SIGNAL TO NOISE RATIO EVALUATION IN SIGNAL

AVERAGED ECG BY DERIVATIVE DYNAMIC TIME WARPING

AND PIECEWISE LINEAR APPROXIMATION

Roberto L. Avitia, Marco A. Reyna, Miguel E. Bravo

Bioengineering Academic Body, University Autonomous of Baja California, Alvaro Obregon Ave., Mexicali, Mexico

Lucio A. Cetto

Computational Biology Department, The MathWorks, Inc., 3 Apple Hill Drive, Natick MA, U.S.A.

Keywords: Signal averaged electrocardiography, Dynamic programming, Piecewise linear approximation, Heartbeat

alignment.

Abstract: Signal Averaged Electrocardiography (SAECG) is a technique widely used as an alternative to improve

signal to noise ratio (SNR), but sometimes patient’s physiology may alter the characteristics of quasi-steady

heartbeats that are assumed in the averaging. This paper evaluates the noise as a parameter for measuring

the alignment heartbeats by Derivative Dynamic Time Warping (DDTW) and using Piecewise Linear

Approximation (PLA) as well. The records were taken from a group of healthy individuals and the results

show that the number of heartbeats averaged necessary to improve the SNR is less than the traditional

method.

1 INTRODUCTION

The High Resolution Electrocardiography (HRECG)

gives us important information about the normal and

abnormal electrical activity of the heart, such as

Ventricular Late Potentials (VLP). Often, these VLP

occur in people who survive to a heart attack (M.E.

Tagluk et al, 1998). Many studies focus the VLP

detection on the QRS complex by means of the

quantification of its duration (A. Illanes et al, 2008;

Z.E. Hadj, 2005 and 2006; T. Bragge et al, 2004).

When HRECG are been recorded, it is very common

that noise masks signals of interest like VLP. To

improve the quality of records, it can be used

multiple techniques such as the well known Signal-

Averaged ECG (SAECG), a widely used technique

in noise reduction for VLPs studies. SAECG assume

that the noise is completely a random signal and

both the signal of interest (i.e., HRECG) and its VLP

pattern (if exists) are quasi-stationary processes,

which are repeating heartbeat to heartbeat at the end

of the QRS complex or at the beginning of ST

segment (G. Breithard, 1991). The noise level is

reduced proportionately as long as more and more

heartbeats are taken into an ensemble. In the results

presented in this paper, the heartbeats had complied

with a correlation coefficient higher than 0.9

compared with a reference or template (G. Breithard

et al, 1993). Alignment of heartbeats is an important

part of the signal averaging, because the

physiological nature of electrocardiographic signals.

This nature alters the behaviour from heartbeat to

heartbeat in lag, in duration, and amplitude.

Variations in time are due to both the heart rate

variability and the elongation in duration. Variations

in amplitude are due to attenuations or

amplifications on the wave forms. It makes the

heartbeats look lagged, shorter or longer in duration,

and higher or lower in amplitude. This would cause

that the ensemble rejects those heartbeats which do

not reach the minimal correlation coefficient

criterion (i.e., 0.9). An alignment technique firstly

used in speech recognition was called dynamic

programming, and now commonly known as

"Dynamic Time Warping” (H. Sakoe et al, 1978). It

has been used in making decisions on segmentation

of ECG signals, showing good results (A. Zifan et

al, 2007).

201

L. Avitia R., A. Reyna M., E. Bravo M. and A. Cetto L. (2010).

SIGNAL TO NOISE RATIO EVALUATION IN SIGNAL AVERAGED ECG BY DERIVATIVE DYNAMIC TIME WARPING AND PIECEWISE LINEAR

APPROXIMATION .

In Proceedings of the Third International Conference on Biomedical Electronics and Devices, pages 201-205

DOI: 10.5220/0002748802010205

 SciTePress

In this paper, we recorded 30 HRECG each of them

including 350 heartbeats taken from 30 healthy

subjects. A method on dynamic programming and

heartbeats segmentation, based on Piecewise Linear

Approximation (PLA) (H.J.L.M. Vullings et al,

1997) was used for heartbeats alignment. Results

show that using PLA it is possible to reach similar

noise levels by mean of the added of less heartbeat

in the ensemble than in conventional method (G.

