DISCRIMINATION OF HEART SOUNDS USING CHOAS ANALYSIS

IN VARIOUS SUBBANDS

D. Kumar, P. Carvalho, M. Antunes

†

, J. Henriques, A. S´a e Melo

†

and J. Habetha

‡

Centre for Informatics and Systems, University of Coimbra, Portugal

†

University Hospital of Coimbra, Portugal

‡

Philips Research Laboratories, Aachen, Germany

Keywords:

Heart sound analysis, Wavelet decomposition, Chaos analysis, Phase reconstruction, Lyapunov exponents,

Correlation dimension, Mechanical valve.

Abstract:

Discrimination among different types of heart sounds has a signiﬁcant impact in designing pHealth systems

based upon this bio-signal, since (i) it enables the optimal selection and tuning of the analysis algorithms

and (ii) it may be applied as a ﬁrst level strategy for heart dysfunction diagnosis. In this paper we introduce

an algorithm for heart sound type discrimination into three classes: healthy heart sounds, heart sounds with

murmur produced by native heart valves and heart sounds produced by prosthetic mechanical heart valves.

The algorithm is based on a nonlinear dynamical model of phase space reconstruction for various frequency

bands. For each frequency sub-band the chaotic nature and the complexity of the signal is assessed using the

largest Lyapunov exponents (LLE) and the correlation dimension (CD). The effectiveness of the method has

been tested with heart sounds of 45 subjects (15 subjects of each class). It was concluded that LLEs and the

CDs exhibit complementary signiﬁcance in the discrimination among different classes of heart sounds.

1 INTRODUCTION

Auscultation has been a popular technique to exam-

ine the mechanical status of the heart. Its capacity to

assess the cardiac mechanical state is comparable to

the electrocardiogram in assessing the cardiac elec-

trical state. It has been proven to be a noninvasive,

inexpensive and effective method for the early detec-

tion of many cardiac disorders (Xiao et al., 2002),

such as prosthetic and native heart valve disorder di-

agnosis and heart failure decompensation assessment.

Besides these more conventional diagnosis functions,

heart sounds may be applied for assessing several im-

portant cardiac reserve parameters for long-term pa-

tient surveillance. For instance, heart sounds may

be applied as the source signal to estimate surrogate

measures of continuous blood pressure, cardiac out-

put and heart contractility as well as to measure the

systolic heart time intervals. Due to its non-invasive

and low intrusive nature it is an interesting bio-signal

for designing systems to support pHealth applications

for continuous and long-term use in several types of

coronary and heart disease management tasks.

Heart sound signals are signiﬁcantly more com-

plex compared to other bio-signals such as the ECG

or PPG. Their main sources of origin are the move-

ments of the atrio-ventricular valves. However, other

more subtle phenomena such as blood turbulence and

heart wall vibration may contribute to the heart sound

signal. These phenomena are highly correlated to

speciﬁc heart dysfunctions and diseases and hence it

is fundamental to design appropriate analysis algo-

rithms that are able to adequately identify and extract

these diagnosis features. A typical heart sound anal-

ysis algorithm pipeline encompasses several stages

related to non-cardiac sound detection and removal,

heart sound segmentation, diagnostic feature extrac-

tion and classiﬁcation (see Figure 1). The degree

of complexity and tuning of the required algorithms

in each stage varies considerably according to the

characteristics of the underlying heart sound. For

instance, the segmentation of a heart sounds with

systolic or diastolic murmur is considerably more

complex and computationally expensive compared to

the segmentation of a heart sound without murmur

(see, for instance (Kumar et al., 2006a)(Kumar et al.,

2006b)). On the other hand, some of the analysis

stages are only required if some speciﬁc disease is

known (or at least suspected) to exist. These issues

are central in designing systems for personnel Health

(pHealth) applications, where low power electronics

369

Kumar D., Carvalho P., Antunes M., Henriques J., Sá e Melo A. and Habetha J. (2009).

