followed by a process of observationsgenerated from an ARIMA (5 1 3) Cases (3a) and (3c) givesimilar results We analyse how the power of the test in (7) isaffected by 120572 and119873 For this analysis we considered 119870 = 5If 120572 was the real probability of the type-I error the powerwould increase as120572 growsWedonot have the real probabilityof the type-I-error but only an upper estimate Neverthelesswe would observe the power growing as 120572 increases Anotherparameter that affects the power of the test is 119873 Again

Table 3 Empirical power varying119873 and the nominal value 120572

119873 = 400 119873 = 600 119873 = 800

120572 = 001 0676305 0873391 0960046120572 = 005 0828791 0945367 0987309120572 = 01 0880587 0967746 0993346

the bigger119873 is the greater the power of Ljung-Box test is Soalso the power of the global test should be raised In Figure 4the output of the method varying 120572 (along the rows) and119873 (along the columns) is shown It can be inferred that thebehavior of the method is consistent since the number oferrors before and after the phenomenon decreases as 120572 and119873 increase as we expected

We consider for different values of 120572 and119873 the empiricaltype-I error probability and the empirical power computedover 40 simulations Table 2 shows that this test is conser-vative but the empirical type-I error probability is not sofar from the nominal level of the test Moreover the resultspresented in Table 3 suggest that once 120572 is fixed it is possibleto increase the power of the test tuning 119873 in a suitable wayThen one could think to set a very high value of 119873 in orderto obtain a satisfactory power However this is not costlessIn fact the higher the value of 119873 is the greater the delay instarting and ending points detection is

Hence the choice of the parameter 119873 is regulated bya tradeoff between the desired power of the test and thedelay in the detection of the phenomenon To concludethe simulationsrsquo analysis we would like to infer about


Stat

us

00

0408

20000 40000Observations

120572 = 001 119873 = 400

(a)

Stat

us

00

0408


120572 = 001 119873 = 600

(b)

Stat

us

00

0408


120572 = 001 119873 = 800

(c)

Stat

us

00408

0 20000 40000

120572 = 005 119873 = 400

Observations

(d)St

atus

00408

0 20000 40000Observations

120572 = 005 119873 = 600

(e)

Stat

us

00408


120572 = 005 119873 = 800

(f)

Stat

us

00408


120572 = 01 119873 = 400

(g)

Stat

us

00408


120572 = 01 119873 = 600

(h)

Stat

us

00408


120572 = 01 119873 = 800

(i)

Figure 4 Output of the method varying 120572 (along the rows) and119873 (along the columns)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 5

(a)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 10

(b)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 15

(c)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 20

(d)

Figure 5 Output of the method varying 119870

the parameter 119870 of the Ljung-Box statistics in order tounderstand if the method is affected by a modification of itsvalue Let consider the situation where observations beforeand after the phenomenon were generated by an ARIMA(5 1 3) and fix 120572 = 001 and119873 = 600 In Figure 5 the outputof the method for different values of119870 (equal to 5 10 15 and20 resp) is shown Although the outputs are different nopattern of dependence on119870 appears

3 Results and Discussion

Let us consider now an application of themethod proposed inthis paper to real data Specifically we analysed RR intervalsof 8 patients during Atrial Fibrillation (AF)

Data have been supplied to authors by Professor LucaMainardi responsible of the Biomedical Signal ProcessingLaboratory of the Department of Bioengineering Politecnico


0 10000 30000 50000

05

1

15

2

Patient 1

Beats

RR in

terv

al (s

)

(a) Tachogram of patient 1

0 2000 6000 10000 14000

05

1

15

2

Patient 4

Beats

RR in

terv

al (s

)

(b) Tachogram of patient 4

Figure 6 Tachogram of two patients For patient 1 (a) AF event comes after and is followed by normal sinus rhythm characterized by lowheart rate variability Patient 4 (b) presents a high rate variability even before and after the AF event

