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ACCURACY ESTIMATION OF THE ECG QRS-COMPLEX REFERENCE
POINT RECOGNITION
O.D. Yurieva1
1Saint-Petersburg
State Electrotechnical University,
e-mail: [email protected]
The results of experimental estimation of the ECG QRS-complex referent point detection
error are presented. Three different methods are considered: based on R-wave maximum,
on QRS area and on squared QRS area. It was shown that the third approach
demonstrated more accurate performance even in case of relatively low sampling
frequency.
Introduction
Analysis of the heart rate variability (HRV) is
one of the widespread methods for quantitative
estimation of autonomous nervous system
condition. The method is based on recognition
and measurement of time intervals between the
ECG R-waves (RR-intervals), generation of
dynamic series of cardiac intervals and
analysis of these series with the use of
different mathematical techniques.
The first stage of the rhythm analysis is RRinterval measurement. RR-interval estimation
from the sampled ECG signal results in errors
caused by discretization. Low sampling
frequency leads to inaccurate reference point
detection of QRS-complex. This fact can
significantly change HRV spectral parameters.
The recommended sampling frequency range
is 250 to 500 Hz [1]. Lower sampling
frequency gives satisfactory results only in
case of the use of specific QRS-complex
reference point detection algorithm based on
interpolation [2].
The choice of sampling frequency depends on
the ECG frequency range, the final
investigation goals and the used analysis
method. The sampling frequency choice is
determined by ECG power spectral density
that is concentrated in the range 0.5-30 Hz [3].
According to Kotelnikoff’s theorem the
sampling frequency 100 Hz is sufficient.
However
the
sampling
frequency
recommended by international standard is 500
Hz [1]. Nevertheless it is allowed to use
sampling frequency 128 Hz [3].
The investigation and quantitative assessment
of the ECG QRS-complex reference point
recognition methods is presented in this work.
The goal of this investigation is correct choice
of the ECG sampling frequency and of the
QRS-complex reference point detection
algorithm.
Approach and techniques
The first stage of the HRV analysis is
measuring of RR-intervals. The RR-intervals
measurement is based on the reference point
detection. Usually the reference point is
determined with the use of the absolute
maximum, of so called “gravity center” or of
the maximum of interpolating curve [4].
The present work is devoted to the
investigation of the sampling frequency
influence on the reference point detection with
the use of two different methods: the use of the
absolute maximum and the “gravity center”.
All calculations were performed with the use
of program package MATLAB.
A set of real three lead ECG recordings was
formed. Data verification was performed for
QRS-complex location determination. The set
is characterized by the following parameters:
total number of records – 16, duration of each
record – 5 min, total number of QRS-
386
complexes – 5136, initial sampling frequency
– 500 Hz.
The noise realization was artificially generated
to analyze the noise immunity of the examined
algorithms. The statistical properties of this
realization were chosen similar to that of white
Gaussian noise. The generated noise was
processed by digital low-pass filter with cutoff frequency 100 Hz. The obtained signal was
set to zero average value and unit standard
deviation. For producing signal with given
signal to noise ratio (SNR) the noise
realization was divided by SNR and added to
the analysed ECG record.
In case the absolute maximum of QRScomplex is used for the reference point
detection,
signal
decimation
causes
displacement of the reference point.
The index of sample corresponding to the
QRS-complex maximum is calculated as
k i  Tmax i  Fd ,
(1)
where Tmax i – time corresponding to QRScomplex maximum , Fd – sampling frequency.
Calculation of RR-interval duration is made
according to:
RRi  (ki  ki 1 )  T ,
I rk
Qk   q i ,
(4)
Ilk
where
0, xi  0.25 Ak
,
qi  
(5)
 xi  0.25 Ak , xi  0.25 Ak
Ak – maximum of QRS-complex, Irk и Ilk –
accordingly right and left borders of the
analysed fragment.
The reference point Ik is determined as the
point where the half of this sum is achieved:
Ik
q
1
 Qk .
