classification of prolapsed mitral valve versus healthy heart from … · 2014-04-23 · and...

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2013 Article ID 376152 10 pageshttpdxdoiorg1011552013376152

Research ArticleClassification of Prolapsed Mitral Valve versus Healthy Heartfrom Phonocardiograms by Multifractal Analysis

Ana Gavrovska12 Goran ZajiT23 Irini Reljin2 and Branimir Reljin1

1 Research and Development Department Innovation Center of the School of Electrical Engineering in BelgradeBulevar Kralja Aleksandra 73 11120 Belgrade Serbia

2 Department of Telecommunications and Information Technology School of Electrical Engineering University of BelgradeBulevar Kralja Aleksandra 73 11120 Belgrade Serbia

3 Department of Telecommunications ICT College of Vocational Studies Zdravka Celara 16 11000 Belgrade Serbia

Correspondence should be addressed to Ana Gavrovska anaga777gmailcom

Received 27 December 2012 Revised 11 April 2013 Accepted 25 April 2013

Academic Editor Reinoud Maex

Copyright copy 2013 Ana Gavrovska et alThis 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

Phonocardiography has shown a great potential for developing low-cost computer-aided diagnosis systems for cardiovascularmonitoring So far most of the work reported regarding cardiosignal analysis using multifractals is oriented towards heartbeatdynamics This paper represents a step towards automatic detection of one of the most common pathological syndromes so-called mitral valve prolapse (MVP) using phonocardiograms and multifractal analysis Subtle features characteristic for MVP inphonocardiograms may be difficult to detect The approach for revealing such features should be locally based rather than globallybased Nevertheless if their appearances are specific and frequent they can affect a multifractal spectrum This has been the casein our experiment with the click syndrome Totally 117 pediatric phonocardiographic recordings (PCGs) 8 seconds long eachobtained from 117 patients were used for PMV automatic detection We propose a two-step algorithm to distinguish PCGs thatbelong to children with healthy hearts and children with prolapsed mitral valves (PMVs) Obtained results show high accuracy ofthe methodWe achieved 9691 accuracy on the dataset (97 recordings) Additionally 90 accuracy is achieved for the evaluationdataset (20 recordings) Content of the datasets is confirmed by the echocardiographic screening

1 Introduction

Cost effectiveness in cardiovascular monitoring representsone of the great challenges [1] Besides traditional ausculta-tion phonocardiography has become a valuable diagnostictool It has shown a great potential for developing low-costcomputer-aided diagnosis (CAD) systems [2ndash4] Efficientphonocardiography analysis can decrease the necessity formore complex methods

Phonocardiograms (PCGs) represent digital records ofheart sounds that are believed to yield valuable clinicalinformation One of the major concerns regarding phono-cardiograms is recognizing and understanding such relevantinformation So far very little work has been reported onautomatic detection of relevant clinical information anddiagnosis through phonocardiography

This paper represents a step towards automatic detectionof one of the most common pathological syndromes so-calledmitral valve prolapse (MVP) using phonocardiogramsand multifractal analysis Even though the examination ofexisting pathological syndromes is possible by observing andlistening to the PCGs it is believed that automatic detectionof a possible abnormality is of great importance It is alsoimportant to draw attention of a physician or an examinerto such cardiac events

Characteristic midsystolic click with possible late systolicmurmur represents a typical auscultatory finding whenMVPis diagnosed [5ndash10] In phonocardiography this property isdescribed in terms of the pathological functionality of mitralvalve leaflets Time domain visual analysis of such clicks isa demanding and an error-prone process The process of

2 Computational and Mathematical Methods in Medicine

examination of each beat separately within a PCG record isalso time consuming

The dynamics of nonstationary medical signals such ascardiosignals may be analyzed by different signal processingtools where fractals multifractals and wavelets are of par-ticular interest [11ndash16] The nature of self-similarity enablesfinding features on one scale which resemble the featuresfrom another scale despite the complexity of the analyzedobject or system dynamics

So far the multifractal analysis shows to be suitable forinvestigating heartbeat dynamics [15] Multifractal behaviourof the cardiovascular system is investigated through analysisof Holder exponents and fractal behavior using differentapproaches such as detrended fluctuation analysis (DFA) andself-affine fractal variability analysis of heartbeat dynamics[17 18] local variability analysis [19 20] analysis of healthyand pathological dynamics from the aspect of respiratory ratevariability [21] and brain activity in healthy patients [21 22]analysis of Holder exponents using laser Doppler flowmetrytechnique [23] analysis of progressive central hypovolemiainfluence [24 25] estimation of heart rate variability (HRV)large deviations [26] and arrhythmia [27]Many variations ofcardiosignals are examined using multifractality age-relatedchanges [28 29] as well as changes in heart dynamics beforeand after particular treatment [30] for different human races[31] body positions [23] and during wake and sleep phases[32 33] Heartbeat dynamics is compared between a groupof healthy patients and a group of patients with heart failures[17]The records of the heart failure group show a loss ofmul-tifractality and narrowing of the multifractal spectra Long-range multiscale properties are investigated for congestiveheart failure (CHF) disease and primary autonomic failure(PAF) disease Differences in singularity spectra of the heartrate signals are shown for healthy CHF and PAF group [34]

Very little research is reported in the literature regardingphonocardio diagnostics from the multifractal viewpointMultifractality in heartbeat dynamics can be consideredthrough acoustic heartbeats Both global and local (inter-beat) techniques are introduced in heartbeat dynamics fordetection of abnormalities [35] Although the global-basedconcept such as Legendremultifractal spectrum seems to beblind to subtle features in case of large heart rate deviations[26] we show in this paper that this is not the case withdetection of PCG records of patients with PMV in a datasetconsisting of records from both healthy patients and patientswith PMV

We propose a novel approach for distinguishing PCGsthat belong to patients with PMVs and healthy patients basedon a multifractal analysis Multifractal analysis is used in aglobal manner (without click event segmentation in the timedomain)

The paper is organized as follows In Section 2 the datasetacquisition procedure is shortly explained Section 3 givesthe fundamental background of PMV and phonocardiogrammorphology in patients with PMV Furthermore it providesan introduction to the fundamentals of multifractals andtheir suitability for medical signal analysis In Section 4 wepropose an algorithm for distinguishing records with PMV

Figure 1 The equipment for acquisition of phonocardiograms

and healthy records using phonocardiography Obtainedresults are presented in Section 5 Finally we give conclusionsbased on the proposed algorithm

2 Data Acquisition

In the study 117 children (7ndash19 years old) contributed toacquisition of 117 recordings There were 54 male and 63female patients (119872 = 54 119865 = 63) No multiple-dayrecordings weremade From this dataset 97 recordings (119872 =

45 119865 = 52) are used for setting of the parameters ofthe classifier The rest of the recordings are included in thevalidation study