DISCRIMINATION OF HEART SOUNDS USING CHOAS ANALYSIS IN VARIOUS SUBBANDS.

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing, pages 369-375

DOI: 10.5220/0001554003690375

 SciTePress

are a typical design constraint and therefore limit the

amount of computation that is available. For these

reasons, it is observed that the discrimination among

different types of heart sounds has a signiﬁcant im-

pact in designing pHealth systems, since it enables

the optimal selection and tuning of the analysis algo-

rithms and (ii) it may be applied as a ﬁrst level of heart

dysfunction diagnosis strategy. In this paper we intro-

duce an algorithm for heart sound type discrimination

into three types of classes: healthy heart sounds, heart

sounds with murmur produced by native heart valves

and heart sounds produced by prosthetic mechanical

heart valves (see Figure 1).

Heart Sound produced

by native valve

Heart sound with

murmur produced by

native valve

Heart sound

produced by

mechanical valve

Feature extraction

Suitable segmentation

algorithm for the class

of heart sounds

non-cardiac sound

removal

In case of heart sound

with murmur :

murmur classification

Heart Sound

Figure 1: Main blocks for heart sound analysis framework

where blocks under dotted square is for discrimination for

the three groups of sounds.

In the best knowledge of the authors, no work has

been proposed thus far that has attempted to solve

the addressed problem in this paper. However, heart

sounds with murmurs classiﬁcation and heart sounds

produced by mechanical valve have been separately

investigated in the literature. Nevertheless, heart mur-

mur classiﬁcation provides insights for the addressed

problem. Heart murmur segmentation and its recog-

nition involves feature extraction and classiﬁcation.

Some of the recent works on heart murmur classiﬁca-

tion are based upon decision tree methods (Pavlopou-

los et al., 2004), nonlinear dynamic methods using

recurrent statistic analysis (Ahlstrom et al., 2006)

and using features from nonlinear dynamical system

(chaos and correlation dimension) analysis (Delgado

et al., 2007).

This paper presents chaos and complexity mea-

surement in different frequency bands of heart sounds

in order to achieve the best distinction among three

classes of heart sounds. Considering the range of fre-

quency spectrum in each group, the signals are de-

composed into 6 successive signals in decreasing fre-

quency bands based on the wavelet decomposition

technique. For each band, the phase space is recon-

structed using one of the nonlinear times series meth-

ods, i.e. time delay embedding method. The chaos

and complexity features are measured in the form of

the largest Lyapunov exponents (LLE) and the corre-

lation dimension (CD). Consequently, statistical anal-

ysis is performed to test the features’ potential in dis-

tinction of these three groups of heart sounds.

The paper is structured as follows: section 2

presents a brief introduction of the applied method

using phase space features, Lyapunov exponents and

correlation dimension is presented. Section 3 contains

the details of the method. In section 4 the achieved

results using the test database composed by heart

sounds of 45 subjects are presented and discussed. Fi-

nally, in section 4 some main conclusions and future

working directions are outlined.

2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1

−0.4

−0.2

0.2

0.4

Amplitude (Unit)

0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

−1

−0.5

0.5

Amplitude (Unit)

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

−0.2

−0.1

0.1

0.2

0.3

Amplitude (Unit)

Time (Sec.)

Figure 2: Three classes of heart sounds: a) Heart sound

without any known cardiac disorder. b) Heart sound with

systolic murmur, c) Heart sound collected from a heart with

a mechanical valve implant.

2 METHOD

The proposed method for the discrimination between

different classes of heart sounds is composed by three

main steps, as it is summarized in Figure 3: 1) sig-

nal decomposition into different subbands using the

wavelet transform technique, 2) chaos and complex-

ity feature extraction using the nonlinear dynamic

approach of phase reconstruction and 3) relevance

assessment of the results using statistical analysis.