Breithard, 1991).

2 MATERIALS AND METHODS

A CARDIAX PC-ECG system was used at 500 Hz

sampling rate for electrocardiography tracings.

Interpolation to a rate of 2 was applied achieving a

double sampling frequency. Simple smoothing was

applied to remove the high frequency noise. Each of

the obtained curves was separated into heartbeats

using a conventional method for R peak detection.

Those, that meet a correlation higher than 0.9, i.e.

100 to 350 beats were selected and averaged. Then

the level of the noise in the ST segment (G.

Breithard, 1991) was assessed and the beats were

approximated by straight lines using the method of

Piecewise Linear Approximation (PLA) from which

alignments will be compared with the same

heartbeat reference using dynamic programming

(DTW), and then perform the averaging of the

heartbeats and re-evaluate the noise level in the ST

segment.

2.1 Preprocessing

A moving average band pass Butterworth filter (1 to

100 Hz) of order 5 was applied first removing the

high frequency noise like interspersions and muscle

noise. Next, a previous segmentation was done by

selecting QRS complex with the classical Pan and

Tompkins algorithm (J. Pan et al, 1985), after that

we selected a region around the R-peak, 150 samples

before and 250 samples after the R-peak. Then the

region around the R-peak, 150 samples before and

250 samples after the R-peak were selected and the

template beat is decomposed in three different parts:

a) before the QRS complex (P wave and PQ

segment); b) the QRS complex part and c) after the

QRS complex (ST segment and T wave).

2.2 Piecewise Linear Approximation

The PLA algorithm was used to represent adaptively

any signal trough straight lines. We propose to

approximate the ECG with a series of line segments.

The ECG is regarded as a vector

[ (1),...... ( )]

xxn=

where

()

(1 )in

≤

is the voltage of the ECG at

time

. The first proposed segment consist of the

first samples of

. We approximate this segment

with a straight line connecting the first and the last

sample. As long as this line approximates the

original segment with an acceptable error

samples are added to the segment. To calculate the

error consider figure 1, where

samples are

approximated by the straight line

()yi ai b=+

. The

error

()ei

for sample

(1 )iij≤≤

should never

exceed an empirical determined threshold calculated

as:

We add s more samples to the segment, until (1)

does not hold. Then, we start shrinking the segment

in order to obtain a segment which does not

exceed

∈

. The new end-point of the segment is the

point

for which

()ei

is maximal. If the error on the

new segment remains below

∈, the line segment to

approximate a part of the ECG is found. The new

segment will start at the end-point of the previous

segment. However, if the error is still not below

∈

we shrink the segment again and again, until (1)

holds.

Figure 1: The error

()ei

for a segment.

A complete heartbeat consists of a sequence of lines

which can be displayed in string format. One line

can be represented as a combination of slope and a

horizontal length

(, )ax

, which enable us to

describe the heartbeat in terms of segment lines as

illustrated in figure 2, where template heartbeat is

represented using PLA i.e. using lines defined by a

slope and number of samples taken in account by

these lines.

() ()

()

xi yi

−

<∈

(1)

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202

Since alignment is an important part of SAECG, a

method to perform it is described as follow.

Figure 2: PLA of a heartbeat taken as template.

2.3 Derivative Dynamic Time Warping

In order to overcome some limitations of the classic

DTW algorithm the Derivative Dynamic Time

Warping algorithm (DDTW) was applied. To find

the similarity between two sequences, DTW looks

for the best alignment, which is generally referred to

as Warp-Path, and thus warps the time axis of one of

the series and calculates the distance between the

two sequences. In some cases it can produce some

misalignments, for instance when multiple points on

one time series correspond to only one point in the

matching time series, or when the two sequences

strongly vary in the Y-axis. Figure 3 shows the

limitations of DTW (S. Chu. et al, 2002).

Figure 3: Alignment produced by DTW. Alignment fails

because of differences in the “y” axis.