Auscultation and phonocardiogram acquisitionwere per-formed at the Health Center ldquoZvezdarardquo Belgrade Serbiausing an electronic stethoscope (3M Littman 4100WS elec-tronic stethoscope Figure 1) All patients were in a sit-ting position during standard auscultative examination inthe morning session (09ndash12 h AM) Data acquisition startswhen a physician determines that the child is calm Duringthe recording of a PCG patients did not perform anyphysical activity (or intellectual activity such as reading)Phonocardiogram acquisition was made by an expert in thestandard cardiology protocol Low-quality recordings (due topatient movement or similar reasons) have been rejected asnonrelevant Only healthy children and children with PMVswere selected for generating the dataset used in this paperBesides the PMV children with other cardiac diseases likeacute infection anemia or tachycardia are excluded from theexperiment Such recordings are not a part of the analyzeddataset

The recordings were carefully examined by the pediatriccardiology expert An additional examination (echocardio-graphic confirmation) was made at the University ChildrenHospital Belgrade Serbia for the patients in the test dataset

Computational and Mathematical Methods in Medicine 3

(97 recordings)The test PCGdatasetwas further divided intotwo groups

(i) healthy group (children with healthy hearts) and(ii) PMV group (children with PMVs)

Echocardiography was used in order to confirm contentvalidity of the groups There are 49 children in Healthy and48 children in PMV group

Each phonocardiographic recording lasts for 8 secondsPCGs were recorded with a sampling frequency of 8 kHzwith 16 bit amplitude resolution The recordings were con-verted to wav format and downsampled to 1 kHz for furtheranalysis

3 Background

31 Prolapsed Mitral Valve (PMV) or Mitral Valve Prolapse(MVP) Is Also Known as Systolic Click Syndrome It is acommon valvular disorder and is often benign Howeverit is also assumed as a disease which may cause seriouscardiac disorders [5 6] There is no accordance regarding theprevalence ofMVP as reported in [5] the occurrence ofMVPranges from 5 to 15 and even up to 35 while in [6] MVPis around 2-3

Various symptoms including electrocardiographic(ECG) repolarisation have been associated with PMV Aphysician is most likely to use his stethoscope for initialPMV detection by auscultation (and phonocardiography)Auscultation still represents an important tool in pediatriccardiology The misperception of a wide range of nonspecificsymptoms led to the practice of acquiring screeningechocardiograms from patients [6]

In phonocardiography PMV is usually manifested via amidsystolic click as an isolated cardiac event or just beforethe systolic murmur (heart noise) appearance The clicksyndrome is sometimes difficult to notice in the systole andits detection depends on the skills of the physician [7] Systoleis defined as an interval between two fundamental heartsounds S1 and S2 (ie tic-tac) visualized in a quasiperiodicphonocardiogram An example of a PCG signal recorded ona patient with PMV is shown in Figure 2 where large ampli-tudes correspond to S1 and S2 sounds S1 sounds are foundafter an electrocardiogramrsquos R waves Fluctuation in betweensuch large peaks (heart beats) does appear to be interestingA click as a singularity may be found difficult to follow inintervals between S1s and S2s (ie within systoles) This clickexistence is not always apparent to an average eyeear

There is a possibility of fault prognosis provided byphonocardiography leading to misleading conclusionswhether the signal corresponds to a healthy patient or apatient with PMV Searching for specific cardiac eventsand features associated with PMV diagnosis in PCGs isan error-prone task Such cardiac events within PCGs arecrucial indicating that findings may not be benign

In early research of PMV treatment in the 1970s echocar-diography was seen as an excellent method for diagnosingPMV Echocardiography as a specific noninvasive techniquecan provide visualization of both mitral valve leaflets [8 9]

06

04

05

010

0

02

minus02

minus01

minus02

minus03

minus04

minus06

minus08

0 1

1

2 3 4 5 6 7 8

Am

plitu

de

Time (s)

Murmur

Click

BeatS1 S2

S1 S2

S1

Figure 2 Phonocardiogram that corresponds to a child withprolapsed mitral valve (PMV)

Clinical features of theMVPwhich can be associatedwith theclick (click andmurmur) as previously noted are relatedwithechocardiographically documented findings [10] Bearing inmind the availability of appropriate equipment the reliabilityof PMV detection is expected to increase This paper dealswith the global difference between a Healthy group and aPMV group of PCG recordings due to the fact that thedifference between these two groups is not often obvious

32 Multifractals in Medical Signal Analysis Self-similaritybehaviour is an interesting property found in many naturalobjects and phenomena For instance the structure of rivernetworks a cloud the nervous system of humans thestructure of a tree cauliflower and so forth have self-similarproperty by observing such structures in different scales(almost) the same shape arises Such objects (structures)are known as fractals because they can be characterizedby noninteger (fractional) dimension 119863

119865[11] The fractal

dimension numerically describes how the irregular structureof objects andor phenomena is replicated in an iterative wayfrom small to large scales or vice versa and can be used forobjective comparison andor classification of different com-plex structures The fractal dimension 119863

119865can be estimated

in different ways One simple but efficient method is knownas the box-counting method This method involves the useof 119899-dimensional grid of nonoverlapping boxes of the sidelength 120576within the space occupied by observed structure andcounts the number of boxes119873(120576) covering the structureThegrid dimension equals 119899 = 119864 + 1 where 119864 is an appropriateEuclidean dimension 119864 = 1 2 or 3 for line surface orvolume respectively If boxes of recursively different sizes areused for covering fractal object the limiting value of N(120576)when 120576 tends to zero follows the power law

119873(120576) sim 120576119863119865 (1)

that establishes the fractal dimension to be estimated [11 12]For artificially generated fractals generated by using some


predetermined rules fractal dimension is scale invariant thatis it has the same value regardless of the observation scaleSuch objects are known as monofractals [12 13] Converselynatural fractals are characterized by fractal dimension whichvaries depending on the scale Such objects are referred to asmultifractals

Multifractals are derived as an extension of fractals thatis appropriate for situations where a unique dimension isnot enough They were introduced by Mandelbrot in the1980s for the purpose of measuring turbulent flow velocity[11] In analysis of the regularity of a flow with velocityv irregularities are concluded to be found These eventssuch as rapid singularity changes occur in different instants(from the Lebesgue measure in R3 space viewpoint) Holderexponent h (119909

0) is assigned to each signal point 119909

0Therefore

each exponent value h corresponds to an appropriate setof points 119878

ℎ Multifractality can be seen as a wide range of

Holder exponents Mapping hrarr 119863ℎ defines a multifractal

spectrumof a signal in away that for each fixed value h (set ofpoints 119878

ℎ) the Hausdorff dimension119863

ℎis calculated Holder

exponent h is a measure of irregularity of a function 119892 atobserved point (a local feature) There exists a polynomial oforder n 119875

119899(x) and such a constant K so

1003816100381610038161003816119892 (119909) minus 119875119899 (119909 minus 1199090)1003816100381610038161003816 le 119870

1003816100381610038161003816119909 minus 11990901003816100381610038161003816

ℎ (2)

stands for all the points 119909 in the neighborhood of 1199090 The

spectrum is calculated using multifractal formalism

119863ℎ= inf119902(119902 sdot ℎ minus 120591 (119902) + 119896) (3)

where 119902 is a real parameter used to describe the singularityof structure and determines the multifractal dimensions 119863

ℎ

120591(q) is a nonlinear function and 119896 is a constant For 119902 gt 1

strongly singular structures are emphasized for 119902 lt 1 lesssingular structures are emphasized while for 119902 = 1119863