Wavelet decomposition is chosen to decompose heart

sound signal over the traditional Fourier transform

based band-pass ﬁlter bank due to its advantage of

time-frequency localization, multirate ﬁltering and

scale-space analysis. For computational efﬁciency

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

370

the discrete wavelet transform with dyadic scales and

translations is chosen. Mathematical background of

the technique is out of the scope of the paper. How-

ever, an introductory explanation of nonlinear dynam-

ical systems features is provided in this section, which

will be further applied on the original as well as on the

decomposed signals.

Heart Sound

1- without murmur

produced by Native Valve

2- with murmur produced

by Native Valve

3- produced by Mechanical

Valve

Original Signal

x

(25Hz -22.5kHZ )

Wavelet Decomposition

ca6 (25Hz -344Hz )

cd6 (0.3- 0.6kHz )

cd5 (0.6- 1.3kHz )

cd4 (1.3- 2.7kHz )

cd3 (2.7- 5.5kHz )

cd2 (5.5.- 11kHz )

cd1 (11-22.5 kHz)

Phase

Reconstruction

Largest Lyapunov

Exponents

Correlation

Dimension

Statistical

Analysis

for the Potential

discrimination

between the groups

Figure 3: Workﬂow for the chaos analysis in the three

groups of heart sounds.

2.1 Phase Space Reconstruction

In order to see the structures in chaotic behavior of

a dynamical system through the time series produced

by itself, a method of attractor reconstruction is ap-

plied. Attractor is a distribution of points in the phase

or the state space that is characterized by the density

of points. Suppose the heart is considered as a non-

linear dynamical system which state space is given as

X = [X

, X

....., X

]

, (1)

where X

is the state of the system at discrete time

i, that generates the N-point heart sound time series

, x

, ...x

}. A method of delay is applied to recon-

struct the attractor in the multidimensional space or

embedding space P, i.e.

= [x

, x

i−τ

, ....., x

i+(m−1)τ)

] ∈ IR

(2)

where i = 1, 2, 3...P and X

are row vectors of the em-

bedding matrix X of size P × m. Application of an

(m, τ) window to a time series of N data points results

in a sequence of P = N−(m−1) vectors. In the phase

space reconstruction, it is important that the two inte-

ger parameters (m, τ) are suitably estimated. The τ

parameter is estimated as the time lag where the ﬁrst

minimum occurs in the mutual information between

data vector {x

, x

, ...x

} and time lagged data vec-

tor X

. Using the estimated τ, the embedded matrix

dimension m is estimated by utilizing Cao’s method

(Cao, 1997). The method exhibits invariance with re-

spect to the data length (Cao, 1997). An example of

reconstructed phase space using in murmur include

heart sound is shown in Figure 4.

1 2 3 4 5 6 7 8 9

−0.2

0.2

0.4

(a)

unit

Sec.

Figure 4: (a) A heart sound signal with murmur. (b) Recon-

structed phase space with τ = 195 and embedding dimen-

sion m = 4.

In order to know the attractor’s behaviors in the

phase space, two signiﬁcant incidents can be ob-

served: the ﬁrst one is the rate of divergence or con-

vergence of the trajectories and the second one is the

geometry of the attractor. These can be quantiﬁed

by the Lyapunov exponents and the correlation di-

mension. The fundamental reason of choosing Lya-

punov exponents and correlation dimension for the

time series characterization is to enhance the knowl-

edge about the underlying system rather than simply

compressing many measurements into a number. This

can not be achieved by many statistics measurements.

A quantity which can serve this objective must be

independent of measurement procedure, coordinates

chosen, noise, etc. According to their deﬁnition, cor-

relation dimensions and Lyapunov exponents nearly

fulﬁl these criteria.