Table 4 Duration and number of beats of the event of AF

Pat no Duration AF (min) Beats1 521 410852 613 431783 433 529374 13 10665 56 43266 442 526617 319 282298 229 17989

di Milano Before patients underwent an ablation interven-tion a seven-day Holter trace had been recorded using aone-channel Del Mar Reynolds Holter recorder with samplefrequency equal to 128Hz This protocol of data collection isin accordance with the Declaration of Helsinki for researchwith human beings The data available are the RR intervalsof such patients from two hours before to two hours afteran event of AF The duration of the phenomenon is differentbetween patients and it is displayed in Table 4

We want to detect the event of AF from the studyof tachogram series In some cases the variability of RRintervals during AF is very high with respect to the physi-ological heartbeat However this remarkable change in thevariability of the phenomenon could be absent as highlightedin Figure 6This is an example where the traditional methodsbased on detection of changes in the process variability areineffective in detecting AF starting point

The first step consists in the identification of a modelfor the RR intervals during AF We used the autocorrelationand partial autocorrelation functions to determine a suit-able model As it is shown in Figure 7 the autocorrelation

function of nabla119911119905 is truncated after the lag number one whilethat of nabla2119911119905 is zero after the lag two This behavior is typicalof an ARIMA (0 1 1) and (0 2 2)Then we set RP equiv ARIMA(0 1 1) The same analysis done on the RR time series of pre-and post-AF does not lead to the same conclusions Indeedautocorrelation and partial autocorrelation functions do nothighlight these characteristics Hence the assumption thatduring Atrial Fibrillation the stochastic process generatingthe RR time series is different from the one that models otherphases seems reasonable Then we would like to analyse theperformance of themethod in detecting start and end of sucha phenomenon

In order to achieve this goal let us fix the following valuesfor parameters 119870 = 5 120572 = 0001 and 119872 = 100 Sincein Section 24 the parameter 119873 has been highlighted as themost important in affecting the performance of the proposedmethod we analyse the output as 119873 varies In Figure 8 theoutputs of the method applied to patients 1 and 5 are shownWe present here only the output for two patients because theresults for the other patients are quite similar

Some considerations can be extrapolated observingFigure 8 First we may point out to the behavior of themethod as119873 increases It can be seen that this behavior is inagreement with conclusions drawn from simulations Thenwe may analyse the delay in the detection of start and end ofAF and the number of errors

Dealing with the delay since each observation is the timebetween an R peak and the following one we can evaluate thetime of the delay in the detection of the event of AF and notonly the number of observations As it is shown in Table 5 thedelay in detecting the phenomenon is negligible if comparedwith the duration of AF except for patient 4 affected by a veryshort AF event Moreover in some cases the method is ableto detect the AF event in advance


0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08

1Differences of order zero

Lag

Differences of order two

Differences of order one

Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF

Differences of order zero

Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)

Figure 7 Patient 1 autocorrelation (a) and partial autocorrelation (b) functions for the time series of RR intervals of the differences of orderone and of the differences of order two


Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)

Figure 8 Output of the method for the patients 1 (a) and 5 (b) varying119873

Table 5 Delays of the methodrsquos output

(a) Delays detecting the start of AF

Pat num 119873 = 400 (min) 119873 = 600 (min) 119873 = 800 (min)1 43 49 542 45 61 733 minus24 02 minus464 39 59 845 minus14 27 566 minus22 1 287 166 168 2918 48 61 75

(b) Delays detecting the end of AF

Pat num 119873 = 400 (min) 119873 = 600 (min) 119873 = 800 (min)1 32 46 62 56 85 123 68 72 894 73 98 1015 51 5 336 minus33 minus69 minus637 32 53 78 33 53 72

Another important point we want to focus on is thenumber of errors made by the proposed method From afirst insight of Figure 8 we can observe that the most partof the errors seems to involve a few number of consecutiveobservations

Table 6 Number of errors before (bef corr) and after (aft corr) theintroduction of the artificial time delay (we fixed119873 = 600)

Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16

Then a correction can be implemented in order to reducethe number of errors (in this case the whole time intervaldetected in a wrong way is considered as an error) Weintroduced an artificial time delay after the first instant ofoutput switching from zero to one (or vice versa) we wait fora given time to declare the AF event started (or ended) onlyif after this time the method is still indicating the presence(or absence) of the phenomenon we can detect it Theintroduction of this correction and its duration are problemdriven Since AF is not a dead risk pathology the problemconcerning the number of errors is more important than thedetection delay and so we chose to insert an artificial timedelay of 3minutes Doing that we decreased considerably thenumber of errors as shown in Table 6