ℎequals

information dimensionThere is yet another approach for introduction of mul-

tifractality Fractal dimension 119891ℎ can be defined for a set

of Holder exponents of points that are within the range [hℎ + Δℎ] Such set may be considered monofractal Legendretransform can be used for the relation between function 120591(q)and a multifractal dimension 119891

ℎ

120591 (119902) = 119902 sdot ℎ (119902) minus 119891ℎ ℎ (119902) cong 120572 (119902) =

119889120591 (119902)

119889119902 (4)

Parameter120572 represents an approximation of theHolder expo-nent h where maximum of spectrum (h 119891

ℎ) corresponds to

the Hausdorff dimension 119863ℎ[13] In order to point out the

multifractal formalism and thus to explain the alpha (120572) asan approximation of Holder exponent we have introducedthe expression (4)

In general multifractality is verified in the literature aseffective concept in analysis of medical signals and images[13 15 16] Legendre singularity spectrum can be calculatedfor different values of 120572 and shows a global aspect of thecontent in a medical signal It results in a smooth concave(decaying) function of Holder exponent f (120572) that gives a

06 07 08 09 1 11 12 13Time (s)

1205761Level11987181198738 = 2

11987171198737 = 2

11987161198736 = 11

11987151198735 = 12

11987141198734 = 9

11987131198733 = 4

11987121198732 = 1

11987111198731 = 1

(a)

Level

06 07 08 09 1 11 12 13Time (s)

12057621198711611987316 = 01198711511987315 = 21198711411987314 = 21198711311987313 = 311987112 11987312 = 311987111 11987311 = 1011987110 11987310 = 2311987191198739 = 2311987181198738 = 1511987171198737 = 811987161198736 = 611987151198735 = 311987141198734 = 211987131198733 = 111987121198732 = 111987111198731 = 1

(b)

Figure 3 An illustration of the box-counting technique as a basisfor the histogram method (a) 120576

1= 112 (b) 120576

2= 124

general information about behavior of the analyzed set ofpoints A simple and efficient method for estimating themultifractal spectrum is the histogram method (and it isbased on the box-counting method) [16]

Figure 3 gives an illustration of the box-counting tech-nique as a basis for the histogram method It is applied to agiven structure S (eg to a part of the PMV record Figure 2)which is then divided into the nonoverlapping boxes 119861

119894of

size 120576 so that 119878 = cup119894119861119894 Each box 119861

119894is characterized by

measure 120583(119861119894) (here the signal level is used as a measure 120583

Figure 3(a)) The coarse Holder exponent of the subset 119861119894

corresponding to given measure 120583 is calculated as

120572119894=ln (120583 (119861

119894))

ln (120576) (5)

By changing the box size Figure 3(b) the value of the coarseHolder exponent changes as well In the limiting procedureas box size tends to zero Holder exponent 120572 at a specific loca-tion within the observed signal (structure) becomes moreprecise The Holder exponent describes the local regularityof structure 119878 Finally the distribution of 120572 exponents f (120572)that is the multifractal spectrum (Legendre spectrum) isdetermined The multifractal spectrum describes the globalregularity of observed structure In this paper the estimationof Legendre spectrum (based on the box-counting technique)is performed using FracLab software [36]


4 Healthy versus PMV Phonocardiograms-Multifractal Explanation

41 Initial Examination We considered 97 PCG records thatbelong either to healthy patients or patients with PMV wherediagnoses are confirmed by the analysis of phonocardiogramsand echocardiograms (echos) There are 49 recordings from49 healthy children and 48 recordings from 48 children withPMV

In Figure 4 we show curves of multifractal spectracalculated for healthy children (49) One can notice themultifractality of the PCGs

Multifractality is also evident in the group of childrenwith PMVs In order to compare the spectra between thegroups Legendremultifractal spectra for PMVrecordings arecalculated under the same conditions as spectra of the healthypatients A certain number of PMVrecordingswere displayedas points (as ldquomonofractalsrdquo Figure 5) Spectra calculationunder the same conditions is based on the use of predefinedparameters which are calculated for healthy patients Theparameters are related to alpha values corresponding tohealthy recordings calculated by [36] Multifractal spectrumcurve (120572 119891(120572)) could not be displayed for a certain numberof PMV signals This implies that previously calculated set ofvalues determined for the healthy patients do not correspondto the abovementioned PMV recordings

Since the spectra are calculated under the same condi-tions that correspond to healthy recordings the fact that onlyPMV signals were displayed as points is used in the classifi-cation algorithm Each phonocardiogram that is displayed asa point is automatically classified as a signal that belongs toa patient with PMV The rest of PMV signals (24 recordings)were displayed as curves in themultifractal domain Our goalis to further examine their multifractal spectra in order tomake a distinction between them and Healthy group The 73signals from both groups are shown in Figure 6 where theyare presented by multifractal curves The similarity betweenthe spectra in Figure 6 is expected since the distinction isdifficult to make by eyeear

411 Feature AnalysismdashHealthy versus PMV ClassificationObtained multifractal spectra curves 119862

119895 (119895 = 1 73) are

sets of points (120572(119899119895) 119891(120572(119899

119895))) 119899119895= 119871119895minus 119873119895+ 1 119871

119895

We examined several features of such sets shapes of thecurves for Healthy and PMV group (width of a curve andarea under a curve) location of maxima characteristics ofa curve shape for large alpha values and so forth Figure 7shows an example of a multifractal spectrum curve withtested characteristics width (W) area (A) alpha value of themaxima (120572MAX) and slope of the curve (120579)

Width of a spectrum is calculated as a difference betweenalpha values in ending points of the curve as 119882 = 120572(119871) minus

120572(119871minus119873+1) AreaA is calculated among lines119891(120572) = 02 120572 =

120572MAX and a multifractal spectrum curve If a signal spectrumis displayed as a single point areaA andwidthW will be zeroFigure 8 shows calculatedA andW values for 97 patientsTherelevance of these features for threshold settings may be seenin their sorted presentation By visual inspection we notice a

06

08

1

04

0

02

minus02

120572

05 1 15 2 25

119891(120572)

Figure 4 Legendre multifractal spectra calculated for healthypatients (findings confirmed by echo analysis)

06

08

1

12

04

0

02

minus02

120572

0 1

1

1051

095

2 3 4 5

15

119891(120572)

Figure 5 Calculated Legendremultifractal spectra for patients withPMV (findings confirmed by echo analysis)

06

08

1

12

04

0

02

120572

0 1 2 3 4 5

minus02

119891(120572)

Figure 6Multifractal spectra of the PCGdataset (excluding spectraof signals displayed as points)


0

02

1

A-area

W-width

(120572MAX 1)

120572MAX

120579 = 119905119892120573

120573

120572

120572119871-119873+1 120572119871-3 120572119871

119891(120572)

Figure 7 An example of a multifractal spectrum curve withanalyzed parameters

5

4

3

2

1

0

A-ar

ea v

alue

W-w

idth

val

ue

5 10 15 20 25 30 35 40 45Number of recording

06506

05505

045

36 38 40 42 44 46

Areas for Healthy classAreas for PMV class

Widths for Healthy classWidths for PMV class

Whealthy

Ahealthy

WPMV

APMV

Atr

Figure 8 Widths and areas for Healthy and PMV group respec-tively presented in increasing order

range of areas (and widths) where most of the signals (bothnormal and PMV) concentrate