2.2 Lyapunov Exponents

In a phase space plot, it is observed that the trajecto-

ries diverge over a course of time very slowly in peri-

odic time series. Chaos is thought to be present only

if divergence is exponentially fast. The averaged ex-

ponents of increase or decrease of separation quanti-

ﬁes the strength of chaos, which is known as the Lya-

punov exponents (Kantz and Schreiber, 1997). One

of the most robust and computationally fast methods

is the one introduced by Rosentein (Rosenstein et al.,

1993) is adopted.

DISCRIMINATION OF HEART SOUNDS USING CHOAS ANALYSIS IN VARIOUS SUBBANDS

371

There are many Lyapunov exponents for the at-

tractor, only the largest is computed that is signiﬁcant

to represent the level of chaos in heart sound signals.

The largest Lyapunov exponent (LLE) may have neg-

ative, positive or zero value. Time series from a dis-

sipative system may yield LLE negative values, while

marginally stable systems zero LLE. Positive value of

LLE denotes chaos in the system.

2.3 Correlation Dimension

Correlation dimension is a measure of self-similarity

(geometry of the attractor) in the time series. This

quantity is computed through correlation sum C(r),

that is a fraction of all possible pairs of points which

are closer than a given radial distance r in a particu-

lar norm. The sum counts the pair whose distance is

smaller than r. Since at large number of points corre-

lation sum follows power law, correlation dimension

can be deﬁned with the logarithmic change in correla-

tion sum with respect to the logarithm of the distance

r. More mathematical explanation can be found in

(Kantz and Schreiber, 1997).

3 APPLICATION AND RESULTS

3.1 Data Collection

Heart sounds containing murmurs produced by na-

tive heart valve as well as heart sounds produced by

heart with a mechanical valve implant, were collected

from the Cardiothoracic Surgery Center of the Uni-

versity Hospital of Coimbra. Heart sounds produced

by mechanical valves were recorded 2-3 weeks af-

ter valve surgery and do not exhibit murmurs. Some

heart sound samples of healthy subjects (who did

not have any kind of CVD) were collected from re-

searchers at the University of Coimbra and Philips

Research Laboratories. For this purpose, a quiet loca-

tion was chosen where subjects were asked to avoid

movements during measurements. In most cases, the

supine position was adopted as the best auscultation

position for the subjects and the best auscultation site

(near to the second or the third intercostal space) was

selected based on the loudness of the heart sounds.

The prepared database was categorized into the three

groups: group H; heart sounds produced by native

valve, group M; heart sounds with murmur produced

by native valves, and group V; heart sounds produced

by mechanical valve.

Data acquisition was performed with an electronic

stethoscope from Meditron. The stethoscope presents

excellent signal to noise ratio characteristic and an ex-

tended frequency range (20 - 20,000 Hz). The normal

amplitude can be regulated up to a maximum of 93

dB. Sound samples can be sampled up to a maximum

sampling rate of 44.1kHz and digitized with a 16-bit

ADC. All collected heart sound samples were sam-

pled at the rate of 44.1kHz for at most one minute.

Later, only 9 seconds length of heart sounds of each

subject is applied for the discrimination test.

3.2 Pre-processing and Wavelet

Decomposition

All collected heart sounds are ﬁrst preprocessed using

a 4th order Butterworth high pass ﬁlter with a cut-off

frequency of 25Hz in order to eliminate low frequen-

cies produced by muscle and stethoscope movements.

The resultant heart sounds are decomposed into

seven frequency bands with the range of 25Hz-

22.5kHz. It should be noticed that various frequency

bands are present in heart sounds produced by native

or mechanical valve. For instance, mechanical valve

produces frequency up to 50kHz (Zhang et al., 1998),

whereas the heart sounds produced by native valves,

even with murmurs, fall into a frequency range of

25Hz-600Hz (Erickson, 2003).

As it has already been mentioned, the heart sounds

are decomposed using the wavelet decomposition

technique. Given the Daubechies wavelet’s properties

related to the suppression of the instrumental defects

( i.e. polynomial components) and the absence of the

Gibbs phenomenon (no ripple in frequency response)

(Strang and Nguyen, 1996), it is chosen to correlate

with the heart sound signals.