4 Conclusions

In this paper we proposed a statistical tool to identify startingand ending points of an event of AF (a common cardiacarrhythmia characterized by an irregular heartbeat) startingfrom the analysis of the RR intervals series We presented amethod based on time series analysis and we performed astatistical test to automatically recognize the phases ldquopre-AFrdquoldquoAFrdquo and ldquopost AFrdquo especially in those situations where theAF event does not follow a physiological time slot andor theirregular heartbeat is still present when the event finishesThe novelty of this work consists in looking at a structuralchange of the order (119901 119889 or 119902) of ARIMAmodel fitted on theRR time series for the AF event with respect to the ldquopre-AFrdquoand ldquopost-AFrdquo phases We tested the proposed method ondifferent simulated data taking a referenceARIMAmodel forthe AF phase and varying the model of ldquopre-AFrdquo and ldquopost-AFrdquo phases

Then we applied the method to real RR intervals dataThe results we obtained confirmed the goodness of theproposed method which seems to be able to identify startingand ending points of an event of AF even when AF followsor comes before irregular heartbeat time slots This is theinnovative feature of our method because the large variety oftechniques that deal with the detection of AF do not take intoaccount this particular situation Since our method analyzesstructural changes of the order of the ARIMA model it candetect AF episodes also in those particular cases when beforeandor after the AF event the heartbeat does not follow anormal sinus rhythm characterized by a significative lowervariability This fact confirms that this methodology maybecome a helpful tool for the online andor offline detectionof AF In particular this method could be useful in an offlinecontrol of Atrial Fibrillation events such as a Holter monitorthat is a prolonged type of ECG tracing Since the traditionaldetection of AF through the analysis of the P wave might belong and hard and in general it is simpler to extract the RRintervals from aHolter the proposedmethod could representan automatic diagnostic tool that simplifies the detection ofAF events

Acknowledgments

The authors wish to thank Professor Luca Mainardi respon-sible of the Biomedical Signal Processing Laboratory ofthe Department of Bioengineering Politecnico di Milanofor supplying the data and Dr Valeria Vitelli for technicalsupport in the statistical analysis

References

[1] M Malik and A J Camm Eds Heart Rate Variability FuturaPublishing Company Armonk NY USA 1995

[2] M Malik ldquoHeart rate variability standards of measurementphysiological interpretation and clinical userdquo Circulation vol93 no 5 pp 1043ndash1065 1996

[3] N Chattipakorn T Incharoen N Kanlop and S ChattipakornldquoHeart rate variability in myocardial infarction and heartfailurerdquo International Journal of Cardiology vol 120 no 3 pp289ndash296 2007

[4] T Kinoshita T Asai T Ishigaki T Suzuki A Kambara andK Matsubayashi ldquoPreoperative heart rate variability predictsatrial fibrillation after coronary bypass graftingrdquo The Annals ofThoracic Surgery vol 91 no 4 pp 1176ndash1182 2011

[5] L Mourot N Tordi M Bouhaddi D Teffaha C Monpereand J Regnard ldquoHeart rate variability to assess ventilatorythresholds reliable in cardiac diseaserdquo European Journal ofPreventive Cardiology vol 19 pp 1272ndash1280 2012

[6] B Xhyheri O Manfrini M Mazzolini C Pizzi and R Bugia-rdini ldquoHeart rate variability todayrdquo Progress in CardiovascularDiseases vol 55 pp 321ndash331 2012

[7] S Akselrod D Gordon F A Ubel D C Shannon A CBerger and R J Cohen ldquoPower spectrum analysis of heart ratefluctuation a quantitative probe of beat-to-beat cardiovascularcontrolrdquo Science vol 213 no 4504 pp 220ndash222 1981

[8] G Baselli D Bolis S Cerutti and C Freschi ldquoAutoregres-sive modeling and power spectral estimate of R-R intervaltime series in arrhythmic patientsrdquo Computers and BiomedicalResearch vol 18 no 6 pp 510ndash530 1985