In order to compare the similar multifractal spectra inthe proposed approach we move the maxima of all the 119891(120572)curves to the point (MaxPos 1) The location of this pointMaxPos is calculated as an average of all maxima locations120572119872119860119883

This gives a better insight into the shape characteristicsof the curves For the comparison of the multifractal curvesthe Legendre multifractal spectrum with maximum value 1 iscalculated for every signal

In the analysis of multifractal spectra we noticed thatrelative changes of curve shapes on their right sides maycarry valuable clinical information in accordance with themultifractal theory Actually we noticed that the slope angles

06

08

1

12

04

0

02

minus02

120572

0 1 2

2

3

1816

060504030201

0

4 5

HealthyPMV

119891(120572)

Figure 9 Slopes of the curves in the right side of spectra for Healthyand PMV group

as features of the curves may be relevant (Figure 9)The slopeparameter for a curve 119862 is calculated as

120579 =

1003816100381610038161003816119891 (120572 (119871)) minus 119891 (120572 (119871 minus 3))1003816100381610038161003816

(120572 (119871) minus 120572 (119871 minus 3)) (6)

The parameter 120579 is assumed to be significant and it is used inthe classification procedure When multifractal spectrum ofa signal is displayed as a point the slope parameter has zerovalue

42 Proposed Algorithm We propose a two-step algorithmfor distinguishing healthy records from PMV ones based onthe Legendre multifractal spectra According to the featureanalysis of the curves we noticed that the slope parametermay be decisive We also noticed that most of the spectra fallwithin a narrow range of area values

For obtained multifractal spectra curves we apply a two-step algorithm

(1) dividing spectra into two sets based on area featureA and

(2) differentiation in two classes (Healthy and PMV)based on the slope parameters calculated for bothof the sets (obtained according to area values in theprevious step)

The first step in the classification is realized using thethreshold 119860 tr for dividing curves into two sets For 119860 gt

119860 tr curves that have large area values are selected Theycan possibly be considered as outliers when displaying thespectra Most of the curves are selected for 119860 le 119860 trWe arbitrarily chose the first intersection of area trends inFigure 7 for the threshold value119860 tr (055)The curves selectedfor 119860 gt 119860 tr and 119860 le 119860 tr are represented in Figures 10 and 11respectively


06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

Right side ofspectra forcalculationareas (A)

A gt Atr

120572

119891(120572)

Figure 10 The large-area spectra selection

06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

120572

A lt Atr or A = Atr

119891(120572)

Figure 11 Spectra selected for 119860 le 119860 tr

In the second step of the algorithm parameter 120579 iscalculated for curves from both sets (shown in Figures 10 and11) If 119860 gt 119860 tr the slope 120579 is compared with predefined slopethreshold 120579

1198791 If slope value 120579 is less than the threshold value

120579 lt 1205791198791 (7)

recording is automatically classified as a recordingwith a clicksyndrome (PMV class) This is shown in Figure 12

If 119860 le 119860 tr the slope parameter 120579 is compared with thepredefined threshold 120579

1198792 If slope parameter 120579 is less than the

threshold

120579 lt 1205791198792 (8)

recording is classified as PMV Otherwise it is classified asan element of the Healthy class In the case of 119860 le 119860 tr by

1 2 3 4 5 6 7 8Samples

145

14

135

13

125

12

115

11

Slop

e par

amet

er v

alue

120579healthy

1205791198791

120579PMV

SlopemdashHealthySlopemdashPMV

Figure 12The slope parameter differentiation for large-area spectra(119860 gt 119860 tr)

visual inspection we also noticed thatmost of the curves have120572MAX values lower than theMaxPos value Spectra displayedas points have higher values (120572MAX) than theMaxPos In theproposed algorithm 120572MAX values (andMaxPos) are not usedfor the classificationThe relevance of 120572MAX parameter is stillquestionable

All threshold values (119860 tr 1205791198791 1205791198792) are chosen empiricallyby observing the spectra with respect to particular tolerance(offset) when determining the value Empirical lines ofseparation are set by examination Figures 12 and 13 representcalculated slope parameters for the set of curves with largearea values (119860 gt 119860 tr) and small area values (119860 le 119860 tr)respectively In Figure 12 twelve values of slope parametersare showed for 12 curves (119860 gt 119860 tr) where four among thembelong to PMV class

The slope parameter is relevant for the other group aswell In Figure 13 the rest of PCG signals (61 recordings)are presented via slope values We can freely add 24 PCGrecordings to this group of signals since they were notmanifested asmultifractal curves (areaA and slope parameter120579 have zero value threshold 120579

1198792is real positive constant)

5 Simulation Results

51 Results of the Proposed Algorithm In the set of 97 PCGrecordings we achieved an accuracy of 9691 Obtainedresults of the simulation are shown in Table 1

Even in the case of overlapping of the spectra curvesthe algorithm gives excellent results in differentiating PMVrecordings from healthy recordings In Figure 14 three mis-classified spectra are shown and two correctly classifiedspectra for each group For the purpose of presentation wekeep colors for signal differentiation (bluemdashfor Healthy andredmdashfor PMV recordings)

In the validation study we analyzed additional 20 PCGrecordings that were not used for setting the thresholds (naive


5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV


Figure 13The values of slope parameter for Healthy and PMV classfor 119860 le 119860 tr

Table 1 Simulation results

ClassNumber of

recordings (withecho confirmation)

Number of hits (theproposed PCG-based

algorithm)Accuracy

Healthy 49 48 9796PMV 48 46 9583Total 97 94 9691

dataset) Totally 20 children (119872 = 9 119865 = 11) contributedto the realization of this dataset (one patient - one signal)Their class (healthy or PMV) affiliation was not known to theauthors during testing the dataset The results in validationstudy will be explained in the following subsection

52 Echocardiographic Confirmation and Validation ResultsThe examination of recorded PCG dataset is followed byechocardiographic examination at the University ChildrenHospital in Belgrade It is confirmed which of 117 recordedphonocardiograms belong to which (Healthy or PMV) classOur analysis is performed only on these groups In standardphonocardiographic analysis cardiology experts may haveuncertainties among such dataset which are resolved with theechocardiographic study

As previously mentioned we tested 20 additional PCGsignals provided by the physician using the proposed algo-rithm (test) with the fixed thresholds Our algorithm gavesatisfying results in comparison to the echocardiographicstudy The validation results are presented in Table 2 All 10PMV recordings were predicted correctly as PMV Two outof 10 healthy recordings were misclassified

The proposed procedure is shown to be efficient and sim-ple Even though the box-counting technique is sometimesneglected because of masking the singularities the proposedalgorithm has overcome this limitation

05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)

Miss HealthyHit Healthy

Miss PMVHit PMV

Figure 14 Examples of correctly classified spectra andmisclassifiedspectra

Table 2 Validation results

ClassNumber of recordings

(with echoconfirmation)


algorithm)Healthy 10 8PMV 10 10Total 20 18

The multifractal spectra calculation is also simpler forrealization than wavelet-based methods Particular anomalyis detected using characteristic features of the multifractalspectra curves Figure 9 points out the part where parameter120572 is large The click syndrome is expected to have an effecton the right side of the spectra unlike the recordings fromthe healthy group where such clicks have not been found (orwhere the particular behaviour in the systole is not a long-term event)