The heart sound signals are subjected to 6 decom-

position level using 6

- order Daubechies wavelet

transform. The band limited (25Hz-22.5kHz) heart

sounds, x, are decomposed into two frequency bands

signals: ca1 that contains frequency bands (25Hz-

11.025kHz), and cd1 (11.025-22.5kHz). The ca1

is further decomposed into band limited signals ca2

(25Hz-5.5kHz) and cd2 (5.5-11kHz). The approach

is repeated until four following frequency band sig-

nals : cd3 (2.7-5.5kHz), cd4 (1.3-2.7kHz), cd5 (0.6-

1.3kHz), cd6 (0.3-0.6kHz) and ca6 (25-344Hz), as

can be seen in Figure 5. The subbands signals

ca6, cd6, cd5, cd4, cd3, cd2 and cd1 reconstruct the

original signal. The differences in the subbands ex-

hibit physiological signiﬁcance. For instance, heart

sounds produced by healthy hearts should have their

energy concentrated mainly in ca6 band, while heart

sounds with murmur typically exhibits a signiﬁ-

cant amount of energy in the cd6 or even in cd5

band. Heart sounds produced by prosthetic mechan-

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

372

ical heart valve usually exhibit high frequency con-

tents.

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

−0.4

−0.2

0.2

0.4

0.5 1 1.5 2 2.5 3

−2

ca6

0.5 1 1.5 2 2.5 3

−0.1

0.1

cd6

0.5 1 1.5 2 2.5 3

−0.2

−0.1

0.1

cd5

0.5 1 1.5 2 2.5 3

−0.1

0.1

cd4

0.5 1 1.5 2 2.5 3

−0.02

0.02

cd3

0.5 1 1.5 2 2.5 3

−0.02

0.02

cd2

0.5 1 1.5 2 2.5 3

−0.01

0.01

cd1

Time (Sec.)

Figure 5: Level 6 decomposition of a Heart sound with

murmur sound samples using Daubechies 6

order (where,

x = ca6+

∑

k=1

3.3 Attractor Reconstruction and

Chaotic Features Computation

The required parameters for the attractor reconstruc-

tion (τ, m) are estimated for each heart sound in each

group. The time delay parameter, τ, is computed as

the ﬁrst local minimum in the plot of the mutual infor-

mation. The embedding dimension is obtained using

the well known Cao’s method (Cao, 1997).

The Lyapunov exponents are computed based on

well known Wolf’s (Rosenstein et al., 1993) method.

The single largest Lyapunov exponent (LLE) of the

heart sound is computed using least square ﬁt in the

plot of logarithm of divergence over increasing time

steps, as depicted in Figure (6). The slope of the line

ﬁtted to the data is computed as the largest Lyapunov

exponent.

In the correlation dimension computation, the

only crucial variable is the radial distance (r) for the

0 20 40 60 80 100 120

−1

(a)

time step

divergence

−3 −2 −1 0 1 2 3

−16

−14

−12

−10

−8

−6

−4

−2

(b)

ln(r)

ln(C(r))

linear fit

Figure 6: Embedding features computation by linear least

square ﬁtting : (a) Largest Lyapunov exponent (b) Correla-

tion dimension.

identiﬁcation of the number of neighbors of the refer-

ence point. In case of a very small radius not enough

points are captured. On the other hand, in case of

a large value, most of the available points are cap-

tured. Both situations mislead the correlation dimen-

sion computation. Care must be taken in choosing

the value, which led to experiment with range of r,

i.e. 5%-25% of the attractor size. This range of ra-

dius enables the fair estimate values of CD, which do

not predominantly vary from each other. In our im-

plementation, we have chosen experimentally a 8%

distance value (r) for further statistical analysis. The

CD is nothing but a slope of the line which can be ap-

proximately ﬁt with the logarithm of correlation sum

(C(r)). In the Figure 6(b), the CD is computed using

the plot of correlation sum over distance.