[9] R G Mark and G B Moody ldquoECG arrhythmia analysis designand evaluation strategiesrdquo inAdvances in Processing and PatternAnalysis of Biological Signals I Gath and G F Inbar Edschapter 18 pp 251ndash272 Plenum Press New York NY USA1996

[10] S S Chugh J L Blackshear W K Shen S C Hammill andB J Gersh ldquoEpidemiology and natural history of atrial fibril-lation clinical implicationsrdquo Journal of the American College ofCardiology vol 37 no 2 pp 371ndash378 2001

[11] A Houghton and D GrayMaking Sense of the ECG 1997[12] A E Lindsay ldquoECG learning centrerdquo 2006 httpecgutah

edu[13] B K Bootsma A J Hoelsen J Strackee and F L Meijler

ldquoAnalysis of R-R intervals in patients with atrial fibrillation atrest and during exerciserdquoCirculation vol 41 no 5 pp 783ndash7941970

[14] R Couceiro P Carvalho J Henriques M Antunes M Harrisand J Habetha ldquoDetection of Atrial Fibrillation using model-based ECG analysisrdquo in Proceedings of the 19th InternationalConference on Pattern Recognition (ICPR rsquo08) December 2008

[15] L Mainardi L Sornmo and S Cerutti Understanding AtrialFibrillation the Signal Processing Contribution Morgan andClaypoll Publishers 2008

[16] K Tateno and LGlass ldquoAutomatic detection of atrial fibrillationusing the coefficient of variation and density histograms ofRR and ΔRR intervalsrdquoMedical and Biological Engineering andComputing vol 39 no 6 pp 664ndash671 2001

[17] A Boardman F S Schlindwein A P Rocha and A Leite ldquoAstudy on the optimum order of autoregressive models for heartrate variabilityrdquo Physiological Measurement vol 23 no 2 pp325ndash336 2002

[18] R A Davis D Huang and Y C You ldquoTesting for a change inthe parameter values and order in autoregressive modelsrdquo TheAnnals of Statistics vol 23 no 1 pp 282ndash304 1995

[19] S Ling ldquoTesting for change points in time series models andlimiting theorems for NED sequencesrdquoThe Annals of Statisticsvol 35 no 3 pp 1213ndash1237 2007

[20] D Picard ldquoTesting and estimating change-points in time seriesrdquoAdvances in Applied Probability vol 17 no 4 pp 841ndash867 1985

[21] S Cerutti L TMainardi A Porta and AM Bianchi ldquoAnalysisof the dynamics of RR interval series for the detection of AtrialFibrillation episodesrdquo in Proceedings of the 24th AnnualMeetingon Computers in Cardiology pp 77ndash80 September 1997


[22] C Cammarota and E Rogora ldquoIndependence and symbolicindependence of nonstationary heartbeat series during atrialfibrillationrdquo Physica A vol 353 no 1ndash4 pp 323ndash335 2005

[23] RDevelopment Core Team R A Language and Environment forStatistical Computing R Foundation for Statistical ComputingVienna Austria 2011 httpwwwr-projectorg

[24] P Diggle Time Series A Biostatistical Introduction ClarendonPress Oxford UK 1990

[25] G E P Box and D A Pierce ldquoDistribution of residual auto-correlations in autoregressive-integrated moving average timeseries modelsrdquo Journal of the American Statistical Associationvol 65 pp 1509ndash1526 1970

[26] GM Ljung andG E P Box ldquoOn ameasure of lack of fit in timeseries modelsrdquo Biometrika vol 65 no 2 pp 297ndash303 1978

[27] D C Montgomery Introduction to Statistical Quality ControlMcGraw-Hill New York NY USA 2005

[28] R J Simes ldquoAn improved bonferroni procedure for multipletests of significancerdquoBiometrika vol 73 no 3 pp 751ndash754 1986

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


0 1000 2000 3000 4000

RR intervals during normal sinus rhythm

Beat number

0

1000

2500

RR in

terv

al (m

s)