Even though the whole recording was used large ampli-tudes in time domain that correspond to S1s (and S2s)are not relevant in the proposed classification procedurewhich is based on multifractal analysis The existence ofnonregular cardiac events (possible clicks) affects the rightside of multifractal spectra curves as opposed to the regularheart sounds (S1s and S2s) Time localization of the clicks wasnot a part of this analysis

This and similar approaches can indicate signal irreg-ularities to users of electronic stethoscopes without largeexperience or skills in auscultation and phonocardiographyIn this way the misinterpretation of phonocardiograms maybe significantly decreased

6 Conclusion

We have been primarily focused on the criteria for obtainingthe clear distinction between patients with diagnosed PMV


and healthy patients using phonocardiography We havetested 97 PCG recordings where each record is 8 secondslong with downsampled frequency of 1 kHz Echocardio-graphic examination confirmed clinical findings in PCGsproposed algorithm achieves high accuracy (9691) In theevaluation step of the study we used additional 20 PCGsignals from another set of patients (20 children) Only twosignals weremisclassified according to the echocardiographicexamination

At this point the research about automatization of thethresholds has not been finished Nevertheless there are clearindications about the direction of future research especiallywith respect to robustness We want to emphasize thateach record is obtained from a different patient and givesa representation of a different ldquopumping machinerdquo (heart)function Therefore the features thresholds and generallythe algorithm can be considered robust for a large populationAn increase of the training dataset may set thresholds moreaccurately

Further research will be primarily oriented towards fur-ther evaluation This involves the use of additional classesof signals (signals belonging neither to Healthy nor PMVgroup) We believe that applying well-known signal pro-cessing techniques may contribute to the development ofa cost-effective computer-aided diagnosis system based onphonocardiograms Decreasing the use of complex equip-ment for screening by efficient low-cost approaches may beof great importance It is necessary to have large datasets ofphonocardiograms for this purposewith confirmeddiagnosisand labeled cardiac events

Conflict of Interests

The authors of this paper do not have a direct financialrelation with any commercial software mentioned in thepaper that might lead to a conflict of interests for any of theauthors

Acknowledgments

This research is partially funded by the Serbian Ministry ofEducation Science and Technological Development throughthe project of Integrated and Interdisciplinary ResearchProgram no III44009 Authors are grateful to MD VesnaBogdanovic fromHealth Center ldquoZvezdarardquo Belgrade Serbiafor providing data and medical support for the presentedresearch

References

[1] G A Meininger ldquoGrand challenges in vascular physiologyrdquoFrontiers in Physiology vol 1 article 18 2010

[2] M E Tavel ldquoCardiac auscultation a glorious pastmdashbut does ithave a futurerdquo Circulation vol 93 no 6 pp 1250ndash1253 1996

[3] T R Reed N E Reed and P Fritzson ldquoHeart sound analysis forsymptom detection and computer-aided diagnosisrdquo SimulationModelling Practice and Theory vol 12 no 2 pp 129ndash146 2004

[4] MAChizner ldquoCardiac auscultation rediscovering the lost artrdquoCurrent Problems inCardiology vol 33 no 7 pp 326ndash408 2008

[5] L A Freed D Levy R A Levine et al ldquoPrevalence and clinicaloutcome of mitral-valve prolapserdquo The New England Journal ofMedicine vol 341 no 1 pp 1ndash7 1999

[6] E Hayek C N Gring and B P Griffin ldquoMitral valve prolapserdquoThe Lancet vol 365 no 9458 pp 507ndash518 2005

[7] J M Criley K B Lewis J O Humphries and R S Ross ldquoPro-lapse of the mitral valve clinical and cine-angiocardiographicfindingsrdquoBritishHeart Journal vol 28 no 4 pp 488ndash496 1966

[8] J C Dillon C L Haine S Chang and H Feigenbaum ldquoUseof echocardiography in patients with prolapsed mitral valverdquoCirculation vol 43 no 4 pp 503ndash507 1971

[9] A N Weiss J W Mimbs P A Ludbrook and B E SobelldquoEchocardiographic detection of mitral valve prolapse Exclu-sion of false positive diagnosis and determination of inheri-tancerdquo Circulation vol 52 no 6 pp 1091ndash1096 1975

[10] R B Devereux R Kramer-Fox and W T Brown ldquoRelationbetween clinical features of the mitral prolapse syndromeand echocardiographically documented mitral valve prolapserdquoJournal of the American College of Cardiology vol 8 no 4 pp763ndash772 1986

[11] B MandelbrotThe Fractal Geometry of Nature W H FreemanNew York NY USA 1982

[12] J Feder Fractals Plenum Press New York NY USA 1988[13] R Lopes and N Betrouni ldquoFractal and multifractal analysis a

reviewrdquoMedical ImageAnalysis vol 13 no 4 pp 634ndash649 2009[14] P C Ivanov A L Goldberger S Havlin C K Peng M

G Rosenblum and H E Stanley ldquoWavelets in medicine andphysiologyrdquo in Wavelets in Physics H van der Berg EdCambridge University Press Cambridge UK 1998

[15] P C Ivanov L A Nunes Amaral A L Goldberger et alldquoMultifractality in humanheartbeat dynamicsrdquoNature vol 399no 6735 pp 461ndash465 1999

[16] I S Reljin and B D Reljin ldquoFractal geometry and multifractalsin analyzing and processing medical data and imagesrdquo Archiveof Oncology vol 10 no 4 pp 283ndash293 2002

[17] P C Ivanov L A Nunes Amaral A L Goldberger et al ldquoFrom1f noise tomultifractal cascades in heartbeat dynamicsrdquoChaosvol 11 no 3 pp 641ndash652 2001

[18] M Meyer and O Stiedl ldquoSelf-affine fractal variability of humanheartbeat interval dynamics in health and diseaserdquo EuropeanJournal of Applied Physiology vol 90 no 3-4 pp 305ndash316 2003

[19] Z R Struzik ldquoRevealing local variability properties of humanheartbeat intervals with the local effective Holder exponentrdquoFractals vol 9 no 1 pp 77ndash93 2001

[20] O Barriere and J Levy-Vehel ldquoLocal holder regularity-basedmodeling of RR intervalsrdquo in Proceedings of the IEEE Interna-tional Symposium on Computer-Based Medical Systems (CBMSrsquo08) Jyvaskyla Finland June 2008

[21] B Suki A M Alencar U Frey et al ldquoFluctuations noise andscaling in the cardio-pulmonary systemrdquo Fluctuations andNoiseLetters vol 3 no 1 pp R1ndashR25 2003

[22] D C Lin and A Sharif ldquoCommon multifractality in the heartrate variability and brain activity of healthy humansrdquoChaos vol20 no 2 pp 1ndash7 2010

[23] D C Lin and A Sharif ldquoIntegrated central-autonomic mul-tifractal complexity in the heart rate variability of healthyhumansrdquo Frontiers in Physiology vol 2 article 123 2011