3.4 Statistical Analysis

The computation of the features based on the embed-

ded matrix of the heart sound samples have been pre-

sented in the previous section. It has been applied

to all the 45 data samples of the three groups, where

each group contains 15 heart sound samples from dif-

ferent subjects. The average value of LLE and CD of

the original and decomposed signal are listed in Table

1. The values are not monotonically increasing or de-

creasing in the descending frequency subbands in ei-

ther of these groups. Instead, some values are nearly

overlapping among the groups. Therefore, there is a

risk to apply a hard threshold to these measures in dis-

tinction between the groups.

From the LLE values in Table 1, it can be observed

that the original heart sound signals and the subband

signals of each group differ signiﬁcantly. The LLE

DISCRIMINATION OF HEART SOUNDS USING CHOAS ANALYSIS IN VARIOUS SUBBANDS

373

of the original signal of the group V (0.123) is signiﬁ-

cantly higher than those of group M (0.073)and group

H (0.073). The values are found to be lower for sub-

band cd1 and cd2 in group V (0.233 and 0.249 ) than

in group H (0.042 and 0.073), though the difference

is not considerably high, whereas in the other sub-

bands the values are higher in group V than in group

M and H. Hence, it can be deduced that heart sounds

of group V is more chaotic in nature than the other

groups in the original band signal and the subbands

ca6, cd6, cd4, and cd3. That can be explained based

upon the single-tilting disk mechanical valve closing

which produces a vast frequency range (up to 50kHz)

of sound. However, it is more chaotic than the group

H but less than the group M in the subbands cd2 and

cd1. The most interesting observation is to ﬁnd that

the values of the group M higher than those of group

H in all subbands. The attractor of the healthy heart

sound is less chaotic compared to the attractors ob-

tained from heart sounds produced by hearts with dis-

orders.

Table 1: Averaged Largest Lyapunov Exponents (LLE) val-

ues for all three data groups. Standard deviations are in

parenthesis.

Signal Group H Group M Group V

x 0.042 (0.018) 0.073 (0.048) 0.123 (0.049)

ca6 0.215 (0.080) 0.246 (0.115) 0.308 (0.116)

cd6 0.279 (0.100) 0.331 (0.139) 0.489 (0.132)

cd5 0.236 (0.101) 0.269 (0.141) 0.431 (0.207)

cd4 0.178 (0.110) 0.259 (0.134) 0.366 (0.111)

cd3 0.170 (0.071) 0.249 (0.065) 0.305 (0.067)

cd2 0.242 (0.117) 0.304 (0.198) 0.249 (0.094)

cd1 0.222 (0.059) 0.302 (0.189) 0.233 (0.126)

From the CD values in Table 2, it can be observed

that the original band limited heart sounds, x, of all the

groups do not exhibits considerable difference among

each other. This implies that the complexity in non-

linear dynamics of the attractors is almost the same

for all heart sounds. The subbands ca6, cd6, cd5, cd4

and cd3 yield almost similar values of CD in each

group. The values suggest moderate variation in com-

plexity of the groups in these subbands. However, in

subband cd2, the group V (4.18) appears to be sig-

niﬁcantly higher compare to the group H (3.66) and

reasonably above the value of group M (3.97). Fur-

thermore, subband cd1 also yields a larger value of

CD for the group V (4.43) than for group M and H. It

indicates increased complexity of the group V, which

may be used in the discrimination of the group.

In the further discussion about the yielded values

of LLE, a signiﬁcance analysis is performed using

one-way variance analysis (ANOVA) with 99% con-

Table 2: Averaged Correlation Dimension (CD) values for

all three data groups using 8% distance of the attractor for

neighbor search from the reference point. Standard devia-

tions are in parenthesis.