(a)

0 1000 2000 3000 4000

0

1000

2500RR intervals during Atrial Fibrillation

Beat number

RR in

terv

al (m

s)

(b)

Figure 1 Typical series of RR intervals during normal sinus rhythm (a) and during Atrial Fibrillation (b)

P-R

P-R

QRSinterval

interval

interval

Q-T interval

S-T

S-T

segmentseg-ment

5mm

5mm

05mV

02 s

1mm 004 s 1mm 01mV

25mms 10mmmV

R

P

Q

S

T

U

Figure 2 Stylized shape of a physiological single beat recorded on ECG graph paper Main relevant points segments and waves arehighlighted

when the ventricles recharge for the next contraction namedrepolarization (see [12] for more details on ECG)

Concerning the ECG detection of AF events character-istic findings are the absence of P waves with unorganizedelectrical activity in their place and irregular RR intervals dueto irregular conduction of impulses to the ventricles Whilethe analysis of P wave is quite complicate the study of RRintervals is simpler Hence it could be an effective way toinvestigate the presence of AF and to detect when a singleevent starts and ends Several examples exist in the literature(see [13ndash16]) which are focused on the peculiar variance ofRR intervals during the AF process and this variance is muchgreater than the one during the physiological heartbeat

Anyway in many situations an AF event does not followa physiological time slot but comes after other types ofarrythmia At the same time in many cases the irregu-lar heartbeat does not disappear when the event finishesAccording to these problems it may be possible to look atan irregular heartbeat even when the AF event itself has notalready started or has already finished So a method basedon detection of changes in the variance of the process canlead to inaccurate results and can fail as described previouslyHence methods which are not based on the analysis of theprocess variance are needed in order to identify suitablequantities to characterize the different phases say ldquopre- AFrdquoldquoAFrdquo and ldquopost- AFrdquo To this aim efforts are usually focused









120601 (119861) nabla119889119911119905 = 120579 (119861) 119886119905 (1)


120601 (119861) = 1 minus

119901

sum

119895=1

120601119895119861119895 120579 (119861) = 1 minus

119902

sum

ℎ=1

120579ℎ119861ℎ (2)



119886119905 = 120579minus1(119861) 120601 (119861) nabla

119889119911119905 (3)


119876 = 119899 (119899 + 2)

119870

sum

119896=1

1199032

119896(119886)

(119899 minus 119896)(4)








1198670 119901 = 119901 and 119889 = 119889 and 119902 = 119902 versus

1198671 119901 = 119901 or 119889 = 119889 or 119902 = 119902

(5)


119901(119895) le119895120572

119872 (6)






s and 11015840








(7)





Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us0

0

02

04

06

08

1

10000 20000 30000 40000 50000Observations




ARIMA 1206011 1206012 1206013 1206014 1206015 1205791 1205792 1205793



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0004547 0005300 0004969120572 = 005 0025889 0028244 0027377120572 = 01 0051221 0055458 0058005



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0676305 0873391 0960046120572 = 005 0828791 0945367 0987309120572 = 01 0880587 0967746 0993346





Stat

us

00

0408


120572 = 001 119873 = 400

(a)

Stat

us

00

0408


120572 = 001 119873 = 600

(b)

Stat

us

00

0408


120572 = 001 119873 = 800

(c)

Stat

us

00408

0 20000 40000

120572 = 005 119873 = 400

Observations

(d)St

atus

00408


120572 = 005 119873 = 600

(e)

Stat

us

00408


120572 = 005 119873 = 800

(f)

Stat

us

00408


120572 = 01 119873 = 400

(g)

Stat

us

00408


120572 = 01 119873 = 600

(h)

Stat

us

00408


120572 = 01 119873 = 800

(i)


Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 5

(a)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 10

(b)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 15

(c)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 20

(d)







0 10000 30000 50000

05

1

15

2

Patient 1

Beats

RR in

terv

al (s

)


0 2000 6000 10000 14000

05

1

15

2

Patient 4

Beats

RR in

terv

al (s

)













0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08


Lag



Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF


Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)



Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
























120601 (119861) nabla119889119911119905 = 120579 (119861) 119886119905 (1)