[24] A Humeau F Chapeau-Blondeau D Rousseau M TartasB Fromy and P Abraham ldquoMultifractality in the peripheralcardiovascular system from pointwise holder exponents of laser


Doppler flowmetry signalsrdquo Biophysical Journal vol 93 no 12pp L59ndashL61 2007

[25] B J West N Scafetta W H Cooke and R Balocchi ldquoInfluenceof progressive central hypovolemia on holder exponent dis-tributions of cardiac interbeat intervalsrdquo Annals of BiomedicalEngineering vol 32 no 8 pp 1077ndash1087 2004

[26] P Loiseaua CMedigueb P Goncalvesc et al ldquoLarge deviationsestimates for the multiscale analysis of heart rate variabilityrdquoPhysica A vol 391 pp 5658ndash5671 2012

[27] A Echelard and J L Vehel ldquoSelf-regulating processes-basedmodeling for arrhythmia characterizationrdquo in Proceedings of the2nd IASTED International Symposia on Imaging and Signal Pro-cessing in Health Care and Technology (ISPHT rsquo12) BaltimoreMd USA May 2012

[28] L Guzman-Vargas E Calleja-Quevedo and F Angulo-BrownldquoOn fractal analysis of cardiac interbeat time seriesrdquo AIPConference Proceedings vol 682 pp 226ndash231 2003 The 7thMexican Symposium on Medical Physics

[29] A Humeau F Chapeau-Blondeau D Rousseau P RousseauW Trzepizur and P Abraham ldquoMultifractality sample entropyand wavelet analyses for age-related changes in the peripheralcardiovascular system preliminary resultsrdquo Medical Physicsvol 35 no 2 pp 717ndash723 2008

[30] M Rudinac M Uscumlic S Rudinac B Milovanovic I Reljinand B Reljin ldquoFractal and multifractal analysis of heart ratevariabilityrdquo in Proceedings of the 8th International Conference onTelecommunications inModern Satellite Cable and BroadcastingServices (TELSIKS rsquo07) pp 325ndash328 Nis Serbia September2007

[31] E Wesfreid V L Billat and Y Meyer ldquoMultifractal analysis ofheartbeat time series in human racesrdquo Applied and Computa-tional Harmonic Analysis vol 18 no 3 pp 329ndash335 2005

[32] A M Diosdado H R Cruz D B Hernandez and G GCoyt ldquoAnalysis of correlations in heart dynamics in wake andsleep phasesrdquo in Proceedings of the 29th Annual InternationalConference of the IEEE EMBS Cite Internationale pp 23ndash26Lyon France August 2007

[33] R Hernandez-Perez L Guzman-Vargas I Reyes-Ramırez andF Angulo-Brown ldquoDifferences in the stability of the heartinterbeat rate during wake and sleep periodsrdquo Fluctuation andNoise Letters vol 10 pp 405ndash416 2011

[34] K Kotani Z R Struzik K Takamasu H E Stanley and YYamamoto ldquoModel for complex heart rate dynamics in healthand diseasesrdquo Physical Review E vol 72 no 4 Article ID041904 8 pages 2005

[35] J G Samaniego L R Juarez J M V Arcos et al ldquoPhonocardio-graph signals acquisition and analysis systemrdquo in Proceedings ofthe 1st International Congress on Instrumentation and AppliedSciences Cancun Mexico October 2010

[36] J L Vehel FracLab httpfraclabsaclayinriafr

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


examination of each beat separately within a PCG record isalso time consuming

The dynamics of nonstationary medical signals such ascardiosignals may be analyzed by different signal processingtools where fractals multifractals and wavelets are of par-ticular interest [11ndash16] The nature of self-similarity enablesfinding features on one scale which resemble the featuresfrom another scale despite the complexity of the analyzedobject or system dynamics

So far the multifractal analysis shows to be suitable forinvestigating heartbeat dynamics [15] Multifractal behaviourof the cardiovascular system is investigated through analysisof Holder exponents and fractal behavior using differentapproaches such as detrended fluctuation analysis (DFA) andself-affine fractal variability analysis of heartbeat dynamics[17 18] local variability analysis [19 20] analysis of healthyand pathological dynamics from the aspect of respiratory ratevariability [21] and brain activity in healthy patients [21 22]analysis of Holder exponents using laser Doppler flowmetrytechnique [23] analysis of progressive central hypovolemiainfluence [24 25] estimation of heart rate variability (HRV)large deviations [26] and arrhythmia [27]Many variations ofcardiosignals are examined using multifractality age-relatedchanges [28 29] as well as changes in heart dynamics beforeand after particular treatment [30] for different human races[31] body positions [23] and during wake and sleep phases[32 33] Heartbeat dynamics is compared between a groupof healthy patients and a group of patients with heart failures[17]The records of the heart failure group show a loss ofmul-tifractality and narrowing of the multifractal spectra Long-range multiscale properties are investigated for congestiveheart failure (CHF) disease and primary autonomic failure(PAF) disease Differences in singularity spectra of the heartrate signals are shown for healthy CHF and PAF group [34]

Very little research is reported in the literature regardingphonocardio diagnostics from the multifractal viewpointMultifractality in heartbeat dynamics can be consideredthrough acoustic heartbeats Both global and local (inter-beat) techniques are introduced in heartbeat dynamics fordetection of abnormalities [35] Although the global-basedconcept such as Legendremultifractal spectrum seems to beblind to subtle features in case of large heart rate deviations[26] we show in this paper that this is not the case withdetection of PCG records of patients with PMV in a datasetconsisting of records from both healthy patients and patientswith PMV

We propose a novel approach for distinguishing PCGsthat belong to patients with PMVs and healthy patients basedon a multifractal analysis Multifractal analysis is used in aglobal manner (without click event segmentation in the timedomain)

The paper is organized as follows In Section 2 the datasetacquisition procedure is shortly explained Section 3 givesthe fundamental background of PMV and phonocardiogrammorphology in patients with PMV Furthermore it providesan introduction to the fundamentals of multifractals andtheir suitability for medical signal analysis In Section 4 wepropose an algorithm for distinguishing records with PMV

Figure 1 The equipment for acquisition of phonocardiograms

and healthy records using phonocardiography Obtainedresults are presented in Section 5 Finally we give conclusionsbased on the proposed algorithm

2 Data Acquisition

In the study 117 children (7ndash19 years old) contributed toacquisition of 117 recordings There were 54 male and 63female patients (119872 = 54 119865 = 63) No multiple-dayrecordings weremade From this dataset 97 recordings (119872 =

45 119865 = 52) are used for setting of the parameters ofthe classifier The rest of the recordings are included in thevalidation study

Auscultation and phonocardiogram acquisitionwere per-formed at the Health Center ldquoZvezdarardquo Belgrade Serbiausing an electronic stethoscope (3M Littman 4100WS elec-tronic stethoscope Figure 1) All patients were in a sit-ting position during standard auscultative examination inthe morning session (09ndash12 h AM) Data acquisition startswhen a physician determines that the child is calm Duringthe recording of a PCG patients did not perform anyphysical activity (or intellectual activity such as reading)Phonocardiogram acquisition was made by an expert in thestandard cardiology protocol Low-quality recordings (due topatient movement or similar reasons) have been rejected asnonrelevant Only healthy children and children with PMVswere selected for generating the dataset used in this paperBesides the PMV children with other cardiac diseases likeacute infection anemia or tachycardia are excluded from theexperiment Such recordings are not a part of the analyzeddataset