2
i
I lk
(6)
The second method uses the same approach,
but the sum of sample squares is calculated
instead of the sum of samples themselves:
Ik
q
I lk
2
i
1
 Qk .
2
(7)
(2)
where T – sampling interval.
Standard deviation of the QRS-complex
reference point is defined as:
N
SQ 
 ( RR
i 1
0i
 RR pi ) 2
N 1
,
(3)
where RR0 и RRp – RR-interval duration of
initial and decimated signals accordingly, (p –
decimation coefficient), N – the numder of
QRS-complexes.
The “gravity center” method includes the
following steps. The module of first signal
difference is calculated to delete the constant
component of the signal. A threshold is chosen
that is equal to the product of the coefficient k
(k<1) and the QRS-complex maximum values.
The sum of the signal values exceeding the
threshold within the fragment corresponding to
QRS-complex is calculated:
Fig. 1. Illustration of the “gravity center” method
Results
The module of difference between the values
of RR-interval durations of initial and
decimated signal was taken as the error
measure of the reference point detection. The
mean-square error (MSE) was calculated for
each examined method. The decimation
coefficient changes from 1 to 5. Fig. 2 presents
the dependence between mean-square error
and the decimation coefficient. The following
387
designations are used in this figure: method 1
– the method based on R-wave maximum,
method 2 – the method based on the QRS area
and method 3 – the method based on the
squared QRS area.
A comparative analysis of the two “gravity
center” methods was performed. The
dependences between mean-square error and
decimation coefficient were investigated for
the signals without noise and with different
SNR values. The results of this investigation
are presented at the Table.
Fig. 2. The dependence between mean-square error and
decimation coefficient
Table. A summary table of error values of
the “gravity center” methods
MSE, ×104
Noise
QRS
Squared
Threshold
level
area
QRS area
No
noise
SNR=20
SNR=15
S=0.5
S=0.6
S=0.7
S=0.8
S=0.9
S=0.5
S=0.6
S=0.7
S=0.8
S=0.9
S=0.5
S=0.6
S=0.7
S=0.8
S=0.9
7.1
6.4
6.1
6.1
6.0
7.5
6.8
6.4
6.4
6.1
7.9
7.2
6.7
6.5
6.4
6.1
6.0
6.0
6.0
5.9
6.1
6.0
6.0
6.0
5.9
6.1
6.1
6.0
6.0
6.0
Conclusion
The following conclusions can be made as the
result of the experimental investigation
presented. The reference point recognition
method based on the absolute maximum that is
used by most authors is very sensitive to the
sampling frequency reduction. The “gravity
center” methods can be used as alternative
methods for the reference point detection. The
method based on the squared QRS area is
more tolerant to the sampling frequency
reduction and gives the better results. The
reference point definition accuracy depends on
signal to noise ratio and threshold value for
this method. The error of the reference point
recognition increases as the threshold and
signal to noise ratio decrease.
Similar investigations are planed to perform
for other QRS-complex reference point
recognition techniques. Also estimation of
influence of accuracy measurement of RRintervals on the HRV parameters calculation is
scheduled. The best reference point
determination methods are likely to be the
methods that are based on the cumulative
characteristics
of
the
QRS-complex
description.
References
1. Heart Rate Variability - Standards of Measurement,
Physiological Interpretation, and Clinical Use, Task
Force of the European Society of Cardiology and the
North American Society of Pacing and
Electrophysiology // Circulation. – 1996. – Vol. 93.
P. 1043-1065.
2. S. Abboud, O. Barnea. Errors due to sampling
frequency of the electrocardiogram in spectral
analysis of heart rate signals with low variability //
Computers in Cardiology. – 1995. – P. 461-464.
3. M. Merri, David S. Farden, et al. Sampling
frequency of the electrocardiogram for spectral
analysis of the heart rate variability // IEEE
Transaction on Biomedical Engineering. – 1990. –
P. 99-102.
4. S. Ward, et al. Electrocardiogram sampling
frequency errors in PR-interval spectral analysis //
Proc. IEEE PGBIOMED’04. – 2004.