120601 (119861) = 1 minus

119901

sum

119895=1

120601119895119861119895 120579 (119861) = 1 minus

119902

sum

ℎ=1

120579ℎ119861ℎ (2)



119886119905 = 120579minus1(119861) 120601 (119861) nabla

119889119911119905 (3)


119876 = 119899 (119899 + 2)

119870

sum

119896=1

1199032

119896(119886)

(119899 minus 119896)(4)








1198670 119901 = 119901 and 119889 = 119889 and 119902 = 119902 versus

1198671 119901 = 119901 or 119889 = 119889 or 119902 = 119902

(5)


119901(119895) le119895120572

119872 (6)






s and 11015840








(7)





Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us0

0

02

04

06

08

1

10000 20000 30000 40000 50000Observations




ARIMA 1206011 1206012 1206013 1206014 1206015 1205791 1205792 1205793



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0004547 0005300 0004969120572 = 005 0025889 0028244 0027377120572 = 01 0051221 0055458 0058005



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0676305 0873391 0960046120572 = 005 0828791 0945367 0987309120572 = 01 0880587 0967746 0993346





Stat

us

00

0408


120572 = 001 119873 = 400

(a)

Stat

us

00

0408


120572 = 001 119873 = 600

(b)

Stat

us

00

0408


120572 = 001 119873 = 800

(c)

Stat

us

00408

0 20000 40000

120572 = 005 119873 = 400

Observations

(d)St

atus

00408


120572 = 005 119873 = 600

(e)

Stat

us

00408


120572 = 005 119873 = 800

(f)

Stat

us

00408


120572 = 01 119873 = 400

(g)

Stat

us

00408


120572 = 01 119873 = 600

(h)

Stat

us

00408


120572 = 01 119873 = 800

(i)


Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 5

(a)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 10

(b)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 15

(c)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 20

(d)







0 10000 30000 50000

05

1

15

2

Patient 1

Beats

RR in

terv

al (s

)


0 2000 6000 10000 14000

05

1

15

2

Patient 4

Beats

RR in

terv

al (s

)













0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08


Lag



Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF


Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)



Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















1198670 119901 = 119901 and 119889 = 119889 and 119902 = 119902 versus

1198671 119901 = 119901 or 119889 = 119889 or 119902 = 119902

(5)


119901(119895) le119895120572

119872 (6)






s and 11015840








(7)





Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us0

0

02

04

06

08

1

10000 20000 30000 40000 50000Observations




ARIMA 1206011 1206012 1206013 1206014 1206015 1205791 1205792 1205793



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0004547 0005300 0004969120572 = 005 0025889 0028244 0027377120572 = 01 0051221 0055458 0058005



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0676305 0873391 0960046120572 = 005 0828791 0945367 0987309120572 = 01 0880587 0967746 0993346





Stat

us

00

0408


120572 = 001 119873 = 400

(a)

Stat

us

00

0408


120572 = 001 119873 = 600

(b)

Stat

us

00

0408


120572 = 001 119873 = 800

(c)

Stat

us

00408

0 20000 40000

120572 = 005 119873 = 400

Observations

(d)St

atus

00408


120572 = 005 119873 = 600

(e)

Stat

us

00408


120572 = 005 119873 = 800

(f)

Stat

us

00408


120572 = 01 119873 = 400

(g)

Stat

us

00408


120572 = 01 119873 = 600

(h)

Stat

us

00408


120572 = 01 119873 = 800

(i)


Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 5

(a)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 10

(b)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 15

(c)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 20

(d)







0 10000 30000 50000

05

1

15

2

Patient 1

Beats

RR in

terv

al (s

)


0 2000 6000 10000 14000

05

1

15

2

Patient 4

Beats

RR in

terv

al (s

)













0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08


Lag



Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF


Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)



Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us

00

02

04

06

08

1

10000 20000 30000 40000 50000Observations


Stat

us0

0

02

04

06

08

1

10000 20000 30000 40000 50000Observations




ARIMA 1206011 1206012 1206013 1206014 1206015 1205791 1205792 1205793



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0004547 0005300 0004969120572 = 005 0025889 0028244 0027377120572 = 01 0051221 0055458 0058005