The recordings were carefully examined by the pediatriccardiology expert An additional examination (echocardio-graphic confirmation) was made at the University ChildrenHospital Belgrade Serbia for the patients in the test dataset






3 Background






06

04

05

010

0

02

minus02

minus01

minus02

minus03

minus04

minus06

minus08

0 1

1

2 3 4 5 6 7 8

Am

plitu

de

Time (s)

Murmur

Click

BeatS1 S2

S1 S2

S1








119873(120576) sim 120576119863119865 (1)






0Therefore









1003816100381610038161003816119892 (119909) minus 119875119899 (119909 minus 1199090)1003816100381610038161003816 le 119870

1003816100381610038161003816119909 minus 11990901003816100381610038161003816

ℎ (2)



119863ℎ= inf119902(119902 sdot ℎ minus 120591 (119902) + 119896) (3)


ℎ



ℎequals




ℎ


119889120591 (119902)

119889119902 (4)


ℎ) corresponds to




06 07 08 09 1 11 12 13Time (s)

1205761Level11987181198738 = 2

11987171198737 = 2

11987161198736 = 11

11987151198735 = 12

11987141198734 = 9

11987131198733 = 4

11987121198732 = 1

11987111198731 = 1

(a)

Level

06 07 08 09 1 11 12 13Time (s)

12057621198711611987316 = 01198711511987315 = 21198711411987314 = 21198711311987313 = 311987112 11987312 = 311987111 11987311 = 1011987110 11987310 = 2311987191198739 = 2311987181198738 = 1511987171198737 = 811987161198736 = 611987151198735 = 311987141198734 = 211987131198733 = 111987121198732 = 111987111198731 = 1

(b)


1= 112 (b) 120576

2= 124



119894of






120572119894=ln (120583 (119861

119894))

ln (120576) (5)









119895 (119895 = 1 73) are

sets of points (120572(119899119895) 119891(120572(119899

119895))) 119899119895= 119871119895minus 119873119895+ 1 119871

119895





06

08

1

04

0

02

minus02

120572

05 1 15 2 25

119891(120572)


06

08

1

12

04

0

02

minus02

120572

0 1

1

1051

095

2 3 4 5

15

119891(120572)


06

08

1

12

04

0

02

120572

0 1 2 3 4 5

minus02

119891(120572)



0

02

1

A-area

W-width

(120572MAX 1)

120572MAX

120579 = 119905119892120573

120573

120572

120572119871-119873+1 120572119871-3 120572119871

119891(120572)


5

4

3

2

1

0

A-ar

ea v

alue

W-w

idth

val

ue


06506

05505

045

36 38 40 42 44 46



Whealthy

Ahealthy

WPMV

APMV

Atr






06

08

1

12

04

0

02

minus02

120572

0 1 2

2

3

1816

060504030201

0

4 5

HealthyPMV

119891(120572)



120579 =

1003816100381610038161003816119891 (120572 (119871)) minus 119891 (120572 (119871 minus 3))1003816100381610038161003816

(120572 (119871) minus 120572 (119871 minus 3)) (6)









06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV


A gt Atr

120572

119891(120572)


06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

120572

A lt Atr or A = Atr

119891(120572)




120579 lt 1205791198791 (7)




threshold

120579 lt 1205791198792 (8)


1 2 3 4 5 6 7 8Samples

145

14

135

13

125

12

115

11

Slop

e par

amet

er v

alue

120579healthy

1205791198791

120579PMV












5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV




ClassNumber of



algorithm)Accuracy






05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)


Miss PMVHit PMV










6 Conclusion








Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of





















3 Background






06

04

05

010

0

02

minus02

minus01

minus02

minus03

minus04

minus06

minus08

0 1

1

2 3 4 5 6 7 8

Am

plitu

de

Time (s)

Murmur

Click

BeatS1 S2

S1 S2

S1








119873(120576) sim 120576119863119865 (1)






0Therefore









1003816100381610038161003816119892 (119909) minus 119875119899 (119909 minus 1199090)1003816100381610038161003816 le 119870

1003816100381610038161003816119909 minus 11990901003816100381610038161003816

ℎ (2)



119863ℎ= inf119902(119902 sdot ℎ minus 120591 (119902) + 119896) (3)


ℎ



ℎequals




ℎ


119889120591 (119902)

119889119902 (4)


ℎ) corresponds to




06 07 08 09 1 11 12 13Time (s)

1205761Level11987181198738 = 2

11987171198737 = 2

11987161198736 = 11

11987151198735 = 12

11987141198734 = 9

11987131198733 = 4

11987121198732 = 1

11987111198731 = 1

(a)

Level

06 07 08 09 1 11 12 13Time (s)

12057621198711611987316 = 01198711511987315 = 21198711411987314 = 21198711311987313 = 311987112 11987312 = 311987111 11987311 = 1011987110 11987310 = 2311987191198739 = 2311987181198738 = 1511987171198737 = 811987161198736 = 611987151198735 = 311987141198734 = 211987131198733 = 111987121198732 = 111987111198731 = 1

(b)


1= 112 (b) 120576

2= 124



119894of






120572119894=ln (120583 (119861

119894))

ln (120576) (5)









119895 (119895 = 1 73) are

sets of points (120572(119899119895) 119891(120572(119899

119895))) 119899119895= 119871119895minus 119873119895+ 1 119871

119895





06

08

1

04

0

02

minus02

120572

05 1 15 2 25

119891(120572)


06

08

1

12

04

0

02

minus02

120572

0 1

1

1051

095

2 3 4 5

15

119891(120572)


06

08

1

12

04

0

02

120572

0 1 2 3 4 5

minus02

119891(120572)



0

02

1

A-area

W-width

(120572MAX 1)

120572MAX

120579 = 119905119892120573

120573

120572

120572119871-119873+1 120572119871-3 120572119871

119891(120572)


5

4

3

2

1

0

A-ar

ea v

alue

W-w

idth

val

ue


06506

05505

045

36 38 40 42 44 46



Whealthy

Ahealthy

WPMV

APMV

Atr






06

08

1

12

04

0

02

minus02

120572

0 1 2

2

3

1816

060504030201

0

4 5

HealthyPMV

119891(120572)



120579 =

1003816100381610038161003816119891 (120572 (119871)) minus 119891 (120572 (119871 minus 3))1003816100381610038161003816

(120572 (119871) minus 120572 (119871 minus 3)) (6)









06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV


A gt Atr

120572

119891(120572)


06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

120572

A lt Atr or A = Atr

119891(120572)




120579 lt 1205791198791 (7)




threshold

120579 lt 1205791198792 (8)


1 2 3 4 5 6 7 8Samples

145

14

135

13

125

12

115

11

Slop

e par

amet

er v

alue

120579healthy

1205791198791

120579PMV












5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV




ClassNumber of



algorithm)Accuracy






05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)