Signal Group H Group M Group V

x 4.25 (0.44) 3.88 (0.21) 4.12 (0.23)

ca6 3.94 (0.36) 3.65 (0.65) 3.89 (0.31)

cd6 3.70 (0.27) 3.46 (0.42) 3.80 (0.32)

cd5 3.63 (0.64) 3.58 (0.49) 3.60 (0.36)

cd4 3.68 (0.66) 3.87 (1.19) 3.75 (0.31)

cd3 3.72 (0.81) 3.95 (0.72) 3.89 (0.60)

cd2 3.66 (0.88) 3.97 (0.88) 4.18 (0.62)

cd1 3.19 (0.73) 3.42 (0.92) 4.43 (0.59)

ﬁdence level. Let α be the conﬁdence level at which

the null hypothesis (similar averaged value groups)

can be rejected, variance in the values of LLE and

CD is searched greater to 99% (α = 0.01) when F-

statistic is below 0.001. The achieved results exhibit

the same results as it has already been presented in

Table 1. It can be seen in Figure 7(a) that LLE of

the original sounds of group H, group M and group

V can be discriminated from the original heart sounds

(F=0.0006689). However, band cd3 (F = 0.0000952)

has better potential to discriminate all the three groups

from each other, see Figure 7(b). The cd2 is able to

distinct group V from group H and group M.

On the other hand, it can be seen in Figure 7(c)

that the CD values of cd6 are able to discriminate

group V from group H and M (F=0.0000952). Fur-

thermore, CD values of ca6 are able to discriminate

group M from group H and group V (F=0.00066896),

see in Figure 7(d).

H M V

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Values

(a)

H M V

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Values

(b)

H M V

1.5

2.5

3.5

4.5

Values

(c)

H M V

3.4

3.6

3.8

4.2

4.4

4.6

4.8

Values

(d)

Figure 7: Conﬁdence interval plots of LLE ((a) original

heart sound, (b) cd3) and CD ((c) cd6, (d) ca6) value of

in all the groups.

BIOSIGNALS 2009 - International Conference on Bio-inspired Systems and Signal Processing

374

4 CONCLUSIONS AND FUTURE

WORKS

Chaos and complexity analysis in seven frequency

subbands (ca6, cd6, cd5, cd4, cd3, cd2, cd1) of three

groups of heart sounds were computed in order to dis-

criminate these groups of heart sounds. The three

groups of heart sounds are heart sounds produced

by native valve, heart sounds with murmur produced

by native valve and heart sounds produced by me-

chanical valves. These are compared with respect to

their degree of chaos which was quantiﬁed as largest

Lyapunov exponents (LLE) as well as complexity in

the form of the correlation dimension (CD). These

quantities were computed for seven frequency bands,

which were achieved by applying a wavelet decompo-

sition. Then statistical analysis was performed to test

the method’s effectiveness. The LLE values of sub-

band cd3 is found to be the best for group discrimi-

nation from each other and CD values of subband ca6

are found to be the best signals to discriminate heart

sound with murmur produced by native valves from

the rest of the two groups.

The decomposition of the original heart sound

into seven subbands alters the original phase space,

and exhibit different chaotic and complex behaviors.

Observing the results, one may conclude that only

LLE can discriminate among the three groups of heart

sounds. However, it is observed that CD can be used

to discriminate one group of heart sound from the rest

of the two groups in the speciﬁc bands with greater

conﬁdence level. Therefore, it can be concluded that

heart dynamics are not spread out equally across the

spectrum of heart sounds, but instead, are limited to

certain frequency band.

In the near future, work will include testing the

method with large database as well as the ﬁne tuning

of the frequency bands for analysis.

ACKNOWLEDGEMENTS

This work was performed under the IST FP6 project

MyHeart (IST-2002-507816) supported by the Euro-

pean Union, and is being continued under the Sound-

ForLife project (PTDC/EIA-68620/2006)ﬁnanced by

FCT.

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