In the present case, each input signal is considered

as a sequence of

samples

[ (1), (2)....... ( )],

xx xn=

and the template is a sequence of

samples

[ (1), (2),...... ( )]yyy ym=

. DTW builds a

matrix

[]Dn m×

in which each element represents

the distance between the

ith−

element of

()

and

the

jth

−

element of

()yj

. Then, a new matrix

introduced, with:

(,) (,) min[( 1, 1), (, 1), ( 1,)]

i d ji j i ji j i

θθθ

+−−−−

(2)

So, that each element is the sum between the local

distance

(,)dji

and the minimum of the total

distances of the neighbor elements.

The warping path

, is a contiguous set of matrix

elements that defines a mapping between

and

The

kelement

−

is defined as

(, )

Wij=

, ,....

Www w

max( , ) 1nm k n m<<+−

(3)

The warping path generally undergoes to several

constraints: among them, the requirement for the

warping path to start and finish in diagonally

opposite corner cells of the matrix, restriction to the

number of allowable steps in the warping path to

adjacent cells and monotonicity in time.

Among all the warping paths that satisfy the above

conditions, for recognition/classification purposes of

interest is in the path that minimizes the warping

cost:

DDTW differs from DTW by considering the square

of the difference of the estimated derivatives of

and

instead of the original time series:

A simple representative block diagram of procedure

is shown in Figure 4. It is very important to say that

averaging has not been made with heartbeat-

segmented, but with heartbeat-aligned, and SNR

evaluation has been made in the ST segment only.

(, ) min

DTW x y w

⎧

⎫

⎪

⎨

⎬

⎪

⎩⎭

∑

(4)

111

()( )/2

() ,1

ii i i

xx x x

xin

−+−

−

+−

(5)

SIGNAL TO NOISE RATIO EVALUATION IN SIGNAL AVERAGED ECG BY DERIVATIVE DYNAMIC TIME

WARPING AND PIECEWISE LINEAR APPROXIMATION

203

Representation of every

segmented-hearbeat by their

corresponding samples.

Selection of template by

visual criterion.

Hearbeats separation from

ECG trace.

Segmentation of every

heartbeat using PLA.

Segmented-heartbeats

Alignment using DDTW

Application of averaging to

heartbeats-aligned ensemble.

SNR evaluation in heartbeat

aligned and averaged.

Figure 4: Method used representation by a simple block

diagram.

3 RESULTS

Each heartbeat to be segmented has a distance

matrix alignment much smaller than if it were made

with all samples of the signals, as shown in Figure 5.

Derivative Time Warping alignment technique

produces an alignment based on the slopes of the

lines generated and amplitude values no matter.

Q (QRS for warping)

C (QRS for Template)

Warping Path (Red)

2 4 6 8 10 12 14 16 18

Figure 5: The segmentation produces a smaller matrix

alignment.

For instance two heartbeats with high difference in

amplitude can be aligned almost completely, as

shown in Figure 6.

Figure 6: Alignment produced by DDTW (a) Aligning

segments P, QRS and T, (b) Heartbeats aligned according

to segment slope. Template reference (red), heartbeat to

align (blue) and heartbeat aligned (black).

Making signal average with no alignment heartbeats

(just those which present high correlation) and

aligning with DDTW and PLA noise level could be

computed using ST segment variance or

where

R is the number of heartbeat taken in account to be

averaged (G. Breithard et al, 1993).

A graphical representation is shown in figure 7,

where four individuals ECG records were noise

measured.

()/(()/)

RMS i i i i

nxRxR

μμ

=−−−

∑∑

(6)

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Figure 7: Four patients ECG noise measured in typical

SAECG (Blue) and using DDTW and PLA (Red).

4 CONCLUSIONS

The alignment algorithm developed based on

DDTW and PLA provides similar results in noise

reduction compared with traditional method based

on high correlation for same number of heartbeats.

For less number of heartbeats however, it reaches

lower noise levels excluding thus the need to reject

as much as traditional method.

ACKNOWLEDGEMENTS

We would like to thank Dr. Zlatev Roumen

Koytchev for his valuable participation as technical

advisor in this paper.

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SIGNAL TO NOISE RATIO EVALUATION IN SIGNAL AVERAGED ECG BY DERIVATIVE DYNAMIC TIME

WARPING AND PIECEWISE LINEAR APPROXIMATION

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