Miss PMVHit PMV










6 Conclusion








Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of




















0Therefore









1003816100381610038161003816119892 (119909) minus 119875119899 (119909 minus 1199090)1003816100381610038161003816 le 119870

1003816100381610038161003816119909 minus 11990901003816100381610038161003816

ℎ (2)



119863ℎ= inf119902(119902 sdot ℎ minus 120591 (119902) + 119896) (3)


ℎ



ℎequals




ℎ


119889120591 (119902)

119889119902 (4)


ℎ) corresponds to




06 07 08 09 1 11 12 13Time (s)

1205761Level11987181198738 = 2

11987171198737 = 2

11987161198736 = 11

11987151198735 = 12

11987141198734 = 9

11987131198733 = 4

11987121198732 = 1

11987111198731 = 1

(a)

Level

06 07 08 09 1 11 12 13Time (s)

12057621198711611987316 = 01198711511987315 = 21198711411987314 = 21198711311987313 = 311987112 11987312 = 311987111 11987311 = 1011987110 11987310 = 2311987191198739 = 2311987181198738 = 1511987171198737 = 811987161198736 = 611987151198735 = 311987141198734 = 211987131198733 = 111987121198732 = 111987111198731 = 1

(b)


1= 112 (b) 120576

2= 124



119894of






120572119894=ln (120583 (119861

119894))

ln (120576) (5)









119895 (119895 = 1 73) are

sets of points (120572(119899119895) 119891(120572(119899

119895))) 119899119895= 119871119895minus 119873119895+ 1 119871

119895





06

08

1

04

0

02

minus02

120572

05 1 15 2 25

119891(120572)


06

08

1

12

04

0

02

minus02

120572

0 1

1

1051

095

2 3 4 5

15

119891(120572)


06

08

1

12

04

0

02

120572

0 1 2 3 4 5

minus02

119891(120572)



0

02

1

A-area

W-width

(120572MAX 1)

120572MAX

120579 = 119905119892120573

120573

120572

120572119871-119873+1 120572119871-3 120572119871

119891(120572)


5

4

3

2

1

0

A-ar

ea v

alue

W-w

idth

val

ue


06506

05505

045

36 38 40 42 44 46



Whealthy

Ahealthy

WPMV

APMV

Atr






06

08

1

12

04

0

02

minus02

120572

0 1 2

2

3

1816

060504030201

0

4 5

HealthyPMV

119891(120572)



120579 =

1003816100381610038161003816119891 (120572 (119871)) minus 119891 (120572 (119871 minus 3))1003816100381610038161003816

(120572 (119871) minus 120572 (119871 minus 3)) (6)









06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV


A gt Atr

120572

119891(120572)


06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

120572

A lt Atr or A = Atr

119891(120572)




120579 lt 1205791198791 (7)




threshold

120579 lt 1205791198792 (8)


1 2 3 4 5 6 7 8Samples

145

14

135

13

125

12

115

11

Slop

e par

amet

er v

alue

120579healthy

1205791198791

120579PMV












5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV




ClassNumber of



algorithm)Accuracy






05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)


Miss PMVHit PMV










6 Conclusion








Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of























119895 (119895 = 1 73) are

sets of points (120572(119899119895) 119891(120572(119899

119895))) 119899119895= 119871119895minus 119873119895+ 1 119871

119895





06

08

1

04

0

02

minus02

120572

05 1 15 2 25

119891(120572)


06

08

1

12

04

0

02

minus02

120572

0 1

1

1051

095

2 3 4 5

15

119891(120572)


06

08

1

12

04

0

02

120572

0 1 2 3 4 5

minus02

119891(120572)



0

02

1

A-area

W-width

(120572MAX 1)

120572MAX

120579 = 119905119892120573

120573

120572

120572119871-119873+1 120572119871-3 120572119871

119891(120572)


5

4

3

2

1

0

A-ar

ea v

alue

W-w

idth

val

ue


06506

05505

045

36 38 40 42 44 46



Whealthy

Ahealthy

WPMV

APMV

Atr






06

08

1

12

04

0

02

minus02

120572

0 1 2

2

3

1816

060504030201

0

4 5

HealthyPMV

119891(120572)



120579 =

1003816100381610038161003816119891 (120572 (119871)) minus 119891 (120572 (119871 minus 3))1003816100381610038161003816

(120572 (119871) minus 120572 (119871 minus 3)) (6)









06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV


A gt Atr

120572

119891(120572)


06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

120572

A lt Atr or A = Atr

119891(120572)




120579 lt 1205791198791 (7)




threshold

120579 lt 1205791198792 (8)


1 2 3 4 5 6 7 8Samples

145

14

135

13

125

12

115

11

Slop

e par

amet

er v

alue

120579healthy

1205791198791

120579PMV












5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV




ClassNumber of



algorithm)Accuracy






05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)


Miss PMVHit PMV










6 Conclusion








Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















0

02

1

A-area

W-width

(120572MAX 1)

120572MAX

120579 = 119905119892120573

120573

120572

120572119871-119873+1 120572119871-3 120572119871

119891(120572)


5

4

3

2

1

0

A-ar

ea v

alue

W-w

idth

val

ue


06506

05505

045

36 38 40 42 44 46



Whealthy

Ahealthy

WPMV

APMV

Atr






06

08

1

12

04

0

02

minus02

120572

0 1 2

2

3

1816

060504030201

0

4 5

HealthyPMV

119891(120572)



120579 =

1003816100381610038161003816119891 (120572 (119871)) minus 119891 (120572 (119871 minus 3))1003816100381610038161003816

(120572 (119871) minus 120572 (119871 minus 3)) (6)









06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV


A gt Atr

120572

119891(120572)


06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

120572

A lt Atr or A = Atr

119891(120572)




120579 lt 1205791198791 (7)




threshold

120579 lt 1205791198792 (8)


1 2 3 4 5 6 7 8Samples

145

14

135

13

125

12

115

11

Slop

e par

amet

er v

alue

120579healthy

1205791198791

120579PMV












5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV




ClassNumber of



algorithm)Accuracy






05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)


Miss PMVHit PMV










6 Conclusion








Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV


A gt Atr

120572

119891(120572)


06

08

1

12

04

0

02

minus02

0 1 2 3 4 5

HealthyPMV

120572

A lt Atr or A = Atr

119891(120572)




120579 lt 1205791198791 (7)




threshold

120579 lt 1205791198792 (8)


1 2 3 4 5 6 7 8Samples

145

14

135

13

125

12

115

11

Slop

e par

amet

er v

alue

120579healthy

1205791198791

120579PMV












5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV




ClassNumber of



algorithm)Accuracy






05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)


Miss PMVHit PMV










6 Conclusion








Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















5 10 15 20 25 30 35 40Samples

5

45

4

35

3

25

1211

2

1

15

Slop

e par

amet

er v

alue

120579healthy

120579healthy

1205791198792

1205791198792120579PMV

120579PMV




ClassNumber of



algorithm)Accuracy






05

06

07

08

09

1

04

0

02

03

01

120572

05 1 15 2

119891(120572)


Miss PMVHit PMV










6 Conclusion








Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of






















Acknowledgments


References












































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of



































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















classification of prolapsed mitral valve versus healthy heart from … · 2014-04-23 · and...

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