119873 = 400 119873 = 600 119873 = 800

120572 = 001 0676305 0873391 0960046120572 = 005 0828791 0945367 0987309120572 = 01 0880587 0967746 0993346





Stat

us

00

0408


120572 = 001 119873 = 400

(a)

Stat

us

00

0408


120572 = 001 119873 = 600

(b)

Stat

us

00

0408


120572 = 001 119873 = 800

(c)

Stat

us

00408

0 20000 40000

120572 = 005 119873 = 400

Observations

(d)St

atus

00408


120572 = 005 119873 = 600

(e)

Stat

us

00408


120572 = 005 119873 = 800

(f)

Stat

us

00408


120572 = 01 119873 = 400

(g)

Stat

us

00408


120572 = 01 119873 = 600

(h)

Stat

us

00408


120572 = 01 119873 = 800

(i)


Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 5

(a)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 10

(b)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 15

(c)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 20

(d)







0 10000 30000 50000

05

1

15

2

Patient 1

Beats

RR in

terv

al (s

)


0 2000 6000 10000 14000

05

1

15

2

Patient 4

Beats

RR in

terv

al (s

)













0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08


Lag



Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF


Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)



Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Stat

us

00

0408


120572 = 001 119873 = 400

(a)

Stat

us

00

0408


120572 = 001 119873 = 600

(b)

Stat

us

00

0408


120572 = 001 119873 = 800

(c)

Stat

us

00408

0 20000 40000

120572 = 005 119873 = 400

Observations

(d)St

atus

00408


120572 = 005 119873 = 600

(e)

Stat

us

00408


120572 = 005 119873 = 800

(f)

Stat

us

00408


120572 = 01 119873 = 400

(g)

Stat

us

00408


120572 = 01 119873 = 600

(h)

Stat

us

00408


120572 = 01 119873 = 800

(i)


Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 5

(a)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 10

(b)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 15

(c)

Stat

us

00

02040608

1

10000 20000 30000 40000 50000Observations

119870 = 20

(d)







0 10000 30000 50000

05

1

15

2

Patient 1

Beats

RR in

terv

al (s

)


0 2000 6000 10000 14000

05

1

15

2

Patient 4

Beats

RR in

terv

al (s

)













0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08


Lag



Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF


Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)



Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















0 10000 30000 50000

05

1

15

2

Patient 1

Beats

RR in

terv

al (s

)


0 2000 6000 10000 14000

05

1

15

2

Patient 4

Beats

RR in

terv

al (s

)













0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08


Lag



Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF


Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)



Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















0 10 15 20Lag

ACF

ACF

ACF

0

0

02

1

05

04

06

08


Lag



Lag

5

0 10 15 205

0 10 15 205

minus05

0

1

05

minus05

(a)

0

005

01

015

Lag

Part

ial A

CF

Part

ial A

CF

Part

ial A

CF


Lag



Lag10 15 205

10 15 205

10 15 205

minus05

minus04

minus03

minus02

minus01

0

minus05

minus04

minus02

minus03

minus01

0

(b)



Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Stat

us

00

0408

10000 20000 30000 40000 50000 60000Beats

Patient 1 119873 = 400

Patient 1 119873 = 600

Patient 1 119873 = 800

(a)St

atus

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Stat

us

00

0408

5000 10000 15000Beats

Patient 5 119873 = 400

Patient 5 119873 = 600

Patient 5 119873 = 800

(b)









Patno

Type-Ierrors

(bef corr)

Type-Ierrors

(aft corr)

Type-IIerrors

(bef corr)

Type-IIerrors

(after corr)

DurationAF

(min)1 0 0 4 1 5212 1 0 0 0 6133 16 6 1 1 4334 0 0 4 4 135 1 0 2 0 566 23 5 3 1 4427 8 1 8 3 3198 0 0 10 6 229Total 49 12 32 16



4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















4 Conclusions



Acknowledgments


References



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





























of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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Research Article Detection of Structural Changes in Tachogram …downloads.hindawi.com/journals/cmmm/2013/373401.pdf · 2019-07-31 · Research Article Detection of Structural Changes